%------------------------------------------------------------------------------
% File : ConnectPP---0.7.2
% Problem : SEU146+2 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/connect++ --verbosity 1 --no-colour --tptp-proof --schedule default --timeout 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n020.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Sep 24 08:58:12 AM UTC 2026
% Result : Theorem 189.15s 189.40s
% Output : Proof 189.67s
% Verified :
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)
% Comments :
%------------------------------------------------------------------------------
fof(antisymmetry_r2_hidden,axiom,
! [A,B] :
( in(A,B)
=> ~ in(B,A) ),
file('theBenchmark.p',antisymmetry_r2_hidden) ).
fof(antisymmetry_r2_xboole_0,axiom,
! [A,B] :
( proper_subset(A,B)
=> ~ proper_subset(B,A) ),
file('theBenchmark.p',antisymmetry_r2_xboole_0) ).
fof(commutativity_k2_tarski,axiom,
! [A,B] : unordered_pair(A,B) = unordered_pair(B,A),
file('theBenchmark.p',commutativity_k2_tarski) ).
fof(commutativity_k2_xboole_0,axiom,
! [A,B] : set_union2(A,B) = set_union2(B,A),
file('theBenchmark.p',commutativity_k2_xboole_0) ).
fof(commutativity_k3_xboole_0,axiom,
! [A,B] : set_intersection2(A,B) = set_intersection2(B,A),
file('theBenchmark.p',commutativity_k3_xboole_0) ).
fof(d10_xboole_0,axiom,
! [A,B] :
( A = B
<=> ( subset(B,A)
& subset(A,B) ) ),
file('theBenchmark.p',d10_xboole_0) ).
fof(d1_tarski,axiom,
! [A,B] :
( B = singleton(A)
<=> ! [C] :
( in(C,B)
<=> C = A ) ),
file('theBenchmark.p',d1_tarski) ).
fof(d1_xboole_0,axiom,
! [A] :
( A = empty_set
<=> ! [B] : ~ in(B,A) ),
file('theBenchmark.p',d1_xboole_0) ).
fof(d2_tarski,axiom,
! [A,B,C] :
( C = unordered_pair(A,B)
<=> ! [D] :
( in(D,C)
<=> ( D = B
| D = A ) ) ),
file('theBenchmark.p',d2_tarski) ).
fof(d2_xboole_0,axiom,
! [A,B,C] :
( C = set_union2(A,B)
<=> ! [D] :
( in(D,C)
<=> ( in(D,B)
| in(D,A) ) ) ),
file('theBenchmark.p',d2_xboole_0) ).
fof(d3_tarski,axiom,
! [A,B] :
( subset(A,B)
<=> ! [C] :
( in(C,A)
=> in(C,B) ) ),
file('theBenchmark.p',d3_tarski) ).
fof(d3_xboole_0,axiom,
! [A,B,C] :
( C = set_intersection2(A,B)
<=> ! [D] :
( in(D,C)
<=> ( in(D,B)
& in(D,A) ) ) ),
file('theBenchmark.p',d3_xboole_0) ).
fof(d4_xboole_0,axiom,
! [A,B,C] :
( C = set_difference(A,B)
<=> ! [D] :
( in(D,C)
<=> ( ~ in(D,B)
& in(D,A) ) ) ),
file('theBenchmark.p',d4_xboole_0) ).
fof(d7_xboole_0,axiom,
! [A,B] :
( disjoint(A,B)
<=> set_intersection2(A,B) = empty_set ),
file('theBenchmark.p',d7_xboole_0) ).
fof(d8_xboole_0,axiom,
! [A,B] :
( proper_subset(A,B)
<=> ( A != B
& subset(A,B) ) ),
file('theBenchmark.p',d8_xboole_0) ).
fof(dt_k1_tarski,axiom,
$true,
file('theBenchmark.p',dt_k1_tarski) ).
fof(dt_k1_xboole_0,axiom,
$true,
file('theBenchmark.p',dt_k1_xboole_0) ).
fof(dt_k2_tarski,axiom,
$true,
file('theBenchmark.p',dt_k2_tarski) ).
fof(dt_k2_xboole_0,axiom,
$true,
file('theBenchmark.p',dt_k2_xboole_0) ).
fof(dt_k3_xboole_0,axiom,
$true,
file('theBenchmark.p',dt_k3_xboole_0) ).
fof(dt_k4_xboole_0,axiom,
$true,
file('theBenchmark.p',dt_k4_xboole_0) ).
fof(fc1_xboole_0,axiom,
empty(empty_set),
file('theBenchmark.p',fc1_xboole_0) ).
fof(fc2_xboole_0,axiom,
! [A,B] :
( ~ empty(A)
=> ~ empty(set_union2(A,B)) ),
file('theBenchmark.p',fc2_xboole_0) ).
fof(fc3_xboole_0,axiom,
! [A,B] :
( ~ empty(A)
=> ~ empty(set_union2(B,A)) ),
file('theBenchmark.p',fc3_xboole_0) ).
fof(idempotence_k2_xboole_0,axiom,
! [A,B] : set_union2(A,A) = A,
file('theBenchmark.p',idempotence_k2_xboole_0) ).
fof(idempotence_k3_xboole_0,axiom,
! [A,B] : set_intersection2(A,A) = A,
file('theBenchmark.p',idempotence_k3_xboole_0) ).
fof(irreflexivity_r2_xboole_0,axiom,
! [A,B] : ~ proper_subset(A,A),
file('theBenchmark.p',irreflexivity_r2_xboole_0) ).
fof(l1_zfmisc_1,lemma,
! [A] : singleton(A) != empty_set,
file('theBenchmark.p',l1_zfmisc_1) ).
fof(l2_zfmisc_1,lemma,
! [A,B] :
( subset(singleton(A),B)
<=> in(A,B) ),
file('theBenchmark.p',l2_zfmisc_1) ).
fof(l32_xboole_1,lemma,
! [A,B] :
( set_difference(A,B) = empty_set
<=> subset(A,B) ),
file('theBenchmark.p',l32_xboole_1) ).
fof(l3_zfmisc_1,lemma,
! [A,B,C] :
( subset(A,B)
=> ( subset(A,set_difference(B,singleton(C)))
| in(C,A) ) ),
file('theBenchmark.p',l3_zfmisc_1) ).
fof(l4_zfmisc_1,conjecture,
! [A,B] :
( subset(A,singleton(B))
<=> ( A = singleton(B)
| A = empty_set ) ),
file('theBenchmark.p',l4_zfmisc_1) ).
fof(rc1_xboole_0,axiom,
? [A] : empty(A),
file('theBenchmark.p',rc1_xboole_0) ).
fof(rc2_xboole_0,axiom,
? [A] : ~ empty(A),
file('theBenchmark.p',rc2_xboole_0) ).
fof(reflexivity_r1_tarski,axiom,
! [A,B] : subset(A,A),
file('theBenchmark.p',reflexivity_r1_tarski) ).
fof(symmetry_r1_xboole_0,axiom,
! [A,B] :
( disjoint(A,B)
=> disjoint(B,A) ),
file('theBenchmark.p',symmetry_r1_xboole_0) ).
fof(t12_xboole_1,lemma,
! [A,B] :
( subset(A,B)
=> set_union2(A,B) = B ),
file('theBenchmark.p',t12_xboole_1) ).
fof(t17_xboole_1,lemma,
! [A,B] : subset(set_intersection2(A,B),A),
file('theBenchmark.p',t17_xboole_1) ).
fof(t19_xboole_1,lemma,
! [A,B,C] :
( ( subset(A,C)
& subset(A,B) )
=> subset(A,set_intersection2(B,C)) ),
file('theBenchmark.p',t19_xboole_1) ).
fof(t1_boole,axiom,
! [A] : set_union2(A,empty_set) = A,
file('theBenchmark.p',t1_boole) ).
fof(t1_xboole_1,lemma,
! [A,B,C] :
( ( subset(B,C)
& subset(A,B) )
=> subset(A,C) ),
file('theBenchmark.p',t1_xboole_1) ).
fof(t26_xboole_1,lemma,
! [A,B,C] :
( subset(A,B)
=> subset(set_intersection2(A,C),set_intersection2(B,C)) ),
file('theBenchmark.p',t26_xboole_1) ).
fof(t28_xboole_1,lemma,
! [A,B] :
( subset(A,B)
=> set_intersection2(A,B) = A ),
file('theBenchmark.p',t28_xboole_1) ).
fof(t2_boole,axiom,
! [A] : set_intersection2(A,empty_set) = empty_set,
file('theBenchmark.p',t2_boole) ).
fof(t2_tarski,axiom,
! [A,B] :
( ! [C] :
( in(C,A)
<=> in(C,B) )
=> A = B ),
file('theBenchmark.p',t2_tarski) ).
fof(t2_xboole_1,lemma,
! [A] : subset(empty_set,A),
file('theBenchmark.p',t2_xboole_1) ).
fof(t33_xboole_1,lemma,
! [A,B,C] :
( subset(A,B)
=> subset(set_difference(A,C),set_difference(B,C)) ),
file('theBenchmark.p',t33_xboole_1) ).
fof(t36_xboole_1,lemma,
! [A,B] : subset(set_difference(A,B),A),
file('theBenchmark.p',t36_xboole_1) ).
fof(t37_xboole_1,lemma,
! [A,B] :
( set_difference(A,B) = empty_set
<=> subset(A,B) ),
file('theBenchmark.p',t37_xboole_1) ).
fof(t39_xboole_1,lemma,
! [A,B] : set_union2(A,set_difference(B,A)) = set_union2(A,B),
file('theBenchmark.p',t39_xboole_1) ).
fof(t3_boole,axiom,
! [A] : set_difference(A,empty_set) = A,
file('theBenchmark.p',t3_boole) ).
fof(t3_xboole_0,lemma,
! [A,B] :
( ~ ( disjoint(A,B)
& ? [C] :
( in(C,B)
& in(C,A) ) )
& ~ ( ! [C] :
~ ( in(C,B)
& in(C,A) )
& ~ disjoint(A,B) ) ),
file('theBenchmark.p',t3_xboole_0) ).
fof(t3_xboole_1,lemma,
! [A] :
( subset(A,empty_set)
=> A = empty_set ),
file('theBenchmark.p',t3_xboole_1) ).
fof(t40_xboole_1,lemma,
! [A,B] : set_difference(set_union2(A,B),B) = set_difference(A,B),
file('theBenchmark.p',t40_xboole_1) ).
fof(t45_xboole_1,lemma,
! [A,B] :
( subset(A,B)
=> B = set_union2(A,set_difference(B,A)) ),
file('theBenchmark.p',t45_xboole_1) ).
fof(t48_xboole_1,lemma,
! [A,B] : set_difference(A,set_difference(A,B)) = set_intersection2(A,B),
file('theBenchmark.p',t48_xboole_1) ).
fof(t4_boole,axiom,
! [A] : set_difference(empty_set,A) = empty_set,
file('theBenchmark.p',t4_boole) ).
fof(t4_xboole_0,lemma,
! [A,B] :
( ~ ( disjoint(A,B)
& ? [C] : in(C,set_intersection2(A,B)) )
& ~ ( ! [C] : ~ in(C,set_intersection2(A,B))
& ~ disjoint(A,B) ) ),
file('theBenchmark.p',t4_xboole_0) ).
fof(t60_xboole_1,lemma,
! [A,B] :
~ ( proper_subset(B,A)
& subset(A,B) ),
file('theBenchmark.p',t60_xboole_1) ).
fof(t63_xboole_1,lemma,
! [A,B,C] :
( ( disjoint(B,C)
& subset(A,B) )
=> disjoint(A,C) ),
file('theBenchmark.p',t63_xboole_1) ).
fof(t69_enumset1,lemma,
! [A] : unordered_pair(A,A) = singleton(A),
file('theBenchmark.p',t69_enumset1) ).
fof(t6_boole,axiom,
! [A] :
( empty(A)
=> A = empty_set ),
file('theBenchmark.p',t6_boole) ).
fof(t7_boole,axiom,
! [A,B] :
~ ( empty(B)
& in(A,B) ),
file('theBenchmark.p',t7_boole) ).
fof(t7_xboole_1,lemma,
! [A,B] : subset(A,set_union2(A,B)),
file('theBenchmark.p',t7_xboole_1) ).
fof(t83_xboole_1,lemma,
! [A,B] :
( disjoint(A,B)
<=> set_difference(A,B) = A ),
file('theBenchmark.p',t83_xboole_1) ).
fof(t8_boole,axiom,
! [A,B] :
~ ( empty(B)
& A != B
& empty(A) ),
file('theBenchmark.p',t8_boole) ).
fof(t8_xboole_1,lemma,
! [A,B,C] :
( ( subset(C,B)
& subset(A,B) )
=> subset(set_union2(A,C),B) ),
file('theBenchmark.p',t8_xboole_1) ).
fof(f_1_1,plain,
! [A,B] :
( ~ in(B,A)
| ~ in(A,B) ),
inference(fof_nnf,[status(thm)],[antisymmetry_r2_hidden]) ).
fof(f_1_2,plain,
! [U_1,U_0] :
( ~ in(U_0,U_1)
| ~ in(U_1,U_0) ),
inference(variable_rename,[status(thm)],[f_1_1]) ).
fof(f_1_3,plain,
! [U_1,U_0] :
( ~ in(U_0,U_1)
| ~ in(U_1,U_0) ),
inference(definitional_conversion,[status(esa)],[f_1_2]) ).
cnf(f_1_4,plain,
( ~ in(U_0,U_1)
| ~ in(U_1,U_0) ),
inference(clausify,[status(thm)],[f_1_3]) ).
fof(f_2_1,plain,
! [A,B] :
( ~ proper_subset(B,A)
| ~ proper_subset(A,B) ),
inference(fof_nnf,[status(thm)],[antisymmetry_r2_xboole_0]) ).
fof(f_2_2,plain,
! [U_3,U_2] :
( ~ proper_subset(U_2,U_3)
| ~ proper_subset(U_3,U_2) ),
inference(variable_rename,[status(thm)],[f_2_1]) ).
fof(f_2_3,plain,
! [U_3,U_2] :
( ~ proper_subset(U_2,U_3)
| ~ proper_subset(U_3,U_2) ),
inference(definitional_conversion,[status(esa)],[f_2_2]) ).
cnf(f_2_4,plain,
( ~ proper_subset(U_2,U_3)
| ~ proper_subset(U_3,U_2) ),
inference(clausify,[status(thm)],[f_2_3]) ).
fof(f_3_1,plain,
! [A,B] : unordered_pair(A,B) = unordered_pair(B,A),
inference(fof_nnf,[status(thm)],[commutativity_k2_tarski]) ).
fof(f_3_2,plain,
! [U_5,U_4] : unordered_pair(U_5,U_4) = unordered_pair(U_4,U_5),
inference(variable_rename,[status(thm)],[f_3_1]) ).
fof(f_3_3,plain,
! [U_4,U_5] : unordered_pair(U_5,U_4) = unordered_pair(U_4,U_5),
inference(definitional_conversion,[status(esa)],[f_3_2]) ).
cnf(f_3_4,plain,
unordered_pair(U_5,U_4) = unordered_pair(U_4,U_5),
inference(clausify,[status(thm)],[f_3_3]) ).
fof(f_4_1,plain,
! [A,B] : set_union2(A,B) = set_union2(B,A),
inference(fof_nnf,[status(thm)],[commutativity_k2_xboole_0]) ).
fof(f_4_2,plain,
! [U_7,U_6] : set_union2(U_7,U_6) = set_union2(U_6,U_7),
inference(variable_rename,[status(thm)],[f_4_1]) ).
fof(f_4_3,plain,
! [U_6,U_7] : set_union2(U_7,U_6) = set_union2(U_6,U_7),
inference(definitional_conversion,[status(esa)],[f_4_2]) ).
