%------------------------------------------------------------------------------
% File : ConnectPP---0.7.2
% Problem : SEU139+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 08:58:10 AM UTC 2026
% Result : Theorem 0.13s 15.68s
% Output : Proof 0.13s
% 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_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_xboole_0,axiom,
! [A] :
( A = empty_set
<=> ! [B] : ~ in(B,A) ),
file('theBenchmark.p',d1_xboole_0) ).
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_xboole_0,axiom,
$true,
file('theBenchmark.p',dt_k1_xboole_0) ).
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,conjecture,
! [A,B] :
~ ( proper_subset(B,A)
& subset(A,B) ),
file('theBenchmark.p',t60_xboole_1) ).
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(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] : set_union2(A,B) = set_union2(B,A),
inference(fof_nnf,[status(thm)],[commutativity_k2_xboole_0]) ).
fof(f_3_2,plain,
! [U_5,U_4] : set_union2(U_5,U_4) = set_union2(U_4,U_5),
inference(variable_rename,[status(thm)],[f_3_1]) ).
cnf(f_3_3,plain,
set_union2(U_5,U_4) = set_union2(U_4,U_5),
inference(clausify,[status(thm)],[f_3_2]) ).
fof(f_4_1,plain,
! [A,B] : set_intersection2(A,B) = set_intersection2(B,A),
inference(fof_nnf,[status(thm)],[commutativity_k3_xboole_0]) ).
fof(f_4_2,plain,
! [U_7,U_6] : set_intersection2(U_7,U_6) = set_intersection2(U_6,U_7),
inference(variable_rename,[status(thm)],[f_4_1]) ).
cnf(f_4_3,plain,
set_intersection2(U_7,U_6) = set_intersection2(U_6,U_7),
inference(clausify,[status(thm)],[f_4_2]) ).
fof(f_5_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_5_2,plain,
! [U_9,U_8] :
( ( U_9 = U_8
| ~ subset(U_8,U_9)
| ~ subset(U_9,U_8) )
& ( ( subset(U_8,U_9)
& subset(U_9,U_8) )
| U_9 != U_8 ) ),
inference(variable_rename,[status(thm)],[f_5_1]) ).
fof(f_5_3,plain,
( ! [U_13,U_11] :
( U_13 = U_11
| ~ subset(U_11,U_13)
| ~ subset(U_13,U_11) )
& ! [U_12,U_10] :
( ( subset(U_10,U_12)
& subset(U_12,U_10) )
| U_12 != U_10 ) ),
inference(miniscope,[status(thm)],[f_5_2]) ).
cnf(f_5_4,plain,
( subset(U_12,U_10)
| U_12 != U_10 ),
inference(clausify,[status(thm)],[f_5_3]) ).
cnf(f_5_5,plain,
( subset(U_10,U_12)
| U_12 != U_10 ),
inference(clausify,[status(thm)],[f_5_3]) ).
cnf(f_5_6,plain,
( U_13 = U_11
| ~ subset(U_11,U_13)
| ~ subset(U_13,U_11) ),
inference(clausify,[status(thm)],[f_5_3]) ).
fof(f_6_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_6_2,plain,
! [U_16] :
( ( U_16 = empty_set
| ? [U_15] : in(U_15,U_16) )
& ( ! [U_14] : ~ in(U_14,U_16)
| U_16 != empty_set ) ),
inference(variable_rename,[status(thm)],[f_6_1]) ).
fof(f_6_3,plain,
( ! [U_18] :
( U_18 = empty_set
| ? [U_15] : in(U_15,U_18) )
& ! [U_17] :
( ! [U_14] : ~ in(U_14,U_17)
| U_17 != empty_set ) ),
inference(miniscope,[status(thm)],[f_6_2]) ).
fof(f_6_4,plain,
( ! [U_18] :
( U_18 = empty_set
| in(sK1(U_18),U_18) )
& ! [U_17] :
( ! [U_14] : ~ in(U_14,U_17)
| U_17 != empty_set ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(U_15,sK1(U_18))],[f_6_3]) ).
cnf(f_6_5,plain,
( ~ in(U_14,U_17)
| U_17 != empty_set ),
inference(clausify,[status(thm)],[f_6_4]) ).
cnf(f_6_6,plain,
( U_18 = empty_set
| in(sK1(U_18),U_18) ),
inference(clausify,[status(thm)],[f_6_4]) ).
fof(f_7_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_7_2,plain,
! [U_23,U_22,U_21] :
( ( U_21 = set_union2(U_23,U_22)
| ? [U_20] :
( ( ~ in(U_20,U_21)
& ( in(U_20,U_22)
| in(U_20,U_23) ) )
| ( ~ in(U_20,U_22)
& ~ in(U_20,U_23)
& in(U_20,U_21) ) ) )
& ( ! [U_19] :
( ( in(U_19,U_21)
| ( ~ in(U_19,U_22)
& ~ in(U_19,U_23) ) )
& ( in(U_19,U_22)
| in(U_19,U_23)
| ~ in(U_19,U_21) ) )
| U_21 != set_union2(U_23,U_22) ) ),
inference(variable_rename,[status(thm)],[f_7_1]) ).
fof(f_7_3,plain,
( ! [U_33,U_31,U_29] :
( U_29 = set_union2(U_33,U_31)
| ? [U_27] :
( ~ in(U_27,U_29)
& ( in(U_27,U_31)
| in(U_27,U_33) ) )
| ? [U_26] :
( ~ in(U_26,U_31)
& ~ in(U_26,U_33)
& in(U_26,U_29) ) )
& ! [U_32,U_30,U_28] :
( ( ! [U_25] :
( in(U_25,U_28)
| ( ~ in(U_25,U_30)
& ~ in(U_25,U_32) ) )
& ! [U_24] :
( in(U_24,U_30)
| in(U_24,U_32)
| ~ in(U_24,U_28) ) )
| U_28 != set_union2(U_32,U_30) ) ),
inference(miniscope,[status(thm)],[f_7_2]) ).
fof(f_7_4,plain,
( ! [U_33,U_31,U_29] :
( U_29 = set_union2(U_33,U_31)
| ? [U_27] :
( ~ in(U_27,U_29)
& ( in(U_27,U_31)
| in(U_27,U_33) ) )
| ( ~ in(sK2(U_33,U_31,U_29),U_31)
& ~ in(sK2(U_33,U_31,U_29),U_33)
& in(sK2(U_33,U_31,U_29),U_29) ) )
& ! [U_32,U_30,U_28] :
( ( ! [U_25] :
( in(U_25,U_28)
| ( ~ in(U_25,U_30)
& ~ in(U_25,U_32) ) )
& ! [U_24] :
( in(U_24,U_30)
| in(U_24,U_32)
| ~ in(U_24,U_28) ) )
| U_28 != set_union2(U_32,U_30) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2]),skolemize(U_26,sK2(U_33,U_31,U_29))],[f_7_3]) ).
