%------------------------------------------------------------------------------
% File : ConnectPP---0.7.2
% Problem : SEU142+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 : n008.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 08:58:11 AM UTC 2026
% Result : Theorem 6.35s 6.63s
% Output : Proof 6.41s
% 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(l32_xboole_1,lemma,
! [A,B] :
( set_difference(A,B) = empty_set
<=> subset(A,B) ),
file('theBenchmark.p',l32_xboole_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,conjecture,
! [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]) ).
cnf(f_1_3,plain,
( ~ in(U_0,U_1)
| ~ in(U_1,U_0) ),
inference(clausify,[status(thm)],[f_1_2]) ).
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]) ).
cnf(f_2_3,plain,
( ~ proper_subset(U_2,U_3)
| ~ proper_subset(U_3,U_2) ),
inference(clausify,[status(thm)],[f_2_2]) ).
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]) ).
cnf(f_3_3,plain,
unordered_pair(U_5,U_4) = unordered_pair(U_4,U_5),
inference(clausify,[status(thm)],[f_3_2]) ).
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]) ).
cnf(f_4_3,plain,
set_union2(U_7,U_6) = set_union2(U_6,U_7),
inference(clausify,[status(thm)],[f_4_2]) ).
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]) ).
cnf(f_5_3,plain,
set_intersection2(U_9,U_8) = set_intersection2(U_8,U_9),
inference(clausify,[status(thm)],[f_5_2]) ).
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]) ).
cnf(f_6_4,plain,
( subset(U_14,U_12)
| U_14 != U_12 ),
inference(clausify,[status(thm)],[f_6_3]) ).
cnf(f_6_5,plain,
( subset(U_12,U_14)
| U_14 != U_12 ),
inference(clausify,[status(thm)],[f_6_3]) ).
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_3]) ).
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]) ).
cnf(f_7_6,plain,
( U_20 = U_26
| ~ in(U_20,U_24)
| U_24 != singleton(U_26) ),
inference(clausify,[status(thm)],[f_7_5]) ).
cnf(f_7_7,plain,
( in(U_21,U_24)
| U_21 != U_26
| U_24 != singleton(U_26) ),
inference(clausify,[status(thm)],[f_7_5]) ).
cnf(f_7_8,plain,
( sK2(U_27,U_25) = U_27
| in(sK1(U_27,U_25),U_25)
| U_25 = singleton(U_27) ),
inference(clausify,[status(thm)],[f_7_5]) ).
cnf(f_7_9,plain,
( ~ in(sK2(U_27,U_25),U_25)
| in(sK1(U_27,U_25),U_25)
| U_25 = singleton(U_27) ),
inference(clausify,[status(thm)],[f_7_5]) ).
cnf(f_7_10,plain,
( sK2(U_27,U_25) = U_27
| sK1(U_27,U_25) != U_27
| U_25 = singleton(U_27) ),
inference(clausify,[status(thm)],[f_7_5]) ).
cnf(f_7_11,plain,
( ~ in(sK2(U_27,U_25),U_25)
| sK1(U_27,U_25) != U_27
| U_25 = singleton(U_27) ),
inference(clausify,[status(thm)],[f_7_5]) ).
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]) ).
cnf(f_8_5,plain,
( ~ in(U_28,U_31)
| U_31 != empty_set ),
inference(clausify,[status(thm)],[f_8_4]) ).
cnf(f_8_6,plain,
( U_32 = empty_set
| in(sK3(U_32),U_32) ),
inference(clausify,[status(thm)],[f_8_4]) ).
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]) ).
cnf(f_9_6,plain,
( U_38 = U_44
| U_38 = U_46
| ~ in(U_38,U_42)
| U_42 != unordered_pair(U_46,U_44) ),
inference(clausify,[status(thm)],[f_9_5]) ).
cnf(f_9_7,plain,
( U_39 != U_46
| in(U_39,U_42)
| U_42 != unordered_pair(U_46,U_44) ),
inference(clausify,[status(thm)],[f_9_5]) ).
cnf(f_9_8,plain,
( U_39 != U_44
| in(U_39,U_42)
| U_42 != unordered_pair(U_46,U_44) ),
inference(clausify,[status(thm)],[f_9_5]) ).
cnf(f_9_9,plain,
( sK5(U_47,U_45,U_43) = U_45
| sK5(U_47,U_45,U_43) = U_47
| in(sK4(U_47,U_45,U_43),U_43)
| U_43 = unordered_pair(U_47,U_45) ),
inference(clausify,[status(thm)],[f_9_5]) ).
cnf(f_9_10,plain,
( ~ in(sK5(U_47,U_45,U_43),U_43)
| in(sK4(U_47,U_45,U_43),U_43)
| U_43 = unordered_pair(U_47,U_45) ),
inference(clausify,[status(thm)],[f_9_5]) ).
cnf(f_9_11,plain,
( sK4(U_47,U_45,U_43) != U_47
| sK5(U_47,U_45,U_43) = U_45
| sK5(U_47,U_45,U_43) = U_47
| U_43 = unordered_pair(U_47,U_45) ),
inference(clausify,[status(thm)],[f_9_5]) ).
cnf(f_9_12,plain,
( sK4(U_47,U_45,U_43) != U_45
| sK5(U_47,U_45,U_43) = U_45
| sK5(U_47,U_45,U_43) = U_47
| U_43 = unordered_pair(U_47,U_45) ),
inference(clausify,[status(thm)],[f_9_5]) ).
cnf(f_9_13,plain,
( sK4(U_47,U_45,U_43) != U_47
| ~ in(sK5(U_47,U_45,U_43),U_43)
| U_43 = unordered_pair(U_47,U_45) ),
inference(clausify,[status(thm)],[f_9_5]) ).
cnf(f_9_14,plain,
( sK4(U_47,U_45,U_43) != U_45
| ~ in(sK5(U_47,U_45,U_43),U_43)
| U_43 = unordered_pair(U_47,U_45) ),
inference(clausify,[status(thm)],[f_9_5]) ).