cnf(f_4_4,plain,
set_union2(U_7,U_6) = set_union2(U_6,U_7),
inference(clausify,[status(thm)],[f_4_3]) ).
fof(f_5_1,plain,
! [A,B] : set_intersection2(A,B) = set_intersection2(B,A),
inference(fof_nnf,[status(thm)],[commutativity_k3_xboole_0]) ).
fof(f_5_2,plain,
! [U_9,U_8] : set_intersection2(U_9,U_8) = set_intersection2(U_8,U_9),
inference(variable_rename,[status(thm)],[f_5_1]) ).
fof(f_5_3,plain,
! [U_8,U_9] : set_intersection2(U_9,U_8) = set_intersection2(U_8,U_9),
inference(definitional_conversion,[status(esa)],[f_5_2]) ).
cnf(f_5_4,plain,
set_intersection2(U_9,U_8) = set_intersection2(U_8,U_9),
inference(clausify,[status(thm)],[f_5_3]) ).
fof(f_6_1,plain,
! [A,B] :
( ( A = B
| ~ subset(B,A)
| ~ subset(A,B) )
& ( ( subset(B,A)
& subset(A,B) )
| A != B ) ),
inference(fof_nnf,[status(thm)],[d10_xboole_0]) ).
fof(f_6_2,plain,
! [U_11,U_10] :
( ( U_11 = U_10
| ~ subset(U_10,U_11)
| ~ subset(U_11,U_10) )
& ( ( subset(U_10,U_11)
& subset(U_11,U_10) )
| U_11 != U_10 ) ),
inference(variable_rename,[status(thm)],[f_6_1]) ).
fof(f_6_3,plain,
( ! [U_15,U_13] :
( U_15 = U_13
| ~ subset(U_13,U_15)
| ~ subset(U_15,U_13) )
& ! [U_14,U_12] :
( ( subset(U_12,U_14)
& subset(U_14,U_12) )
| U_14 != U_12 ) ),
inference(miniscope,[status(thm)],[f_6_2]) ).
fof(f_6_4,plain,
( ! [U_12,U_14] :
( subset(U_12,U_14)
| ~ sP0(U_12,U_14) )
& ! [U_12,U_14] :
( subset(U_14,U_12)
| ~ sP0(U_12,U_14) )
& ! [U_13,U_15] :
( U_15 = U_13
| ~ subset(U_13,U_15)
| ~ subset(U_15,U_13) )
& ! [U_12,U_14] :
( sP0(U_12,U_14)
| U_14 != U_12 ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP0])],[f_6_3]) ).
cnf(f_6_5,plain,
( sP0(U_12,U_14)
| U_14 != U_12 ),
inference(clausify,[status(thm)],[f_6_4]) ).
cnf(f_6_6,plain,
( U_15 = U_13
| ~ subset(U_13,U_15)
| ~ subset(U_15,U_13) ),
inference(clausify,[status(thm)],[f_6_4]) ).
cnf(f_6_7,plain,
( subset(U_14,U_12)
| ~ sP0(U_12,U_14) ),
inference(clausify,[status(thm)],[f_6_4]) ).
cnf(f_6_8,plain,
( subset(U_12,U_14)
| ~ sP0(U_12,U_14) ),
inference(clausify,[status(thm)],[f_6_4]) ).
fof(f_7_1,plain,
! [A,B] :
( ( B = singleton(A)
| ? [C] :
( ( ~ in(C,B)
& C = A )
| ( C != A
& in(C,B) ) ) )
& ( ! [C] :
( ( in(C,B)
| C != A )
& ( C = A
| ~ in(C,B) ) )
| B != singleton(A) ) ),
inference(fof_nnf,[status(thm)],[d1_tarski]) ).
fof(f_7_2,plain,
! [U_19,U_18] :
( ( U_18 = singleton(U_19)
| ? [U_17] :
( ( ~ in(U_17,U_18)
& U_17 = U_19 )
| ( U_17 != U_19
& in(U_17,U_18) ) ) )
& ( ! [U_16] :
( ( in(U_16,U_18)
| U_16 != U_19 )
& ( U_16 = U_19
| ~ in(U_16,U_18) ) )
| U_18 != singleton(U_19) ) ),
inference(variable_rename,[status(thm)],[f_7_1]) ).
fof(f_7_3,plain,
( ! [U_27,U_25] :
( U_25 = singleton(U_27)
| ? [U_23] :
( ~ in(U_23,U_25)
& U_23 = U_27 )
| ? [U_22] :
( U_22 != U_27
& in(U_22,U_25) ) )
& ! [U_26,U_24] :
( ( ! [U_21] :
( in(U_21,U_24)
| U_21 != U_26 )
& ! [U_20] :
( U_20 = U_26
| ~ in(U_20,U_24) ) )
| U_24 != singleton(U_26) ) ),
inference(miniscope,[status(thm)],[f_7_2]) ).
fof(f_7_4,plain,
( ! [U_27,U_25] :
( U_25 = singleton(U_27)
| ? [U_23] :
( ~ in(U_23,U_25)
& U_23 = U_27 )
| ( sK1(U_27,U_25) != U_27
& in(sK1(U_27,U_25),U_25) ) )
& ! [U_26,U_24] :
( ( ! [U_21] :
( in(U_21,U_24)
| U_21 != U_26 )
& ! [U_20] :
( U_20 = U_26
| ~ in(U_20,U_24) ) )
| U_24 != singleton(U_26) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(U_22,sK1(U_27,U_25))],[f_7_3]) ).
fof(f_7_5,plain,
( ! [U_27,U_25] :
( U_25 = singleton(U_27)
| ( ~ in(sK2(U_27,U_25),U_25)
& sK2(U_27,U_25) = U_27 )
| ( sK1(U_27,U_25) != U_27
& in(sK1(U_27,U_25),U_25) ) )
& ! [U_26,U_24] :
( ( ! [U_21] :
( in(U_21,U_24)
| U_21 != U_26 )
& ! [U_20] :
( U_20 = U_26
| ~ in(U_20,U_24) ) )
| U_24 != singleton(U_26) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2]),skolemize(U_23,sK2(U_27,U_25))],[f_7_4]) ).
fof(f_7_6,plain,
( ! [U_25,U_27] :
( ~ in(sK2(U_27,U_25),U_25)
| ~ sP3(U_25,U_27) )
& ! [U_25,U_27] :
( sK2(U_27,U_25) = U_27
| ~ sP3(U_25,U_27) )
& ! [U_25,U_27] :
( sK1(U_27,U_25) != U_27
| ~ sP2(U_25,U_27) )
& ! [U_25,U_27] :
( in(sK1(U_27,U_25),U_25)
| ~ sP2(U_25,U_27) )
& ! [U_21,U_26,U_20,U_24] :
( in(U_21,U_24)
| U_21 != U_26
| ~ sP1(U_21,U_26,U_20,U_24) )
& ! [U_21,U_26,U_20,U_24] :
( U_20 = U_26
| ~ in(U_20,U_24)
| ~ sP1(U_21,U_26,U_20,U_24) )
& ! [U_25,U_27] :
( U_25 = singleton(U_27)
| sP3(U_25,U_27)
| sP2(U_25,U_27) )
& ! [U_21,U_26,U_20,U_24] :
( sP1(U_21,U_26,U_20,U_24)
| U_24 != singleton(U_26) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP1,sP2,sP3])],[f_7_5]) ).
cnf(f_7_7,plain,
( sP1(U_21,U_26,U_20,U_24)
| U_24 != singleton(U_26) ),
inference(clausify,[status(thm)],[f_7_6]) ).
cnf(f_7_8,plain,
( U_25 = singleton(U_27)
| sP3(U_25,U_27)
| sP2(U_25,U_27) ),
inference(clausify,[status(thm)],[f_7_6]) ).
cnf(f_7_9,plain,
( U_20 = U_26
| ~ in(U_20,U_24)
| ~ sP1(U_21,U_26,U_20,U_24) ),
inference(clausify,[status(thm)],[f_7_6]) ).
cnf(f_7_10,plain,
( in(U_21,U_24)
| U_21 != U_26
| ~ sP1(U_21,U_26,U_20,U_24) ),
inference(clausify,[status(thm)],[f_7_6]) ).
cnf(f_7_11,plain,
( in(sK1(U_27,U_25),U_25)
| ~ sP2(U_25,U_27) ),
inference(clausify,[status(thm)],[f_7_6]) ).
cnf(f_7_12,plain,
( sK1(U_27,U_25) != U_27
| ~ sP2(U_25,U_27) ),
inference(clausify,[status(thm)],[f_7_6]) ).
cnf(f_7_13,plain,
( sK2(U_27,U_25) = U_27
| ~ sP3(U_25,U_27) ),
inference(clausify,[status(thm)],[f_7_6]) ).
cnf(f_7_14,plain,
( ~ in(sK2(U_27,U_25),U_25)
| ~ sP3(U_25,U_27) ),
inference(clausify,[status(thm)],[f_7_6]) ).
fof(f_8_1,plain,
! [A] :
( ( A = empty_set
| ? [B] : in(B,A) )
& ( ! [B] : ~ in(B,A)
| A != empty_set ) ),
inference(fof_nnf,[status(thm)],[d1_xboole_0]) ).
fof(f_8_2,plain,
! [U_30] :
( ( U_30 = empty_set
| ? [U_29] : in(U_29,U_30) )
& ( ! [U_28] : ~ in(U_28,U_30)
| U_30 != empty_set ) ),
inference(variable_rename,[status(thm)],[f_8_1]) ).
fof(f_8_3,plain,
( ! [U_32] :
( U_32 = empty_set
| ? [U_29] : in(U_29,U_32) )
& ! [U_31] :
( ! [U_28] : ~ in(U_28,U_31)
| U_31 != empty_set ) ),
inference(miniscope,[status(thm)],[f_8_2]) ).
fof(f_8_4,plain,
( ! [U_32] :
( U_32 = empty_set
| in(sK3(U_32),U_32) )
& ! [U_31] :
( ! [U_28] : ~ in(U_28,U_31)
| U_31 != empty_set ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3]),skolemize(U_29,sK3(U_32))],[f_8_3]) ).
fof(f_8_5,plain,
( ! [U_32] :
( U_32 = empty_set
| in(sK3(U_32),U_32) )
& ! [U_28,U_31] :
( ~ in(U_28,U_31)
| U_31 != empty_set ) ),
inference(definitional_conversion,[status(esa)],[f_8_4]) ).
cnf(f_8_6,plain,
( ~ in(U_28,U_31)
| U_31 != empty_set ),
inference(clausify,[status(thm)],[f_8_5]) ).
cnf(f_8_7,plain,
( U_32 = empty_set
| in(sK3(U_32),U_32) ),
inference(clausify,[status(thm)],[f_8_5]) ).
fof(f_9_1,plain,
! [A,B,C] :
( ( C = unordered_pair(A,B)
| ? [D] :
( ( ~ in(D,C)
& ( D = B
| D = A ) )
| ( D != B
& D != A
& in(D,C) ) ) )
& ( ! [D] :
( ( in(D,C)
| ( D != B
& D != A ) )
& ( D = B
| D = A
| ~ in(D,C) ) )
| C != unordered_pair(A,B) ) ),
inference(fof_nnf,[status(thm)],[d2_tarski]) ).
fof(f_9_2,plain,
! [U_37,U_36,U_35] :
( ( U_35 = unordered_pair(U_37,U_36)
| ? [U_34] :
( ( ~ in(U_34,U_35)
& ( U_34 = U_36
| U_34 = U_37 ) )
| ( U_34 != U_36
& U_34 != U_37
& in(U_34,U_35) ) ) )
& ( ! [U_33] :
( ( in(U_33,U_35)
| ( U_33 != U_36
& U_33 != U_37 ) )
& ( U_33 = U_36
| U_33 = U_37
| ~ in(U_33,U_35) ) )
| U_35 != unordered_pair(U_37,U_36) ) ),
inference(variable_rename,[status(thm)],[f_9_1]) ).
fof(f_9_3,plain,
( ! [U_47,U_45,U_43] :
( U_43 = unordered_pair(U_47,U_45)
| ? [U_41] :
( ~ in(U_41,U_43)
& ( U_41 = U_45
| U_41 = U_47 ) )
| ? [U_40] :
( U_40 != U_45
& U_40 != U_47
& in(U_40,U_43) ) )
& ! [U_46,U_44,U_42] :
( ( ! [U_39] :
( in(U_39,U_42)
| ( U_39 != U_44
& U_39 != U_46 ) )
& ! [U_38] :
( U_38 = U_44
| U_38 = U_46
| ~ in(U_38,U_42) ) )
| U_42 != unordered_pair(U_46,U_44) ) ),
inference(miniscope,[status(thm)],[f_9_2]) ).
fof(f_9_4,plain,
( ! [U_47,U_45,U_43] :
( U_43 = unordered_pair(U_47,U_45)
| ? [U_41] :
( ~ in(U_41,U_43)
& ( U_41 = U_45
| U_41 = U_47 ) )
| ( sK4(U_47,U_45,U_43) != U_45
& sK4(U_47,U_45,U_43) != U_47
& in(sK4(U_47,U_45,U_43),U_43) ) )
& ! [U_46,U_44,U_42] :
( ( ! [U_39] :
( in(U_39,U_42)
| ( U_39 != U_44
& U_39 != U_46 ) )
& ! [U_38] :
( U_38 = U_44
| U_38 = U_46
| ~ in(U_38,U_42) ) )
| U_42 != unordered_pair(U_46,U_44) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4]),skolemize(U_40,sK4(U_47,U_45,U_43))],[f_9_3]) ).
fof(f_9_5,plain,
( ! [U_47,U_45,U_43] :
( U_43 = unordered_pair(U_47,U_45)
| ( ~ in(sK5(U_47,U_45,U_43),U_43)
& ( sK5(U_47,U_45,U_43) = U_45
| sK5(U_47,U_45,U_43) = U_47 ) )
| ( sK4(U_47,U_45,U_43) != U_45
& sK4(U_47,U_45,U_43) != U_47
& in(sK4(U_47,U_45,U_43),U_43) ) )
& ! [U_46,U_44,U_42] :
( ( ! [U_39] :
( in(U_39,U_42)
| ( U_39 != U_44
& U_39 != U_46 ) )
& ! [U_38] :
( U_38 = U_44
| U_38 = U_46
| ~ in(U_38,U_42) ) )
| U_42 != unordered_pair(U_46,U_44) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK5]),skolemize(U_41,sK5(U_47,U_45,U_43))],[f_9_4]) ).
fof(f_9_6,plain,
( ! [U_43,U_45,U_47] :
( ~ in(sK5(U_47,U_45,U_43),U_43)
| ~ sP7(U_43,U_45,U_47) )
& ! [U_43,U_45,U_47] :
( sK5(U_47,U_45,U_43) = U_45
| sK5(U_47,U_45,U_43) = U_47
| ~ sP7(U_43,U_45,U_47) )
& ! [U_43,U_45,U_47] :
( sK4(U_47,U_45,U_43) != U_45
| ~ sP6(U_43,U_45,U_47) )
& ! [U_43,U_45,U_47] :
( sK4(U_47,U_45,U_43) != U_47
| ~ sP6(U_43,U_45,U_47) )
& ! [U_43,U_45,U_47] :
( in(sK4(U_47,U_45,U_43),U_43)
| ~ sP6(U_43,U_45,U_47) )
& ! [U_44,U_39,U_46] :
( U_39 != U_44
| ~ sP4(U_44,U_39,U_46) )
& ! [U_44,U_39,U_46] :
( U_39 != U_46
| ~ sP4(U_44,U_39,U_46) )
& ! [U_44,U_42,U_38,U_39,U_46] :
( in(U_39,U_42)
| sP4(U_44,U_39,U_46)
| ~ sP5(U_44,U_42,U_38,U_39,U_46) )
& ! [U_44,U_42,U_38,U_39,U_46] :
( U_38 = U_44
| U_38 = U_46
| ~ in(U_38,U_42)
| ~ sP5(U_44,U_42,U_38,U_39,U_46) )
& ! [U_43,U_45,U_47] :
( U_43 = unordered_pair(U_47,U_45)
| sP7(U_43,U_45,U_47)
| sP6(U_43,U_45,U_47) )
& ! [U_44,U_42,U_38,U_39,U_46] :
( sP5(U_44,U_42,U_38,U_39,U_46)
| U_42 != unordered_pair(U_46,U_44) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP4,sP5,sP6,sP7])],[f_9_5]) ).