fof(f_7_5,plain,
( ! [U_33,U_31,U_29] :
( U_29 = set_union2(U_33,U_31)
| ( ~ in(sK3(U_33,U_31,U_29),U_29)
& ( in(sK3(U_33,U_31,U_29),U_31)
| in(sK3(U_33,U_31,U_29),U_33) ) )
| ( ~ in(sK2(U_33,U_31,U_29),U_31)
& ~ in(sK2(U_33,U_31,U_29),U_33)
& in(sK2(U_33,U_31,U_29),U_29) ) )
& ! [U_32,U_30,U_28] :
( ( ! [U_25] :
( in(U_25,U_28)
| ( ~ in(U_25,U_30)
& ~ in(U_25,U_32) ) )
& ! [U_24] :
( in(U_24,U_30)
| in(U_24,U_32)
| ~ in(U_24,U_28) ) )
| U_28 != set_union2(U_32,U_30) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3]),skolemize(U_27,sK3(U_33,U_31,U_29))],[f_7_4]) ).
cnf(f_7_6,plain,
( in(U_24,U_30)
| in(U_24,U_32)
| ~ in(U_24,U_28)
| U_28 != set_union2(U_32,U_30) ),
inference(clausify,[status(thm)],[f_7_5]) ).
cnf(f_7_7,plain,
( ~ in(U_25,U_32)
| in(U_25,U_28)
| U_28 != set_union2(U_32,U_30) ),
inference(clausify,[status(thm)],[f_7_5]) ).
cnf(f_7_8,plain,
( ~ in(U_25,U_30)
| in(U_25,U_28)
| U_28 != set_union2(U_32,U_30) ),
inference(clausify,[status(thm)],[f_7_5]) ).
cnf(f_7_9,plain,
( in(sK3(U_33,U_31,U_29),U_31)
| in(sK3(U_33,U_31,U_29),U_33)
| in(sK2(U_33,U_31,U_29),U_29)
| U_29 = set_union2(U_33,U_31) ),
inference(clausify,[status(thm)],[f_7_5]) ).
cnf(f_7_10,plain,
( ~ in(sK3(U_33,U_31,U_29),U_29)
| in(sK2(U_33,U_31,U_29),U_29)
| U_29 = set_union2(U_33,U_31) ),
inference(clausify,[status(thm)],[f_7_5]) ).
cnf(f_7_11,plain,
( ~ in(sK2(U_33,U_31,U_29),U_33)
| in(sK3(U_33,U_31,U_29),U_31)
| in(sK3(U_33,U_31,U_29),U_33)
| U_29 = set_union2(U_33,U_31) ),
inference(clausify,[status(thm)],[f_7_5]) ).
cnf(f_7_12,plain,
( ~ in(sK2(U_33,U_31,U_29),U_31)
| in(sK3(U_33,U_31,U_29),U_31)
| in(sK3(U_33,U_31,U_29),U_33)
| U_29 = set_union2(U_33,U_31) ),
inference(clausify,[status(thm)],[f_7_5]) ).
cnf(f_7_13,plain,
( ~ in(sK2(U_33,U_31,U_29),U_33)
| ~ in(sK3(U_33,U_31,U_29),U_29)
| U_29 = set_union2(U_33,U_31) ),
inference(clausify,[status(thm)],[f_7_5]) ).
cnf(f_7_14,plain,
( ~ in(sK2(U_33,U_31,U_29),U_31)
| ~ in(sK3(U_33,U_31,U_29),U_29)
| U_29 = set_union2(U_33,U_31) ),
inference(clausify,[status(thm)],[f_7_5]) ).
fof(f_8_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_8_2,plain,
! [U_37,U_36] :
( ( subset(U_37,U_36)
| ? [U_35] :
( ~ in(U_35,U_36)
& in(U_35,U_37) ) )
& ( ! [U_34] :
( in(U_34,U_36)
| ~ in(U_34,U_37) )
| ~ subset(U_37,U_36) ) ),
inference(variable_rename,[status(thm)],[f_8_1]) ).
fof(f_8_3,plain,
( ! [U_41,U_39] :
( subset(U_41,U_39)
| ? [U_35] :
( ~ in(U_35,U_39)
& in(U_35,U_41) ) )
& ! [U_40,U_38] :
( ! [U_34] :
( in(U_34,U_38)
| ~ in(U_34,U_40) )
| ~ subset(U_40,U_38) ) ),
inference(miniscope,[status(thm)],[f_8_2]) ).
fof(f_8_4,plain,
( ! [U_41,U_39] :
( subset(U_41,U_39)
| ( ~ in(sK4(U_41,U_39),U_39)
& in(sK4(U_41,U_39),U_41) ) )
& ! [U_40,U_38] :
( ! [U_34] :
( in(U_34,U_38)
| ~ in(U_34,U_40) )
| ~ subset(U_40,U_38) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4]),skolemize(U_35,sK4(U_41,U_39))],[f_8_3]) ).
cnf(f_8_5,plain,
( in(U_34,U_38)
| ~ in(U_34,U_40)
| ~ subset(U_40,U_38) ),
inference(clausify,[status(thm)],[f_8_4]) ).
cnf(f_8_6,plain,
( in(sK4(U_41,U_39),U_41)
| subset(U_41,U_39) ),
inference(clausify,[status(thm)],[f_8_4]) ).
cnf(f_8_7,plain,
( ~ in(sK4(U_41,U_39),U_39)
| subset(U_41,U_39) ),
inference(clausify,[status(thm)],[f_8_4]) ).
fof(f_9_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_9_2,plain,
! [U_46,U_45,U_44] :
( ( U_44 = set_intersection2(U_46,U_45)
| ? [U_43] :
( ( ~ in(U_43,U_44)
& in(U_43,U_45)
& in(U_43,U_46) )
| ( ( ~ in(U_43,U_45)
| ~ in(U_43,U_46) )
& in(U_43,U_44) ) ) )
& ( ! [U_42] :
( ( in(U_42,U_44)
| ~ in(U_42,U_45)
| ~ in(U_42,U_46) )
& ( ( in(U_42,U_45)
& in(U_42,U_46) )
| ~ in(U_42,U_44) ) )
| U_44 != set_intersection2(U_46,U_45) ) ),
inference(variable_rename,[status(thm)],[f_9_1]) ).
fof(f_9_3,plain,
( ! [U_56,U_54,U_52] :
( U_52 = set_intersection2(U_56,U_54)
| ? [U_50] :
( ~ in(U_50,U_52)
& in(U_50,U_54)
& in(U_50,U_56) )
| ? [U_49] :
( ( ~ in(U_49,U_54)
| ~ in(U_49,U_56) )
& in(U_49,U_52) ) )
& ! [U_55,U_53,U_51] :
( ( ! [U_48] :
( in(U_48,U_51)
| ~ in(U_48,U_53)
| ~ in(U_48,U_55) )
& ! [U_47] :
( ( in(U_47,U_53)
& in(U_47,U_55) )
| ~ in(U_47,U_51) ) )
| U_51 != set_intersection2(U_55,U_53) ) ),
inference(miniscope,[status(thm)],[f_9_2]) ).
