TSTP Solution File: SEU265+1 by Metis---2.4
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : SEU265+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n027.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 12:39:49 EDT 2022
% Result : Theorem 3.91s 4.09s
% Output : CNFRefutation 3.91s
% Verified :
% SZS Type : Refutation
% Derivation depth : 28
% Number of leaves : 29
% Syntax : Number of formulae : 221 ( 55 unt; 0 def)
% Number of atoms : 496 ( 114 equ)
% Maximal formula atoms : 16 ( 2 avg)
% Number of connectives : 503 ( 228 ~; 209 |; 32 &)
% ( 15 <=>; 19 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 4 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 9 ( 6 usr; 1 prp; 0-3 aty)
% Number of functors : 20 ( 20 usr; 8 con; 0-3 aty)
% Number of variables : 322 ( 15 sgn 196 !; 23 ?)
% Comments :
%------------------------------------------------------------------------------
fof(cc1_relset_1,axiom,
! [A,B,C] :
( element(C,powerset(cartesian_product2(A,B)))
=> relation(C) ) ).
fof(d4_relat_1,axiom,
! [A] :
( relation(A)
=> ! [B] :
( B = relation_dom(A)
<=> ! [C] :
( in(C,B)
<=> ? [D] : in(ordered_pair(C,D),A) ) ) ) ).
fof(dt_k4_relset_1,axiom,
! [A,B,C] :
( relation_of2(C,A,B)
=> element(relation_dom_as_subset(A,B,C),powerset(A)) ) ).
fof(dt_m2_relset_1,axiom,
! [A,B,C] :
( relation_of2_as_subset(C,A,B)
=> element(C,powerset(cartesian_product2(A,B))) ) ).
fof(existence_m1_subset_1,axiom,
! [A] :
? [B] : element(B,A) ).
fof(fc1_xboole_0,axiom,
empty(empty_set) ).
fof(redefinition_k4_relset_1,axiom,
! [A,B,C] :
( relation_of2(C,A,B)
=> relation_dom_as_subset(A,B,C) = relation_dom(C) ) ).
fof(redefinition_m2_relset_1,axiom,
! [A,B,C] :
( relation_of2_as_subset(C,A,B)
<=> relation_of2(C,A,B) ) ).
fof(t1_subset,axiom,
! [A,B] :
( in(A,B)
=> element(A,B) ) ).
fof(t20_relat_1,axiom,
! [A,B,C] :
( relation(C)
=> ( in(ordered_pair(A,B),C)
=> ( in(A,relation_dom(C))
& in(B,relation_rng(C)) ) ) ) ).
fof(t22_relset_1,conjecture,
! [A,B,C] :
( relation_of2_as_subset(C,B,A)
=> ( ! [D] :
~ ( in(D,B)
& ! [E] : ~ in(ordered_pair(D,E),C) )
<=> relation_dom_as_subset(B,A,C) = B ) ) ).
fof(t2_subset,axiom,
! [A,B] :
( element(A,B)
=> ( empty(B)
| in(A,B) ) ) ).
fof(t2_tarski,axiom,
! [A,B] :
( ! [C] :
( in(C,A)
<=> in(C,B) )
=> A = B ) ).
fof(t4_subset,axiom,
! [A,B,C] :
( ( in(A,B)
& element(B,powerset(C)) )
=> element(A,C) ) ).
fof(t5_subset,axiom,
! [A,B,C] :
~ ( in(A,B)
& element(B,powerset(C))
& empty(C) ) ).
fof(t6_boole,axiom,
! [A] :
( empty(A)
=> A = empty_set ) ).
fof(subgoal_0,plain,
! [A,B,C] :
( ( relation_of2_as_subset(C,B,A)
& ! [D] :
~ ( in(D,B)
& ! [E] : ~ in(ordered_pair(D,E),C) ) )
=> relation_dom_as_subset(B,A,C) = B ),
inference(strip,[],[t22_relset_1]) ).
fof(subgoal_1,plain,
! [A,B,C] :
( ( relation_of2_as_subset(C,B,A)
& relation_dom_as_subset(B,A,C) = B )
=> ! [D] :
( in(D,B)
=> ~ ! [E] : ~ in(ordered_pair(D,E),C) ) ),
inference(strip,[],[t22_relset_1]) ).
fof(negate_0_0,plain,
~ ! [A,B,C] :
( ( relation_of2_as_subset(C,B,A)
& ! [D] :
~ ( in(D,B)
& ! [E] : ~ in(ordered_pair(D,E),C) ) )
=> relation_dom_as_subset(B,A,C) = B ),
inference(negate,[],[subgoal_0]) ).
fof(normalize_0_0,plain,
? [A,B,C] :
( relation_dom_as_subset(B,A,C) != B
& relation_of2_as_subset(C,B,A)
& ! [D] :
( ~ in(D,B)
| ? [E] : in(ordered_pair(D,E),C) ) ),
inference(canonicalize,[],[negate_0_0]) ).
fof(normalize_0_1,plain,
( relation_dom_as_subset(skolemFOFtoCNF_B_1,skolemFOFtoCNF_A_2,skolemFOFtoCNF_C_4) != skolemFOFtoCNF_B_1
& relation_of2_as_subset(skolemFOFtoCNF_C_4,skolemFOFtoCNF_B_1,skolemFOFtoCNF_A_2)
& ! [D] :
( ~ in(D,skolemFOFtoCNF_B_1)
| ? [E] : in(ordered_pair(D,E),skolemFOFtoCNF_C_4) ) ),
inference(skolemize,[],[normalize_0_0]) ).
fof(normalize_0_2,plain,
relation_dom_as_subset(skolemFOFtoCNF_B_1,skolemFOFtoCNF_A_2,skolemFOFtoCNF_C_4) != skolemFOFtoCNF_B_1,
inference(conjunct,[],[normalize_0_1]) ).
fof(normalize_0_3,plain,
relation_of2_as_subset(skolemFOFtoCNF_C_4,skolemFOFtoCNF_B_1,skolemFOFtoCNF_A_2),
inference(conjunct,[],[normalize_0_1]) ).
fof(normalize_0_4,plain,
! [A,B,C] :
( ~ relation_of2(C,A,B)
<=> ~ relation_of2_as_subset(C,A,B) ),
inference(canonicalize,[],[redefinition_m2_relset_1]) ).
fof(normalize_0_5,plain,
! [A,B,C] :
( ~ relation_of2(C,A,B)
<=> ~ relation_of2_as_subset(C,A,B) ),
inference(specialize,[],[normalize_0_4]) ).
fof(normalize_0_6,plain,
! [A,B,C] :
( ( ~ relation_of2(C,A,B)
| relation_of2_as_subset(C,A,B) )
& ( ~ relation_of2_as_subset(C,A,B)
| relation_of2(C,A,B) ) ),
inference(clausify,[],[normalize_0_5]) ).
fof(normalize_0_7,plain,
! [A,B,C] :
( ~ relation_of2_as_subset(C,A,B)
| relation_of2(C,A,B) ),
inference(conjunct,[],[normalize_0_6]) ).
fof(normalize_0_8,plain,
! [A,B,C] :
( ~ relation_of2(C,A,B)
| relation_dom_as_subset(A,B,C) = relation_dom(C) ),
inference(canonicalize,[],[redefinition_k4_relset_1]) ).
fof(normalize_0_9,plain,
! [A,B,C] :
( ~ relation_of2(C,A,B)
| relation_dom_as_subset(A,B,C) = relation_dom(C) ),
inference(specialize,[],[normalize_0_8]) ).
fof(normalize_0_10,plain,
! [A,B,C] :
( ~ relation_of2(C,A,B)
| element(relation_dom_as_subset(A,B,C),powerset(A)) ),
inference(canonicalize,[],[dt_k4_relset_1]) ).
fof(normalize_0_11,plain,
! [A,B,C] :
( ~ relation_of2(C,A,B)
| element(relation_dom_as_subset(A,B,C),powerset(A)) ),
inference(specialize,[],[normalize_0_10]) ).
fof(normalize_0_12,plain,
! [A,B,C] :
( ~ element(B,powerset(C))
| ~ empty(C)
| ~ in(A,B) ),
inference(canonicalize,[],[t5_subset]) ).
fof(normalize_0_13,plain,
! [A,B,C] :
( ~ element(B,powerset(C))
| ~ empty(C)
| ~ in(A,B) ),
inference(specialize,[],[normalize_0_12]) ).
fof(normalize_0_14,plain,
! [A] :
? [B] : element(B,A),
inference(canonicalize,[],[existence_m1_subset_1]) ).
fof(normalize_0_15,plain,
! [A] :
? [B] : element(B,A),
inference(specialize,[],[normalize_0_14]) ).
fof(normalize_0_16,plain,
! [A] : element(skolemFOFtoCNF_B(A),A),
inference(skolemize,[],[normalize_0_15]) ).
fof(normalize_0_17,plain,
! [A] :
( ~ empty(A)
| A = empty_set ),
inference(canonicalize,[],[t6_boole]) ).
fof(normalize_0_18,plain,
! [A] :
( ~ empty(A)
| A = empty_set ),
inference(specialize,[],[normalize_0_17]) ).
fof(normalize_0_19,plain,
empty(empty_set),
inference(canonicalize,[],[fc1_xboole_0]) ).