cnf(f_9_7,plain,
( sP5(U_44,U_42,U_38,U_39,U_46)
| U_42 != unordered_pair(U_46,U_44) ),
inference(clausify,[status(thm)],[f_9_6]) ).
cnf(f_9_8,plain,
( U_43 = unordered_pair(U_47,U_45)
| sP7(U_43,U_45,U_47)
| sP6(U_43,U_45,U_47) ),
inference(clausify,[status(thm)],[f_9_6]) ).
cnf(f_9_9,plain,
( U_38 = U_44
| U_38 = U_46
| ~ in(U_38,U_42)
| ~ sP5(U_44,U_42,U_38,U_39,U_46) ),
inference(clausify,[status(thm)],[f_9_6]) ).
cnf(f_9_10,plain,
( in(U_39,U_42)
| sP4(U_44,U_39,U_46)
| ~ sP5(U_44,U_42,U_38,U_39,U_46) ),
inference(clausify,[status(thm)],[f_9_6]) ).
cnf(f_9_11,plain,
( U_39 != U_46
| ~ sP4(U_44,U_39,U_46) ),
inference(clausify,[status(thm)],[f_9_6]) ).
cnf(f_9_12,plain,
( U_39 != U_44
| ~ sP4(U_44,U_39,U_46) ),
inference(clausify,[status(thm)],[f_9_6]) ).
cnf(f_9_13,plain,
( in(sK4(U_47,U_45,U_43),U_43)
| ~ sP6(U_43,U_45,U_47) ),
inference(clausify,[status(thm)],[f_9_6]) ).
cnf(f_9_14,plain,
( sK4(U_47,U_45,U_43) != U_47
| ~ sP6(U_43,U_45,U_47) ),
inference(clausify,[status(thm)],[f_9_6]) ).
cnf(f_9_15,plain,
( sK4(U_47,U_45,U_43) != U_45
| ~ sP6(U_43,U_45,U_47) ),
inference(clausify,[status(thm)],[f_9_6]) ).
cnf(f_9_16,plain,
( sK5(U_47,U_45,U_43) = U_45
| sK5(U_47,U_45,U_43) = U_47
| ~ sP7(U_43,U_45,U_47) ),
inference(clausify,[status(thm)],[f_9_6]) ).
cnf(f_9_17,plain,
( ~ in(sK5(U_47,U_45,U_43),U_43)
| ~ sP7(U_43,U_45,U_47) ),
inference(clausify,[status(thm)],[f_9_6]) ).
fof(f_10_1,plain,
! [A,B,C] :
( ( C = set_union2(A,B)
| ? [D] :
( ( ~ in(D,C)
& ( in(D,B)
| in(D,A) ) )
| ( ~ in(D,B)
& ~ in(D,A)
& in(D,C) ) ) )
& ( ! [D] :
( ( in(D,C)
| ( ~ in(D,B)
& ~ in(D,A) ) )
& ( in(D,B)
| in(D,A)
| ~ in(D,C) ) )
| C != set_union2(A,B) ) ),
inference(fof_nnf,[status(thm)],[d2_xboole_0]) ).
fof(f_10_2,plain,
! [U_52,U_51,U_50] :
( ( U_50 = set_union2(U_52,U_51)
| ? [U_49] :
( ( ~ in(U_49,U_50)
& ( in(U_49,U_51)
| in(U_49,U_52) ) )
| ( ~ in(U_49,U_51)
& ~ in(U_49,U_52)
& in(U_49,U_50) ) ) )
& ( ! [U_48] :
( ( in(U_48,U_50)
| ( ~ in(U_48,U_51)
& ~ in(U_48,U_52) ) )
& ( in(U_48,U_51)
| in(U_48,U_52)
| ~ in(U_48,U_50) ) )
| U_50 != set_union2(U_52,U_51) ) ),
inference(variable_rename,[status(thm)],[f_10_1]) ).
fof(f_10_3,plain,
( ! [U_62,U_60,U_58] :
( U_58 = set_union2(U_62,U_60)
| ? [U_56] :
( ~ in(U_56,U_58)
& ( in(U_56,U_60)
| in(U_56,U_62) ) )
| ? [U_55] :
( ~ in(U_55,U_60)
& ~ in(U_55,U_62)
& in(U_55,U_58) ) )
& ! [U_61,U_59,U_57] :
( ( ! [U_54] :
( in(U_54,U_57)
| ( ~ in(U_54,U_59)
& ~ in(U_54,U_61) ) )
& ! [U_53] :
( in(U_53,U_59)
| in(U_53,U_61)
| ~ in(U_53,U_57) ) )
| U_57 != set_union2(U_61,U_59) ) ),
inference(miniscope,[status(thm)],[f_10_2]) ).
fof(f_10_4,plain,
( ! [U_62,U_60,U_58] :
( U_58 = set_union2(U_62,U_60)
| ? [U_56] :
( ~ in(U_56,U_58)
& ( in(U_56,U_60)
| in(U_56,U_62) ) )
| ( ~ in(sK6(U_62,U_60,U_58),U_60)
& ~ in(sK6(U_62,U_60,U_58),U_62)
& in(sK6(U_62,U_60,U_58),U_58) ) )
& ! [U_61,U_59,U_57] :
( ( ! [U_54] :
( in(U_54,U_57)
| ( ~ in(U_54,U_59)
& ~ in(U_54,U_61) ) )
& ! [U_53] :
( in(U_53,U_59)
| in(U_53,U_61)
| ~ in(U_53,U_57) ) )
| U_57 != set_union2(U_61,U_59) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK6]),skolemize(U_55,sK6(U_62,U_60,U_58))],[f_10_3]) ).
fof(f_10_5,plain,
( ! [U_62,U_60,U_58] :
( U_58 = set_union2(U_62,U_60)
| ( ~ in(sK7(U_62,U_60,U_58),U_58)
& ( in(sK7(U_62,U_60,U_58),U_60)
| in(sK7(U_62,U_60,U_58),U_62) ) )
| ( ~ in(sK6(U_62,U_60,U_58),U_60)
& ~ in(sK6(U_62,U_60,U_58),U_62)
& in(sK6(U_62,U_60,U_58),U_58) ) )
& ! [U_61,U_59,U_57] :
( ( ! [U_54] :
( in(U_54,U_57)
| ( ~ in(U_54,U_59)
& ~ in(U_54,U_61) ) )
& ! [U_53] :
( in(U_53,U_59)
| in(U_53,U_61)
| ~ in(U_53,U_57) ) )
| U_57 != set_union2(U_61,U_59) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK7]),skolemize(U_56,sK7(U_62,U_60,U_58))],[f_10_4]) ).
fof(f_10_6,plain,
( ! [U_58,U_60,U_62] :
( ~ in(sK7(U_62,U_60,U_58),U_58)
| ~ sP11(U_58,U_60,U_62) )
& ! [U_58,U_60,U_62] :
( in(sK7(U_62,U_60,U_58),U_60)
| in(sK7(U_62,U_60,U_58),U_62)
| ~ sP11(U_58,U_60,U_62) )
& ! [U_58,U_60,U_62] :
( ~ in(sK6(U_62,U_60,U_58),U_60)
| ~ sP10(U_58,U_60,U_62) )
& ! [U_58,U_60,U_62] :
( ~ in(sK6(U_62,U_60,U_58),U_62)
| ~ sP10(U_58,U_60,U_62) )
& ! [U_58,U_60,U_62] :
( in(sK6(U_62,U_60,U_58),U_58)
| ~ sP10(U_58,U_60,U_62) )
& ! [U_61,U_59,U_54] :
( ~ in(U_54,U_59)
| ~ sP8(U_61,U_59,U_54) )
& ! [U_61,U_59,U_54] :
( ~ in(U_54,U_61)
| ~ sP8(U_61,U_59,U_54) )
& ! [U_53,U_57,U_61,U_59,U_54] :
( in(U_54,U_57)
| sP8(U_61,U_59,U_54)
| ~ sP9(U_53,U_57,U_61,U_59,U_54) )
& ! [U_53,U_57,U_61,U_59,U_54] :
( in(U_53,U_59)
| in(U_53,U_61)
| ~ in(U_53,U_57)
| ~ sP9(U_53,U_57,U_61,U_59,U_54) )
& ! [U_58,U_60,U_62] :
( U_58 = set_union2(U_62,U_60)
| sP11(U_58,U_60,U_62)
| sP10(U_58,U_60,U_62) )
& ! [U_53,U_57,U_61,U_59,U_54] :
( sP9(U_53,U_57,U_61,U_59,U_54)
| U_57 != set_union2(U_61,U_59) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP8,sP9,sP10,sP11])],[f_10_5]) ).
cnf(f_10_7,plain,
( sP9(U_53,U_57,U_61,U_59,U_54)
| U_57 != set_union2(U_61,U_59) ),
inference(clausify,[status(thm)],[f_10_6]) ).
cnf(f_10_8,plain,
( U_58 = set_union2(U_62,U_60)
| sP11(U_58,U_60,U_62)
| sP10(U_58,U_60,U_62) ),
inference(clausify,[status(thm)],[f_10_6]) ).
cnf(f_10_9,plain,
( in(U_53,U_59)
| in(U_53,U_61)
| ~ in(U_53,U_57)
| ~ sP9(U_53,U_57,U_61,U_59,U_54) ),
inference(clausify,[status(thm)],[f_10_6]) ).
cnf(f_10_10,plain,
( in(U_54,U_57)
| sP8(U_61,U_59,U_54)
| ~ sP9(U_53,U_57,U_61,U_59,U_54) ),
inference(clausify,[status(thm)],[f_10_6]) ).
cnf(f_10_11,plain,
( ~ in(U_54,U_61)
| ~ sP8(U_61,U_59,U_54) ),
inference(clausify,[status(thm)],[f_10_6]) ).
cnf(f_10_12,plain,
( ~ in(U_54,U_59)
| ~ sP8(U_61,U_59,U_54) ),
inference(clausify,[status(thm)],[f_10_6]) ).
cnf(f_10_13,plain,
( in(sK6(U_62,U_60,U_58),U_58)
| ~ sP10(U_58,U_60,U_62) ),
inference(clausify,[status(thm)],[f_10_6]) ).
cnf(f_10_14,plain,
( ~ in(sK6(U_62,U_60,U_58),U_62)
| ~ sP10(U_58,U_60,U_62) ),
inference(clausify,[status(thm)],[f_10_6]) ).
cnf(f_10_15,plain,
( ~ in(sK6(U_62,U_60,U_58),U_60)
| ~ sP10(U_58,U_60,U_62) ),
inference(clausify,[status(thm)],[f_10_6]) ).
cnf(f_10_16,plain,
( in(sK7(U_62,U_60,U_58),U_60)
| in(sK7(U_62,U_60,U_58),U_62)
| ~ sP11(U_58,U_60,U_62) ),
inference(clausify,[status(thm)],[f_10_6]) ).
cnf(f_10_17,plain,
( ~ in(sK7(U_62,U_60,U_58),U_58)
| ~ sP11(U_58,U_60,U_62) ),
inference(clausify,[status(thm)],[f_10_6]) ).
fof(f_11_1,plain,
! [A,B] :
( ( subset(A,B)
| ? [C] :
( ~ in(C,B)
& in(C,A) ) )
& ( ! [C] :
( in(C,B)
| ~ in(C,A) )
| ~ subset(A,B) ) ),
inference(fof_nnf,[status(thm)],[d3_tarski]) ).
fof(f_11_2,plain,
! [U_66,U_65] :
( ( subset(U_66,U_65)
| ? [U_64] :
( ~ in(U_64,U_65)
& in(U_64,U_66) ) )
& ( ! [U_63] :
( in(U_63,U_65)
| ~ in(U_63,U_66) )
| ~ subset(U_66,U_65) ) ),
inference(variable_rename,[status(thm)],[f_11_1]) ).
fof(f_11_3,plain,
( ! [U_70,U_68] :
( subset(U_70,U_68)
| ? [U_64] :
( ~ in(U_64,U_68)
& in(U_64,U_70) ) )
& ! [U_69,U_67] :
( ! [U_63] :
( in(U_63,U_67)
| ~ in(U_63,U_69) )
| ~ subset(U_69,U_67) ) ),
inference(miniscope,[status(thm)],[f_11_2]) ).
fof(f_11_4,plain,
( ! [U_70,U_68] :
( subset(U_70,U_68)
| ( ~ in(sK8(U_70,U_68),U_68)
& in(sK8(U_70,U_68),U_70) ) )
& ! [U_69,U_67] :
( ! [U_63] :
( in(U_63,U_67)
| ~ in(U_63,U_69) )
| ~ subset(U_69,U_67) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK8]),skolemize(U_64,sK8(U_70,U_68))],[f_11_3]) ).
fof(f_11_5,plain,
( ! [U_68,U_70] :
( ~ in(sK8(U_70,U_68),U_68)
| ~ sP12(U_68,U_70) )
& ! [U_68,U_70] :
( in(sK8(U_70,U_68),U_70)
| ~ sP12(U_68,U_70) )
& ! [U_68,U_70] :
( subset(U_70,U_68)
| sP12(U_68,U_70) )
& ! [U_69,U_67,U_63] :
( in(U_63,U_67)
| ~ in(U_63,U_69)
| ~ subset(U_69,U_67) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP12])],[f_11_4]) ).
cnf(f_11_6,plain,
( in(U_63,U_67)
| ~ in(U_63,U_69)
| ~ subset(U_69,U_67) ),
inference(clausify,[status(thm)],[f_11_5]) ).
cnf(f_11_7,plain,
( subset(U_70,U_68)
| sP12(U_68,U_70) ),
inference(clausify,[status(thm)],[f_11_5]) ).
cnf(f_11_8,plain,
( in(sK8(U_70,U_68),U_70)
| ~ sP12(U_68,U_70) ),
inference(clausify,[status(thm)],[f_11_5]) ).
cnf(f_11_9,plain,
( ~ in(sK8(U_70,U_68),U_68)
| ~ sP12(U_68,U_70) ),
inference(clausify,[status(thm)],[f_11_5]) ).
fof(f_12_1,plain,
! [A,B,C] :
( ( C = set_intersection2(A,B)
| ? [D] :
( ( ~ in(D,C)
& in(D,B)
& in(D,A) )
| ( ( ~ in(D,B)
| ~ in(D,A) )
& in(D,C) ) ) )
& ( ! [D] :
( ( in(D,C)
| ~ in(D,B)
| ~ in(D,A) )
& ( ( in(D,B)
& in(D,A) )
| ~ in(D,C) ) )
| C != set_intersection2(A,B) ) ),
inference(fof_nnf,[status(thm)],[d3_xboole_0]) ).