fof(f_9_4,plain,
( ! [U_56,U_54,U_52] :
( U_52 = set_intersection2(U_56,U_54)
| ? [U_50] :
( ~ in(U_50,U_52)
& in(U_50,U_54)
& in(U_50,U_56) )
| ( ( ~ in(sK5(U_56,U_54,U_52),U_54)
| ~ in(sK5(U_56,U_54,U_52),U_56) )
& in(sK5(U_56,U_54,U_52),U_52) ) )
& ! [U_55,U_53,U_51] :
( ( ! [U_48] :
( in(U_48,U_51)
| ~ in(U_48,U_53)
| ~ in(U_48,U_55) )
& ! [U_47] :
( ( in(U_47,U_53)
& in(U_47,U_55) )
| ~ in(U_47,U_51) ) )
| U_51 != set_intersection2(U_55,U_53) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK5]),skolemize(U_49,sK5(U_56,U_54,U_52))],[f_9_3]) ).
fof(f_9_5,plain,
( ! [U_56,U_54,U_52] :
( U_52 = set_intersection2(U_56,U_54)
| ( ~ in(sK6(U_56,U_54,U_52),U_52)
& in(sK6(U_56,U_54,U_52),U_54)
& in(sK6(U_56,U_54,U_52),U_56) )
| ( ( ~ in(sK5(U_56,U_54,U_52),U_54)
| ~ in(sK5(U_56,U_54,U_52),U_56) )
& in(sK5(U_56,U_54,U_52),U_52) ) )
& ! [U_55,U_53,U_51] :
( ( ! [U_48] :
( in(U_48,U_51)
| ~ in(U_48,U_53)
| ~ in(U_48,U_55) )
& ! [U_47] :
( ( in(U_47,U_53)
& in(U_47,U_55) )
| ~ in(U_47,U_51) ) )
| U_51 != set_intersection2(U_55,U_53) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK6]),skolemize(U_50,sK6(U_56,U_54,U_52))],[f_9_4]) ).
cnf(f_9_6,plain,
( in(U_47,U_55)
| ~ in(U_47,U_51)
| U_51 != set_intersection2(U_55,U_53) ),
inference(clausify,[status(thm)],[f_9_5]) ).
cnf(f_9_7,plain,
( in(U_47,U_53)
| ~ in(U_47,U_51)
| U_51 != set_intersection2(U_55,U_53) ),
inference(clausify,[status(thm)],[f_9_5]) ).
cnf(f_9_8,plain,
( in(U_48,U_51)
| ~ in(U_48,U_53)
| ~ in(U_48,U_55)
| U_51 != set_intersection2(U_55,U_53) ),
inference(clausify,[status(thm)],[f_9_5]) ).
cnf(f_9_9,plain,
( in(sK6(U_56,U_54,U_52),U_56)
| in(sK5(U_56,U_54,U_52),U_52)
| U_52 = set_intersection2(U_56,U_54) ),
inference(clausify,[status(thm)],[f_9_5]) ).
cnf(f_9_10,plain,
( in(sK6(U_56,U_54,U_52),U_54)
| in(sK5(U_56,U_54,U_52),U_52)
| U_52 = set_intersection2(U_56,U_54) ),
inference(clausify,[status(thm)],[f_9_5]) ).
cnf(f_9_11,plain,
( ~ in(sK6(U_56,U_54,U_52),U_52)
| in(sK5(U_56,U_54,U_52),U_52)
| U_52 = set_intersection2(U_56,U_54) ),
inference(clausify,[status(thm)],[f_9_5]) ).
cnf(f_9_12,plain,
( in(sK6(U_56,U_54,U_52),U_56)
| ~ in(sK5(U_56,U_54,U_52),U_54)
| ~ in(sK5(U_56,U_54,U_52),U_56)
| U_52 = set_intersection2(U_56,U_54) ),
inference(clausify,[status(thm)],[f_9_5]) ).
cnf(f_9_13,plain,
( in(sK6(U_56,U_54,U_52),U_54)
| ~ in(sK5(U_56,U_54,U_52),U_54)
| ~ in(sK5(U_56,U_54,U_52),U_56)
| U_52 = set_intersection2(U_56,U_54) ),
inference(clausify,[status(thm)],[f_9_5]) ).
cnf(f_9_14,plain,
( ~ in(sK6(U_56,U_54,U_52),U_52)
| ~ in(sK5(U_56,U_54,U_52),U_54)
| ~ in(sK5(U_56,U_54,U_52),U_56)
| U_52 = set_intersection2(U_56,U_54) ),
inference(clausify,[status(thm)],[f_9_5]) ).
fof(f_10_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_10_2,plain,
! [U_61,U_60,U_59] :
( ( U_59 = set_difference(U_61,U_60)
| ? [U_58] :
( ( ~ in(U_58,U_59)
& ~ in(U_58,U_60)
& in(U_58,U_61) )
| ( ( in(U_58,U_60)
| ~ in(U_58,U_61) )
& in(U_58,U_59) ) ) )
& ( ! [U_57] :
( ( in(U_57,U_59)
| in(U_57,U_60)
| ~ in(U_57,U_61) )
& ( ( ~ in(U_57,U_60)
& in(U_57,U_61) )
| ~ in(U_57,U_59) ) )
| U_59 != set_difference(U_61,U_60) ) ),
inference(variable_rename,[status(thm)],[f_10_1]) ).
fof(f_10_3,plain,
( ! [U_71,U_69,U_67] :
( U_67 = set_difference(U_71,U_69)
| ? [U_65] :
( ~ in(U_65,U_67)
& ~ in(U_65,U_69)
& in(U_65,U_71) )
| ? [U_64] :
( ( in(U_64,U_69)
| ~ in(U_64,U_71) )
& in(U_64,U_67) ) )
& ! [U_70,U_68,U_66] :
( ( ! [U_63] :
( in(U_63,U_66)
| in(U_63,U_68)
| ~ in(U_63,U_70) )
& ! [U_62] :
( ( ~ in(U_62,U_68)
& in(U_62,U_70) )
| ~ in(U_62,U_66) ) )
| U_66 != set_difference(U_70,U_68) ) ),
inference(miniscope,[status(thm)],[f_10_2]) ).