fof(normalize_0_20,plain,
! [A,B] :
( ~ element(A,B)
| empty(B)
| in(A,B) ),
inference(canonicalize,[],[t2_subset]) ).
fof(normalize_0_21,plain,
! [A,B] :
( ~ element(A,B)
| empty(B)
| in(A,B) ),
inference(specialize,[],[normalize_0_20]) ).
fof(normalize_0_22,plain,
! [A,B] :
( A = B
| ? [C] :
( ~ in(C,A)
<=> in(C,B) ) ),
inference(canonicalize,[],[t2_tarski]) ).
fof(normalize_0_23,plain,
! [A,B] :
( A = B
| ? [C] :
( ~ in(C,A)
<=> in(C,B) ) ),
inference(specialize,[],[normalize_0_22]) ).
fof(normalize_0_24,plain,
! [A,B] :
( ( ~ in(skolemFOFtoCNF_C_3(A,B),A)
| ~ in(skolemFOFtoCNF_C_3(A,B),B)
| A = B )
& ( A = B
| in(skolemFOFtoCNF_C_3(A,B),A)
| in(skolemFOFtoCNF_C_3(A,B),B) ) ),
inference(clausify,[],[normalize_0_23]) ).
fof(normalize_0_25,plain,
! [A,B] :
( A = B
| in(skolemFOFtoCNF_C_3(A,B),A)
| in(skolemFOFtoCNF_C_3(A,B),B) ),
inference(conjunct,[],[normalize_0_24]) ).
fof(normalize_0_26,plain,
! [A,B] :
( ~ in(A,B)
| element(A,B) ),
inference(canonicalize,[],[t1_subset]) ).
fof(normalize_0_27,plain,
! [A,B] :
( ~ in(A,B)
| element(A,B) ),
inference(specialize,[],[normalize_0_26]) ).
fof(normalize_0_28,plain,
! [A,B,C] :
( ~ element(B,powerset(C))
| ~ in(A,B)
| element(A,C) ),
inference(canonicalize,[],[t4_subset]) ).
fof(normalize_0_29,plain,
! [A,B,C] :
( ~ element(B,powerset(C))
| ~ in(A,B)
| element(A,C) ),
inference(specialize,[],[normalize_0_28]) ).
fof(normalize_0_30,plain,
! [A,B] :
( ~ in(skolemFOFtoCNF_C_3(A,B),A)
| ~ in(skolemFOFtoCNF_C_3(A,B),B)
| A = B ),
inference(conjunct,[],[normalize_0_24]) ).
fof(normalize_0_31,plain,
! [D] :
( ~ in(D,skolemFOFtoCNF_B_1)
| ? [E] : in(ordered_pair(D,E),skolemFOFtoCNF_C_4) ),
inference(conjunct,[],[normalize_0_1]) ).
fof(normalize_0_32,plain,
! [D] :
( ~ in(D,skolemFOFtoCNF_B_1)
| ? [E] : in(ordered_pair(D,E),skolemFOFtoCNF_C_4) ),
inference(specialize,[],[normalize_0_31]) ).
fof(normalize_0_33,plain,
! [D] :
( ~ in(D,skolemFOFtoCNF_B_1)
| in(ordered_pair(D,skolemFOFtoCNF_E(D)),skolemFOFtoCNF_C_4) ),
inference(clausify,[],[normalize_0_32]) ).
fof(normalize_0_34,plain,
! [A,B,C] :
( ~ in(ordered_pair(A,B),C)
| ~ relation(C)
| ( in(A,relation_dom(C))
& in(B,relation_rng(C)) ) ),
inference(canonicalize,[],[t20_relat_1]) ).
fof(normalize_0_35,plain,
! [A,B,C] :
( ~ in(ordered_pair(A,B),C)
| ~ relation(C)
| ( in(A,relation_dom(C))
& in(B,relation_rng(C)) ) ),
inference(specialize,[],[normalize_0_34]) ).
fof(normalize_0_36,plain,
! [A,B,C] :
( ( ~ in(ordered_pair(A,B),C)
| ~ relation(C)
| in(A,relation_dom(C)) )
& ( ~ in(ordered_pair(A,B),C)
| ~ relation(C)
| in(B,relation_rng(C)) ) ),
inference(clausify,[],[normalize_0_35]) ).
fof(normalize_0_37,plain,
! [A,B,C] :
( ~ in(ordered_pair(A,B),C)
| ~ relation(C)
| in(A,relation_dom(C)) ),
inference(conjunct,[],[normalize_0_36]) ).
fof(normalize_0_38,plain,
! [A,B,C] :
( ~ element(C,powerset(cartesian_product2(A,B)))
| relation(C) ),
inference(canonicalize,[],[cc1_relset_1]) ).
fof(normalize_0_39,plain,
! [A,B,C] :
( ~ element(C,powerset(cartesian_product2(A,B)))
| relation(C) ),
inference(specialize,[],[normalize_0_38]) ).
fof(normalize_0_40,plain,
! [A,B,C] :
( ~ relation_of2_as_subset(C,A,B)
| element(C,powerset(cartesian_product2(A,B))) ),
inference(canonicalize,[],[dt_m2_relset_1]) ).
fof(normalize_0_41,plain,
! [A,B,C] :
( ~ relation_of2_as_subset(C,A,B)
| element(C,powerset(cartesian_product2(A,B))) ),
inference(specialize,[],[normalize_0_40]) ).
cnf(refute_0_0,plain,
relation_dom_as_subset(skolemFOFtoCNF_B_1,skolemFOFtoCNF_A_2,skolemFOFtoCNF_C_4) != skolemFOFtoCNF_B_1,
inference(canonicalize,[],[normalize_0_2]) ).
cnf(refute_0_1,plain,
relation_of2_as_subset(skolemFOFtoCNF_C_4,skolemFOFtoCNF_B_1,skolemFOFtoCNF_A_2),
inference(canonicalize,[],[normalize_0_3]) ).
cnf(refute_0_2,plain,
( ~ relation_of2_as_subset(C,A,B)
| relation_of2(C,A,B) ),
inference(canonicalize,[],[normalize_0_7]) ).
cnf(refute_0_3,plain,
( ~ relation_of2_as_subset(skolemFOFtoCNF_C_4,skolemFOFtoCNF_B_1,skolemFOFtoCNF_A_2)
| relation_of2(skolemFOFtoCNF_C_4,skolemFOFtoCNF_B_1,skolemFOFtoCNF_A_2) ),
inference(subst,[],[refute_0_2:[bind(A,$fot(skolemFOFtoCNF_B_1)),bind(B,$fot(skolemFOFtoCNF_A_2)),bind(C,$fot(skolemFOFtoCNF_C_4))]]) ).
cnf(refute_0_4,plain,
relation_of2(skolemFOFtoCNF_C_4,skolemFOFtoCNF_B_1,skolemFOFtoCNF_A_2),
inference(resolve,[$cnf( relation_of2_as_subset(skolemFOFtoCNF_C_4,skolemFOFtoCNF_B_1,skolemFOFtoCNF_A_2) )],[refute_0_1,refute_0_3]) ).
cnf(refute_0_5,plain,
( ~ relation_of2(C,A,B)
| relation_dom_as_subset(A,B,C) = relation_dom(C) ),
inference(canonicalize,[],[normalize_0_9]) ).
cnf(refute_0_6,plain,
( ~ relation_of2(skolemFOFtoCNF_C_4,skolemFOFtoCNF_B_1,skolemFOFtoCNF_A_2)
| relation_dom_as_subset(skolemFOFtoCNF_B_1,skolemFOFtoCNF_A_2,skolemFOFtoCNF_C_4) = relation_dom(skolemFOFtoCNF_C_4) ),
inference(subst,[],[refute_0_5:[bind(A,$fot(skolemFOFtoCNF_B_1)),bind(B,$fot(skolemFOFtoCNF_A_2)),bind(C,$fot(skolemFOFtoCNF_C_4))]]) ).
cnf(refute_0_7,plain,
relation_dom_as_subset(skolemFOFtoCNF_B_1,skolemFOFtoCNF_A_2,skolemFOFtoCNF_C_4) = relation_dom(skolemFOFtoCNF_C_4),
inference(resolve,[$cnf( relation_of2(skolemFOFtoCNF_C_4,skolemFOFtoCNF_B_1,skolemFOFtoCNF_A_2) )],[refute_0_4,refute_0_6]) ).
cnf(refute_0_8,plain,
( relation_dom(skolemFOFtoCNF_C_4) != skolemFOFtoCNF_B_1
| relation_dom_as_subset(skolemFOFtoCNF_B_1,skolemFOFtoCNF_A_2,skolemFOFtoCNF_C_4) != relation_dom(skolemFOFtoCNF_C_4)
| relation_dom_as_subset(skolemFOFtoCNF_B_1,skolemFOFtoCNF_A_2,skolemFOFtoCNF_C_4) = skolemFOFtoCNF_B_1 ),
introduced(tautology,[equality,[$cnf( $equal(relation_dom_as_subset(skolemFOFtoCNF_B_1,skolemFOFtoCNF_A_2,skolemFOFtoCNF_C_4),relation_dom(skolemFOFtoCNF_C_4)) ),[1],$fot(skolemFOFtoCNF_B_1)]]) ).