fof(f_12_2,plain,
! [U_75,U_74,U_73] :
( ( U_73 = set_intersection2(U_75,U_74)
| ? [U_72] :
( ( ~ in(U_72,U_73)
& in(U_72,U_74)
& in(U_72,U_75) )
| ( ( ~ in(U_72,U_74)
| ~ in(U_72,U_75) )
& in(U_72,U_73) ) ) )
& ( ! [U_71] :
( ( in(U_71,U_73)
| ~ in(U_71,U_74)
| ~ in(U_71,U_75) )
& ( ( in(U_71,U_74)
& in(U_71,U_75) )
| ~ in(U_71,U_73) ) )
| U_73 != set_intersection2(U_75,U_74) ) ),
inference(variable_rename,[status(thm)],[f_12_1]) ).
fof(f_12_3,plain,
( ! [U_85,U_83,U_81] :
( U_81 = set_intersection2(U_85,U_83)
| ? [U_79] :
( ~ in(U_79,U_81)
& in(U_79,U_83)
& in(U_79,U_85) )
| ? [U_78] :
( ( ~ in(U_78,U_83)
| ~ in(U_78,U_85) )
& in(U_78,U_81) ) )
& ! [U_84,U_82,U_80] :
( ( ! [U_77] :
( in(U_77,U_80)
| ~ in(U_77,U_82)
| ~ in(U_77,U_84) )
& ! [U_76] :
( ( in(U_76,U_82)
& in(U_76,U_84) )
| ~ in(U_76,U_80) ) )
| U_80 != set_intersection2(U_84,U_82) ) ),
inference(miniscope,[status(thm)],[f_12_2]) ).
fof(f_12_4,plain,
( ! [U_85,U_83,U_81] :
( U_81 = set_intersection2(U_85,U_83)
| ? [U_79] :
( ~ in(U_79,U_81)
& in(U_79,U_83)
& in(U_79,U_85) )
| ( ( ~ in(sK9(U_85,U_83,U_81),U_83)
| ~ in(sK9(U_85,U_83,U_81),U_85) )
& in(sK9(U_85,U_83,U_81),U_81) ) )
& ! [U_84,U_82,U_80] :
( ( ! [U_77] :
( in(U_77,U_80)
| ~ in(U_77,U_82)
| ~ in(U_77,U_84) )
& ! [U_76] :
( ( in(U_76,U_82)
& in(U_76,U_84) )
| ~ in(U_76,U_80) ) )
| U_80 != set_intersection2(U_84,U_82) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK9]),skolemize(U_78,sK9(U_85,U_83,U_81))],[f_12_3]) ).
fof(f_12_5,plain,
( ! [U_85,U_83,U_81] :
( U_81 = set_intersection2(U_85,U_83)
| ( ~ in(sK10(U_85,U_83,U_81),U_81)
& in(sK10(U_85,U_83,U_81),U_83)
& in(sK10(U_85,U_83,U_81),U_85) )
| ( ( ~ in(sK9(U_85,U_83,U_81),U_83)
| ~ in(sK9(U_85,U_83,U_81),U_85) )
& in(sK9(U_85,U_83,U_81),U_81) ) )
& ! [U_84,U_82,U_80] :
( ( ! [U_77] :
( in(U_77,U_80)
| ~ in(U_77,U_82)
| ~ in(U_77,U_84) )
& ! [U_76] :
( ( in(U_76,U_82)
& in(U_76,U_84) )
| ~ in(U_76,U_80) ) )
| U_80 != set_intersection2(U_84,U_82) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK10]),skolemize(U_79,sK10(U_85,U_83,U_81))],[f_12_4]) ).
fof(f_12_6,plain,
( ! [U_81,U_85,U_83] :
( ~ in(sK10(U_85,U_83,U_81),U_81)
| ~ sP16(U_81,U_85,U_83) )
& ! [U_81,U_85,U_83] :
( in(sK10(U_85,U_83,U_81),U_83)
| ~ sP16(U_81,U_85,U_83) )
& ! [U_81,U_85,U_83] :
( in(sK10(U_85,U_83,U_81),U_85)
| ~ sP16(U_81,U_85,U_83) )
& ! [U_81,U_85,U_83] :
( ~ in(sK9(U_85,U_83,U_81),U_83)
| ~ in(sK9(U_85,U_83,U_81),U_85)
| ~ sP15(U_81,U_85,U_83) )
& ! [U_81,U_85,U_83] :
( in(sK9(U_85,U_83,U_81),U_81)
| ~ sP15(U_81,U_85,U_83) )
& ! [U_82,U_76,U_84] :
( in(U_76,U_82)
| ~ sP13(U_82,U_76,U_84) )
& ! [U_82,U_76,U_84] :
( in(U_76,U_84)
| ~ sP13(U_82,U_76,U_84) )
& ! [U_82,U_76,U_84,U_77,U_80] :
( in(U_77,U_80)
| ~ in(U_77,U_82)
| ~ in(U_77,U_84)
| ~ sP14(U_82,U_76,U_84,U_77,U_80) )
& ! [U_82,U_76,U_84,U_77,U_80] :
( sP13(U_82,U_76,U_84)
| ~ in(U_76,U_80)
| ~ sP14(U_82,U_76,U_84,U_77,U_80) )
& ! [U_81,U_85,U_83] :
( U_81 = set_intersection2(U_85,U_83)
| sP16(U_81,U_85,U_83)
| sP15(U_81,U_85,U_83) )
& ! [U_82,U_76,U_84,U_77,U_80] :
( sP14(U_82,U_76,U_84,U_77,U_80)
| U_80 != set_intersection2(U_84,U_82) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP13,sP14,sP15,sP16])],[f_12_5]) ).
cnf(f_12_7,plain,
( sP14(U_82,U_76,U_84,U_77,U_80)
| U_80 != set_intersection2(U_84,U_82) ),
inference(clausify,[status(thm)],[f_12_6]) ).
cnf(f_12_8,plain,
( U_81 = set_intersection2(U_85,U_83)
| sP16(U_81,U_85,U_83)
| sP15(U_81,U_85,U_83) ),
inference(clausify,[status(thm)],[f_12_6]) ).
cnf(f_12_9,plain,
( sP13(U_82,U_76,U_84)
| ~ in(U_76,U_80)
| ~ sP14(U_82,U_76,U_84,U_77,U_80) ),
inference(clausify,[status(thm)],[f_12_6]) ).
cnf(f_12_10,plain,
( in(U_77,U_80)
| ~ in(U_77,U_82)
| ~ in(U_77,U_84)
| ~ sP14(U_82,U_76,U_84,U_77,U_80) ),
inference(clausify,[status(thm)],[f_12_6]) ).
cnf(f_12_11,plain,
( in(U_76,U_84)
| ~ sP13(U_82,U_76,U_84) ),
inference(clausify,[status(thm)],[f_12_6]) ).
cnf(f_12_12,plain,
( in(U_76,U_82)
| ~ sP13(U_82,U_76,U_84) ),
inference(clausify,[status(thm)],[f_12_6]) ).
cnf(f_12_13,plain,
( in(sK9(U_85,U_83,U_81),U_81)
| ~ sP15(U_81,U_85,U_83) ),
inference(clausify,[status(thm)],[f_12_6]) ).
cnf(f_12_14,plain,
( ~ in(sK9(U_85,U_83,U_81),U_83)
| ~ in(sK9(U_85,U_83,U_81),U_85)
| ~ sP15(U_81,U_85,U_83) ),
inference(clausify,[status(thm)],[f_12_6]) ).
cnf(f_12_15,plain,
( in(sK10(U_85,U_83,U_81),U_85)
| ~ sP16(U_81,U_85,U_83) ),
inference(clausify,[status(thm)],[f_12_6]) ).
cnf(f_12_16,plain,
( in(sK10(U_85,U_83,U_81),U_83)
| ~ sP16(U_81,U_85,U_83) ),
inference(clausify,[status(thm)],[f_12_6]) ).
cnf(f_12_17,plain,
( ~ in(sK10(U_85,U_83,U_81),U_81)
| ~ sP16(U_81,U_85,U_83) ),
inference(clausify,[status(thm)],[f_12_6]) ).
fof(f_13_1,plain,
! [A,B,C] :
( ( C = set_difference(A,B)
| ? [D] :
( ( ~ in(D,C)
& ~ in(D,B)
& in(D,A) )
| ( ( in(D,B)
| ~ in(D,A) )
& in(D,C) ) ) )
& ( ! [D] :
( ( in(D,C)
| in(D,B)
| ~ in(D,A) )
& ( ( ~ in(D,B)
& in(D,A) )
| ~ in(D,C) ) )
| C != set_difference(A,B) ) ),
inference(fof_nnf,[status(thm)],[d4_xboole_0]) ).
fof(f_13_2,plain,
! [U_90,U_89,U_88] :
( ( U_88 = set_difference(U_90,U_89)
| ? [U_87] :
( ( ~ in(U_87,U_88)
& ~ in(U_87,U_89)
& in(U_87,U_90) )
| ( ( in(U_87,U_89)
| ~ in(U_87,U_90) )
& in(U_87,U_88) ) ) )
& ( ! [U_86] :
( ( in(U_86,U_88)
| in(U_86,U_89)
| ~ in(U_86,U_90) )
& ( ( ~ in(U_86,U_89)
& in(U_86,U_90) )
| ~ in(U_86,U_88) ) )
| U_88 != set_difference(U_90,U_89) ) ),
inference(variable_rename,[status(thm)],[f_13_1]) ).
fof(f_13_3,plain,
( ! [U_100,U_98,U_96] :
( U_96 = set_difference(U_100,U_98)
| ? [U_94] :
( ~ in(U_94,U_96)
& ~ in(U_94,U_98)
& in(U_94,U_100) )
| ? [U_93] :
( ( in(U_93,U_98)
| ~ in(U_93,U_100) )
& in(U_93,U_96) ) )
& ! [U_99,U_97,U_95] :
( ( ! [U_92] :
( in(U_92,U_95)
| in(U_92,U_97)
| ~ in(U_92,U_99) )
& ! [U_91] :
( ( ~ in(U_91,U_97)
& in(U_91,U_99) )
| ~ in(U_91,U_95) ) )
| U_95 != set_difference(U_99,U_97) ) ),
inference(miniscope,[status(thm)],[f_13_2]) ).
fof(f_13_4,plain,
( ! [U_100,U_98,U_96] :
( U_96 = set_difference(U_100,U_98)
| ? [U_94] :
( ~ in(U_94,U_96)
& ~ in(U_94,U_98)
& in(U_94,U_100) )
| ( ( in(sK11(U_100,U_98,U_96),U_98)
| ~ in(sK11(U_100,U_98,U_96),U_100) )
& in(sK11(U_100,U_98,U_96),U_96) ) )
& ! [U_99,U_97,U_95] :
( ( ! [U_92] :
( in(U_92,U_95)
| in(U_92,U_97)
| ~ in(U_92,U_99) )
& ! [U_91] :
( ( ~ in(U_91,U_97)
& in(U_91,U_99) )
| ~ in(U_91,U_95) ) )
| U_95 != set_difference(U_99,U_97) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK11]),skolemize(U_93,sK11(U_100,U_98,U_96))],[f_13_3]) ).
fof(f_13_5,plain,
( ! [U_100,U_98,U_96] :
( U_96 = set_difference(U_100,U_98)
| ( ~ in(sK12(U_100,U_98,U_96),U_96)
& ~ in(sK12(U_100,U_98,U_96),U_98)
& in(sK12(U_100,U_98,U_96),U_100) )
| ( ( in(sK11(U_100,U_98,U_96),U_98)
| ~ in(sK11(U_100,U_98,U_96),U_100) )
& in(sK11(U_100,U_98,U_96),U_96) ) )
& ! [U_99,U_97,U_95] :
( ( ! [U_92] :
( in(U_92,U_95)
| in(U_92,U_97)
| ~ in(U_92,U_99) )
& ! [U_91] :
( ( ~ in(U_91,U_97)
& in(U_91,U_99) )
| ~ in(U_91,U_95) ) )
| U_95 != set_difference(U_99,U_97) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK12]),skolemize(U_94,sK12(U_100,U_98,U_96))],[f_13_4]) ).
fof(f_13_6,plain,
( ! [U_96,U_100,U_98] :
( ~ in(sK12(U_100,U_98,U_96),U_96)
| ~ sP20(U_96,U_100,U_98) )
& ! [U_96,U_100,U_98] :
( ~ in(sK12(U_100,U_98,U_96),U_98)
| ~ sP20(U_96,U_100,U_98) )
& ! [U_96,U_100,U_98] :
( in(sK12(U_100,U_98,U_96),U_100)
| ~ sP20(U_96,U_100,U_98) )
& ! [U_96,U_100,U_98] :
( in(sK11(U_100,U_98,U_96),U_98)
| ~ in(sK11(U_100,U_98,U_96),U_100)
| ~ sP19(U_96,U_100,U_98) )
& ! [U_96,U_100,U_98] :
( in(sK11(U_100,U_98,U_96),U_96)
| ~ sP19(U_96,U_100,U_98) )
& ! [U_97,U_91,U_99] :
( ~ in(U_91,U_97)
| ~ sP17(U_97,U_91,U_99) )
& ! [U_97,U_91,U_99] :
( in(U_91,U_99)
| ~ sP17(U_97,U_91,U_99) )
& ! [U_92,U_97,U_95,U_91,U_99] :
( in(U_92,U_95)
| in(U_92,U_97)
| ~ in(U_92,U_99)
| ~ sP18(U_92,U_97,U_95,U_91,U_99) )
& ! [U_92,U_97,U_95,U_91,U_99] :
( sP17(U_97,U_91,U_99)
| ~ in(U_91,U_95)
| ~ sP18(U_92,U_97,U_95,U_91,U_99) )
& ! [U_96,U_100,U_98] :
( U_96 = set_difference(U_100,U_98)
| sP20(U_96,U_100,U_98)
| sP19(U_96,U_100,U_98) )
& ! [U_92,U_97,U_95,U_91,U_99] :
( sP18(U_92,U_97,U_95,U_91,U_99)
| U_95 != set_difference(U_99,U_97) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP17,sP18,sP19,sP20])],[f_13_5]) ).
cnf(f_13_7,plain,
( sP18(U_92,U_97,U_95,U_91,U_99)
| U_95 != set_difference(U_99,U_97) ),
inference(clausify,[status(thm)],[f_13_6]) ).
cnf(f_13_8,plain,
( U_96 = set_difference(U_100,U_98)
| sP20(U_96,U_100,U_98)
| sP19(U_96,U_100,U_98) ),
inference(clausify,[status(thm)],[f_13_6]) ).
cnf(f_13_9,plain,
( sP17(U_97,U_91,U_99)
| ~ in(U_91,U_95)
| ~ sP18(U_92,U_97,U_95,U_91,U_99) ),
inference(clausify,[status(thm)],[f_13_6]) ).
cnf(f_13_10,plain,
( in(U_92,U_95)
| in(U_92,U_97)
| ~ in(U_92,U_99)
| ~ sP18(U_92,U_97,U_95,U_91,U_99) ),
inference(clausify,[status(thm)],[f_13_6]) ).
cnf(f_13_11,plain,
( in(U_91,U_99)
| ~ sP17(U_97,U_91,U_99) ),
inference(clausify,[status(thm)],[f_13_6]) ).
cnf(f_13_12,plain,
( ~ in(U_91,U_97)
| ~ sP17(U_97,U_91,U_99) ),
inference(clausify,[status(thm)],[f_13_6]) ).
cnf(f_13_13,plain,
( in(sK11(U_100,U_98,U_96),U_96)
| ~ sP19(U_96,U_100,U_98) ),
inference(clausify,[status(thm)],[f_13_6]) ).
cnf(f_13_14,plain,
( in(sK11(U_100,U_98,U_96),U_98)
| ~ in(sK11(U_100,U_98,U_96),U_100)
| ~ sP19(U_96,U_100,U_98) ),
inference(clausify,[status(thm)],[f_13_6]) ).