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]) ).
cnf(f_10_6,plain,
( in(U_53,U_59)
| in(U_53,U_61)
| ~ in(U_53,U_57)
| U_57 != set_union2(U_61,U_59) ),
inference(clausify,[status(thm)],[f_10_5]) ).
cnf(f_10_7,plain,
( ~ in(U_54,U_61)
| in(U_54,U_57)
| U_57 != set_union2(U_61,U_59) ),
inference(clausify,[status(thm)],[f_10_5]) ).
cnf(f_10_8,plain,
( ~ in(U_54,U_59)
| in(U_54,U_57)
| U_57 != set_union2(U_61,U_59) ),
inference(clausify,[status(thm)],[f_10_5]) ).
cnf(f_10_9,plain,
( 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_58)
| U_58 = set_union2(U_62,U_60) ),
inference(clausify,[status(thm)],[f_10_5]) ).
cnf(f_10_10,plain,
( ~ in(sK7(U_62,U_60,U_58),U_58)
| in(sK6(U_62,U_60,U_58),U_58)
| U_58 = set_union2(U_62,U_60) ),
inference(clausify,[status(thm)],[f_10_5]) ).
cnf(f_10_11,plain,
( ~ in(sK6(U_62,U_60,U_58),U_62)
| in(sK7(U_62,U_60,U_58),U_60)
| in(sK7(U_62,U_60,U_58),U_62)
| U_58 = set_union2(U_62,U_60) ),
inference(clausify,[status(thm)],[f_10_5]) ).
cnf(f_10_12,plain,
( ~ in(sK6(U_62,U_60,U_58),U_60)
| in(sK7(U_62,U_60,U_58),U_60)
| in(sK7(U_62,U_60,U_58),U_62)
| U_58 = set_union2(U_62,U_60) ),
inference(clausify,[status(thm)],[f_10_5]) ).
cnf(f_10_13,plain,
( ~ in(sK6(U_62,U_60,U_58),U_62)
| ~ in(sK7(U_62,U_60,U_58),U_58)
| U_58 = set_union2(U_62,U_60) ),
inference(clausify,[status(thm)],[f_10_5]) ).
cnf(f_10_14,plain,
( ~ in(sK6(U_62,U_60,U_58),U_60)
| ~ in(sK7(U_62,U_60,U_58),U_58)
| U_58 = set_union2(U_62,U_60) ),
inference(clausify,[status(thm)],[f_10_5]) ).
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]) ).
cnf(f_11_5,plain,
( in(U_63,U_67)
| ~ in(U_63,U_69)
| ~ subset(U_69,U_67) ),
inference(clausify,[status(thm)],[f_11_4]) ).
cnf(f_11_6,plain,
( in(sK8(U_70,U_68),U_70)
| subset(U_70,U_68) ),
inference(clausify,[status(thm)],[f_11_4]) ).
cnf(f_11_7,plain,
( ~ in(sK8(U_70,U_68),U_68)
| subset(U_70,U_68) ),
inference(clausify,[status(thm)],[f_11_4]) ).
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]) ).
cnf(f_12_6,plain,
( in(U_76,U_84)
| ~ in(U_76,U_80)
| U_80 != set_intersection2(U_84,U_82) ),
inference(clausify,[status(thm)],[f_12_5]) ).
cnf(f_12_7,plain,
( in(U_76,U_82)
| ~ in(U_76,U_80)
| U_80 != set_intersection2(U_84,U_82) ),
inference(clausify,[status(thm)],[f_12_5]) ).
cnf(f_12_8,plain,
( in(U_77,U_80)
| ~ in(U_77,U_82)
| ~ in(U_77,U_84)
| U_80 != set_intersection2(U_84,U_82) ),
inference(clausify,[status(thm)],[f_12_5]) ).
cnf(f_12_9,plain,
( in(sK10(U_85,U_83,U_81),U_85)
| in(sK9(U_85,U_83,U_81),U_81)
| U_81 = set_intersection2(U_85,U_83) ),
inference(clausify,[status(thm)],[f_12_5]) ).
cnf(f_12_10,plain,
( in(sK10(U_85,U_83,U_81),U_83)
| in(sK9(U_85,U_83,U_81),U_81)
| U_81 = set_intersection2(U_85,U_83) ),
inference(clausify,[status(thm)],[f_12_5]) ).
cnf(f_12_11,plain,
( ~ in(sK10(U_85,U_83,U_81),U_81)
| in(sK9(U_85,U_83,U_81),U_81)
| U_81 = set_intersection2(U_85,U_83) ),
inference(clausify,[status(thm)],[f_12_5]) ).
cnf(f_12_12,plain,
( 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)
| U_81 = set_intersection2(U_85,U_83) ),
inference(clausify,[status(thm)],[f_12_5]) ).
cnf(f_12_13,plain,
( in(sK10(U_85,U_83,U_81),U_83)
| ~ in(sK9(U_85,U_83,U_81),U_83)
| ~ in(sK9(U_85,U_83,U_81),U_85)
| U_81 = set_intersection2(U_85,U_83) ),
inference(clausify,[status(thm)],[f_12_5]) ).
cnf(f_12_14,plain,
( ~ in(sK10(U_85,U_83,U_81),U_81)
| ~ in(sK9(U_85,U_83,U_81),U_83)
| ~ in(sK9(U_85,U_83,U_81),U_85)
| U_81 = set_intersection2(U_85,U_83) ),
inference(clausify,[status(thm)],[f_12_5]) ).