fof(f_10_4,plain,
( ! [U_71,U_69,U_67] :
( U_67 = set_difference(U_71,U_69)
| ? [U_65] :
( ~ in(U_65,U_67)
& ~ in(U_65,U_69)
& in(U_65,U_71) )
| ( ( in(sK7(U_71,U_69,U_67),U_69)
| ~ in(sK7(U_71,U_69,U_67),U_71) )
& in(sK7(U_71,U_69,U_67),U_67) ) )
& ! [U_70,U_68,U_66] :
( ( ! [U_63] :
( in(U_63,U_66)
| in(U_63,U_68)
| ~ in(U_63,U_70) )
& ! [U_62] :
( ( ~ in(U_62,U_68)
& in(U_62,U_70) )
| ~ in(U_62,U_66) ) )
| U_66 != set_difference(U_70,U_68) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK7]),skolemize(U_64,sK7(U_71,U_69,U_67))],[f_10_3]) ).
fof(f_10_5,plain,
( ! [U_71,U_69,U_67] :
( U_67 = set_difference(U_71,U_69)
| ( ~ in(sK8(U_71,U_69,U_67),U_67)
& ~ in(sK8(U_71,U_69,U_67),U_69)
& in(sK8(U_71,U_69,U_67),U_71) )
| ( ( in(sK7(U_71,U_69,U_67),U_69)
| ~ in(sK7(U_71,U_69,U_67),U_71) )
& in(sK7(U_71,U_69,U_67),U_67) ) )
& ! [U_70,U_68,U_66] :
( ( ! [U_63] :
( in(U_63,U_66)
| in(U_63,U_68)
| ~ in(U_63,U_70) )
& ! [U_62] :
( ( ~ in(U_62,U_68)
& in(U_62,U_70) )
| ~ in(U_62,U_66) ) )
| U_66 != set_difference(U_70,U_68) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK8]),skolemize(U_65,sK8(U_71,U_69,U_67))],[f_10_4]) ).
cnf(f_10_6,plain,
( in(U_62,U_70)
| ~ in(U_62,U_66)
| U_66 != set_difference(U_70,U_68) ),
inference(clausify,[status(thm)],[f_10_5]) ).
cnf(f_10_7,plain,
( ~ in(U_62,U_68)
| ~ in(U_62,U_66)
| U_66 != set_difference(U_70,U_68) ),
inference(clausify,[status(thm)],[f_10_5]) ).
cnf(f_10_8,plain,
( in(U_63,U_66)
| in(U_63,U_68)
| ~ in(U_63,U_70)
| U_66 != set_difference(U_70,U_68) ),
inference(clausify,[status(thm)],[f_10_5]) ).
cnf(f_10_9,plain,
( in(sK8(U_71,U_69,U_67),U_71)
| in(sK7(U_71,U_69,U_67),U_67)
| U_67 = set_difference(U_71,U_69) ),
inference(clausify,[status(thm)],[f_10_5]) ).
cnf(f_10_10,plain,
( ~ in(sK8(U_71,U_69,U_67),U_69)
| in(sK7(U_71,U_69,U_67),U_67)
| U_67 = set_difference(U_71,U_69) ),
inference(clausify,[status(thm)],[f_10_5]) ).
cnf(f_10_11,plain,
( ~ in(sK8(U_71,U_69,U_67),U_67)
| in(sK7(U_71,U_69,U_67),U_67)
| U_67 = set_difference(U_71,U_69) ),
inference(clausify,[status(thm)],[f_10_5]) ).
cnf(f_10_12,plain,
( in(sK8(U_71,U_69,U_67),U_71)
| in(sK7(U_71,U_69,U_67),U_69)
| ~ in(sK7(U_71,U_69,U_67),U_71)
| U_67 = set_difference(U_71,U_69) ),
inference(clausify,[status(thm)],[f_10_5]) ).
cnf(f_10_13,plain,
( ~ in(sK8(U_71,U_69,U_67),U_69)
| in(sK7(U_71,U_69,U_67),U_69)
| ~ in(sK7(U_71,U_69,U_67),U_71)
| U_67 = set_difference(U_71,U_69) ),
inference(clausify,[status(thm)],[f_10_5]) ).
cnf(f_10_14,plain,
( ~ in(sK8(U_71,U_69,U_67),U_67)
| in(sK7(U_71,U_69,U_67),U_69)
| ~ in(sK7(U_71,U_69,U_67),U_71)
| U_67 = set_difference(U_71,U_69) ),
inference(clausify,[status(thm)],[f_10_5]) ).
fof(f_11_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_11_2,plain,
! [U_73,U_72] :
( ( disjoint(U_73,U_72)
| set_intersection2(U_73,U_72) != empty_set )
& ( set_intersection2(U_73,U_72) = empty_set
| ~ disjoint(U_73,U_72) ) ),
inference(variable_rename,[status(thm)],[f_11_1]) ).
fof(f_11_3,plain,
( ! [U_77,U_75] :
( disjoint(U_77,U_75)
| set_intersection2(U_77,U_75) != empty_set )
& ! [U_76,U_74] :
( set_intersection2(U_76,U_74) = empty_set
| ~ disjoint(U_76,U_74) ) ),
inference(miniscope,[status(thm)],[f_11_2]) ).
cnf(f_11_4,plain,
( set_intersection2(U_76,U_74) = empty_set
| ~ disjoint(U_76,U_74) ),
inference(clausify,[status(thm)],[f_11_3]) ).
cnf(f_11_5,plain,
( disjoint(U_77,U_75)
| set_intersection2(U_77,U_75) != empty_set ),
inference(clausify,[status(thm)],[f_11_3]) ).
fof(f_12_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_12_2,plain,
! [U_79,U_78] :
( ( proper_subset(U_79,U_78)
| U_79 = U_78
| ~ subset(U_79,U_78) )
& ( ( U_79 != U_78
& subset(U_79,U_78) )
| ~ proper_subset(U_79,U_78) ) ),
inference(variable_rename,[status(thm)],[f_12_1]) ).
fof(f_12_3,plain,
( ! [U_83,U_81] :
( proper_subset(U_83,U_81)
| U_83 = U_81
| ~ subset(U_83,U_81) )
& ! [U_82,U_80] :
( ( U_82 != U_80
& subset(U_82,U_80) )
| ~ proper_subset(U_82,U_80) ) ),
inference(miniscope,[status(thm)],[f_12_2]) ).
cnf(f_12_4,plain,
( subset(U_82,U_80)
| ~ proper_subset(U_82,U_80) ),
inference(clausify,[status(thm)],[f_12_3]) ).
cnf(f_12_5,plain,
( U_82 != U_80
| ~ proper_subset(U_82,U_80) ),
inference(clausify,[status(thm)],[f_12_3]) ).
cnf(f_12_6,plain,
( proper_subset(U_83,U_81)
| U_83 = U_81
| ~ subset(U_83,U_81) ),
inference(clausify,[status(thm)],[f_12_3]) ).
fof(f_13_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_k1_xboole_0]) ).
cnf(f_13_2,plain,
$true,
inference(clausify,[status(thm)],[f_13_1]) ).