cnf(refute_0_9,plain,
( relation_dom(skolemFOFtoCNF_C_4) != skolemFOFtoCNF_B_1
| relation_dom_as_subset(skolemFOFtoCNF_B_1,skolemFOFtoCNF_A_2,skolemFOFtoCNF_C_4) = skolemFOFtoCNF_B_1 ),
inference(resolve,[$cnf( $equal(relation_dom_as_subset(skolemFOFtoCNF_B_1,skolemFOFtoCNF_A_2,skolemFOFtoCNF_C_4),relation_dom(skolemFOFtoCNF_C_4)) )],[refute_0_7,refute_0_8]) ).
cnf(refute_0_10,plain,
relation_dom(skolemFOFtoCNF_C_4) != skolemFOFtoCNF_B_1,
inference(resolve,[$cnf( $equal(relation_dom_as_subset(skolemFOFtoCNF_B_1,skolemFOFtoCNF_A_2,skolemFOFtoCNF_C_4),skolemFOFtoCNF_B_1) )],[refute_0_9,refute_0_0]) ).
cnf(refute_0_11,plain,
( ~ relation_of2(C,A,B)
| element(relation_dom_as_subset(A,B,C),powerset(A)) ),
inference(canonicalize,[],[normalize_0_11]) ).
cnf(refute_0_12,plain,
( ~ relation_of2(skolemFOFtoCNF_C_4,skolemFOFtoCNF_B_1,skolemFOFtoCNF_A_2)
| element(relation_dom_as_subset(skolemFOFtoCNF_B_1,skolemFOFtoCNF_A_2,skolemFOFtoCNF_C_4),powerset(skolemFOFtoCNF_B_1)) ),
inference(subst,[],[refute_0_11:[bind(A,$fot(skolemFOFtoCNF_B_1)),bind(B,$fot(skolemFOFtoCNF_A_2)),bind(C,$fot(skolemFOFtoCNF_C_4))]]) ).
cnf(refute_0_13,plain,
element(relation_dom_as_subset(skolemFOFtoCNF_B_1,skolemFOFtoCNF_A_2,skolemFOFtoCNF_C_4),powerset(skolemFOFtoCNF_B_1)),
inference(resolve,[$cnf( relation_of2(skolemFOFtoCNF_C_4,skolemFOFtoCNF_B_1,skolemFOFtoCNF_A_2) )],[refute_0_4,refute_0_12]) ).
cnf(refute_0_14,plain,
( relation_dom_as_subset(skolemFOFtoCNF_B_1,skolemFOFtoCNF_A_2,skolemFOFtoCNF_C_4) != relation_dom(skolemFOFtoCNF_C_4)
| ~ element(relation_dom_as_subset(skolemFOFtoCNF_B_1,skolemFOFtoCNF_A_2,skolemFOFtoCNF_C_4),powerset(skolemFOFtoCNF_B_1))
| element(relation_dom(skolemFOFtoCNF_C_4),powerset(skolemFOFtoCNF_B_1)) ),
introduced(tautology,[equality,[$cnf( element(relation_dom_as_subset(skolemFOFtoCNF_B_1,skolemFOFtoCNF_A_2,skolemFOFtoCNF_C_4),powerset(skolemFOFtoCNF_B_1)) ),[0],$fot(relation_dom(skolemFOFtoCNF_C_4))]]) ).
cnf(refute_0_15,plain,
( ~ element(relation_dom_as_subset(skolemFOFtoCNF_B_1,skolemFOFtoCNF_A_2,skolemFOFtoCNF_C_4),powerset(skolemFOFtoCNF_B_1))
| element(relation_dom(skolemFOFtoCNF_C_4),powerset(skolemFOFtoCNF_B_1)) ),
inference(resolve,[$cnf( $equal(relation_dom_as_subset(skolemFOFtoCNF_B_1,skolemFOFtoCNF_A_2,skolemFOFtoCNF_C_4),relation_dom(skolemFOFtoCNF_C_4)) )],[refute_0_7,refute_0_14]) ).
cnf(refute_0_16,plain,
element(relation_dom(skolemFOFtoCNF_C_4),powerset(skolemFOFtoCNF_B_1)),
inference(resolve,[$cnf( element(relation_dom_as_subset(skolemFOFtoCNF_B_1,skolemFOFtoCNF_A_2,skolemFOFtoCNF_C_4),powerset(skolemFOFtoCNF_B_1)) )],[refute_0_13,refute_0_15]) ).
cnf(refute_0_17,plain,
( ~ element(B,powerset(C))
| ~ empty(C)
| ~ in(A,B) ),
inference(canonicalize,[],[normalize_0_13]) ).
cnf(refute_0_18,plain,
( ~ element(relation_dom(skolemFOFtoCNF_C_4),powerset(skolemFOFtoCNF_B_1))
| ~ empty(skolemFOFtoCNF_B_1)
| ~ in(X_160,relation_dom(skolemFOFtoCNF_C_4)) ),
inference(subst,[],[refute_0_17:[bind(A,$fot(X_160)),bind(B,$fot(relation_dom(skolemFOFtoCNF_C_4))),bind(C,$fot(skolemFOFtoCNF_B_1))]]) ).
cnf(refute_0_19,plain,
( ~ empty(skolemFOFtoCNF_B_1)
| ~ in(X_160,relation_dom(skolemFOFtoCNF_C_4)) ),
inference(resolve,[$cnf( element(relation_dom(skolemFOFtoCNF_C_4),powerset(skolemFOFtoCNF_B_1)) )],[refute_0_16,refute_0_18]) ).
cnf(refute_0_20,plain,
( ~ empty(skolemFOFtoCNF_B_1)
| ~ in(skolemFOFtoCNF_C_3(empty_set,relation_dom(skolemFOFtoCNF_C_4)),relation_dom(skolemFOFtoCNF_C_4)) ),
inference(subst,[],[refute_0_19:[bind(X_160,$fot(skolemFOFtoCNF_C_3(empty_set,relation_dom(skolemFOFtoCNF_C_4))))]]) ).
cnf(refute_0_21,plain,
element(skolemFOFtoCNF_B(A),A),
inference(canonicalize,[],[normalize_0_16]) ).
cnf(refute_0_22,plain,
element(skolemFOFtoCNF_B(powerset(X_162)),powerset(X_162)),
inference(subst,[],[refute_0_21:[bind(A,$fot(powerset(X_162)))]]) ).
cnf(refute_0_23,plain,
( ~ element(skolemFOFtoCNF_B(powerset(X_162)),powerset(X_162))
| ~ empty(X_162)
| ~ in(X_160,skolemFOFtoCNF_B(powerset(X_162))) ),
inference(subst,[],[refute_0_17:[bind(A,$fot(X_160)),bind(B,$fot(skolemFOFtoCNF_B(powerset(X_162)))),bind(C,$fot(X_162))]]) ).
cnf(refute_0_24,plain,
( ~ empty(X_162)
| ~ in(X_160,skolemFOFtoCNF_B(powerset(X_162))) ),
inference(resolve,[$cnf( element(skolemFOFtoCNF_B(powerset(X_162)),powerset(X_162)) )],[refute_0_22,refute_0_23]) ).
cnf(refute_0_25,plain,
( ~ empty(empty_set)
| ~ in(X_160,skolemFOFtoCNF_B(powerset(empty_set))) ),
inference(subst,[],[refute_0_24:[bind(X_162,$fot(empty_set))]]) ).
cnf(refute_0_26,plain,
( ~ empty(A)
| A = empty_set ),
inference(canonicalize,[],[normalize_0_18]) ).
cnf(refute_0_27,plain,
( ~ empty(skolemFOFtoCNF_B(powerset(empty_set)))
| skolemFOFtoCNF_B(powerset(empty_set)) = empty_set ),
inference(subst,[],[refute_0_26:[bind(A,$fot(skolemFOFtoCNF_B(powerset(empty_set))))]]) ).
cnf(refute_0_28,plain,
empty(empty_set),
inference(canonicalize,[],[normalize_0_19]) ).
cnf(refute_0_29,plain,
element(skolemFOFtoCNF_B(X_67),X_67),
inference(subst,[],[refute_0_21:[bind(A,$fot(X_67))]]) ).
cnf(refute_0_30,plain,
( ~ element(A,B)
| empty(B)
| in(A,B) ),
inference(canonicalize,[],[normalize_0_21]) ).
cnf(refute_0_31,plain,
( ~ element(skolemFOFtoCNF_B(X_67),X_67)
| empty(X_67)
| in(skolemFOFtoCNF_B(X_67),X_67) ),
inference(subst,[],[refute_0_30:[bind(A,$fot(skolemFOFtoCNF_B(X_67))),bind(B,$fot(X_67))]]) ).
cnf(refute_0_32,plain,
( empty(X_67)
| in(skolemFOFtoCNF_B(X_67),X_67) ),
inference(resolve,[$cnf( element(skolemFOFtoCNF_B(X_67),X_67) )],[refute_0_29,refute_0_31]) ).
cnf(refute_0_33,plain,
( empty(skolemFOFtoCNF_B(powerset(X_166)))
| in(skolemFOFtoCNF_B(skolemFOFtoCNF_B(powerset(X_166))),skolemFOFtoCNF_B(powerset(X_166))) ),
inference(subst,[],[refute_0_32:[bind(X_67,$fot(skolemFOFtoCNF_B(powerset(X_166))))]]) ).