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]) ).
cnf(f_13_6,plain,
( in(U_91,U_99)
| ~ in(U_91,U_95)
| U_95 != set_difference(U_99,U_97) ),
inference(clausify,[status(thm)],[f_13_5]) ).
cnf(f_13_7,plain,
( ~ in(U_91,U_97)
| ~ in(U_91,U_95)
| U_95 != set_difference(U_99,U_97) ),
inference(clausify,[status(thm)],[f_13_5]) ).
cnf(f_13_8,plain,
( in(U_92,U_95)
| in(U_92,U_97)
| ~ in(U_92,U_99)
| U_95 != set_difference(U_99,U_97) ),
inference(clausify,[status(thm)],[f_13_5]) ).
cnf(f_13_9,plain,
( in(sK12(U_100,U_98,U_96),U_100)
| in(sK11(U_100,U_98,U_96),U_96)
| U_96 = set_difference(U_100,U_98) ),
inference(clausify,[status(thm)],[f_13_5]) ).
cnf(f_13_10,plain,
( ~ in(sK12(U_100,U_98,U_96),U_98)
| in(sK11(U_100,U_98,U_96),U_96)
| U_96 = set_difference(U_100,U_98) ),
inference(clausify,[status(thm)],[f_13_5]) ).
cnf(f_13_11,plain,
( ~ in(sK12(U_100,U_98,U_96),U_96)
| in(sK11(U_100,U_98,U_96),U_96)
| U_96 = set_difference(U_100,U_98) ),
inference(clausify,[status(thm)],[f_13_5]) ).
cnf(f_13_12,plain,
( 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)
| U_96 = set_difference(U_100,U_98) ),
inference(clausify,[status(thm)],[f_13_5]) ).
cnf(f_13_13,plain,
( ~ in(sK12(U_100,U_98,U_96),U_98)
| in(sK11(U_100,U_98,U_96),U_98)
| ~ in(sK11(U_100,U_98,U_96),U_100)
| U_96 = set_difference(U_100,U_98) ),
inference(clausify,[status(thm)],[f_13_5]) ).
cnf(f_13_14,plain,
( ~ in(sK12(U_100,U_98,U_96),U_96)
| in(sK11(U_100,U_98,U_96),U_98)
| ~ in(sK11(U_100,U_98,U_96),U_100)
| U_96 = set_difference(U_100,U_98) ),
inference(clausify,[status(thm)],[f_13_5]) ).
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]) ).
cnf(f_14_4,plain,
( set_intersection2(U_105,U_103) = empty_set
| ~ disjoint(U_105,U_103) ),
inference(clausify,[status(thm)],[f_14_3]) ).
cnf(f_14_5,plain,
( disjoint(U_106,U_104)
| set_intersection2(U_106,U_104) != empty_set ),
inference(clausify,[status(thm)],[f_14_3]) ).
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]) ).
cnf(f_15_4,plain,
( subset(U_111,U_109)
| ~ proper_subset(U_111,U_109) ),
inference(clausify,[status(thm)],[f_15_3]) ).
cnf(f_15_5,plain,
( U_111 != U_109
| ~ proper_subset(U_111,U_109) ),
inference(clausify,[status(thm)],[f_15_3]) ).
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_3]) ).
fof(f_16_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_k1_tarski]) ).
cnf(f_16_2,plain,
$true,
inference(clausify,[status(thm)],[f_16_1]) ).
fof(f_17_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_k1_xboole_0]) ).
cnf(f_17_2,plain,
$true,
inference(clausify,[status(thm)],[f_17_1]) ).
fof(f_18_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_k2_tarski]) ).
cnf(f_18_2,plain,
$true,
inference(clausify,[status(thm)],[f_18_1]) ).
fof(f_19_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_k2_xboole_0]) ).
cnf(f_19_2,plain,
$true,
inference(clausify,[status(thm)],[f_19_1]) ).
fof(f_20_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_k3_xboole_0]) ).
cnf(f_20_2,plain,
$true,
inference(clausify,[status(thm)],[f_20_1]) ).
fof(f_21_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_k4_xboole_0]) ).
cnf(f_21_2,plain,
$true,
inference(clausify,[status(thm)],[f_21_1]) ).
fof(f_22_1,plain,
empty(empty_set),
inference(fof_nnf,[status(thm)],[fc1_xboole_0]) ).
cnf(f_22_2,plain,
empty(empty_set),
inference(clausify,[status(thm)],[f_22_1]) ).
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]) ).
cnf(f_23_4,plain,
( ~ empty(set_union2(U_114,U_113))
| empty(U_114) ),
inference(clausify,[status(thm)],[f_23_3]) ).
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]) ).
cnf(f_24_4,plain,
( ~ empty(set_union2(U_115,U_116))
| empty(U_116) ),
inference(clausify,[status(thm)],[f_24_3]) ).
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]) ).
cnf(f_25_4,plain,
set_union2(U_118,U_118) = U_118,
inference(clausify,[status(thm)],[f_25_3]) ).
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]) ).
cnf(f_26_4,plain,
set_intersection2(U_120,U_120) = U_120,
inference(clausify,[status(thm)],[f_26_3]) ).