cnf(f_13_15,plain,
( in(sK12(U_100,U_98,U_96),U_100)
| ~ sP20(U_96,U_100,U_98) ),
inference(clausify,[status(thm)],[f_13_6]) ).
cnf(f_13_16,plain,
( ~ in(sK12(U_100,U_98,U_96),U_98)
| ~ sP20(U_96,U_100,U_98) ),
inference(clausify,[status(thm)],[f_13_6]) ).
cnf(f_13_17,plain,
( ~ in(sK12(U_100,U_98,U_96),U_96)
| ~ sP20(U_96,U_100,U_98) ),
inference(clausify,[status(thm)],[f_13_6]) ).
fof(f_14_1,plain,
! [A,B] :
( ( disjoint(A,B)
| set_intersection2(A,B) != empty_set )
& ( set_intersection2(A,B) = empty_set
| ~ disjoint(A,B) ) ),
inference(fof_nnf,[status(thm)],[d7_xboole_0]) ).
fof(f_14_2,plain,
! [U_102,U_101] :
( ( disjoint(U_102,U_101)
| set_intersection2(U_102,U_101) != empty_set )
& ( set_intersection2(U_102,U_101) = empty_set
| ~ disjoint(U_102,U_101) ) ),
inference(variable_rename,[status(thm)],[f_14_1]) ).
fof(f_14_3,plain,
( ! [U_106,U_104] :
( disjoint(U_106,U_104)
| set_intersection2(U_106,U_104) != empty_set )
& ! [U_105,U_103] :
( set_intersection2(U_105,U_103) = empty_set
| ~ disjoint(U_105,U_103) ) ),
inference(miniscope,[status(thm)],[f_14_2]) ).
fof(f_14_4,plain,
( ! [U_104,U_106] :
( disjoint(U_106,U_104)
| set_intersection2(U_106,U_104) != empty_set )
& ! [U_103,U_105] :
( set_intersection2(U_105,U_103) = empty_set
| ~ disjoint(U_105,U_103) ) ),
inference(definitional_conversion,[status(esa)],[f_14_3]) ).
cnf(f_14_5,plain,
( set_intersection2(U_105,U_103) = empty_set
| ~ disjoint(U_105,U_103) ),
inference(clausify,[status(thm)],[f_14_4]) ).
cnf(f_14_6,plain,
( disjoint(U_106,U_104)
| set_intersection2(U_106,U_104) != empty_set ),
inference(clausify,[status(thm)],[f_14_4]) ).
fof(f_15_1,plain,
! [A,B] :
( ( proper_subset(A,B)
| A = B
| ~ subset(A,B) )
& ( ( A != B
& subset(A,B) )
| ~ proper_subset(A,B) ) ),
inference(fof_nnf,[status(thm)],[d8_xboole_0]) ).
fof(f_15_2,plain,
! [U_108,U_107] :
( ( proper_subset(U_108,U_107)
| U_108 = U_107
| ~ subset(U_108,U_107) )
& ( ( U_108 != U_107
& subset(U_108,U_107) )
| ~ proper_subset(U_108,U_107) ) ),
inference(variable_rename,[status(thm)],[f_15_1]) ).
fof(f_15_3,plain,
( ! [U_112,U_110] :
( proper_subset(U_112,U_110)
| U_112 = U_110
| ~ subset(U_112,U_110) )
& ! [U_111,U_109] :
( ( U_111 != U_109
& subset(U_111,U_109) )
| ~ proper_subset(U_111,U_109) ) ),
inference(miniscope,[status(thm)],[f_15_2]) ).
fof(f_15_4,plain,
( ! [U_109,U_111] :
( U_111 != U_109
| ~ sP21(U_109,U_111) )
& ! [U_109,U_111] :
( subset(U_111,U_109)
| ~ sP21(U_109,U_111) )
& ! [U_110,U_112] :
( proper_subset(U_112,U_110)
| U_112 = U_110
| ~ subset(U_112,U_110) )
& ! [U_109,U_111] :
( sP21(U_109,U_111)
| ~ proper_subset(U_111,U_109) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP21])],[f_15_3]) ).
cnf(f_15_5,plain,
( sP21(U_109,U_111)
| ~ proper_subset(U_111,U_109) ),
inference(clausify,[status(thm)],[f_15_4]) ).
cnf(f_15_6,plain,
( proper_subset(U_112,U_110)
| U_112 = U_110
| ~ subset(U_112,U_110) ),
inference(clausify,[status(thm)],[f_15_4]) ).
cnf(f_15_7,plain,
( subset(U_111,U_109)
| ~ sP21(U_109,U_111) ),
inference(clausify,[status(thm)],[f_15_4]) ).
cnf(f_15_8,plain,
( U_111 != U_109
| ~ sP21(U_109,U_111) ),
inference(clausify,[status(thm)],[f_15_4]) ).
fof(f_16_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_k1_tarski]) ).
fof(f_16_2,plain,
$true,
inference(definitional_conversion,[status(esa)],[f_16_1]) ).
cnf(f_16_3,plain,
$true,
inference(clausify,[status(thm)],[f_16_2]) ).
fof(f_17_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_k1_xboole_0]) ).
fof(f_17_2,plain,
$true,
inference(definitional_conversion,[status(esa)],[f_17_1]) ).
cnf(f_17_3,plain,
$true,
inference(clausify,[status(thm)],[f_17_2]) ).
fof(f_18_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_k2_tarski]) ).
fof(f_18_2,plain,
$true,
inference(definitional_conversion,[status(esa)],[f_18_1]) ).
cnf(f_18_3,plain,
$true,
inference(clausify,[status(thm)],[f_18_2]) ).
fof(f_19_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_k2_xboole_0]) ).
fof(f_19_2,plain,
$true,
inference(definitional_conversion,[status(esa)],[f_19_1]) ).
cnf(f_19_3,plain,
$true,
inference(clausify,[status(thm)],[f_19_2]) ).
fof(f_20_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_k3_xboole_0]) ).
fof(f_20_2,plain,
$true,
inference(definitional_conversion,[status(esa)],[f_20_1]) ).
cnf(f_20_3,plain,
$true,
inference(clausify,[status(thm)],[f_20_2]) ).
fof(f_21_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_k4_xboole_0]) ).
fof(f_21_2,plain,
$true,
inference(definitional_conversion,[status(esa)],[f_21_1]) ).
cnf(f_21_3,plain,
$true,
inference(clausify,[status(thm)],[f_21_2]) ).
fof(f_22_1,plain,
empty(empty_set),
inference(fof_nnf,[status(thm)],[fc1_xboole_0]) ).
fof(f_22_2,plain,
empty(empty_set),
inference(definitional_conversion,[status(esa)],[f_22_1]) ).
cnf(f_22_3,plain,
empty(empty_set),
inference(clausify,[status(thm)],[f_22_2]) ).
fof(f_23_1,plain,
! [A,B] :
( ~ empty(set_union2(A,B))
| empty(A) ),
inference(fof_nnf,[status(thm)],[fc2_xboole_0]) ).
fof(f_23_2,plain,
! [U_114,U_113] :
( ~ empty(set_union2(U_114,U_113))
| empty(U_114) ),
inference(variable_rename,[status(thm)],[f_23_1]) ).
fof(f_23_3,plain,
! [U_114] :
( ! [U_113] : ~ empty(set_union2(U_114,U_113))
| empty(U_114) ),
inference(miniscope,[status(thm)],[f_23_2]) ).
fof(f_23_4,plain,
! [U_113,U_114] :
( ~ empty(set_union2(U_114,U_113))
| empty(U_114) ),
inference(definitional_conversion,[status(esa)],[f_23_3]) ).
cnf(f_23_5,plain,
( ~ empty(set_union2(U_114,U_113))
| empty(U_114) ),
inference(clausify,[status(thm)],[f_23_4]) ).
fof(f_24_1,plain,
! [A,B] :
( ~ empty(set_union2(B,A))
| empty(A) ),
inference(fof_nnf,[status(thm)],[fc3_xboole_0]) ).
fof(f_24_2,plain,
! [U_116,U_115] :
( ~ empty(set_union2(U_115,U_116))
| empty(U_116) ),
inference(variable_rename,[status(thm)],[f_24_1]) ).
fof(f_24_3,plain,
! [U_116] :
( ! [U_115] : ~ empty(set_union2(U_115,U_116))
| empty(U_116) ),
inference(miniscope,[status(thm)],[f_24_2]) ).
fof(f_24_4,plain,
! [U_115,U_116] :
( ~ empty(set_union2(U_115,U_116))
| empty(U_116) ),
inference(definitional_conversion,[status(esa)],[f_24_3]) ).
cnf(f_24_5,plain,
( ~ empty(set_union2(U_115,U_116))
| empty(U_116) ),
inference(clausify,[status(thm)],[f_24_4]) ).
fof(f_25_1,plain,
! [A,B] : set_union2(A,A) = A,
inference(fof_nnf,[status(thm)],[idempotence_k2_xboole_0]) ).
fof(f_25_2,plain,
! [U_118,U_117] : set_union2(U_118,U_118) = U_118,
inference(variable_rename,[status(thm)],[f_25_1]) ).
fof(f_25_3,plain,
! [U_118] : set_union2(U_118,U_118) = U_118,
inference(miniscope,[status(thm)],[f_25_2]) ).
fof(f_25_4,plain,
! [U_118] : set_union2(U_118,U_118) = U_118,
inference(definitional_conversion,[status(esa)],[f_25_3]) ).
cnf(f_25_5,plain,
set_union2(U_118,U_118) = U_118,
inference(clausify,[status(thm)],[f_25_4]) ).
fof(f_26_1,plain,
! [A,B] : set_intersection2(A,A) = A,
inference(fof_nnf,[status(thm)],[idempotence_k3_xboole_0]) ).
fof(f_26_2,plain,
! [U_120,U_119] : set_intersection2(U_120,U_120) = U_120,
inference(variable_rename,[status(thm)],[f_26_1]) ).
fof(f_26_3,plain,
! [U_120] : set_intersection2(U_120,U_120) = U_120,
inference(miniscope,[status(thm)],[f_26_2]) ).
fof(f_26_4,plain,
! [U_120] : set_intersection2(U_120,U_120) = U_120,
inference(definitional_conversion,[status(esa)],[f_26_3]) ).
cnf(f_26_5,plain,
set_intersection2(U_120,U_120) = U_120,
inference(clausify,[status(thm)],[f_26_4]) ).
fof(f_27_1,plain,
! [A,B] : ~ proper_subset(A,A),
inference(fof_nnf,[status(thm)],[irreflexivity_r2_xboole_0]) ).
fof(f_27_2,plain,
! [U_122,U_121] : ~ proper_subset(U_122,U_122),
inference(variable_rename,[status(thm)],[f_27_1]) ).
fof(f_27_3,plain,
! [U_122] : ~ proper_subset(U_122,U_122),
inference(miniscope,[status(thm)],[f_27_2]) ).
fof(f_27_4,plain,
! [U_122] : ~ proper_subset(U_122,U_122),
inference(definitional_conversion,[status(esa)],[f_27_3]) ).
cnf(f_27_5,plain,
~ proper_subset(U_122,U_122),
inference(clausify,[status(thm)],[f_27_4]) ).
fof(f_28_1,plain,
! [A] : singleton(A) != empty_set,
inference(fof_nnf,[status(thm)],[l1_zfmisc_1]) ).
fof(f_28_2,plain,
! [U_123] : singleton(U_123) != empty_set,
inference(variable_rename,[status(thm)],[f_28_1]) ).
fof(f_28_3,plain,
! [U_123] : singleton(U_123) != empty_set,
inference(definitional_conversion,[status(esa)],[f_28_2]) ).
cnf(f_28_4,plain,
singleton(U_123) != empty_set,
inference(clausify,[status(thm)],[f_28_3]) ).
fof(f_29_1,plain,
! [A,B] :
( ( subset(singleton(A),B)
| ~ in(A,B) )
& ( in(A,B)
| ~ subset(singleton(A),B) ) ),
inference(fof_nnf,[status(thm)],[l2_zfmisc_1]) ).
fof(f_29_2,plain,
! [U_125,U_124] :
( ( subset(singleton(U_125),U_124)
| ~ in(U_125,U_124) )
& ( in(U_125,U_124)
| ~ subset(singleton(U_125),U_124) ) ),
inference(variable_rename,[status(thm)],[f_29_1]) ).
fof(f_29_3,plain,
( ! [U_129,U_127] :
( subset(singleton(U_129),U_127)
| ~ in(U_129,U_127) )
& ! [U_128,U_126] :
( in(U_128,U_126)
| ~ subset(singleton(U_128),U_126) ) ),
inference(miniscope,[status(thm)],[f_29_2]) ).
fof(f_29_4,plain,
( ! [U_127,U_129] :
( subset(singleton(U_129),U_127)
| ~ in(U_129,U_127) )
& ! [U_126,U_128] :
( in(U_128,U_126)
| ~ subset(singleton(U_128),U_126) ) ),
inference(definitional_conversion,[status(esa)],[f_29_3]) ).
cnf(f_29_5,plain,
( in(U_128,U_126)
| ~ subset(singleton(U_128),U_126) ),
inference(clausify,[status(thm)],[f_29_4]) ).
cnf(f_29_6,plain,
( subset(singleton(U_129),U_127)
| ~ in(U_129,U_127) ),
inference(clausify,[status(thm)],[f_29_4]) ).
fof(f_30_1,plain,
! [A,B] :
( ( set_difference(A,B) = empty_set
| ~ subset(A,B) )
& ( subset(A,B)
| set_difference(A,B) != empty_set ) ),
inference(fof_nnf,[status(thm)],[l32_xboole_1]) ).
fof(f_30_2,plain,
! [U_131,U_130] :
( ( set_difference(U_131,U_130) = empty_set
| ~ subset(U_131,U_130) )
& ( subset(U_131,U_130)
| set_difference(U_131,U_130) != empty_set ) ),
inference(variable_rename,[status(thm)],[f_30_1]) ).
fof(f_30_3,plain,
( ! [U_135,U_133] :
( set_difference(U_135,U_133) = empty_set
| ~ subset(U_135,U_133) )
& ! [U_134,U_132] :
( subset(U_134,U_132)
| set_difference(U_134,U_132) != empty_set ) ),
inference(miniscope,[status(thm)],[f_30_2]) ).
fof(f_30_4,plain,
( ! [U_133,U_135] :
( set_difference(U_135,U_133) = empty_set
| ~ subset(U_135,U_133) )
& ! [U_132,U_134] :
( subset(U_134,U_132)
| set_difference(U_134,U_132) != empty_set ) ),
inference(definitional_conversion,[status(esa)],[f_30_3]) ).
cnf(f_30_5,plain,
( subset(U_134,U_132)
| set_difference(U_134,U_132) != empty_set ),
inference(clausify,[status(thm)],[f_30_4]) ).
cnf(f_30_6,plain,
( set_difference(U_135,U_133) = empty_set
| ~ subset(U_135,U_133) ),
inference(clausify,[status(thm)],[f_30_4]) ).
fof(f_31_1,plain,
! [A,B,C] :
( subset(A,set_difference(B,singleton(C)))
| in(C,A)
| ~ subset(A,B) ),
inference(fof_nnf,[status(thm)],[l3_zfmisc_1]) ).
fof(f_31_2,plain,
! [U_138,U_137,U_136] :
( subset(U_138,set_difference(U_137,singleton(U_136)))
| in(U_136,U_138)
| ~ subset(U_138,U_137) ),
inference(variable_rename,[status(thm)],[f_31_1]) ).
fof(f_31_3,plain,
! [U_138,U_137] :
( ! [U_136] :
( subset(U_138,set_difference(U_137,singleton(U_136)))
| in(U_136,U_138) )
| ~ subset(U_138,U_137) ),
inference(miniscope,[status(thm)],[f_31_2]) ).