cnf(refute_0_34,plain,
( ~ empty(X_166)
| ~ in(skolemFOFtoCNF_B(skolemFOFtoCNF_B(powerset(X_166))),skolemFOFtoCNF_B(powerset(X_166))) ),
inference(subst,[],[refute_0_24:[bind(X_160,$fot(skolemFOFtoCNF_B(skolemFOFtoCNF_B(powerset(X_166))))),bind(X_162,$fot(X_166))]]) ).
cnf(refute_0_35,plain,
( ~ empty(X_166)
| empty(skolemFOFtoCNF_B(powerset(X_166))) ),
inference(resolve,[$cnf( in(skolemFOFtoCNF_B(skolemFOFtoCNF_B(powerset(X_166))),skolemFOFtoCNF_B(powerset(X_166))) )],[refute_0_33,refute_0_34]) ).
cnf(refute_0_36,plain,
( ~ empty(empty_set)
| empty(skolemFOFtoCNF_B(powerset(empty_set))) ),
inference(subst,[],[refute_0_35:[bind(X_166,$fot(empty_set))]]) ).
cnf(refute_0_37,plain,
empty(skolemFOFtoCNF_B(powerset(empty_set))),
inference(resolve,[$cnf( empty(empty_set) )],[refute_0_28,refute_0_36]) ).
cnf(refute_0_38,plain,
skolemFOFtoCNF_B(powerset(empty_set)) = empty_set,
inference(resolve,[$cnf( empty(skolemFOFtoCNF_B(powerset(empty_set))) )],[refute_0_37,refute_0_27]) ).
cnf(refute_0_39,plain,
( skolemFOFtoCNF_B(powerset(empty_set)) != empty_set
| ~ in(X_160,empty_set)
| in(X_160,skolemFOFtoCNF_B(powerset(empty_set))) ),
introduced(tautology,[equality,[$cnf( ~ in(X_160,skolemFOFtoCNF_B(powerset(empty_set))) ),[1],$fot(empty_set)]]) ).
cnf(refute_0_40,plain,
( ~ in(X_160,empty_set)
| in(X_160,skolemFOFtoCNF_B(powerset(empty_set))) ),
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_B(powerset(empty_set)),empty_set) )],[refute_0_38,refute_0_39]) ).
cnf(refute_0_41,plain,
( ~ empty(empty_set)
| ~ in(X_160,empty_set) ),
inference(resolve,[$cnf( in(X_160,skolemFOFtoCNF_B(powerset(empty_set))) )],[refute_0_40,refute_0_25]) ).
cnf(refute_0_42,plain,
~ in(X_160,empty_set),
inference(resolve,[$cnf( empty(empty_set) )],[refute_0_28,refute_0_41]) ).
cnf(refute_0_43,plain,
~ in(skolemFOFtoCNF_C_3(empty_set,X_211),empty_set),
inference(subst,[],[refute_0_42:[bind(X_160,$fot(skolemFOFtoCNF_C_3(empty_set,X_211)))]]) ).
cnf(refute_0_44,plain,
( A = B
| in(skolemFOFtoCNF_C_3(A,B),A)
| in(skolemFOFtoCNF_C_3(A,B),B) ),
inference(canonicalize,[],[normalize_0_25]) ).
cnf(refute_0_45,plain,
( empty_set = X_211
| in(skolemFOFtoCNF_C_3(empty_set,X_211),X_211)
| in(skolemFOFtoCNF_C_3(empty_set,X_211),empty_set) ),
inference(subst,[],[refute_0_44:[bind(A,$fot(empty_set)),bind(B,$fot(X_211))]]) ).
cnf(refute_0_46,plain,
( empty_set = X_211
| in(skolemFOFtoCNF_C_3(empty_set,X_211),X_211) ),
inference(resolve,[$cnf( in(skolemFOFtoCNF_C_3(empty_set,X_211),empty_set) )],[refute_0_45,refute_0_43]) ).
cnf(refute_0_47,plain,
( empty_set = relation_dom(skolemFOFtoCNF_C_4)
| in(skolemFOFtoCNF_C_3(empty_set,relation_dom(skolemFOFtoCNF_C_4)),relation_dom(skolemFOFtoCNF_C_4)) ),
inference(subst,[],[refute_0_46:[bind(X_211,$fot(relation_dom(skolemFOFtoCNF_C_4)))]]) ).
cnf(refute_0_48,plain,
( ~ empty(skolemFOFtoCNF_B_1)
| empty_set = relation_dom(skolemFOFtoCNF_C_4) ),
inference(resolve,[$cnf( in(skolemFOFtoCNF_C_3(empty_set,relation_dom(skolemFOFtoCNF_C_4)),relation_dom(skolemFOFtoCNF_C_4)) )],[refute_0_47,refute_0_20]) ).
cnf(refute_0_49,plain,
( ~ element(skolemFOFtoCNF_C_3(skolemFOFtoCNF_B_1,relation_dom(skolemFOFtoCNF_C_4)),skolemFOFtoCNF_B_1)
| empty(skolemFOFtoCNF_B_1)
| in(skolemFOFtoCNF_C_3(skolemFOFtoCNF_B_1,relation_dom(skolemFOFtoCNF_C_4)),skolemFOFtoCNF_B_1) ),
inference(subst,[],[refute_0_30:[bind(A,$fot(skolemFOFtoCNF_C_3(skolemFOFtoCNF_B_1,relation_dom(skolemFOFtoCNF_C_4)))),bind(B,$fot(skolemFOFtoCNF_B_1))]]) ).
cnf(refute_0_50,plain,
( ~ in(A,B)
| element(A,B) ),
inference(canonicalize,[],[normalize_0_27]) ).
cnf(refute_0_51,plain,
( ~ in(skolemFOFtoCNF_C_3(X_210,X_211),X_210)
| element(skolemFOFtoCNF_C_3(X_210,X_211),X_210) ),
inference(subst,[],[refute_0_50:[bind(A,$fot(skolemFOFtoCNF_C_3(X_210,X_211))),bind(B,$fot(X_210))]]) ).
cnf(refute_0_52,plain,
( X_210 = X_211
| in(skolemFOFtoCNF_C_3(X_210,X_211),X_210)
| in(skolemFOFtoCNF_C_3(X_210,X_211),X_211) ),
inference(subst,[],[refute_0_44:[bind(A,$fot(X_210)),bind(B,$fot(X_211))]]) ).
cnf(refute_0_53,plain,
( X_210 = X_211
| element(skolemFOFtoCNF_C_3(X_210,X_211),X_210)
| in(skolemFOFtoCNF_C_3(X_210,X_211),X_211) ),
inference(resolve,[$cnf( in(skolemFOFtoCNF_C_3(X_210,X_211),X_210) )],[refute_0_52,refute_0_51]) ).
cnf(refute_0_54,plain,
( X_210 = relation_dom(skolemFOFtoCNF_C_4)
| element(skolemFOFtoCNF_C_3(X_210,relation_dom(skolemFOFtoCNF_C_4)),X_210)
| in(skolemFOFtoCNF_C_3(X_210,relation_dom(skolemFOFtoCNF_C_4)),relation_dom(skolemFOFtoCNF_C_4)) ),
inference(subst,[],[refute_0_53:[bind(X_211,$fot(relation_dom(skolemFOFtoCNF_C_4)))]]) ).
cnf(refute_0_55,plain,
( ~ element(B,powerset(C))
| ~ in(A,B)
| element(A,C) ),
inference(canonicalize,[],[normalize_0_29]) ).
cnf(refute_0_56,plain,
( ~ element(relation_dom(skolemFOFtoCNF_C_4),powerset(skolemFOFtoCNF_B_1))
| ~ in(X_233,relation_dom(skolemFOFtoCNF_C_4))
| element(X_233,skolemFOFtoCNF_B_1) ),
inference(subst,[],[refute_0_55:[bind(A,$fot(X_233)),bind(B,$fot(relation_dom(skolemFOFtoCNF_C_4))),bind(C,$fot(skolemFOFtoCNF_B_1))]]) ).
cnf(refute_0_57,plain,
( ~ in(X_233,relation_dom(skolemFOFtoCNF_C_4))
| element(X_233,skolemFOFtoCNF_B_1) ),
inference(resolve,[$cnf( element(relation_dom(skolemFOFtoCNF_C_4),powerset(skolemFOFtoCNF_B_1)) )],[refute_0_16,refute_0_56]) ).
cnf(refute_0_58,plain,
( ~ in(skolemFOFtoCNF_C_3(X_210,relation_dom(skolemFOFtoCNF_C_4)),relation_dom(skolemFOFtoCNF_C_4))
| element(skolemFOFtoCNF_C_3(X_210,relation_dom(skolemFOFtoCNF_C_4)),skolemFOFtoCNF_B_1) ),
inference(subst,[],[refute_0_57:[bind(X_233,$fot(skolemFOFtoCNF_C_3(X_210,relation_dom(skolemFOFtoCNF_C_4))))]]) ).
cnf(refute_0_59,plain,
( X_210 = relation_dom(skolemFOFtoCNF_C_4)
| element(skolemFOFtoCNF_C_3(X_210,relation_dom(skolemFOFtoCNF_C_4)),X_210)
| element(skolemFOFtoCNF_C_3(X_210,relation_dom(skolemFOFtoCNF_C_4)),skolemFOFtoCNF_B_1) ),
inference(resolve,[$cnf( in(skolemFOFtoCNF_C_3(X_210,relation_dom(skolemFOFtoCNF_C_4)),relation_dom(skolemFOFtoCNF_C_4)) )],[refute_0_54,refute_0_58]) ).