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]) ).
cnf(f_27_4,plain,
~ proper_subset(U_122,U_122),
inference(clausify,[status(thm)],[f_27_3]) ).
fof(f_28_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_28_2,plain,
! [U_124,U_123] :
( ( set_difference(U_124,U_123) = empty_set
| ~ subset(U_124,U_123) )
& ( subset(U_124,U_123)
| set_difference(U_124,U_123) != empty_set ) ),
inference(variable_rename,[status(thm)],[f_28_1]) ).
fof(f_28_3,plain,
( ! [U_128,U_126] :
( set_difference(U_128,U_126) = empty_set
| ~ subset(U_128,U_126) )
& ! [U_127,U_125] :
( subset(U_127,U_125)
| set_difference(U_127,U_125) != empty_set ) ),
inference(miniscope,[status(thm)],[f_28_2]) ).
cnf(f_28_4,plain,
( subset(U_127,U_125)
| set_difference(U_127,U_125) != empty_set ),
inference(clausify,[status(thm)],[f_28_3]) ).
cnf(f_28_5,plain,
( set_difference(U_128,U_126) = empty_set
| ~ subset(U_128,U_126) ),
inference(clausify,[status(thm)],[f_28_3]) ).
fof(f_29_1,plain,
? [A] : empty(A),
inference(fof_nnf,[status(thm)],[rc1_xboole_0]) ).
fof(f_29_2,plain,
? [U_129] : empty(U_129),
inference(variable_rename,[status(thm)],[f_29_1]) ).
fof(f_29_3,plain,
empty(sK13),
inference(skolemize,[status(esa),new_symbols(skolem,[sK13]),skolemize(U_129,sK13)],[f_29_2]) ).
cnf(f_29_4,plain,
empty(sK13),
inference(clausify,[status(thm)],[f_29_3]) ).
fof(f_30_1,plain,
? [A] : ~ empty(A),
inference(fof_nnf,[status(thm)],[rc2_xboole_0]) ).
fof(f_30_2,plain,
? [U_130] : ~ empty(U_130),
inference(variable_rename,[status(thm)],[f_30_1]) ).
fof(f_30_3,plain,
~ empty(sK14),
inference(skolemize,[status(esa),new_symbols(skolem,[sK14]),skolemize(U_130,sK14)],[f_30_2]) ).
cnf(f_30_4,plain,
~ empty(sK14),
inference(clausify,[status(thm)],[f_30_3]) ).
fof(f_31_1,plain,
! [A,B] : subset(A,A),
inference(fof_nnf,[status(thm)],[reflexivity_r1_tarski]) ).
fof(f_31_2,plain,
! [U_132,U_131] : subset(U_132,U_132),
inference(variable_rename,[status(thm)],[f_31_1]) ).
fof(f_31_3,plain,
! [U_132] : subset(U_132,U_132),
inference(miniscope,[status(thm)],[f_31_2]) ).
cnf(f_31_4,plain,
subset(U_132,U_132),
inference(clausify,[status(thm)],[f_31_3]) ).
fof(f_32_1,plain,
! [A,B] :
( disjoint(B,A)
| ~ disjoint(A,B) ),
inference(fof_nnf,[status(thm)],[symmetry_r1_xboole_0]) ).
fof(f_32_2,plain,
! [U_134,U_133] :
( disjoint(U_133,U_134)
| ~ disjoint(U_134,U_133) ),
inference(variable_rename,[status(thm)],[f_32_1]) ).
cnf(f_32_3,plain,
( disjoint(U_133,U_134)
| ~ disjoint(U_134,U_133) ),
inference(clausify,[status(thm)],[f_32_2]) ).
fof(f_33_1,plain,
! [A,B] :
( set_union2(A,B) = B
| ~ subset(A,B) ),
inference(fof_nnf,[status(thm)],[t12_xboole_1]) ).
fof(f_33_2,plain,
! [U_136,U_135] :
( set_union2(U_136,U_135) = U_135
| ~ subset(U_136,U_135) ),
inference(variable_rename,[status(thm)],[f_33_1]) ).
cnf(f_33_3,plain,
( set_union2(U_136,U_135) = U_135
| ~ subset(U_136,U_135) ),
inference(clausify,[status(thm)],[f_33_2]) ).
fof(f_34_1,plain,
! [A,B] : subset(set_intersection2(A,B),A),
inference(fof_nnf,[status(thm)],[t17_xboole_1]) ).
fof(f_34_2,plain,
! [U_138,U_137] : subset(set_intersection2(U_138,U_137),U_138),
inference(variable_rename,[status(thm)],[f_34_1]) ).
cnf(f_34_3,plain,
subset(set_intersection2(U_138,U_137),U_138),
inference(clausify,[status(thm)],[f_34_2]) ).
fof(f_35_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_35_2,plain,
! [U_141,U_140,U_139] :
( subset(U_141,set_intersection2(U_140,U_139))
| ~ subset(U_141,U_139)
| ~ subset(U_141,U_140) ),
inference(variable_rename,[status(thm)],[f_35_1]) ).
cnf(f_35_3,plain,
( subset(U_141,set_intersection2(U_140,U_139))
| ~ subset(U_141,U_139)
| ~ subset(U_141,U_140) ),
inference(clausify,[status(thm)],[f_35_2]) ).
fof(f_36_1,plain,
! [A] : set_union2(A,empty_set) = A,
inference(fof_nnf,[status(thm)],[t1_boole]) ).
fof(f_36_2,plain,
! [U_142] : set_union2(U_142,empty_set) = U_142,
inference(variable_rename,[status(thm)],[f_36_1]) ).
cnf(f_36_3,plain,
set_union2(U_142,empty_set) = U_142,
inference(clausify,[status(thm)],[f_36_2]) ).
fof(f_37_1,plain,
! [A,B,C] :
( subset(A,C)
| ~ subset(B,C)
| ~ subset(A,B) ),
inference(fof_nnf,[status(thm)],[t1_xboole_1]) ).