fof(f_31_4,plain,
! [U_137,U_136,U_138] :
( subset(U_138,set_difference(U_137,singleton(U_136)))
| in(U_136,U_138)
| ~ subset(U_138,U_137) ),
inference(definitional_conversion,[status(esa)],[f_31_3]) ).
cnf(f_31_5,plain,
( subset(U_138,set_difference(U_137,singleton(U_136)))
| in(U_136,U_138)
| ~ subset(U_138,U_137) ),
inference(clausify,[status(thm)],[f_31_4]) ).
fof(f_32_1,negated_conjecture,
~ ! [A,B] :
( subset(A,singleton(B))
<=> ( A = singleton(B)
| A = empty_set ) ),
inference(negate,[status(cth)],[l4_zfmisc_1]) ).
fof(f_32_2,negated_conjecture,
? [A,B] :
( ( ~ subset(A,singleton(B))
& ( A = singleton(B)
| A = empty_set ) )
| ( A != singleton(B)
& A != empty_set
& subset(A,singleton(B)) ) ),
inference(fof_nnf,[status(thm)],[f_32_1]) ).
fof(f_32_3,negated_conjecture,
? [U_140,U_139] :
( ( ~ subset(U_140,singleton(U_139))
& ( U_140 = singleton(U_139)
| U_140 = empty_set ) )
| ( U_140 != singleton(U_139)
& U_140 != empty_set
& subset(U_140,singleton(U_139)) ) ),
inference(variable_rename,[status(thm)],[f_32_2]) ).
fof(f_32_4,negated_conjecture,
( ? [U_144,U_142] :
( ~ subset(U_144,singleton(U_142))
& ( U_144 = singleton(U_142)
| U_144 = empty_set ) )
| ? [U_143,U_141] :
( U_143 != singleton(U_141)
& U_143 != empty_set
& subset(U_143,singleton(U_141)) ) ),
inference(miniscope,[status(thm)],[f_32_3]) ).
fof(f_32_5,negated_conjecture,
( ? [U_144,U_142] :
( ~ subset(U_144,singleton(U_142))
& ( U_144 = singleton(U_142)
| U_144 = empty_set ) )
| ? [U_141] :
( sK13 != singleton(U_141)
& sK13 != empty_set
& subset(sK13,singleton(U_141)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK13]),skolemize(U_143,sK13)],[f_32_4]) ).
fof(f_32_6,negated_conjecture,
( ? [U_144,U_142] :
( ~ subset(U_144,singleton(U_142))
& ( U_144 = singleton(U_142)
| U_144 = empty_set ) )
| ( sK13 != singleton(sK14)
& sK13 != empty_set
& subset(sK13,singleton(sK14)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK14]),skolemize(U_141,sK14)],[f_32_5]) ).
fof(f_32_7,negated_conjecture,
( ? [U_142] :
( ~ subset(sK15,singleton(U_142))
& ( sK15 = singleton(U_142)
| sK15 = empty_set ) )
| ( sK13 != singleton(sK14)
& sK13 != empty_set
& subset(sK13,singleton(sK14)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK15]),skolemize(U_144,sK15)],[f_32_6]) ).
fof(f_32_8,negated_conjecture,
( ( ~ subset(sK15,singleton(sK16))
& ( sK15 = singleton(sK16)
| sK15 = empty_set ) )
| ( sK13 != singleton(sK14)
& sK13 != empty_set
& subset(sK13,singleton(sK14)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK16]),skolemize(U_142,sK16)],[f_32_7]) ).
fof(f_32_9,negated_conjecture,
( ( ~ subset(sK15,singleton(sK16))
| ~ sP23 )
& ( sK15 = singleton(sK16)
| sK15 = empty_set
| ~ sP23 )
& ( sK13 != singleton(sK14)
| ~ sP22 )
& ( sK13 != empty_set
| ~ sP22 )
& ( subset(sK13,singleton(sK14))
| ~ sP22 )
& ( sP23
| sP22 ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP22,sP23])],[f_32_8]) ).
cnf(f_32_10,negated_conjecture,
( sP23
| sP22 ),
inference(clausify,[status(thm)],[f_32_9]) ).
cnf(f_32_11,negated_conjecture,
( subset(sK13,singleton(sK14))
| ~ sP22 ),
inference(clausify,[status(thm)],[f_32_9]) ).
cnf(f_32_12,negated_conjecture,
( sK13 != empty_set
| ~ sP22 ),
inference(clausify,[status(thm)],[f_32_9]) ).
cnf(f_32_13,negated_conjecture,
( sK13 != singleton(sK14)
| ~ sP22 ),
inference(clausify,[status(thm)],[f_32_9]) ).
cnf(f_32_14,negated_conjecture,
( sK15 = singleton(sK16)
| sK15 = empty_set
| ~ sP23 ),
inference(clausify,[status(thm)],[f_32_9]) ).
cnf(f_32_15,negated_conjecture,
( ~ subset(sK15,singleton(sK16))
| ~ sP23 ),
inference(clausify,[status(thm)],[f_32_9]) ).
fof(f_33_1,plain,
? [A] : empty(A),
inference(fof_nnf,[status(thm)],[rc1_xboole_0]) ).
fof(f_33_2,plain,
? [U_145] : empty(U_145),
inference(variable_rename,[status(thm)],[f_33_1]) ).
fof(f_33_3,plain,
empty(sK17),
inference(skolemize,[status(esa),new_symbols(skolem,[sK17]),skolemize(U_145,sK17)],[f_33_2]) ).
fof(f_33_4,plain,
empty(sK17),
inference(definitional_conversion,[status(esa)],[f_33_3]) ).
cnf(f_33_5,plain,
empty(sK17),
inference(clausify,[status(thm)],[f_33_4]) ).
fof(f_34_1,plain,
? [A] : ~ empty(A),
inference(fof_nnf,[status(thm)],[rc2_xboole_0]) ).
fof(f_34_2,plain,
? [U_146] : ~ empty(U_146),
inference(variable_rename,[status(thm)],[f_34_1]) ).
fof(f_34_3,plain,
~ empty(sK18),
inference(skolemize,[status(esa),new_symbols(skolem,[sK18]),skolemize(U_146,sK18)],[f_34_2]) ).
fof(f_34_4,plain,
~ empty(sK18),
inference(definitional_conversion,[status(esa)],[f_34_3]) ).
cnf(f_34_5,plain,
~ empty(sK18),
inference(clausify,[status(thm)],[f_34_4]) ).
fof(f_35_1,plain,
! [A,B] : subset(A,A),
inference(fof_nnf,[status(thm)],[reflexivity_r1_tarski]) ).
fof(f_35_2,plain,
! [U_148,U_147] : subset(U_148,U_148),
inference(variable_rename,[status(thm)],[f_35_1]) ).
fof(f_35_3,plain,
! [U_148] : subset(U_148,U_148),
inference(miniscope,[status(thm)],[f_35_2]) ).
fof(f_35_4,plain,
! [U_148] : subset(U_148,U_148),
inference(definitional_conversion,[status(esa)],[f_35_3]) ).
cnf(f_35_5,plain,
subset(U_148,U_148),
inference(clausify,[status(thm)],[f_35_4]) ).
fof(f_36_1,plain,
! [A,B] :
( disjoint(B,A)
| ~ disjoint(A,B) ),
inference(fof_nnf,[status(thm)],[symmetry_r1_xboole_0]) ).
fof(f_36_2,plain,
! [U_150,U_149] :
( disjoint(U_149,U_150)
| ~ disjoint(U_150,U_149) ),
inference(variable_rename,[status(thm)],[f_36_1]) ).
fof(f_36_3,plain,
! [U_149,U_150] :
( disjoint(U_149,U_150)
| ~ disjoint(U_150,U_149) ),
inference(definitional_conversion,[status(esa)],[f_36_2]) ).
cnf(f_36_4,plain,
( disjoint(U_149,U_150)
| ~ disjoint(U_150,U_149) ),
inference(clausify,[status(thm)],[f_36_3]) ).
fof(f_37_1,plain,
! [A,B] :
( set_union2(A,B) = B
| ~ subset(A,B) ),
inference(fof_nnf,[status(thm)],[t12_xboole_1]) ).
fof(f_37_2,plain,
! [U_152,U_151] :
( set_union2(U_152,U_151) = U_151
| ~ subset(U_152,U_151) ),
inference(variable_rename,[status(thm)],[f_37_1]) ).
fof(f_37_3,plain,
! [U_151,U_152] :
( set_union2(U_152,U_151) = U_151
| ~ subset(U_152,U_151) ),
inference(definitional_conversion,[status(esa)],[f_37_2]) ).
cnf(f_37_4,plain,
( set_union2(U_152,U_151) = U_151
| ~ subset(U_152,U_151) ),
inference(clausify,[status(thm)],[f_37_3]) ).
fof(f_38_1,plain,
! [A,B] : subset(set_intersection2(A,B),A),
inference(fof_nnf,[status(thm)],[t17_xboole_1]) ).
fof(f_38_2,plain,
! [U_154,U_153] : subset(set_intersection2(U_154,U_153),U_154),
inference(variable_rename,[status(thm)],[f_38_1]) ).
fof(f_38_3,plain,
! [U_153,U_154] : subset(set_intersection2(U_154,U_153),U_154),
inference(definitional_conversion,[status(esa)],[f_38_2]) ).
cnf(f_38_4,plain,
subset(set_intersection2(U_154,U_153),U_154),
inference(clausify,[status(thm)],[f_38_3]) ).
fof(f_39_1,plain,
! [A,B,C] :
( subset(A,set_intersection2(B,C))
| ~ subset(A,C)
| ~ subset(A,B) ),
inference(fof_nnf,[status(thm)],[t19_xboole_1]) ).
fof(f_39_2,plain,
! [U_157,U_156,U_155] :
( subset(U_157,set_intersection2(U_156,U_155))
| ~ subset(U_157,U_155)
| ~ subset(U_157,U_156) ),
inference(variable_rename,[status(thm)],[f_39_1]) ).
fof(f_39_3,plain,
! [U_155,U_156,U_157] :
( subset(U_157,set_intersection2(U_156,U_155))
| ~ subset(U_157,U_155)
| ~ subset(U_157,U_156) ),
inference(definitional_conversion,[status(esa)],[f_39_2]) ).
cnf(f_39_4,plain,
( subset(U_157,set_intersection2(U_156,U_155))
| ~ subset(U_157,U_155)
| ~ subset(U_157,U_156) ),
inference(clausify,[status(thm)],[f_39_3]) ).
fof(f_40_1,plain,
! [A] : set_union2(A,empty_set) = A,
inference(fof_nnf,[status(thm)],[t1_boole]) ).
fof(f_40_2,plain,
! [U_158] : set_union2(U_158,empty_set) = U_158,
inference(variable_rename,[status(thm)],[f_40_1]) ).
fof(f_40_3,plain,
! [U_158] : set_union2(U_158,empty_set) = U_158,
inference(definitional_conversion,[status(esa)],[f_40_2]) ).
cnf(f_40_4,plain,
set_union2(U_158,empty_set) = U_158,
inference(clausify,[status(thm)],[f_40_3]) ).
fof(f_41_1,plain,
! [A,B,C] :
( subset(A,C)
| ~ subset(B,C)
| ~ subset(A,B) ),
inference(fof_nnf,[status(thm)],[t1_xboole_1]) ).
fof(f_41_2,plain,
! [U_161,U_160,U_159] :
( subset(U_161,U_159)
| ~ subset(U_160,U_159)
| ~ subset(U_161,U_160) ),
inference(variable_rename,[status(thm)],[f_41_1]) ).
fof(f_41_3,plain,
! [U_160,U_159,U_161] :
( subset(U_161,U_159)
| ~ subset(U_160,U_159)
| ~ subset(U_161,U_160) ),
inference(definitional_conversion,[status(esa)],[f_41_2]) ).
cnf(f_41_4,plain,
( subset(U_161,U_159)
| ~ subset(U_160,U_159)
| ~ subset(U_161,U_160) ),
inference(clausify,[status(thm)],[f_41_3]) ).
fof(f_42_1,plain,
! [A,B,C] :
( subset(set_intersection2(A,C),set_intersection2(B,C))
| ~ subset(A,B) ),
inference(fof_nnf,[status(thm)],[t26_xboole_1]) ).
fof(f_42_2,plain,
! [U_164,U_163,U_162] :
( subset(set_intersection2(U_164,U_162),set_intersection2(U_163,U_162))
| ~ subset(U_164,U_163) ),
inference(variable_rename,[status(thm)],[f_42_1]) ).
fof(f_42_3,plain,
! [U_164,U_163] :
( ! [U_162] : subset(set_intersection2(U_164,U_162),set_intersection2(U_163,U_162))
| ~ subset(U_164,U_163) ),
inference(miniscope,[status(thm)],[f_42_2]) ).
fof(f_42_4,plain,
! [U_163,U_162,U_164] :
( subset(set_intersection2(U_164,U_162),set_intersection2(U_163,U_162))
| ~ subset(U_164,U_163) ),
inference(definitional_conversion,[status(esa)],[f_42_3]) ).
cnf(f_42_5,plain,
( subset(set_intersection2(U_164,U_162),set_intersection2(U_163,U_162))
| ~ subset(U_164,U_163) ),
inference(clausify,[status(thm)],[f_42_4]) ).
fof(f_43_1,plain,
! [A,B] :
( set_intersection2(A,B) = A
| ~ subset(A,B) ),
inference(fof_nnf,[status(thm)],[t28_xboole_1]) ).
fof(f_43_2,plain,
! [U_166,U_165] :
( set_intersection2(U_166,U_165) = U_166
| ~ subset(U_166,U_165) ),
inference(variable_rename,[status(thm)],[f_43_1]) ).
fof(f_43_3,plain,
! [U_165,U_166] :
( set_intersection2(U_166,U_165) = U_166
| ~ subset(U_166,U_165) ),
inference(definitional_conversion,[status(esa)],[f_43_2]) ).
cnf(f_43_4,plain,
( set_intersection2(U_166,U_165) = U_166
| ~ subset(U_166,U_165) ),
inference(clausify,[status(thm)],[f_43_3]) ).
fof(f_44_1,plain,
! [A] : set_intersection2(A,empty_set) = empty_set,
inference(fof_nnf,[status(thm)],[t2_boole]) ).
fof(f_44_2,plain,
! [U_167] : set_intersection2(U_167,empty_set) = empty_set,
inference(variable_rename,[status(thm)],[f_44_1]) ).
fof(f_44_3,plain,
! [U_167] : set_intersection2(U_167,empty_set) = empty_set,
inference(definitional_conversion,[status(esa)],[f_44_2]) ).
cnf(f_44_4,plain,
set_intersection2(U_167,empty_set) = empty_set,
inference(clausify,[status(thm)],[f_44_3]) ).
fof(f_45_1,plain,
! [A,B] :
( A = B
| ? [C] :
( ( ~ in(C,A)
& in(C,B) )
| ( ~ in(C,B)
& in(C,A) ) ) ),
inference(fof_nnf,[status(thm)],[t2_tarski]) ).
fof(f_45_2,plain,
! [U_170,U_169] :
( U_170 = U_169
| ? [U_168] :
( ( ~ in(U_168,U_170)
& in(U_168,U_169) )
| ( ~ in(U_168,U_169)
& in(U_168,U_170) ) ) ),
inference(variable_rename,[status(thm)],[f_45_1]) ).
fof(f_45_3,plain,
! [U_170,U_169] :
( U_170 = U_169
| ? [U_172] :
( ~ in(U_172,U_170)
& in(U_172,U_169) )
| ? [U_171] :
( ~ in(U_171,U_169)
& in(U_171,U_170) ) ),
inference(miniscope,[status(thm)],[f_45_2]) ).