cnf(refute_0_60,plain,
( skolemFOFtoCNF_B_1 = relation_dom(skolemFOFtoCNF_C_4)
| element(skolemFOFtoCNF_C_3(skolemFOFtoCNF_B_1,relation_dom(skolemFOFtoCNF_C_4)),skolemFOFtoCNF_B_1) ),
inference(subst,[],[refute_0_59:[bind(X_210,$fot(skolemFOFtoCNF_B_1))]]) ).
cnf(refute_0_61,plain,
X = X,
introduced(tautology,[refl,[$fot(X)]]) ).
cnf(refute_0_62,plain,
( X != X
| X != Y
| Y = X ),
introduced(tautology,[equality,[$cnf( $equal(X,X) ),[0],$fot(Y)]]) ).
cnf(refute_0_63,plain,
( X != Y
| Y = X ),
inference(resolve,[$cnf( $equal(X,X) )],[refute_0_61,refute_0_62]) ).
cnf(refute_0_64,plain,
( skolemFOFtoCNF_B_1 != relation_dom(skolemFOFtoCNF_C_4)
| relation_dom(skolemFOFtoCNF_C_4) = skolemFOFtoCNF_B_1 ),
inference(subst,[],[refute_0_63:[bind(X,$fot(skolemFOFtoCNF_B_1)),bind(Y,$fot(relation_dom(skolemFOFtoCNF_C_4)))]]) ).
cnf(refute_0_65,plain,
skolemFOFtoCNF_B_1 != relation_dom(skolemFOFtoCNF_C_4),
inference(resolve,[$cnf( $equal(relation_dom(skolemFOFtoCNF_C_4),skolemFOFtoCNF_B_1) )],[refute_0_64,refute_0_10]) ).
cnf(refute_0_66,plain,
element(skolemFOFtoCNF_C_3(skolemFOFtoCNF_B_1,relation_dom(skolemFOFtoCNF_C_4)),skolemFOFtoCNF_B_1),
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_B_1,relation_dom(skolemFOFtoCNF_C_4)) )],[refute_0_60,refute_0_65]) ).
cnf(refute_0_67,plain,
( empty(skolemFOFtoCNF_B_1)
| in(skolemFOFtoCNF_C_3(skolemFOFtoCNF_B_1,relation_dom(skolemFOFtoCNF_C_4)),skolemFOFtoCNF_B_1) ),
inference(resolve,[$cnf( element(skolemFOFtoCNF_C_3(skolemFOFtoCNF_B_1,relation_dom(skolemFOFtoCNF_C_4)),skolemFOFtoCNF_B_1) )],[refute_0_66,refute_0_49]) ).
cnf(refute_0_68,plain,
( ~ in(skolemFOFtoCNF_C_3(A,B),A)
| ~ in(skolemFOFtoCNF_C_3(A,B),B)
| A = B ),
inference(canonicalize,[],[normalize_0_30]) ).
cnf(refute_0_69,plain,
( ~ in(skolemFOFtoCNF_C_3(skolemFOFtoCNF_B_1,relation_dom(skolemFOFtoCNF_C_4)),relation_dom(skolemFOFtoCNF_C_4))
| ~ in(skolemFOFtoCNF_C_3(skolemFOFtoCNF_B_1,relation_dom(skolemFOFtoCNF_C_4)),skolemFOFtoCNF_B_1)
| skolemFOFtoCNF_B_1 = relation_dom(skolemFOFtoCNF_C_4) ),
inference(subst,[],[refute_0_68:[bind(A,$fot(skolemFOFtoCNF_B_1)),bind(B,$fot(relation_dom(skolemFOFtoCNF_C_4)))]]) ).
cnf(refute_0_70,plain,
( ~ in(D,skolemFOFtoCNF_B_1)
| in(ordered_pair(D,skolemFOFtoCNF_E(D)),skolemFOFtoCNF_C_4) ),
inference(canonicalize,[],[normalize_0_33]) ).
cnf(refute_0_71,plain,
( ~ in(skolemFOFtoCNF_C_3(skolemFOFtoCNF_B_1,relation_dom(skolemFOFtoCNF_C_4)),skolemFOFtoCNF_B_1)
| in(ordered_pair(skolemFOFtoCNF_C_3(skolemFOFtoCNF_B_1,relation_dom(skolemFOFtoCNF_C_4)),skolemFOFtoCNF_E(skolemFOFtoCNF_C_3(skolemFOFtoCNF_B_1,relation_dom(skolemFOFtoCNF_C_4)))),skolemFOFtoCNF_C_4) ),
inference(subst,[],[refute_0_70:[bind(D,$fot(skolemFOFtoCNF_C_3(skolemFOFtoCNF_B_1,relation_dom(skolemFOFtoCNF_C_4))))]]) ).
cnf(refute_0_72,plain,
( empty(skolemFOFtoCNF_B_1)
| in(ordered_pair(skolemFOFtoCNF_C_3(skolemFOFtoCNF_B_1,relation_dom(skolemFOFtoCNF_C_4)),skolemFOFtoCNF_E(skolemFOFtoCNF_C_3(skolemFOFtoCNF_B_1,relation_dom(skolemFOFtoCNF_C_4)))),skolemFOFtoCNF_C_4) ),
inference(resolve,[$cnf( in(skolemFOFtoCNF_C_3(skolemFOFtoCNF_B_1,relation_dom(skolemFOFtoCNF_C_4)),skolemFOFtoCNF_B_1) )],[refute_0_67,refute_0_71]) ).
cnf(refute_0_73,plain,
( ~ in(ordered_pair(A,B),C)
| ~ relation(C)
| in(A,relation_dom(C)) ),
inference(canonicalize,[],[normalize_0_37]) ).
cnf(refute_0_74,plain,
( ~ in(ordered_pair(skolemFOFtoCNF_C_3(skolemFOFtoCNF_B_1,relation_dom(skolemFOFtoCNF_C_4)),skolemFOFtoCNF_E(skolemFOFtoCNF_C_3(skolemFOFtoCNF_B_1,relation_dom(skolemFOFtoCNF_C_4)))),skolemFOFtoCNF_C_4)
| ~ relation(skolemFOFtoCNF_C_4)
| in(skolemFOFtoCNF_C_3(skolemFOFtoCNF_B_1,relation_dom(skolemFOFtoCNF_C_4)),relation_dom(skolemFOFtoCNF_C_4)) ),
inference(subst,[],[refute_0_73:[bind(A,$fot(skolemFOFtoCNF_C_3(skolemFOFtoCNF_B_1,relation_dom(skolemFOFtoCNF_C_4)))),bind(B,$fot(skolemFOFtoCNF_E(skolemFOFtoCNF_C_3(skolemFOFtoCNF_B_1,relation_dom(skolemFOFtoCNF_C_4))))),bind(C,$fot(skolemFOFtoCNF_C_4))]]) ).
cnf(refute_0_75,plain,
( ~ relation(skolemFOFtoCNF_C_4)
| empty(skolemFOFtoCNF_B_1)
| in(skolemFOFtoCNF_C_3(skolemFOFtoCNF_B_1,relation_dom(skolemFOFtoCNF_C_4)),relation_dom(skolemFOFtoCNF_C_4)) ),
inference(resolve,[$cnf( in(ordered_pair(skolemFOFtoCNF_C_3(skolemFOFtoCNF_B_1,relation_dom(skolemFOFtoCNF_C_4)),skolemFOFtoCNF_E(skolemFOFtoCNF_C_3(skolemFOFtoCNF_B_1,relation_dom(skolemFOFtoCNF_C_4)))),skolemFOFtoCNF_C_4) )],[refute_0_72,refute_0_74]) ).
cnf(refute_0_76,plain,
( ~ element(C,powerset(cartesian_product2(A,B)))
| relation(C) ),
inference(canonicalize,[],[normalize_0_39]) ).
cnf(refute_0_77,plain,
( ~ element(skolemFOFtoCNF_C_4,powerset(cartesian_product2(skolemFOFtoCNF_B_1,skolemFOFtoCNF_A_2)))
| relation(skolemFOFtoCNF_C_4) ),
inference(subst,[],[refute_0_76:[bind(A,$fot(skolemFOFtoCNF_B_1)),bind(B,$fot(skolemFOFtoCNF_A_2)),bind(C,$fot(skolemFOFtoCNF_C_4))]]) ).
cnf(refute_0_78,plain,
( ~ relation_of2_as_subset(C,A,B)
| element(C,powerset(cartesian_product2(A,B))) ),
inference(canonicalize,[],[normalize_0_41]) ).
cnf(refute_0_79,plain,
( ~ relation_of2_as_subset(skolemFOFtoCNF_C_4,skolemFOFtoCNF_B_1,skolemFOFtoCNF_A_2)
| element(skolemFOFtoCNF_C_4,powerset(cartesian_product2(skolemFOFtoCNF_B_1,skolemFOFtoCNF_A_2))) ),
inference(subst,[],[refute_0_78:[bind(A,$fot(skolemFOFtoCNF_B_1)),bind(B,$fot(skolemFOFtoCNF_A_2)),bind(C,$fot(skolemFOFtoCNF_C_4))]]) ).