fof(f_37_2,plain,
! [U_145,U_144,U_143] :
( subset(U_145,U_143)
| ~ subset(U_144,U_143)
| ~ subset(U_145,U_144) ),
inference(variable_rename,[status(thm)],[f_37_1]) ).
cnf(f_37_3,plain,
( subset(U_145,U_143)
| ~ subset(U_144,U_143)
| ~ subset(U_145,U_144) ),
inference(clausify,[status(thm)],[f_37_2]) ).
fof(f_38_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_38_2,plain,
! [U_148,U_147,U_146] :
( subset(set_intersection2(U_148,U_146),set_intersection2(U_147,U_146))
| ~ subset(U_148,U_147) ),
inference(variable_rename,[status(thm)],[f_38_1]) ).
fof(f_38_3,plain,
! [U_148,U_147] :
( ! [U_146] : subset(set_intersection2(U_148,U_146),set_intersection2(U_147,U_146))
| ~ subset(U_148,U_147) ),
inference(miniscope,[status(thm)],[f_38_2]) ).
cnf(f_38_4,plain,
( subset(set_intersection2(U_148,U_146),set_intersection2(U_147,U_146))
| ~ subset(U_148,U_147) ),
inference(clausify,[status(thm)],[f_38_3]) ).
fof(f_39_1,plain,
! [A,B] :
( set_intersection2(A,B) = A
| ~ subset(A,B) ),
inference(fof_nnf,[status(thm)],[t28_xboole_1]) ).
fof(f_39_2,plain,
! [U_150,U_149] :
( set_intersection2(U_150,U_149) = U_150
| ~ subset(U_150,U_149) ),
inference(variable_rename,[status(thm)],[f_39_1]) ).
cnf(f_39_3,plain,
( set_intersection2(U_150,U_149) = U_150
| ~ subset(U_150,U_149) ),
inference(clausify,[status(thm)],[f_39_2]) ).
fof(f_40_1,plain,
! [A] : set_intersection2(A,empty_set) = empty_set,
inference(fof_nnf,[status(thm)],[t2_boole]) ).
fof(f_40_2,plain,
! [U_151] : set_intersection2(U_151,empty_set) = empty_set,
inference(variable_rename,[status(thm)],[f_40_1]) ).
cnf(f_40_3,plain,
set_intersection2(U_151,empty_set) = empty_set,
inference(clausify,[status(thm)],[f_40_2]) ).
fof(f_41_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_41_2,plain,
! [U_154,U_153] :
( U_154 = U_153
| ? [U_152] :
( ( ~ in(U_152,U_154)
& in(U_152,U_153) )
| ( ~ in(U_152,U_153)
& in(U_152,U_154) ) ) ),
inference(variable_rename,[status(thm)],[f_41_1]) ).
fof(f_41_3,plain,
! [U_154,U_153] :
( U_154 = U_153
| ? [U_156] :
( ~ in(U_156,U_154)
& in(U_156,U_153) )
| ? [U_155] :
( ~ in(U_155,U_153)
& in(U_155,U_154) ) ),
inference(miniscope,[status(thm)],[f_41_2]) ).
fof(f_41_4,plain,
! [U_154,U_153] :
( U_154 = U_153
| ? [U_156] :
( ~ in(U_156,U_154)
& in(U_156,U_153) )
| ( ~ in(sK15(U_154,U_153),U_153)
& in(sK15(U_154,U_153),U_154) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK15]),skolemize(U_155,sK15(U_154,U_153))],[f_41_3]) ).
fof(f_41_5,plain,
! [U_154,U_153] :
( U_154 = U_153
| ( ~ in(sK16(U_154,U_153),U_154)
& in(sK16(U_154,U_153),U_153) )
| ( ~ in(sK15(U_154,U_153),U_153)
& in(sK15(U_154,U_153),U_154) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK16]),skolemize(U_156,sK16(U_154,U_153))],[f_41_4]) ).
cnf(f_41_6,plain,
( in(sK16(U_154,U_153),U_153)
| in(sK15(U_154,U_153),U_154)
| U_154 = U_153 ),
inference(clausify,[status(thm)],[f_41_5]) ).
cnf(f_41_7,plain,
( ~ in(sK16(U_154,U_153),U_154)
| in(sK15(U_154,U_153),U_154)
| U_154 = U_153 ),
inference(clausify,[status(thm)],[f_41_5]) ).
cnf(f_41_8,plain,
( in(sK16(U_154,U_153),U_153)
| ~ in(sK15(U_154,U_153),U_153)
| U_154 = U_153 ),
inference(clausify,[status(thm)],[f_41_5]) ).
cnf(f_41_9,plain,
( ~ in(sK16(U_154,U_153),U_154)
| ~ in(sK15(U_154,U_153),U_153)
| U_154 = U_153 ),
inference(clausify,[status(thm)],[f_41_5]) ).
fof(f_42_1,plain,
! [A] : subset(empty_set,A),
inference(fof_nnf,[status(thm)],[t2_xboole_1]) ).
fof(f_42_2,plain,
! [U_157] : subset(empty_set,U_157),
inference(variable_rename,[status(thm)],[f_42_1]) ).
cnf(f_42_3,plain,
subset(empty_set,U_157),
inference(clausify,[status(thm)],[f_42_2]) ).
fof(f_43_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_43_2,plain,
! [U_160,U_159,U_158] :
( subset(set_difference(U_160,U_158),set_difference(U_159,U_158))
| ~ subset(U_160,U_159) ),
inference(variable_rename,[status(thm)],[f_43_1]) ).