fof(f_14_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_k2_xboole_0]) ).
cnf(f_14_2,plain,
$true,
inference(clausify,[status(thm)],[f_14_1]) ).
fof(f_15_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_k3_xboole_0]) ).
cnf(f_15_2,plain,
$true,
inference(clausify,[status(thm)],[f_15_1]) ).
fof(f_16_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_k4_xboole_0]) ).
cnf(f_16_2,plain,
$true,
inference(clausify,[status(thm)],[f_16_1]) ).
fof(f_17_1,plain,
empty(empty_set),
inference(fof_nnf,[status(thm)],[fc1_xboole_0]) ).
cnf(f_17_2,plain,
empty(empty_set),
inference(clausify,[status(thm)],[f_17_1]) ).
fof(f_18_1,plain,
! [A,B] :
( ~ empty(set_union2(A,B))
| empty(A) ),
inference(fof_nnf,[status(thm)],[fc2_xboole_0]) ).
fof(f_18_2,plain,
! [U_85,U_84] :
( ~ empty(set_union2(U_85,U_84))
| empty(U_85) ),
inference(variable_rename,[status(thm)],[f_18_1]) ).
fof(f_18_3,plain,
! [U_85] :
( ! [U_84] : ~ empty(set_union2(U_85,U_84))
| empty(U_85) ),
inference(miniscope,[status(thm)],[f_18_2]) ).
cnf(f_18_4,plain,
( ~ empty(set_union2(U_85,U_84))
| empty(U_85) ),
inference(clausify,[status(thm)],[f_18_3]) ).
fof(f_19_1,plain,
! [A,B] :
( ~ empty(set_union2(B,A))
| empty(A) ),
inference(fof_nnf,[status(thm)],[fc3_xboole_0]) ).
fof(f_19_2,plain,
! [U_87,U_86] :
( ~ empty(set_union2(U_86,U_87))
| empty(U_87) ),
inference(variable_rename,[status(thm)],[f_19_1]) ).
fof(f_19_3,plain,
! [U_87] :
( ! [U_86] : ~ empty(set_union2(U_86,U_87))
| empty(U_87) ),
inference(miniscope,[status(thm)],[f_19_2]) ).
cnf(f_19_4,plain,
( ~ empty(set_union2(U_86,U_87))
| empty(U_87) ),
inference(clausify,[status(thm)],[f_19_3]) ).
fof(f_20_1,plain,
! [A,B] : set_union2(A,A) = A,
inference(fof_nnf,[status(thm)],[idempotence_k2_xboole_0]) ).
fof(f_20_2,plain,
! [U_89,U_88] : set_union2(U_89,U_89) = U_89,
inference(variable_rename,[status(thm)],[f_20_1]) ).
fof(f_20_3,plain,
! [U_89] : set_union2(U_89,U_89) = U_89,
inference(miniscope,[status(thm)],[f_20_2]) ).
cnf(f_20_4,plain,
set_union2(U_89,U_89) = U_89,
inference(clausify,[status(thm)],[f_20_3]) ).
fof(f_21_1,plain,
! [A,B] : set_intersection2(A,A) = A,
inference(fof_nnf,[status(thm)],[idempotence_k3_xboole_0]) ).
fof(f_21_2,plain,
! [U_91,U_90] : set_intersection2(U_91,U_91) = U_91,
inference(variable_rename,[status(thm)],[f_21_1]) ).
fof(f_21_3,plain,
! [U_91] : set_intersection2(U_91,U_91) = U_91,
inference(miniscope,[status(thm)],[f_21_2]) ).
cnf(f_21_4,plain,
set_intersection2(U_91,U_91) = U_91,
inference(clausify,[status(thm)],[f_21_3]) ).
fof(f_22_1,plain,
! [A,B] : ~ proper_subset(A,A),
inference(fof_nnf,[status(thm)],[irreflexivity_r2_xboole_0]) ).
fof(f_22_2,plain,
! [U_93,U_92] : ~ proper_subset(U_93,U_93),
inference(variable_rename,[status(thm)],[f_22_1]) ).
fof(f_22_3,plain,
! [U_93] : ~ proper_subset(U_93,U_93),
inference(miniscope,[status(thm)],[f_22_2]) ).
cnf(f_22_4,plain,
~ proper_subset(U_93,U_93),
inference(clausify,[status(thm)],[f_22_3]) ).
fof(f_23_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_23_2,plain,
! [U_95,U_94] :
( ( set_difference(U_95,U_94) = empty_set
| ~ subset(U_95,U_94) )
& ( subset(U_95,U_94)
| set_difference(U_95,U_94) != empty_set ) ),
inference(variable_rename,[status(thm)],[f_23_1]) ).
fof(f_23_3,plain,
( ! [U_99,U_97] :
( set_difference(U_99,U_97) = empty_set
| ~ subset(U_99,U_97) )
& ! [U_98,U_96] :
( subset(U_98,U_96)
| set_difference(U_98,U_96) != empty_set ) ),
inference(miniscope,[status(thm)],[f_23_2]) ).
cnf(f_23_4,plain,
( subset(U_98,U_96)
| set_difference(U_98,U_96) != empty_set ),
inference(clausify,[status(thm)],[f_23_3]) ).
cnf(f_23_5,plain,
( set_difference(U_99,U_97) = empty_set
| ~ subset(U_99,U_97) ),
inference(clausify,[status(thm)],[f_23_3]) ).
fof(f_24_1,plain,
? [A] : empty(A),
inference(fof_nnf,[status(thm)],[rc1_xboole_0]) ).
fof(f_24_2,plain,
? [U_100] : empty(U_100),
inference(variable_rename,[status(thm)],[f_24_1]) ).
fof(f_24_3,plain,
empty(sK9),
inference(skolemize,[status(esa),new_symbols(skolem,[sK9]),skolemize(U_100,sK9)],[f_24_2]) ).
cnf(f_24_4,plain,
empty(sK9),
inference(clausify,[status(thm)],[f_24_3]) ).
fof(f_25_1,plain,
? [A] : ~ empty(A),
inference(fof_nnf,[status(thm)],[rc2_xboole_0]) ).
fof(f_25_2,plain,
? [U_101] : ~ empty(U_101),
inference(variable_rename,[status(thm)],[f_25_1]) ).
fof(f_25_3,plain,
~ empty(sK10),
inference(skolemize,[status(esa),new_symbols(skolem,[sK10]),skolemize(U_101,sK10)],[f_25_2]) ).
cnf(f_25_4,plain,
~ empty(sK10),
inference(clausify,[status(thm)],[f_25_3]) ).
fof(f_26_1,plain,
! [A,B] : subset(A,A),
inference(fof_nnf,[status(thm)],[reflexivity_r1_tarski]) ).
fof(f_26_2,plain,
! [U_103,U_102] : subset(U_103,U_103),
inference(variable_rename,[status(thm)],[f_26_1]) ).