fof(f_45_4,plain,
! [U_170,U_169] :
( U_170 = U_169
| ? [U_172] :
( ~ in(U_172,U_170)
& in(U_172,U_169) )
| ( ~ in(sK19(U_170,U_169),U_169)
& in(sK19(U_170,U_169),U_170) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK19]),skolemize(U_171,sK19(U_170,U_169))],[f_45_3]) ).
fof(f_45_5,plain,
! [U_170,U_169] :
( U_170 = U_169
| ( ~ in(sK20(U_170,U_169),U_170)
& in(sK20(U_170,U_169),U_169) )
| ( ~ in(sK19(U_170,U_169),U_169)
& in(sK19(U_170,U_169),U_170) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK20]),skolemize(U_172,sK20(U_170,U_169))],[f_45_4]) ).
fof(f_45_6,plain,
( ! [U_169,U_170] :
( ~ in(sK20(U_170,U_169),U_170)
| ~ sP25(U_169,U_170) )
& ! [U_169,U_170] :
( in(sK20(U_170,U_169),U_169)
| ~ sP25(U_169,U_170) )
& ! [U_169,U_170] :
( ~ in(sK19(U_170,U_169),U_169)
| ~ sP24(U_169,U_170) )
& ! [U_169,U_170] :
( in(sK19(U_170,U_169),U_170)
| ~ sP24(U_169,U_170) )
& ! [U_169,U_170] :
( U_170 = U_169
| sP25(U_169,U_170)
| sP24(U_169,U_170) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP24,sP25])],[f_45_5]) ).
cnf(f_45_7,plain,
( U_170 = U_169
| sP25(U_169,U_170)
| sP24(U_169,U_170) ),
inference(clausify,[status(thm)],[f_45_6]) ).
cnf(f_45_8,plain,
( in(sK19(U_170,U_169),U_170)
| ~ sP24(U_169,U_170) ),
inference(clausify,[status(thm)],[f_45_6]) ).
cnf(f_45_9,plain,
( ~ in(sK19(U_170,U_169),U_169)
| ~ sP24(U_169,U_170) ),
inference(clausify,[status(thm)],[f_45_6]) ).
cnf(f_45_10,plain,
( in(sK20(U_170,U_169),U_169)
| ~ sP25(U_169,U_170) ),
inference(clausify,[status(thm)],[f_45_6]) ).
cnf(f_45_11,plain,
( ~ in(sK20(U_170,U_169),U_170)
| ~ sP25(U_169,U_170) ),
inference(clausify,[status(thm)],[f_45_6]) ).
fof(f_46_1,plain,
! [A] : subset(empty_set,A),
inference(fof_nnf,[status(thm)],[t2_xboole_1]) ).
fof(f_46_2,plain,
! [U_173] : subset(empty_set,U_173),
inference(variable_rename,[status(thm)],[f_46_1]) ).
fof(f_46_3,plain,
! [U_173] : subset(empty_set,U_173),
inference(definitional_conversion,[status(esa)],[f_46_2]) ).
cnf(f_46_4,plain,
subset(empty_set,U_173),
inference(clausify,[status(thm)],[f_46_3]) ).
fof(f_47_1,plain,
! [A,B,C] :
( subset(set_difference(A,C),set_difference(B,C))
| ~ subset(A,B) ),
inference(fof_nnf,[status(thm)],[t33_xboole_1]) ).
fof(f_47_2,plain,
! [U_176,U_175,U_174] :
( subset(set_difference(U_176,U_174),set_difference(U_175,U_174))
| ~ subset(U_176,U_175) ),
inference(variable_rename,[status(thm)],[f_47_1]) ).
fof(f_47_3,plain,
! [U_176,U_175] :
( ! [U_174] : subset(set_difference(U_176,U_174),set_difference(U_175,U_174))
| ~ subset(U_176,U_175) ),
inference(miniscope,[status(thm)],[f_47_2]) ).
fof(f_47_4,plain,
! [U_174,U_175,U_176] :
( subset(set_difference(U_176,U_174),set_difference(U_175,U_174))
| ~ subset(U_176,U_175) ),
inference(definitional_conversion,[status(esa)],[f_47_3]) ).
cnf(f_47_5,plain,
( subset(set_difference(U_176,U_174),set_difference(U_175,U_174))
| ~ subset(U_176,U_175) ),
inference(clausify,[status(thm)],[f_47_4]) ).
fof(f_48_1,plain,
! [A,B] : subset(set_difference(A,B),A),
inference(fof_nnf,[status(thm)],[t36_xboole_1]) ).
fof(f_48_2,plain,
! [U_178,U_177] : subset(set_difference(U_178,U_177),U_178),
inference(variable_rename,[status(thm)],[f_48_1]) ).
fof(f_48_3,plain,
! [U_177,U_178] : subset(set_difference(U_178,U_177),U_178),
inference(definitional_conversion,[status(esa)],[f_48_2]) ).
cnf(f_48_4,plain,
subset(set_difference(U_178,U_177),U_178),
inference(clausify,[status(thm)],[f_48_3]) ).
fof(f_49_1,plain,
! [A,B] :
( ( set_difference(A,B) = empty_set
| ~ subset(A,B) )
& ( subset(A,B)
| set_difference(A,B) != empty_set ) ),
inference(fof_nnf,[status(thm)],[t37_xboole_1]) ).
fof(f_49_2,plain,
! [U_180,U_179] :
( ( set_difference(U_180,U_179) = empty_set
| ~ subset(U_180,U_179) )
& ( subset(U_180,U_179)
| set_difference(U_180,U_179) != empty_set ) ),
inference(variable_rename,[status(thm)],[f_49_1]) ).
fof(f_49_3,plain,
( ! [U_184,U_182] :
( set_difference(U_184,U_182) = empty_set
| ~ subset(U_184,U_182) )
& ! [U_183,U_181] :
( subset(U_183,U_181)
| set_difference(U_183,U_181) != empty_set ) ),
inference(miniscope,[status(thm)],[f_49_2]) ).
fof(f_49_4,plain,
( ! [U_184,U_182] :
( set_difference(U_184,U_182) = empty_set
| ~ subset(U_184,U_182) )
& ! [U_183,U_181] :
( subset(U_183,U_181)
| set_difference(U_183,U_181) != empty_set ) ),
inference(definitional_conversion,[status(esa)],[f_49_3]) ).
cnf(f_49_5,plain,
( subset(U_183,U_181)
| set_difference(U_183,U_181) != empty_set ),
inference(clausify,[status(thm)],[f_49_4]) ).
cnf(f_49_6,plain,
( set_difference(U_184,U_182) = empty_set
| ~ subset(U_184,U_182) ),
inference(clausify,[status(thm)],[f_49_4]) ).
fof(f_50_1,plain,
! [A,B] : set_union2(A,set_difference(B,A)) = set_union2(A,B),
inference(fof_nnf,[status(thm)],[t39_xboole_1]) ).
fof(f_50_2,plain,
! [U_186,U_185] : set_union2(U_186,set_difference(U_185,U_186)) = set_union2(U_186,U_185),
inference(variable_rename,[status(thm)],[f_50_1]) ).
fof(f_50_3,plain,
! [U_185,U_186] : set_union2(U_186,set_difference(U_185,U_186)) = set_union2(U_186,U_185),
inference(definitional_conversion,[status(esa)],[f_50_2]) ).
cnf(f_50_4,plain,
set_union2(U_186,set_difference(U_185,U_186)) = set_union2(U_186,U_185),
inference(clausify,[status(thm)],[f_50_3]) ).
fof(f_51_1,plain,
! [A] : set_difference(A,empty_set) = A,
inference(fof_nnf,[status(thm)],[t3_boole]) ).
fof(f_51_2,plain,
! [U_187] : set_difference(U_187,empty_set) = U_187,
inference(variable_rename,[status(thm)],[f_51_1]) ).
fof(f_51_3,plain,
! [U_187] : set_difference(U_187,empty_set) = U_187,
inference(definitional_conversion,[status(esa)],[f_51_2]) ).
cnf(f_51_4,plain,
set_difference(U_187,empty_set) = U_187,
inference(clausify,[status(thm)],[f_51_3]) ).
fof(f_52_1,plain,
! [A,B] :
( ( ~ disjoint(A,B)
| ! [C] :
( ~ in(C,B)
| ~ in(C,A) ) )
& ( ? [C] :
( in(C,B)
& in(C,A) )
| disjoint(A,B) ) ),
inference(fof_nnf,[status(thm)],[t3_xboole_0]) ).
fof(f_52_2,plain,
! [U_191,U_190] :
( ( ~ disjoint(U_191,U_190)
| ! [U_189] :
( ~ in(U_189,U_190)
| ~ in(U_189,U_191) ) )
& ( ? [U_188] :
( in(U_188,U_190)
& in(U_188,U_191) )
| disjoint(U_191,U_190) ) ),
inference(variable_rename,[status(thm)],[f_52_1]) ).
fof(f_52_3,plain,
( ! [U_195,U_193] :
( ~ disjoint(U_195,U_193)
| ! [U_189] :
( ~ in(U_189,U_193)
| ~ in(U_189,U_195) ) )
& ! [U_194,U_192] :
( ? [U_188] :
( in(U_188,U_192)
& in(U_188,U_194) )
| disjoint(U_194,U_192) ) ),
inference(miniscope,[status(thm)],[f_52_2]) ).
fof(f_52_4,plain,
( ! [U_195,U_193] :
( ~ disjoint(U_195,U_193)
| ! [U_189] :
( ~ in(U_189,U_193)
| ~ in(U_189,U_195) ) )
& ! [U_194,U_192] :
( ( in(sK21(U_194,U_192),U_192)
& in(sK21(U_194,U_192),U_194) )
| disjoint(U_194,U_192) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK21]),skolemize(U_188,sK21(U_194,U_192))],[f_52_3]) ).
fof(f_52_5,plain,
( ! [U_192,U_194] :
( in(sK21(U_194,U_192),U_192)
| ~ sP26(U_192,U_194) )
& ! [U_192,U_194] :
( in(sK21(U_194,U_192),U_194)
| ~ sP26(U_192,U_194) )
& ! [U_195,U_189,U_193] :
( ~ disjoint(U_195,U_193)
| ~ in(U_189,U_193)
| ~ in(U_189,U_195) )
& ! [U_192,U_194] :
( sP26(U_192,U_194)
| disjoint(U_194,U_192) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP26])],[f_52_4]) ).
cnf(f_52_6,plain,
( sP26(U_192,U_194)
| disjoint(U_194,U_192) ),
inference(clausify,[status(thm)],[f_52_5]) ).
cnf(f_52_7,plain,
( ~ disjoint(U_195,U_193)
| ~ in(U_189,U_193)
| ~ in(U_189,U_195) ),
inference(clausify,[status(thm)],[f_52_5]) ).
cnf(f_52_8,plain,
( in(sK21(U_194,U_192),U_194)
| ~ sP26(U_192,U_194) ),
inference(clausify,[status(thm)],[f_52_5]) ).
cnf(f_52_9,plain,
( in(sK21(U_194,U_192),U_192)
| ~ sP26(U_192,U_194) ),
inference(clausify,[status(thm)],[f_52_5]) ).
fof(f_53_1,plain,
! [A] :
( A = empty_set
| ~ subset(A,empty_set) ),
inference(fof_nnf,[status(thm)],[t3_xboole_1]) ).
fof(f_53_2,plain,
! [U_196] :
( U_196 = empty_set
| ~ subset(U_196,empty_set) ),
inference(variable_rename,[status(thm)],[f_53_1]) ).
fof(f_53_3,plain,
! [U_196] :
( U_196 = empty_set
| ~ subset(U_196,empty_set) ),
inference(definitional_conversion,[status(esa)],[f_53_2]) ).
cnf(f_53_4,plain,
( U_196 = empty_set
| ~ subset(U_196,empty_set) ),
inference(clausify,[status(thm)],[f_53_3]) ).
fof(f_54_1,plain,
! [A,B] : set_difference(set_union2(A,B),B) = set_difference(A,B),
inference(fof_nnf,[status(thm)],[t40_xboole_1]) ).
fof(f_54_2,plain,
! [U_198,U_197] : set_difference(set_union2(U_198,U_197),U_197) = set_difference(U_198,U_197),
inference(variable_rename,[status(thm)],[f_54_1]) ).
fof(f_54_3,plain,
! [U_198,U_197] : set_difference(set_union2(U_198,U_197),U_197) = set_difference(U_198,U_197),
inference(definitional_conversion,[status(esa)],[f_54_2]) ).
cnf(f_54_4,plain,
set_difference(set_union2(U_198,U_197),U_197) = set_difference(U_198,U_197),
inference(clausify,[status(thm)],[f_54_3]) ).
fof(f_55_1,plain,
! [A,B] :
( B = set_union2(A,set_difference(B,A))
| ~ subset(A,B) ),
inference(fof_nnf,[status(thm)],[t45_xboole_1]) ).
fof(f_55_2,plain,
! [U_200,U_199] :
( U_199 = set_union2(U_200,set_difference(U_199,U_200))
| ~ subset(U_200,U_199) ),
inference(variable_rename,[status(thm)],[f_55_1]) ).
fof(f_55_3,plain,
! [U_200,U_199] :
( U_199 = set_union2(U_200,set_difference(U_199,U_200))
| ~ subset(U_200,U_199) ),
inference(definitional_conversion,[status(esa)],[f_55_2]) ).
cnf(f_55_4,plain,
( U_199 = set_union2(U_200,set_difference(U_199,U_200))
| ~ subset(U_200,U_199) ),
inference(clausify,[status(thm)],[f_55_3]) ).
fof(f_56_1,plain,
! [A,B] : set_difference(A,set_difference(A,B)) = set_intersection2(A,B),
inference(fof_nnf,[status(thm)],[t48_xboole_1]) ).
fof(f_56_2,plain,
! [U_202,U_201] : set_difference(U_202,set_difference(U_202,U_201)) = set_intersection2(U_202,U_201),
inference(variable_rename,[status(thm)],[f_56_1]) ).
fof(f_56_3,plain,
! [U_201,U_202] : set_difference(U_202,set_difference(U_202,U_201)) = set_intersection2(U_202,U_201),
inference(definitional_conversion,[status(esa)],[f_56_2]) ).
cnf(f_56_4,plain,
set_difference(U_202,set_difference(U_202,U_201)) = set_intersection2(U_202,U_201),
inference(clausify,[status(thm)],[f_56_3]) ).
fof(f_57_1,plain,
! [A] : set_difference(empty_set,A) = empty_set,
inference(fof_nnf,[status(thm)],[t4_boole]) ).
fof(f_57_2,plain,
! [U_203] : set_difference(empty_set,U_203) = empty_set,
inference(variable_rename,[status(thm)],[f_57_1]) ).
fof(f_57_3,plain,
! [U_203] : set_difference(empty_set,U_203) = empty_set,
inference(definitional_conversion,[status(esa)],[f_57_2]) ).
cnf(f_57_4,plain,
set_difference(empty_set,U_203) = empty_set,
inference(clausify,[status(thm)],[f_57_3]) ).
fof(f_58_1,plain,
! [A,B] :
( ( ~ disjoint(A,B)
| ! [C] : ~ in(C,set_intersection2(A,B)) )
& ( ? [C] : in(C,set_intersection2(A,B))
| disjoint(A,B) ) ),
inference(fof_nnf,[status(thm)],[t4_xboole_0]) ).
fof(f_58_2,plain,
! [U_207,U_206] :
( ( ~ disjoint(U_207,U_206)
| ! [U_205] : ~ in(U_205,set_intersection2(U_207,U_206)) )
& ( ? [U_204] : in(U_204,set_intersection2(U_207,U_206))
| disjoint(U_207,U_206) ) ),
inference(variable_rename,[status(thm)],[f_58_1]) ).