fof(f_43_3,plain,
! [U_160,U_159] :
( ! [U_158] : subset(set_difference(U_160,U_158),set_difference(U_159,U_158))
| ~ subset(U_160,U_159) ),
inference(miniscope,[status(thm)],[f_43_2]) ).
cnf(f_43_4,plain,
( subset(set_difference(U_160,U_158),set_difference(U_159,U_158))
| ~ subset(U_160,U_159) ),
inference(clausify,[status(thm)],[f_43_3]) ).
fof(f_44_1,plain,
! [A,B] : subset(set_difference(A,B),A),
inference(fof_nnf,[status(thm)],[t36_xboole_1]) ).
fof(f_44_2,plain,
! [U_162,U_161] : subset(set_difference(U_162,U_161),U_162),
inference(variable_rename,[status(thm)],[f_44_1]) ).
cnf(f_44_3,plain,
subset(set_difference(U_162,U_161),U_162),
inference(clausify,[status(thm)],[f_44_2]) ).
fof(f_45_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_45_2,plain,
! [U_164,U_163] :
( ( set_difference(U_164,U_163) = empty_set
| ~ subset(U_164,U_163) )
& ( subset(U_164,U_163)
| set_difference(U_164,U_163) != empty_set ) ),
inference(variable_rename,[status(thm)],[f_45_1]) ).
fof(f_45_3,plain,
( ! [U_168,U_166] :
( set_difference(U_168,U_166) = empty_set
| ~ subset(U_168,U_166) )
& ! [U_167,U_165] :
( subset(U_167,U_165)
| set_difference(U_167,U_165) != empty_set ) ),
inference(miniscope,[status(thm)],[f_45_2]) ).
cnf(f_45_4,plain,
( subset(U_167,U_165)
| set_difference(U_167,U_165) != empty_set ),
inference(clausify,[status(thm)],[f_45_3]) ).
cnf(f_45_5,plain,
( set_difference(U_168,U_166) = empty_set
| ~ subset(U_168,U_166) ),
inference(clausify,[status(thm)],[f_45_3]) ).
fof(f_46_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_46_2,plain,
! [U_170,U_169] : set_union2(U_170,set_difference(U_169,U_170)) = set_union2(U_170,U_169),
inference(variable_rename,[status(thm)],[f_46_1]) ).
cnf(f_46_3,plain,
set_union2(U_170,set_difference(U_169,U_170)) = set_union2(U_170,U_169),
inference(clausify,[status(thm)],[f_46_2]) ).
fof(f_47_1,plain,
! [A] : set_difference(A,empty_set) = A,
inference(fof_nnf,[status(thm)],[t3_boole]) ).
fof(f_47_2,plain,
! [U_171] : set_difference(U_171,empty_set) = U_171,
inference(variable_rename,[status(thm)],[f_47_1]) ).
cnf(f_47_3,plain,
set_difference(U_171,empty_set) = U_171,
inference(clausify,[status(thm)],[f_47_2]) ).
fof(f_48_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_48_2,plain,
! [U_175,U_174] :
( ( ~ disjoint(U_175,U_174)
| ! [U_173] :
( ~ in(U_173,U_174)
| ~ in(U_173,U_175) ) )
& ( ? [U_172] :
( in(U_172,U_174)
& in(U_172,U_175) )
| disjoint(U_175,U_174) ) ),
inference(variable_rename,[status(thm)],[f_48_1]) ).
fof(f_48_3,plain,
( ! [U_179,U_177] :
( ~ disjoint(U_179,U_177)
| ! [U_173] :
( ~ in(U_173,U_177)
| ~ in(U_173,U_179) ) )
& ! [U_178,U_176] :
( ? [U_172] :
( in(U_172,U_176)
& in(U_172,U_178) )
| disjoint(U_178,U_176) ) ),
inference(miniscope,[status(thm)],[f_48_2]) ).
fof(f_48_4,plain,
( ! [U_179,U_177] :
( ~ disjoint(U_179,U_177)
| ! [U_173] :
( ~ in(U_173,U_177)
| ~ in(U_173,U_179) ) )
& ! [U_178,U_176] :
( ( in(sK17(U_178,U_176),U_176)
& in(sK17(U_178,U_176),U_178) )
| disjoint(U_178,U_176) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK17]),skolemize(U_172,sK17(U_178,U_176))],[f_48_3]) ).
cnf(f_48_5,plain,
( in(sK17(U_178,U_176),U_178)
| disjoint(U_178,U_176) ),
inference(clausify,[status(thm)],[f_48_4]) ).
cnf(f_48_6,plain,
( in(sK17(U_178,U_176),U_176)
| disjoint(U_178,U_176) ),
inference(clausify,[status(thm)],[f_48_4]) ).
cnf(f_48_7,plain,
( ~ disjoint(U_179,U_177)
| ~ in(U_173,U_177)
| ~ in(U_173,U_179) ),
inference(clausify,[status(thm)],[f_48_4]) ).
fof(f_49_1,plain,
! [A] :
( A = empty_set
| ~ subset(A,empty_set) ),
inference(fof_nnf,[status(thm)],[t3_xboole_1]) ).
fof(f_49_2,plain,
! [U_180] :
( U_180 = empty_set
| ~ subset(U_180,empty_set) ),
inference(variable_rename,[status(thm)],[f_49_1]) ).
cnf(f_49_3,plain,
( U_180 = empty_set
| ~ subset(U_180,empty_set) ),
inference(clausify,[status(thm)],[f_49_2]) ).
fof(f_50_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_50_2,plain,
! [U_182,U_181] : set_difference(set_union2(U_182,U_181),U_181) = set_difference(U_182,U_181),
inference(variable_rename,[status(thm)],[f_50_1]) ).