fof(f_26_3,plain,
! [U_103] : subset(U_103,U_103),
inference(miniscope,[status(thm)],[f_26_2]) ).
cnf(f_26_4,plain,
subset(U_103,U_103),
inference(clausify,[status(thm)],[f_26_3]) ).
fof(f_27_1,plain,
! [A,B] :
( disjoint(B,A)
| ~ disjoint(A,B) ),
inference(fof_nnf,[status(thm)],[symmetry_r1_xboole_0]) ).
fof(f_27_2,plain,
! [U_105,U_104] :
( disjoint(U_104,U_105)
| ~ disjoint(U_105,U_104) ),
inference(variable_rename,[status(thm)],[f_27_1]) ).
cnf(f_27_3,plain,
( disjoint(U_104,U_105)
| ~ disjoint(U_105,U_104) ),
inference(clausify,[status(thm)],[f_27_2]) ).
fof(f_28_1,plain,
! [A,B] :
( set_union2(A,B) = B
| ~ subset(A,B) ),
inference(fof_nnf,[status(thm)],[t12_xboole_1]) ).
fof(f_28_2,plain,
! [U_107,U_106] :
( set_union2(U_107,U_106) = U_106
| ~ subset(U_107,U_106) ),
inference(variable_rename,[status(thm)],[f_28_1]) ).
cnf(f_28_3,plain,
( set_union2(U_107,U_106) = U_106
| ~ subset(U_107,U_106) ),
inference(clausify,[status(thm)],[f_28_2]) ).
fof(f_29_1,plain,
! [A,B] : subset(set_intersection2(A,B),A),
inference(fof_nnf,[status(thm)],[t17_xboole_1]) ).
fof(f_29_2,plain,
! [U_109,U_108] : subset(set_intersection2(U_109,U_108),U_109),
inference(variable_rename,[status(thm)],[f_29_1]) ).
cnf(f_29_3,plain,
subset(set_intersection2(U_109,U_108),U_109),
inference(clausify,[status(thm)],[f_29_2]) ).
fof(f_30_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_30_2,plain,
! [U_112,U_111,U_110] :
( subset(U_112,set_intersection2(U_111,U_110))
| ~ subset(U_112,U_110)
| ~ subset(U_112,U_111) ),
inference(variable_rename,[status(thm)],[f_30_1]) ).
cnf(f_30_3,plain,
( subset(U_112,set_intersection2(U_111,U_110))
| ~ subset(U_112,U_110)
| ~ subset(U_112,U_111) ),
inference(clausify,[status(thm)],[f_30_2]) ).
fof(f_31_1,plain,
! [A] : set_union2(A,empty_set) = A,
inference(fof_nnf,[status(thm)],[t1_boole]) ).
fof(f_31_2,plain,
! [U_113] : set_union2(U_113,empty_set) = U_113,
inference(variable_rename,[status(thm)],[f_31_1]) ).
cnf(f_31_3,plain,
set_union2(U_113,empty_set) = U_113,
inference(clausify,[status(thm)],[f_31_2]) ).
fof(f_32_1,plain,
! [A,B,C] :
( subset(A,C)
| ~ subset(B,C)
| ~ subset(A,B) ),
inference(fof_nnf,[status(thm)],[t1_xboole_1]) ).
fof(f_32_2,plain,
! [U_116,U_115,U_114] :
( subset(U_116,U_114)
| ~ subset(U_115,U_114)
| ~ subset(U_116,U_115) ),
inference(variable_rename,[status(thm)],[f_32_1]) ).
cnf(f_32_3,plain,
( subset(U_116,U_114)
| ~ subset(U_115,U_114)
| ~ subset(U_116,U_115) ),
inference(clausify,[status(thm)],[f_32_2]) ).
fof(f_33_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_33_2,plain,
! [U_119,U_118,U_117] :
( subset(set_intersection2(U_119,U_117),set_intersection2(U_118,U_117))
| ~ subset(U_119,U_118) ),
inference(variable_rename,[status(thm)],[f_33_1]) ).
fof(f_33_3,plain,
! [U_119,U_118] :
( ! [U_117] : subset(set_intersection2(U_119,U_117),set_intersection2(U_118,U_117))
| ~ subset(U_119,U_118) ),
inference(miniscope,[status(thm)],[f_33_2]) ).
cnf(f_33_4,plain,
( subset(set_intersection2(U_119,U_117),set_intersection2(U_118,U_117))
| ~ subset(U_119,U_118) ),
inference(clausify,[status(thm)],[f_33_3]) ).
fof(f_34_1,plain,
! [A,B] :
( set_intersection2(A,B) = A
| ~ subset(A,B) ),
inference(fof_nnf,[status(thm)],[t28_xboole_1]) ).
fof(f_34_2,plain,
! [U_121,U_120] :
( set_intersection2(U_121,U_120) = U_121
| ~ subset(U_121,U_120) ),
inference(variable_rename,[status(thm)],[f_34_1]) ).
cnf(f_34_3,plain,
( set_intersection2(U_121,U_120) = U_121
| ~ subset(U_121,U_120) ),
inference(clausify,[status(thm)],[f_34_2]) ).
fof(f_35_1,plain,
! [A] : set_intersection2(A,empty_set) = empty_set,
inference(fof_nnf,[status(thm)],[t2_boole]) ).
fof(f_35_2,plain,
! [U_122] : set_intersection2(U_122,empty_set) = empty_set,
inference(variable_rename,[status(thm)],[f_35_1]) ).
cnf(f_35_3,plain,
set_intersection2(U_122,empty_set) = empty_set,
inference(clausify,[status(thm)],[f_35_2]) ).
fof(f_36_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_36_2,plain,
! [U_125,U_124] :
( U_125 = U_124
| ? [U_123] :
( ( ~ in(U_123,U_125)
& in(U_123,U_124) )
| ( ~ in(U_123,U_124)
& in(U_123,U_125) ) ) ),
inference(variable_rename,[status(thm)],[f_36_1]) ).
fof(f_36_3,plain,
! [U_125,U_124] :
( U_125 = U_124
| ? [U_127] :
( ~ in(U_127,U_125)
& in(U_127,U_124) )
| ? [U_126] :
( ~ in(U_126,U_124)
& in(U_126,U_125) ) ),
inference(miniscope,[status(thm)],[f_36_2]) ).
fof(f_36_4,plain,
! [U_125,U_124] :
( U_125 = U_124
| ? [U_127] :
( ~ in(U_127,U_125)
& in(U_127,U_124) )
| ( ~ in(sK11(U_125,U_124),U_124)
& in(sK11(U_125,U_124),U_125) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK11]),skolemize(U_126,sK11(U_125,U_124))],[f_36_3]) ).