fof(f_58_3,plain,
( ! [U_211,U_209] :
( ~ disjoint(U_211,U_209)
| ! [U_205] : ~ in(U_205,set_intersection2(U_211,U_209)) )
& ! [U_210,U_208] :
( ? [U_204] : in(U_204,set_intersection2(U_210,U_208))
| disjoint(U_210,U_208) ) ),
inference(miniscope,[status(thm)],[f_58_2]) ).
fof(f_58_4,plain,
( ! [U_211,U_209] :
( ~ disjoint(U_211,U_209)
| ! [U_205] : ~ in(U_205,set_intersection2(U_211,U_209)) )
& ! [U_210,U_208] :
( in(sK22(U_210,U_208),set_intersection2(U_210,U_208))
| disjoint(U_210,U_208) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK22]),skolemize(U_204,sK22(U_210,U_208))],[f_58_3]) ).
fof(f_58_5,plain,
( ! [U_211,U_205,U_209] :
( ~ disjoint(U_211,U_209)
| ~ in(U_205,set_intersection2(U_211,U_209)) )
& ! [U_210,U_208] :
( in(sK22(U_210,U_208),set_intersection2(U_210,U_208))
| disjoint(U_210,U_208) ) ),
inference(definitional_conversion,[status(esa)],[f_58_4]) ).
cnf(f_58_6,plain,
( in(sK22(U_210,U_208),set_intersection2(U_210,U_208))
| disjoint(U_210,U_208) ),
inference(clausify,[status(thm)],[f_58_5]) ).
cnf(f_58_7,plain,
( ~ disjoint(U_211,U_209)
| ~ in(U_205,set_intersection2(U_211,U_209)) ),
inference(clausify,[status(thm)],[f_58_5]) ).
fof(f_59_1,plain,
! [A,B] :
( ~ proper_subset(B,A)
| ~ subset(A,B) ),
inference(fof_nnf,[status(thm)],[t60_xboole_1]) ).
fof(f_59_2,plain,
! [U_213,U_212] :
( ~ proper_subset(U_212,U_213)
| ~ subset(U_213,U_212) ),
inference(variable_rename,[status(thm)],[f_59_1]) ).
fof(f_59_3,plain,
! [U_212,U_213] :
( ~ proper_subset(U_212,U_213)
| ~ subset(U_213,U_212) ),
inference(definitional_conversion,[status(esa)],[f_59_2]) ).
cnf(f_59_4,plain,
( ~ proper_subset(U_212,U_213)
| ~ subset(U_213,U_212) ),
inference(clausify,[status(thm)],[f_59_3]) ).
fof(f_60_1,plain,
! [A,B,C] :
( disjoint(A,C)
| ~ disjoint(B,C)
| ~ subset(A,B) ),
inference(fof_nnf,[status(thm)],[t63_xboole_1]) ).
fof(f_60_2,plain,
! [U_216,U_215,U_214] :
( disjoint(U_216,U_214)
| ~ disjoint(U_215,U_214)
| ~ subset(U_216,U_215) ),
inference(variable_rename,[status(thm)],[f_60_1]) ).
fof(f_60_3,plain,
! [U_216,U_215,U_214] :
( disjoint(U_216,U_214)
| ~ disjoint(U_215,U_214)
| ~ subset(U_216,U_215) ),
inference(definitional_conversion,[status(esa)],[f_60_2]) ).
cnf(f_60_4,plain,
( disjoint(U_216,U_214)
| ~ disjoint(U_215,U_214)
| ~ subset(U_216,U_215) ),
inference(clausify,[status(thm)],[f_60_3]) ).
fof(f_61_1,plain,
! [A] : unordered_pair(A,A) = singleton(A),
inference(fof_nnf,[status(thm)],[t69_enumset1]) ).
fof(f_61_2,plain,
! [U_217] : unordered_pair(U_217,U_217) = singleton(U_217),
inference(variable_rename,[status(thm)],[f_61_1]) ).
fof(f_61_3,plain,
! [U_217] : unordered_pair(U_217,U_217) = singleton(U_217),
inference(definitional_conversion,[status(esa)],[f_61_2]) ).
cnf(f_61_4,plain,
unordered_pair(U_217,U_217) = singleton(U_217),
inference(clausify,[status(thm)],[f_61_3]) ).
fof(f_62_1,plain,
! [A] :
( A = empty_set
| ~ empty(A) ),
inference(fof_nnf,[status(thm)],[t6_boole]) ).
fof(f_62_2,plain,
! [U_218] :
( U_218 = empty_set
| ~ empty(U_218) ),
inference(variable_rename,[status(thm)],[f_62_1]) ).
fof(f_62_3,plain,
! [U_218] :
( U_218 = empty_set
| ~ empty(U_218) ),
inference(definitional_conversion,[status(esa)],[f_62_2]) ).
cnf(f_62_4,plain,
( U_218 = empty_set
| ~ empty(U_218) ),
inference(clausify,[status(thm)],[f_62_3]) ).
fof(f_63_1,plain,
! [A,B] :
( ~ empty(B)
| ~ in(A,B) ),
inference(fof_nnf,[status(thm)],[t7_boole]) ).
fof(f_63_2,plain,
! [U_220,U_219] :
( ~ empty(U_219)
| ~ in(U_220,U_219) ),
inference(variable_rename,[status(thm)],[f_63_1]) ).
fof(f_63_3,plain,
! [U_219,U_220] :
( ~ empty(U_219)
| ~ in(U_220,U_219) ),
inference(definitional_conversion,[status(esa)],[f_63_2]) ).
cnf(f_63_4,plain,
( ~ empty(U_219)
| ~ in(U_220,U_219) ),
inference(clausify,[status(thm)],[f_63_3]) ).
fof(f_64_1,plain,
! [A,B] : subset(A,set_union2(A,B)),
inference(fof_nnf,[status(thm)],[t7_xboole_1]) ).
fof(f_64_2,plain,
! [U_222,U_221] : subset(U_222,set_union2(U_222,U_221)),
inference(variable_rename,[status(thm)],[f_64_1]) ).
fof(f_64_3,plain,
! [U_221,U_222] : subset(U_222,set_union2(U_222,U_221)),
inference(definitional_conversion,[status(esa)],[f_64_2]) ).
cnf(f_64_4,plain,
subset(U_222,set_union2(U_222,U_221)),
inference(clausify,[status(thm)],[f_64_3]) ).
fof(f_65_1,plain,
! [A,B] :
( ( disjoint(A,B)
| set_difference(A,B) != A )
& ( set_difference(A,B) = A
| ~ disjoint(A,B) ) ),
inference(fof_nnf,[status(thm)],[t83_xboole_1]) ).
fof(f_65_2,plain,
! [U_224,U_223] :
( ( disjoint(U_224,U_223)
| set_difference(U_224,U_223) != U_224 )
& ( set_difference(U_224,U_223) = U_224
| ~ disjoint(U_224,U_223) ) ),
inference(variable_rename,[status(thm)],[f_65_1]) ).
fof(f_65_3,plain,
( ! [U_228,U_226] :
( disjoint(U_228,U_226)
| set_difference(U_228,U_226) != U_228 )
& ! [U_227,U_225] :
( set_difference(U_227,U_225) = U_227
| ~ disjoint(U_227,U_225) ) ),
inference(miniscope,[status(thm)],[f_65_2]) ).
fof(f_65_4,plain,
( ! [U_226,U_228] :
( disjoint(U_228,U_226)
| set_difference(U_228,U_226) != U_228 )
& ! [U_227,U_225] :
( set_difference(U_227,U_225) = U_227
| ~ disjoint(U_227,U_225) ) ),
inference(definitional_conversion,[status(esa)],[f_65_3]) ).
cnf(f_65_5,plain,
( set_difference(U_227,U_225) = U_227
| ~ disjoint(U_227,U_225) ),
inference(clausify,[status(thm)],[f_65_4]) ).
cnf(f_65_6,plain,
( disjoint(U_228,U_226)
| set_difference(U_228,U_226) != U_228 ),
inference(clausify,[status(thm)],[f_65_4]) ).
fof(f_66_1,plain,
! [A,B] :
( ~ empty(B)
| A = B
| ~ empty(A) ),
inference(fof_nnf,[status(thm)],[t8_boole]) ).
fof(f_66_2,plain,
! [U_230,U_229] :
( ~ empty(U_229)
| U_230 = U_229
| ~ empty(U_230) ),
inference(variable_rename,[status(thm)],[f_66_1]) ).
fof(f_66_3,plain,
! [U_230] :
( ! [U_229] :
( ~ empty(U_229)
| U_230 = U_229 )
| ~ empty(U_230) ),
inference(miniscope,[status(thm)],[f_66_2]) ).
fof(f_66_4,plain,
! [U_230,U_229] :
( ~ empty(U_229)
| U_230 = U_229
| ~ empty(U_230) ),
inference(definitional_conversion,[status(esa)],[f_66_3]) ).
cnf(f_66_5,plain,
( ~ empty(U_229)
| U_230 = U_229
| ~ empty(U_230) ),
inference(clausify,[status(thm)],[f_66_4]) ).
fof(f_67_1,plain,
! [A,B,C] :
( subset(set_union2(A,C),B)
| ~ subset(C,B)
| ~ subset(A,B) ),
inference(fof_nnf,[status(thm)],[t8_xboole_1]) ).
fof(f_67_2,plain,
! [U_233,U_232,U_231] :
( subset(set_union2(U_233,U_231),U_232)
| ~ subset(U_231,U_232)
| ~ subset(U_233,U_232) ),
inference(variable_rename,[status(thm)],[f_67_1]) ).
fof(f_67_3,plain,
! [U_232,U_231,U_233] :
( subset(set_union2(U_233,U_231),U_232)
| ~ subset(U_231,U_232)
| ~ subset(U_233,U_232) ),
inference(definitional_conversion,[status(esa)],[f_67_2]) ).
cnf(f_67_4,plain,
( subset(set_union2(U_233,U_231),U_232)
| ~ subset(U_231,U_232)
| ~ subset(U_233,U_232) ),
inference(clausify,[status(thm)],[f_67_3]) ).
cnf(f_16_3_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_16_3]) ).
cnf(f_17_3_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_17_3]) ).
cnf(f_18_3_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_18_3]) ).
cnf(f_19_3_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_19_3]) ).
cnf(f_20_3_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_20_3]) ).
cnf(f_21_3_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_21_3]) ).
cnf(equality_1,axiom,
Eq_x_0 = Eq_x_0,
theory(equality,[reflexivity]) ).
cnf(equality_2,axiom,
( Eq_x_1 = Eq_x_0
| Eq_x_0 != Eq_x_1 ),
theory(equality,[symmetry]) ).
cnf(equality_3,axiom,
( Eq_x_0 = Eq_x_2
| Eq_x_1 != Eq_x_2
| Eq_x_0 != Eq_x_1 ),
theory(equality,[transitivity]) ).
cnf(equality_4,axiom,
( unordered_pair(Eq_x_0,Eq_x_1) = unordered_pair(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_5,axiom,
( set_union2(Eq_x_0,Eq_x_1) = set_union2(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_6,axiom,
( set_intersection2(Eq_x_0,Eq_x_1) = set_intersection2(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_7,axiom,
( singleton(Eq_x_0) = singleton(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_8,axiom,
( set_difference(Eq_x_0,Eq_x_1) = set_difference(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_9,axiom,
( sK1(Eq_x_0,Eq_x_1) = sK1(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_10,axiom,
( sK2(Eq_x_0,Eq_x_1) = sK2(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_11,axiom,
( sK3(Eq_x_0) = sK3(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_12,axiom,
( sK4(Eq_x_0,Eq_x_1,Eq_x_2) = sK4(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_13,axiom,
( sK5(Eq_x_0,Eq_x_1,Eq_x_2) = sK5(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_14,axiom,
( sK6(Eq_x_0,Eq_x_1,Eq_x_2) = sK6(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_15,axiom,
( sK7(Eq_x_0,Eq_x_1,Eq_x_2) = sK7(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_16,axiom,
( sK8(Eq_x_0,Eq_x_1) = sK8(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_17,axiom,
( sK9(Eq_x_0,Eq_x_1,Eq_x_2) = sK9(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_18,axiom,
( sK10(Eq_x_0,Eq_x_1,Eq_x_2) = sK10(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_19,axiom,
( sK11(Eq_x_0,Eq_x_1,Eq_x_2) = sK11(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_20,axiom,
( sK12(Eq_x_0,Eq_x_1,Eq_x_2) = sK12(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_21,axiom,
( sK19(Eq_x_0,Eq_x_1) = sK19(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_22,axiom,
( sK20(Eq_x_0,Eq_x_1) = sK20(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_23,axiom,
( sK21(Eq_x_0,Eq_x_1) = sK21(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_24,axiom,
( sK22(Eq_x_0,Eq_x_1) = sK22(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_25,axiom,
( in(Eq_y_0,Eq_y_1)
| ~ in(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_26,axiom,
( proper_subset(Eq_y_0,Eq_y_1)
| ~ proper_subset(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_27,axiom,
( subset(Eq_y_0,Eq_y_1)
| ~ subset(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_28,axiom,
( disjoint(Eq_y_0,Eq_y_1)
| ~ disjoint(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_29,axiom,
( empty(Eq_y_0)
| ~ empty(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_30,axiom,
( sP0(Eq_y_0,Eq_y_1)
| ~ sP0(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_31,axiom,
( sP1(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| ~ sP1(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_32,axiom,
( sP2(Eq_y_0,Eq_y_1)
| ~ sP2(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_33,axiom,
( sP3(Eq_y_0,Eq_y_1)
| ~ sP3(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_34,axiom,
( sP4(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP4(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_35,axiom,
( sP5(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
| ~ sP5(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4)
| Eq_x_4 != Eq_y_4
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_36,axiom,
( sP6(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP6(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_37,axiom,
( sP7(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP7(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_38,axiom,
( sP8(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP8(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_39,axiom,
( sP9(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
| ~ sP9(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4)
| Eq_x_4 != Eq_y_4
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_40,axiom,
( sP10(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP10(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_41,axiom,
( sP11(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP11(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_42,axiom,
( sP12(Eq_y_0,Eq_y_1)
| ~ sP12(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_43,axiom,
( sP13(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP13(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_44,axiom,
( sP14(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
| ~ sP14(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4)
| Eq_x_4 != Eq_y_4
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_45,axiom,
( sP15(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP15(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_46,axiom,
( sP16(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP16(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_47,axiom,
( sP17(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP17(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_48,axiom,
( sP18(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
| ~ sP18(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4)
| Eq_x_4 != Eq_y_4
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_49,axiom,
( sP19(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP19(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_50,axiom,
( sP20(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP20(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_51,axiom,
( sP21(Eq_y_0,Eq_y_1)
| ~ sP21(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_52,axiom,
( sP24(Eq_y_0,Eq_y_1)
| ~ sP24(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_53,axiom,
( sP25(Eq_y_0,Eq_y_1)
| ~ sP25(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_54,axiom,
( sP26(Eq_y_0,Eq_y_1)
| ~ sP26(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(sat_proved,plain,
$false,
inference(cadical,[status(thm)],[]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU146+2 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.03 This is a FOF_THM_RFO_SEQ problem
% 0.00/0.04 % Command : /export/starexec/sandbox/solver/bin/connect++ --verbosity 1 --no-colour --tptp-proof --schedule default --timeout 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n020.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Sat Sep 19 23:23:18 UTC 2026
% 0.09/0.36 % CPUTime :
% 189.15/189.40 % SZS status Theorem for theBenchmark
% 189.15/189.40 % SZS output start Proof for theBenchmark
% See solution above
%------------------------------------------------------------------------------