cnf(f_50_3,plain,
set_difference(set_union2(U_182,U_181),U_181) = set_difference(U_182,U_181),
inference(clausify,[status(thm)],[f_50_2]) ).
fof(f_51_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_51_2,plain,
! [U_184,U_183] :
( U_183 = set_union2(U_184,set_difference(U_183,U_184))
| ~ subset(U_184,U_183) ),
inference(variable_rename,[status(thm)],[f_51_1]) ).
cnf(f_51_3,plain,
( U_183 = set_union2(U_184,set_difference(U_183,U_184))
| ~ subset(U_184,U_183) ),
inference(clausify,[status(thm)],[f_51_2]) ).
fof(f_52_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_52_2,plain,
! [U_186,U_185] : set_difference(U_186,set_difference(U_186,U_185)) = set_intersection2(U_186,U_185),
inference(variable_rename,[status(thm)],[f_52_1]) ).
cnf(f_52_3,plain,
set_difference(U_186,set_difference(U_186,U_185)) = set_intersection2(U_186,U_185),
inference(clausify,[status(thm)],[f_52_2]) ).
fof(f_53_1,plain,
! [A] : set_difference(empty_set,A) = empty_set,
inference(fof_nnf,[status(thm)],[t4_boole]) ).
fof(f_53_2,plain,
! [U_187] : set_difference(empty_set,U_187) = empty_set,
inference(variable_rename,[status(thm)],[f_53_1]) ).
cnf(f_53_3,plain,
set_difference(empty_set,U_187) = empty_set,
inference(clausify,[status(thm)],[f_53_2]) ).
fof(f_54_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_54_2,plain,
! [U_191,U_190] :
( ( ~ disjoint(U_191,U_190)
| ! [U_189] : ~ in(U_189,set_intersection2(U_191,U_190)) )
& ( ? [U_188] : in(U_188,set_intersection2(U_191,U_190))
| disjoint(U_191,U_190) ) ),
inference(variable_rename,[status(thm)],[f_54_1]) ).
fof(f_54_3,plain,
( ! [U_195,U_193] :
( ~ disjoint(U_195,U_193)
| ! [U_189] : ~ in(U_189,set_intersection2(U_195,U_193)) )
& ! [U_194,U_192] :
( ? [U_188] : in(U_188,set_intersection2(U_194,U_192))
| disjoint(U_194,U_192) ) ),
inference(miniscope,[status(thm)],[f_54_2]) ).
fof(f_54_4,plain,
( ! [U_195,U_193] :
( ~ disjoint(U_195,U_193)
| ! [U_189] : ~ in(U_189,set_intersection2(U_195,U_193)) )
& ! [U_194,U_192] :
( in(sK18(U_194,U_192),set_intersection2(U_194,U_192))
| disjoint(U_194,U_192) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK18]),skolemize(U_188,sK18(U_194,U_192))],[f_54_3]) ).
cnf(f_54_5,plain,
( in(sK18(U_194,U_192),set_intersection2(U_194,U_192))
| disjoint(U_194,U_192) ),
inference(clausify,[status(thm)],[f_54_4]) ).
cnf(f_54_6,plain,
( ~ disjoint(U_195,U_193)
| ~ in(U_189,set_intersection2(U_195,U_193)) ),
inference(clausify,[status(thm)],[f_54_4]) ).
fof(f_55_1,plain,
! [A,B] :
( ~ proper_subset(B,A)
| ~ subset(A,B) ),
inference(fof_nnf,[status(thm)],[t60_xboole_1]) ).
fof(f_55_2,plain,
! [U_197,U_196] :
( ~ proper_subset(U_196,U_197)
| ~ subset(U_197,U_196) ),
inference(variable_rename,[status(thm)],[f_55_1]) ).
cnf(f_55_3,plain,
( ~ proper_subset(U_196,U_197)
| ~ subset(U_197,U_196) ),
inference(clausify,[status(thm)],[f_55_2]) ).
fof(f_56_1,plain,
! [A,B,C] :
( disjoint(A,C)
| ~ disjoint(B,C)
| ~ subset(A,B) ),
inference(fof_nnf,[status(thm)],[t63_xboole_1]) ).
fof(f_56_2,plain,
! [U_200,U_199,U_198] :
( disjoint(U_200,U_198)
| ~ disjoint(U_199,U_198)
| ~ subset(U_200,U_199) ),
inference(variable_rename,[status(thm)],[f_56_1]) ).
cnf(f_56_3,plain,
( disjoint(U_200,U_198)
| ~ disjoint(U_199,U_198)
| ~ subset(U_200,U_199) ),
inference(clausify,[status(thm)],[f_56_2]) ).
fof(f_57_1,negated_conjecture,
~ ! [A] : unordered_pair(A,A) = singleton(A),
inference(negate,[status(cth)],[t69_enumset1]) ).
fof(f_57_2,negated_conjecture,
? [A] : unordered_pair(A,A) != singleton(A),
inference(fof_nnf,[status(thm)],[f_57_1]) ).
fof(f_57_3,negated_conjecture,
? [U_201] : unordered_pair(U_201,U_201) != singleton(U_201),
inference(variable_rename,[status(thm)],[f_57_2]) ).
fof(f_57_4,negated_conjecture,
unordered_pair(sK19,sK19) != singleton(sK19),
inference(skolemize,[status(esa),new_symbols(skolem,[sK19]),skolemize(U_201,sK19)],[f_57_3]) ).
fof(f_57_5,negated_conjecture,
unordered_pair(sK19,sK19) != singleton(sK19),
inference(definitional_conversion,[status(esa)],[f_57_4]) ).