cnf(refute_0_80,plain,
element(skolemFOFtoCNF_C_4,powerset(cartesian_product2(skolemFOFtoCNF_B_1,skolemFOFtoCNF_A_2))),
inference(resolve,[$cnf( relation_of2_as_subset(skolemFOFtoCNF_C_4,skolemFOFtoCNF_B_1,skolemFOFtoCNF_A_2) )],[refute_0_1,refute_0_79]) ).
cnf(refute_0_81,plain,
relation(skolemFOFtoCNF_C_4),
inference(resolve,[$cnf( element(skolemFOFtoCNF_C_4,powerset(cartesian_product2(skolemFOFtoCNF_B_1,skolemFOFtoCNF_A_2))) )],[refute_0_80,refute_0_77]) ).
cnf(refute_0_82,plain,
( empty(skolemFOFtoCNF_B_1)
| in(skolemFOFtoCNF_C_3(skolemFOFtoCNF_B_1,relation_dom(skolemFOFtoCNF_C_4)),relation_dom(skolemFOFtoCNF_C_4)) ),
inference(resolve,[$cnf( relation(skolemFOFtoCNF_C_4) )],[refute_0_81,refute_0_75]) ).
cnf(refute_0_83,plain,
( ~ in(skolemFOFtoCNF_C_3(skolemFOFtoCNF_B_1,relation_dom(skolemFOFtoCNF_C_4)),skolemFOFtoCNF_B_1)
| skolemFOFtoCNF_B_1 = relation_dom(skolemFOFtoCNF_C_4)
| empty(skolemFOFtoCNF_B_1) ),
inference(resolve,[$cnf( in(skolemFOFtoCNF_C_3(skolemFOFtoCNF_B_1,relation_dom(skolemFOFtoCNF_C_4)),relation_dom(skolemFOFtoCNF_C_4)) )],[refute_0_82,refute_0_69]) ).
cnf(refute_0_84,plain,
( ~ in(skolemFOFtoCNF_C_3(skolemFOFtoCNF_B_1,relation_dom(skolemFOFtoCNF_C_4)),skolemFOFtoCNF_B_1)
| empty(skolemFOFtoCNF_B_1) ),
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_B_1,relation_dom(skolemFOFtoCNF_C_4)) )],[refute_0_83,refute_0_65]) ).
cnf(refute_0_85,plain,
empty(skolemFOFtoCNF_B_1),
inference(resolve,[$cnf( in(skolemFOFtoCNF_C_3(skolemFOFtoCNF_B_1,relation_dom(skolemFOFtoCNF_C_4)),skolemFOFtoCNF_B_1) )],[refute_0_67,refute_0_84]) ).
cnf(refute_0_86,plain,
empty_set = relation_dom(skolemFOFtoCNF_C_4),
inference(resolve,[$cnf( empty(skolemFOFtoCNF_B_1) )],[refute_0_85,refute_0_48]) ).
cnf(refute_0_87,plain,
( empty_set != relation_dom(skolemFOFtoCNF_C_4)
| relation_dom(skolemFOFtoCNF_C_4) = empty_set ),
inference(subst,[],[refute_0_63:[bind(X,$fot(empty_set)),bind(Y,$fot(relation_dom(skolemFOFtoCNF_C_4)))]]) ).
cnf(refute_0_88,plain,
relation_dom(skolemFOFtoCNF_C_4) = empty_set,
inference(resolve,[$cnf( $equal(empty_set,relation_dom(skolemFOFtoCNF_C_4)) )],[refute_0_86,refute_0_87]) ).
cnf(refute_0_89,plain,
( empty_set != skolemFOFtoCNF_B_1
| relation_dom(skolemFOFtoCNF_C_4) != empty_set
| relation_dom(skolemFOFtoCNF_C_4) = skolemFOFtoCNF_B_1 ),
introduced(tautology,[equality,[$cnf( $equal(relation_dom(skolemFOFtoCNF_C_4),empty_set) ),[1],$fot(skolemFOFtoCNF_B_1)]]) ).
cnf(refute_0_90,plain,
( empty_set != skolemFOFtoCNF_B_1
| relation_dom(skolemFOFtoCNF_C_4) = skolemFOFtoCNF_B_1 ),
inference(resolve,[$cnf( $equal(relation_dom(skolemFOFtoCNF_C_4),empty_set) )],[refute_0_88,refute_0_89]) ).
cnf(refute_0_91,plain,
( ~ empty(skolemFOFtoCNF_B_1)
| skolemFOFtoCNF_B_1 = empty_set ),
inference(subst,[],[refute_0_26:[bind(A,$fot(skolemFOFtoCNF_B_1))]]) ).
cnf(refute_0_92,plain,
skolemFOFtoCNF_B_1 = empty_set,
inference(resolve,[$cnf( empty(skolemFOFtoCNF_B_1) )],[refute_0_85,refute_0_91]) ).
cnf(refute_0_93,plain,
( empty_set != empty_set
| skolemFOFtoCNF_B_1 != empty_set
| empty_set = skolemFOFtoCNF_B_1 ),
introduced(tautology,[equality,[$cnf( ~ $equal(empty_set,skolemFOFtoCNF_B_1) ),[1],$fot(empty_set)]]) ).
cnf(refute_0_94,plain,
( empty_set != empty_set
| empty_set = skolemFOFtoCNF_B_1 ),
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_B_1,empty_set) )],[refute_0_92,refute_0_93]) ).
cnf(refute_0_95,plain,
( empty_set != empty_set
| relation_dom(skolemFOFtoCNF_C_4) = skolemFOFtoCNF_B_1 ),
inference(resolve,[$cnf( $equal(empty_set,skolemFOFtoCNF_B_1) )],[refute_0_94,refute_0_90]) ).
cnf(refute_0_96,plain,
empty_set != empty_set,
inference(resolve,[$cnf( $equal(relation_dom(skolemFOFtoCNF_C_4),skolemFOFtoCNF_B_1) )],[refute_0_95,refute_0_10]) ).
cnf(refute_0_97,plain,
empty_set = empty_set,
introduced(tautology,[refl,[$fot(empty_set)]]) ).
cnf(refute_0_98,plain,
$false,
inference(resolve,[$cnf( $equal(empty_set,empty_set) )],[refute_0_97,refute_0_96]) ).
fof(negate_1_0,plain,
~ ! [A,B,C] :
( ( relation_of2_as_subset(C,B,A)
& relation_dom_as_subset(B,A,C) = B )
=> ! [D] :
( in(D,B)
=> ~ ! [E] : ~ in(ordered_pair(D,E),C) ) ),
inference(negate,[],[subgoal_1]) ).
fof(normalize_1_0,plain,
? [A,B,C] :
( relation_dom_as_subset(B,A,C) = B
& relation_of2_as_subset(C,B,A)
& ? [D] :
( in(D,B)
& ! [E] : ~ in(ordered_pair(D,E),C) ) ),
inference(canonicalize,[],[negate_1_0]) ).
fof(normalize_1_1,plain,
( relation_dom_as_subset(skolemFOFtoCNF_B_2,skolemFOFtoCNF_A_3,skolemFOFtoCNF_C_5) = skolemFOFtoCNF_B_2
& relation_of2_as_subset(skolemFOFtoCNF_C_5,skolemFOFtoCNF_B_2,skolemFOFtoCNF_A_3)
& ? [D] :
( in(D,skolemFOFtoCNF_B_2)
& ! [E] : ~ in(ordered_pair(D,E),skolemFOFtoCNF_C_5) ) ),
inference(skolemize,[],[normalize_1_0]) ).
fof(normalize_1_2,plain,
? [D] :
( in(D,skolemFOFtoCNF_B_2)
& ! [E] : ~ in(ordered_pair(D,E),skolemFOFtoCNF_C_5) ),
inference(conjunct,[],[normalize_1_1]) ).
fof(normalize_1_3,plain,
( in(skolemFOFtoCNF_D_2,skolemFOFtoCNF_B_2)
& ! [E] : ~ in(ordered_pair(skolemFOFtoCNF_D_2,E),skolemFOFtoCNF_C_5) ),
inference(skolemize,[],[normalize_1_2]) ).
fof(normalize_1_4,plain,
in(skolemFOFtoCNF_D_2,skolemFOFtoCNF_B_2),
inference(conjunct,[],[normalize_1_3]) ).
fof(normalize_1_5,plain,
! [A] :
( ~ relation(A)
| ! [B] :
( B != relation_dom(A)
<=> ? [C] :
( ~ in(C,B)
<=> ? [D] : in(ordered_pair(C,D),A) ) ) ),
inference(canonicalize,[],[d4_relat_1]) ).
fof(normalize_1_6,plain,
! [A] :
( ~ relation(A)
| ! [B] :
( B != relation_dom(A)
<=> ? [C] :
( ~ in(C,B)
<=> ? [D] : in(ordered_pair(C,D),A) ) ) ),
inference(specialize,[],[normalize_1_5]) ).