fof(f_36_5,plain,
! [U_125,U_124] :
( U_125 = U_124
| ( ~ in(sK12(U_125,U_124),U_125)
& in(sK12(U_125,U_124),U_124) )
| ( ~ in(sK11(U_125,U_124),U_124)
& in(sK11(U_125,U_124),U_125) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK12]),skolemize(U_127,sK12(U_125,U_124))],[f_36_4]) ).
cnf(f_36_6,plain,
( in(sK12(U_125,U_124),U_124)
| in(sK11(U_125,U_124),U_125)
| U_125 = U_124 ),
inference(clausify,[status(thm)],[f_36_5]) ).
cnf(f_36_7,plain,
( ~ in(sK12(U_125,U_124),U_125)
| in(sK11(U_125,U_124),U_125)
| U_125 = U_124 ),
inference(clausify,[status(thm)],[f_36_5]) ).
cnf(f_36_8,plain,
( in(sK12(U_125,U_124),U_124)
| ~ in(sK11(U_125,U_124),U_124)
| U_125 = U_124 ),
inference(clausify,[status(thm)],[f_36_5]) ).
cnf(f_36_9,plain,
( ~ in(sK12(U_125,U_124),U_125)
| ~ in(sK11(U_125,U_124),U_124)
| U_125 = U_124 ),
inference(clausify,[status(thm)],[f_36_5]) ).
fof(f_37_1,plain,
! [A] : subset(empty_set,A),
inference(fof_nnf,[status(thm)],[t2_xboole_1]) ).
fof(f_37_2,plain,
! [U_128] : subset(empty_set,U_128),
inference(variable_rename,[status(thm)],[f_37_1]) ).
cnf(f_37_3,plain,
subset(empty_set,U_128),
inference(clausify,[status(thm)],[f_37_2]) ).
fof(f_38_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_38_2,plain,
! [U_131,U_130,U_129] :
( subset(set_difference(U_131,U_129),set_difference(U_130,U_129))
| ~ subset(U_131,U_130) ),
inference(variable_rename,[status(thm)],[f_38_1]) ).
fof(f_38_3,plain,
! [U_131,U_130] :
( ! [U_129] : subset(set_difference(U_131,U_129),set_difference(U_130,U_129))
| ~ subset(U_131,U_130) ),
inference(miniscope,[status(thm)],[f_38_2]) ).
cnf(f_38_4,plain,
( subset(set_difference(U_131,U_129),set_difference(U_130,U_129))
| ~ subset(U_131,U_130) ),
inference(clausify,[status(thm)],[f_38_3]) ).
fof(f_39_1,plain,
! [A,B] : subset(set_difference(A,B),A),
inference(fof_nnf,[status(thm)],[t36_xboole_1]) ).
fof(f_39_2,plain,
! [U_133,U_132] : subset(set_difference(U_133,U_132),U_133),
inference(variable_rename,[status(thm)],[f_39_1]) ).
cnf(f_39_3,plain,
subset(set_difference(U_133,U_132),U_133),
inference(clausify,[status(thm)],[f_39_2]) ).
fof(f_40_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_40_2,plain,
! [U_135,U_134] :
( ( set_difference(U_135,U_134) = empty_set
| ~ subset(U_135,U_134) )
& ( subset(U_135,U_134)
| set_difference(U_135,U_134) != empty_set ) ),
inference(variable_rename,[status(thm)],[f_40_1]) ).
fof(f_40_3,plain,
( ! [U_139,U_137] :
( set_difference(U_139,U_137) = empty_set
| ~ subset(U_139,U_137) )
& ! [U_138,U_136] :
( subset(U_138,U_136)
| set_difference(U_138,U_136) != empty_set ) ),
inference(miniscope,[status(thm)],[f_40_2]) ).
cnf(f_40_4,plain,
( subset(U_138,U_136)
| set_difference(U_138,U_136) != empty_set ),
inference(clausify,[status(thm)],[f_40_3]) ).
cnf(f_40_5,plain,
( set_difference(U_139,U_137) = empty_set
| ~ subset(U_139,U_137) ),
inference(clausify,[status(thm)],[f_40_3]) ).
fof(f_41_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_41_2,plain,
! [U_141,U_140] : set_union2(U_141,set_difference(U_140,U_141)) = set_union2(U_141,U_140),
inference(variable_rename,[status(thm)],[f_41_1]) ).
cnf(f_41_3,plain,
set_union2(U_141,set_difference(U_140,U_141)) = set_union2(U_141,U_140),
inference(clausify,[status(thm)],[f_41_2]) ).
fof(f_42_1,plain,
! [A] : set_difference(A,empty_set) = A,
inference(fof_nnf,[status(thm)],[t3_boole]) ).
fof(f_42_2,plain,
! [U_142] : set_difference(U_142,empty_set) = U_142,
inference(variable_rename,[status(thm)],[f_42_1]) ).
cnf(f_42_3,plain,
set_difference(U_142,empty_set) = U_142,
inference(clausify,[status(thm)],[f_42_2]) ).
fof(f_43_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_43_2,plain,
! [U_146,U_145] :
( ( ~ disjoint(U_146,U_145)
| ! [U_144] :
( ~ in(U_144,U_145)
| ~ in(U_144,U_146) ) )
& ( ? [U_143] :
( in(U_143,U_145)
& in(U_143,U_146) )
| disjoint(U_146,U_145) ) ),
inference(variable_rename,[status(thm)],[f_43_1]) ).
fof(f_43_3,plain,
( ! [U_150,U_148] :
( ~ disjoint(U_150,U_148)
| ! [U_144] :
( ~ in(U_144,U_148)
| ~ in(U_144,U_150) ) )
& ! [U_149,U_147] :
( ? [U_143] :
( in(U_143,U_147)
& in(U_143,U_149) )
| disjoint(U_149,U_147) ) ),
inference(miniscope,[status(thm)],[f_43_2]) ).
fof(f_43_4,plain,
( ! [U_150,U_148] :
( ~ disjoint(U_150,U_148)
| ! [U_144] :
( ~ in(U_144,U_148)
| ~ in(U_144,U_150) ) )
& ! [U_149,U_147] :
( ( in(sK13(U_149,U_147),U_147)
& in(sK13(U_149,U_147),U_149) )
| disjoint(U_149,U_147) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK13]),skolemize(U_143,sK13(U_149,U_147))],[f_43_3]) ).
cnf(f_43_5,plain,
( in(sK13(U_149,U_147),U_149)
| disjoint(U_149,U_147) ),
inference(clausify,[status(thm)],[f_43_4]) ).
cnf(f_43_6,plain,
( in(sK13(U_149,U_147),U_147)
| disjoint(U_149,U_147) ),
inference(clausify,[status(thm)],[f_43_4]) ).
cnf(f_43_7,plain,
( ~ disjoint(U_150,U_148)
| ~ in(U_144,U_148)
| ~ in(U_144,U_150) ),
inference(clausify,[status(thm)],[f_43_4]) ).