cnf(f_57_6,negated_conjecture,
unordered_pair(sK19,sK19) != singleton(sK19),
inference(clausify,[status(thm)],[f_57_5]) ).
fof(f_58_1,plain,
! [A] :
( A = empty_set
| ~ empty(A) ),
inference(fof_nnf,[status(thm)],[t6_boole]) ).
fof(f_58_2,plain,
! [U_202] :
( U_202 = empty_set
| ~ empty(U_202) ),
inference(variable_rename,[status(thm)],[f_58_1]) ).
cnf(f_58_3,plain,
( U_202 = empty_set
| ~ empty(U_202) ),
inference(clausify,[status(thm)],[f_58_2]) ).
fof(f_59_1,plain,
! [A,B] :
( ~ empty(B)
| ~ in(A,B) ),
inference(fof_nnf,[status(thm)],[t7_boole]) ).
fof(f_59_2,plain,
! [U_204,U_203] :
( ~ empty(U_203)
| ~ in(U_204,U_203) ),
inference(variable_rename,[status(thm)],[f_59_1]) ).
cnf(f_59_3,plain,
( ~ empty(U_203)
| ~ in(U_204,U_203) ),
inference(clausify,[status(thm)],[f_59_2]) ).
fof(f_60_1,plain,
! [A,B] : subset(A,set_union2(A,B)),
inference(fof_nnf,[status(thm)],[t7_xboole_1]) ).
fof(f_60_2,plain,
! [U_206,U_205] : subset(U_206,set_union2(U_206,U_205)),
inference(variable_rename,[status(thm)],[f_60_1]) ).
cnf(f_60_3,plain,
subset(U_206,set_union2(U_206,U_205)),
inference(clausify,[status(thm)],[f_60_2]) ).
fof(f_61_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_61_2,plain,
! [U_208,U_207] :
( ( disjoint(U_208,U_207)
| set_difference(U_208,U_207) != U_208 )
& ( set_difference(U_208,U_207) = U_208
| ~ disjoint(U_208,U_207) ) ),
inference(variable_rename,[status(thm)],[f_61_1]) ).
fof(f_61_3,plain,
( ! [U_212,U_210] :
( disjoint(U_212,U_210)
| set_difference(U_212,U_210) != U_212 )
& ! [U_211,U_209] :
( set_difference(U_211,U_209) = U_211
| ~ disjoint(U_211,U_209) ) ),
inference(miniscope,[status(thm)],[f_61_2]) ).
cnf(f_61_4,plain,
( set_difference(U_211,U_209) = U_211
| ~ disjoint(U_211,U_209) ),
inference(clausify,[status(thm)],[f_61_3]) ).
cnf(f_61_5,plain,
( disjoint(U_212,U_210)
| set_difference(U_212,U_210) != U_212 ),
inference(clausify,[status(thm)],[f_61_3]) ).
fof(f_62_1,plain,
! [A,B] :
( ~ empty(B)
| A = B
| ~ empty(A) ),
inference(fof_nnf,[status(thm)],[t8_boole]) ).
fof(f_62_2,plain,
! [U_214,U_213] :
( ~ empty(U_213)
| U_214 = U_213
| ~ empty(U_214) ),
inference(variable_rename,[status(thm)],[f_62_1]) ).
fof(f_62_3,plain,
! [U_214] :
( ! [U_213] :
( ~ empty(U_213)
| U_214 = U_213 )
| ~ empty(U_214) ),
inference(miniscope,[status(thm)],[f_62_2]) ).
cnf(f_62_4,plain,
( ~ empty(U_213)
| U_214 = U_213
| ~ empty(U_214) ),
inference(clausify,[status(thm)],[f_62_3]) ).
fof(f_63_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_63_2,plain,
! [U_217,U_216,U_215] :
( subset(set_union2(U_217,U_215),U_216)
| ~ subset(U_215,U_216)
| ~ subset(U_217,U_216) ),
inference(variable_rename,[status(thm)],[f_63_1]) ).
cnf(f_63_3,plain,
( subset(set_union2(U_217,U_215),U_216)
| ~ subset(U_215,U_216)
| ~ subset(U_217,U_216) ),
inference(clausify,[status(thm)],[f_63_2]) ).
cnf(f_16_2_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_16_2]) ).
cnf(f_17_2_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_17_2]) ).
cnf(f_18_2_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_18_2]) ).
cnf(f_19_2_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_19_2]) ).
cnf(f_20_2_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_20_2]) ).
cnf(f_21_2_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_21_2]) ).
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,
( sK15(Eq_x_0,Eq_x_1) = sK15(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,
( sK16(Eq_x_0,Eq_x_1) = sK16(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,
( sK17(Eq_x_0,Eq_x_1) = sK17(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,
( sK18(Eq_x_0,Eq_x_1) = sK18(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(sat_proved,plain,
$false,
inference(cadical,[status(thm)],[]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU142+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
% 0.09/0.37 % Computer : n008.cluster.edu
% 0.09/0.37 % Model : x86_64 x86_64
% 0.09/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.37 % Memory : 8046.5625MB
% 0.09/0.37 % OS : Linux 6.8.0-71-generic
% 0.09/0.37 % CPULimit : 300
% 0.09/0.37 % WCLimit : 300
% 0.09/0.37 % DateTime : Sat Sep 19 23:22:54 UTC 2026
% 0.09/0.37 % CPUTime :
% 6.35/6.63 % SZS status Theorem for theBenchmark
% 6.35/6.63 % SZS output start Proof for theBenchmark
% See solution above
%------------------------------------------------------------------------------