fof(normalize_1_7,plain,
! [A,B,C,D] :
( ( B != relation_dom(A)
| ~ in(C,B)
| ~ relation(A)
| in(ordered_pair(C,skolemFOFtoCNF_D_1(A,C)),A) )
& ( B != relation_dom(A)
| ~ in(ordered_pair(C,D),A)
| ~ relation(A)
| in(C,B) )
& ( ~ in(ordered_pair(skolemFOFtoCNF_C(A,B),D),A)
| ~ in(skolemFOFtoCNF_C(A,B),B)
| ~ relation(A)
| B = relation_dom(A) )
& ( ~ relation(A)
| B = relation_dom(A)
| in(ordered_pair(skolemFOFtoCNF_C(A,B),skolemFOFtoCNF_D(A,B)),A)
| in(skolemFOFtoCNF_C(A,B),B) ) ),
inference(clausify,[],[normalize_1_6]) ).
fof(normalize_1_8,plain,
! [A,B,C] :
( B != relation_dom(A)
| ~ in(C,B)
| ~ relation(A)
| in(ordered_pair(C,skolemFOFtoCNF_D_1(A,C)),A) ),
inference(conjunct,[],[normalize_1_7]) ).
fof(normalize_1_9,plain,
relation_of2_as_subset(skolemFOFtoCNF_C_5,skolemFOFtoCNF_B_2,skolemFOFtoCNF_A_3),
inference(conjunct,[],[normalize_1_1]) ).
fof(normalize_1_10,plain,
! [A,B,C] :
( ~ relation_of2(C,A,B)
<=> ~ relation_of2_as_subset(C,A,B) ),
inference(canonicalize,[],[redefinition_m2_relset_1]) ).
fof(normalize_1_11,plain,
! [A,B,C] :
( ~ relation_of2(C,A,B)
<=> ~ relation_of2_as_subset(C,A,B) ),
inference(specialize,[],[normalize_1_10]) ).
fof(normalize_1_12,plain,
! [A,B,C] :
( ( ~ relation_of2(C,A,B)
| relation_of2_as_subset(C,A,B) )
& ( ~ relation_of2_as_subset(C,A,B)
| relation_of2(C,A,B) ) ),
inference(clausify,[],[normalize_1_11]) ).
fof(normalize_1_13,plain,
! [A,B,C] :
( ~ relation_of2_as_subset(C,A,B)
| relation_of2(C,A,B) ),
inference(conjunct,[],[normalize_1_12]) ).
fof(normalize_1_14,plain,
! [A,B,C] :
( ~ relation_of2(C,A,B)
| relation_dom_as_subset(A,B,C) = relation_dom(C) ),
inference(canonicalize,[],[redefinition_k4_relset_1]) ).
fof(normalize_1_15,plain,
! [A,B,C] :
( ~ relation_of2(C,A,B)
| relation_dom_as_subset(A,B,C) = relation_dom(C) ),
inference(specialize,[],[normalize_1_14]) ).
fof(normalize_1_16,plain,
relation_dom_as_subset(skolemFOFtoCNF_B_2,skolemFOFtoCNF_A_3,skolemFOFtoCNF_C_5) = skolemFOFtoCNF_B_2,
inference(conjunct,[],[normalize_1_1]) ).
fof(normalize_1_17,plain,
! [A,B,C] :
( ~ element(C,powerset(cartesian_product2(A,B)))
| relation(C) ),
inference(canonicalize,[],[cc1_relset_1]) ).
fof(normalize_1_18,plain,
! [A,B,C] :
( ~ element(C,powerset(cartesian_product2(A,B)))
| relation(C) ),
inference(specialize,[],[normalize_1_17]) ).
fof(normalize_1_19,plain,
! [A,B,C] :
( ~ relation_of2_as_subset(C,A,B)
| element(C,powerset(cartesian_product2(A,B))) ),
inference(canonicalize,[],[dt_m2_relset_1]) ).
fof(normalize_1_20,plain,
! [A,B,C] :
( ~ relation_of2_as_subset(C,A,B)
| element(C,powerset(cartesian_product2(A,B))) ),
inference(specialize,[],[normalize_1_19]) ).
fof(normalize_1_21,plain,
! [E] : ~ in(ordered_pair(skolemFOFtoCNF_D_2,E),skolemFOFtoCNF_C_5),
inference(conjunct,[],[normalize_1_3]) ).
fof(normalize_1_22,plain,
! [E] : ~ in(ordered_pair(skolemFOFtoCNF_D_2,E),skolemFOFtoCNF_C_5),
inference(specialize,[],[normalize_1_21]) ).
cnf(refute_1_0,plain,
in(skolemFOFtoCNF_D_2,skolemFOFtoCNF_B_2),
inference(canonicalize,[],[normalize_1_4]) ).
cnf(refute_1_1,plain,
( B != relation_dom(A)
| ~ in(C,B)
| ~ relation(A)
| in(ordered_pair(C,skolemFOFtoCNF_D_1(A,C)),A) ),
inference(canonicalize,[],[normalize_1_8]) ).
cnf(refute_1_2,plain,
( relation_dom(A) != relation_dom(A)
| ~ in(C,relation_dom(A))
| ~ relation(A)
| in(ordered_pair(C,skolemFOFtoCNF_D_1(A,C)),A) ),
inference(subst,[],[refute_1_1:[bind(B,$fot(relation_dom(A)))]]) ).
cnf(refute_1_3,plain,
relation_dom(A) = relation_dom(A),
introduced(tautology,[refl,[$fot(relation_dom(A))]]) ).
cnf(refute_1_4,plain,
( ~ in(C,relation_dom(A))
| ~ relation(A)
| in(ordered_pair(C,skolemFOFtoCNF_D_1(A,C)),A) ),
inference(resolve,[$cnf( $equal(relation_dom(A),relation_dom(A)) )],[refute_1_3,refute_1_2]) ).
cnf(refute_1_5,plain,
( ~ in(X_497,relation_dom(skolemFOFtoCNF_C_5))
| ~ relation(skolemFOFtoCNF_C_5)
| in(ordered_pair(X_497,skolemFOFtoCNF_D_1(skolemFOFtoCNF_C_5,X_497)),skolemFOFtoCNF_C_5) ),
inference(subst,[],[refute_1_4:[bind(A,$fot(skolemFOFtoCNF_C_5)),bind(C,$fot(X_497))]]) ).
cnf(refute_1_6,plain,
relation_of2_as_subset(skolemFOFtoCNF_C_5,skolemFOFtoCNF_B_2,skolemFOFtoCNF_A_3),
inference(canonicalize,[],[normalize_1_9]) ).
cnf(refute_1_7,plain,
( ~ relation_of2_as_subset(C,A,B)
| relation_of2(C,A,B) ),
inference(canonicalize,[],[normalize_1_13]) ).
cnf(refute_1_8,plain,
( ~ relation_of2_as_subset(skolemFOFtoCNF_C_5,skolemFOFtoCNF_B_2,skolemFOFtoCNF_A_3)
| relation_of2(skolemFOFtoCNF_C_5,skolemFOFtoCNF_B_2,skolemFOFtoCNF_A_3) ),
inference(subst,[],[refute_1_7:[bind(A,$fot(skolemFOFtoCNF_B_2)),bind(B,$fot(skolemFOFtoCNF_A_3)),bind(C,$fot(skolemFOFtoCNF_C_5))]]) ).
cnf(refute_1_9,plain,
relation_of2(skolemFOFtoCNF_C_5,skolemFOFtoCNF_B_2,skolemFOFtoCNF_A_3),
inference(resolve,[$cnf( relation_of2_as_subset(skolemFOFtoCNF_C_5,skolemFOFtoCNF_B_2,skolemFOFtoCNF_A_3) )],[refute_1_6,refute_1_8]) ).
cnf(refute_1_10,plain,
( ~ relation_of2(C,A,B)
| relation_dom_as_subset(A,B,C) = relation_dom(C) ),
inference(canonicalize,[],[normalize_1_15]) ).
cnf(refute_1_11,plain,
( ~ relation_of2(skolemFOFtoCNF_C_5,skolemFOFtoCNF_B_2,skolemFOFtoCNF_A_3)
| relation_dom_as_subset(skolemFOFtoCNF_B_2,skolemFOFtoCNF_A_3,skolemFOFtoCNF_C_5) = relation_dom(skolemFOFtoCNF_C_5) ),
inference(subst,[],[refute_1_10:[bind(A,$fot(skolemFOFtoCNF_B_2)),bind(B,$fot(skolemFOFtoCNF_A_3)),bind(C,$fot(skolemFOFtoCNF_C_5))]]) ).
cnf(refute_1_12,plain,
relation_dom_as_subset(skolemFOFtoCNF_B_2,skolemFOFtoCNF_A_3,skolemFOFtoCNF_C_5) = relation_dom(skolemFOFtoCNF_C_5),
inference(resolve,[$cnf( relation_of2(skolemFOFtoCNF_C_5,skolemFOFtoCNF_B_2,skolemFOFtoCNF_A_3) )],[refute_1_9,refute_1_11]) ).
cnf(refute_1_13,plain,
relation_dom_as_subset(skolemFOFtoCNF_B_2,skolemFOFtoCNF_A_3,skolemFOFtoCNF_C_5) = skolemFOFtoCNF_B_2,
inference(canonicalize,[],[normalize_1_16]) ).
cnf(refute_1_14,plain,
( relation_dom_as_subset(skolemFOFtoCNF_B_2,skolemFOFtoCNF_A_3,skolemFOFtoCNF_C_5) != relation_dom(skolemFOFtoCNF_C_5)
| relation_dom_as_subset(skolemFOFtoCNF_B_2,skolemFOFtoCNF_A_3,skolemFOFtoCNF_C_5) != skolemFOFtoCNF_B_2
| skolemFOFtoCNF_B_2 = relation_dom(skolemFOFtoCNF_C_5) ),
introduced(tautology,[equality,[$cnf( $equal(relation_dom_as_subset(skolemFOFtoCNF_B_2,skolemFOFtoCNF_A_3,skolemFOFtoCNF_C_5),relation_dom(skolemFOFtoCNF_C_5)) ),[0],$fot(skolemFOFtoCNF_B_2)]]) ).
cnf(refute_1_15,plain,
( relation_dom_as_subset(skolemFOFtoCNF_B_2,skolemFOFtoCNF_A_3,skolemFOFtoCNF_C_5) != relation_dom(skolemFOFtoCNF_C_5)
| skolemFOFtoCNF_B_2 = relation_dom(skolemFOFtoCNF_C_5) ),
inference(resolve,[$cnf( $equal(relation_dom_as_subset(skolemFOFtoCNF_B_2,skolemFOFtoCNF_A_3,skolemFOFtoCNF_C_5),skolemFOFtoCNF_B_2) )],[refute_1_13,refute_1_14]) ).
cnf(refute_1_16,plain,
skolemFOFtoCNF_B_2 = relation_dom(skolemFOFtoCNF_C_5),
inference(resolve,[$cnf( $equal(relation_dom_as_subset(skolemFOFtoCNF_B_2,skolemFOFtoCNF_A_3,skolemFOFtoCNF_C_5),relation_dom(skolemFOFtoCNF_C_5)) )],[refute_1_12,refute_1_15]) ).
cnf(refute_1_17,plain,
X = X,
introduced(tautology,[refl,[$fot(X)]]) ).
cnf(refute_1_18,plain,
( X != X
| X != Y
| Y = X ),
introduced(tautology,[equality,[$cnf( $equal(X,X) ),[0],$fot(Y)]]) ).
cnf(refute_1_19,plain,
( X != Y
| Y = X ),
inference(resolve,[$cnf( $equal(X,X) )],[refute_1_17,refute_1_18]) ).
cnf(refute_1_20,plain,
( skolemFOFtoCNF_B_2 != relation_dom(skolemFOFtoCNF_C_5)
| relation_dom(skolemFOFtoCNF_C_5) = skolemFOFtoCNF_B_2 ),
inference(subst,[],[refute_1_19:[bind(X,$fot(skolemFOFtoCNF_B_2)),bind(Y,$fot(relation_dom(skolemFOFtoCNF_C_5)))]]) ).
cnf(refute_1_21,plain,
relation_dom(skolemFOFtoCNF_C_5) = skolemFOFtoCNF_B_2,
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_B_2,relation_dom(skolemFOFtoCNF_C_5)) )],[refute_1_16,refute_1_20]) ).
cnf(refute_1_22,plain,
( relation_dom(skolemFOFtoCNF_C_5) != skolemFOFtoCNF_B_2
| ~ in(X_497,skolemFOFtoCNF_B_2)
| in(X_497,relation_dom(skolemFOFtoCNF_C_5)) ),
introduced(tautology,[equality,[$cnf( ~ in(X_497,relation_dom(skolemFOFtoCNF_C_5)) ),[1],$fot(skolemFOFtoCNF_B_2)]]) ).
cnf(refute_1_23,plain,
( ~ in(X_497,skolemFOFtoCNF_B_2)
| in(X_497,relation_dom(skolemFOFtoCNF_C_5)) ),
inference(resolve,[$cnf( $equal(relation_dom(skolemFOFtoCNF_C_5),skolemFOFtoCNF_B_2) )],[refute_1_21,refute_1_22]) ).
cnf(refute_1_24,plain,
( ~ in(X_497,skolemFOFtoCNF_B_2)
| ~ relation(skolemFOFtoCNF_C_5)
| in(ordered_pair(X_497,skolemFOFtoCNF_D_1(skolemFOFtoCNF_C_5,X_497)),skolemFOFtoCNF_C_5) ),
inference(resolve,[$cnf( in(X_497,relation_dom(skolemFOFtoCNF_C_5)) )],[refute_1_23,refute_1_5]) ).
cnf(refute_1_25,plain,
( ~ element(C,powerset(cartesian_product2(A,B)))
| relation(C) ),
inference(canonicalize,[],[normalize_1_18]) ).
cnf(refute_1_26,plain,
( ~ element(skolemFOFtoCNF_C_5,powerset(cartesian_product2(skolemFOFtoCNF_B_2,skolemFOFtoCNF_A_3)))
| relation(skolemFOFtoCNF_C_5) ),
inference(subst,[],[refute_1_25:[bind(A,$fot(skolemFOFtoCNF_B_2)),bind(B,$fot(skolemFOFtoCNF_A_3)),bind(C,$fot(skolemFOFtoCNF_C_5))]]) ).
cnf(refute_1_27,plain,
( ~ relation_of2_as_subset(C,A,B)
| element(C,powerset(cartesian_product2(A,B))) ),
inference(canonicalize,[],[normalize_1_20]) ).
cnf(refute_1_28,plain,
( ~ relation_of2_as_subset(skolemFOFtoCNF_C_5,skolemFOFtoCNF_B_2,skolemFOFtoCNF_A_3)
| element(skolemFOFtoCNF_C_5,powerset(cartesian_product2(skolemFOFtoCNF_B_2,skolemFOFtoCNF_A_3))) ),
inference(subst,[],[refute_1_27:[bind(A,$fot(skolemFOFtoCNF_B_2)),bind(B,$fot(skolemFOFtoCNF_A_3)),bind(C,$fot(skolemFOFtoCNF_C_5))]]) ).
cnf(refute_1_29,plain,
element(skolemFOFtoCNF_C_5,powerset(cartesian_product2(skolemFOFtoCNF_B_2,skolemFOFtoCNF_A_3))),
inference(resolve,[$cnf( relation_of2_as_subset(skolemFOFtoCNF_C_5,skolemFOFtoCNF_B_2,skolemFOFtoCNF_A_3) )],[refute_1_6,refute_1_28]) ).
cnf(refute_1_30,plain,
relation(skolemFOFtoCNF_C_5),
inference(resolve,[$cnf( element(skolemFOFtoCNF_C_5,powerset(cartesian_product2(skolemFOFtoCNF_B_2,skolemFOFtoCNF_A_3))) )],[refute_1_29,refute_1_26]) ).
cnf(refute_1_31,plain,
( ~ in(X_497,skolemFOFtoCNF_B_2)
| in(ordered_pair(X_497,skolemFOFtoCNF_D_1(skolemFOFtoCNF_C_5,X_497)),skolemFOFtoCNF_C_5) ),
inference(resolve,[$cnf( relation(skolemFOFtoCNF_C_5) )],[refute_1_30,refute_1_24]) ).
cnf(refute_1_32,plain,
( ~ in(skolemFOFtoCNF_D_2,skolemFOFtoCNF_B_2)
| in(ordered_pair(skolemFOFtoCNF_D_2,skolemFOFtoCNF_D_1(skolemFOFtoCNF_C_5,skolemFOFtoCNF_D_2)),skolemFOFtoCNF_C_5) ),
inference(subst,[],[refute_1_31:[bind(X_497,$fot(skolemFOFtoCNF_D_2))]]) ).
cnf(refute_1_33,plain,
in(ordered_pair(skolemFOFtoCNF_D_2,skolemFOFtoCNF_D_1(skolemFOFtoCNF_C_5,skolemFOFtoCNF_D_2)),skolemFOFtoCNF_C_5),
inference(resolve,[$cnf( in(skolemFOFtoCNF_D_2,skolemFOFtoCNF_B_2) )],[refute_1_0,refute_1_32]) ).
cnf(refute_1_34,plain,
~ in(ordered_pair(skolemFOFtoCNF_D_2,E),skolemFOFtoCNF_C_5),
inference(canonicalize,[],[normalize_1_22]) ).
cnf(refute_1_35,plain,
~ in(ordered_pair(skolemFOFtoCNF_D_2,skolemFOFtoCNF_D_1(skolemFOFtoCNF_C_5,skolemFOFtoCNF_D_2)),skolemFOFtoCNF_C_5),
inference(subst,[],[refute_1_34:[bind(E,$fot(skolemFOFtoCNF_D_1(skolemFOFtoCNF_C_5,skolemFOFtoCNF_D_2)))]]) ).
cnf(refute_1_36,plain,
$false,
inference(resolve,[$cnf( in(ordered_pair(skolemFOFtoCNF_D_2,skolemFOFtoCNF_D_1(skolemFOFtoCNF_C_5,skolemFOFtoCNF_D_2)),skolemFOFtoCNF_C_5) )],[refute_1_33,refute_1_35]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11 % Problem : SEU265+1 : TPTP v8.1.0. Released v3.3.0.
% 0.03/0.12 % Command : metis --show proof --show saturation %s
% 0.13/0.33 % Computer : n027.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 600
% 0.13/0.33 % DateTime : Mon Jun 20 02:55:24 EDT 2022
% 0.13/0.33 % CPUTime :
% 0.13/0.34 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 3.91/4.09 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 3.91/4.09
% 3.91/4.09 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 3.91/4.10
%------------------------------------------------------------------------------