fof(f_44_1,plain,
! [A] :
( A = empty_set
| ~ subset(A,empty_set) ),
inference(fof_nnf,[status(thm)],[t3_xboole_1]) ).
fof(f_44_2,plain,
! [U_151] :
( U_151 = empty_set
| ~ subset(U_151,empty_set) ),
inference(variable_rename,[status(thm)],[f_44_1]) ).
cnf(f_44_3,plain,
( U_151 = empty_set
| ~ subset(U_151,empty_set) ),
inference(clausify,[status(thm)],[f_44_2]) ).
fof(f_45_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_45_2,plain,
! [U_153,U_152] : set_difference(set_union2(U_153,U_152),U_152) = set_difference(U_153,U_152),
inference(variable_rename,[status(thm)],[f_45_1]) ).
cnf(f_45_3,plain,
set_difference(set_union2(U_153,U_152),U_152) = set_difference(U_153,U_152),
inference(clausify,[status(thm)],[f_45_2]) ).
fof(f_46_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_46_2,plain,
! [U_155,U_154] :
( U_154 = set_union2(U_155,set_difference(U_154,U_155))
| ~ subset(U_155,U_154) ),
inference(variable_rename,[status(thm)],[f_46_1]) ).
cnf(f_46_3,plain,
( U_154 = set_union2(U_155,set_difference(U_154,U_155))
| ~ subset(U_155,U_154) ),
inference(clausify,[status(thm)],[f_46_2]) ).
fof(f_47_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_47_2,plain,
! [U_157,U_156] : set_difference(U_157,set_difference(U_157,U_156)) = set_intersection2(U_157,U_156),
inference(variable_rename,[status(thm)],[f_47_1]) ).
cnf(f_47_3,plain,
set_difference(U_157,set_difference(U_157,U_156)) = set_intersection2(U_157,U_156),
inference(clausify,[status(thm)],[f_47_2]) ).
fof(f_48_1,plain,
! [A] : set_difference(empty_set,A) = empty_set,
inference(fof_nnf,[status(thm)],[t4_boole]) ).
fof(f_48_2,plain,
! [U_158] : set_difference(empty_set,U_158) = empty_set,
inference(variable_rename,[status(thm)],[f_48_1]) ).
cnf(f_48_3,plain,
set_difference(empty_set,U_158) = empty_set,
inference(clausify,[status(thm)],[f_48_2]) ).
fof(f_49_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_49_2,plain,
! [U_162,U_161] :
( ( ~ disjoint(U_162,U_161)
| ! [U_160] : ~ in(U_160,set_intersection2(U_162,U_161)) )
& ( ? [U_159] : in(U_159,set_intersection2(U_162,U_161))
| disjoint(U_162,U_161) ) ),
inference(variable_rename,[status(thm)],[f_49_1]) ).
fof(f_49_3,plain,
( ! [U_166,U_164] :
( ~ disjoint(U_166,U_164)
| ! [U_160] : ~ in(U_160,set_intersection2(U_166,U_164)) )
& ! [U_165,U_163] :
( ? [U_159] : in(U_159,set_intersection2(U_165,U_163))
| disjoint(U_165,U_163) ) ),
inference(miniscope,[status(thm)],[f_49_2]) ).
fof(f_49_4,plain,
( ! [U_166,U_164] :
( ~ disjoint(U_166,U_164)
| ! [U_160] : ~ in(U_160,set_intersection2(U_166,U_164)) )
& ! [U_165,U_163] :
( in(sK14(U_165,U_163),set_intersection2(U_165,U_163))
| disjoint(U_165,U_163) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK14]),skolemize(U_159,sK14(U_165,U_163))],[f_49_3]) ).
cnf(f_49_5,plain,
( in(sK14(U_165,U_163),set_intersection2(U_165,U_163))
| disjoint(U_165,U_163) ),
inference(clausify,[status(thm)],[f_49_4]) ).
cnf(f_49_6,plain,
( ~ disjoint(U_166,U_164)
| ~ in(U_160,set_intersection2(U_166,U_164)) ),
inference(clausify,[status(thm)],[f_49_4]) ).
fof(f_50_1,negated_conjecture,
~ ! [A,B] :
~ ( proper_subset(B,A)
& subset(A,B) ),
inference(negate,[status(cth)],[t60_xboole_1]) ).
fof(f_50_2,negated_conjecture,
? [A,B] :
( proper_subset(B,A)
& subset(A,B) ),
inference(fof_nnf,[status(thm)],[f_50_1]) ).
fof(f_50_3,negated_conjecture,
? [U_168,U_167] :
( proper_subset(U_167,U_168)
& subset(U_168,U_167) ),
inference(variable_rename,[status(thm)],[f_50_2]) ).
fof(f_50_4,negated_conjecture,
? [U_167] :
( proper_subset(U_167,sK15)
& subset(sK15,U_167) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK15]),skolemize(U_168,sK15)],[f_50_3]) ).
fof(f_50_5,negated_conjecture,
( proper_subset(sK16,sK15)
& subset(sK15,sK16) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK16]),skolemize(U_167,sK16)],[f_50_4]) ).
fof(f_50_6,negated_conjecture,
( proper_subset(sK16,sK15)
& subset(sK15,sK16) ),
inference(definitional_conversion,[status(esa)],[f_50_5]) ).
cnf(f_50_7,negated_conjecture,
subset(sK15,sK16),
inference(clausify,[status(thm)],[f_50_6]) ).
cnf(f_50_8,negated_conjecture,
proper_subset(sK16,sK15),
inference(clausify,[status(thm)],[f_50_6]) ).
fof(f_51_1,plain,
! [A] :
( A = empty_set
| ~ empty(A) ),
inference(fof_nnf,[status(thm)],[t6_boole]) ).
fof(f_51_2,plain,
! [U_169] :
( U_169 = empty_set
| ~ empty(U_169) ),
inference(variable_rename,[status(thm)],[f_51_1]) ).
cnf(f_51_3,plain,
( U_169 = empty_set
| ~ empty(U_169) ),
inference(clausify,[status(thm)],[f_51_2]) ).
fof(f_52_1,plain,
! [A,B] :
( ~ empty(B)
| ~ in(A,B) ),
inference(fof_nnf,[status(thm)],[t7_boole]) ).
fof(f_52_2,plain,
! [U_171,U_170] :
( ~ empty(U_170)
| ~ in(U_171,U_170) ),
inference(variable_rename,[status(thm)],[f_52_1]) ).
cnf(f_52_3,plain,
( ~ empty(U_170)
| ~ in(U_171,U_170) ),
inference(clausify,[status(thm)],[f_52_2]) ).
fof(f_53_1,plain,
! [A,B] : subset(A,set_union2(A,B)),
inference(fof_nnf,[status(thm)],[t7_xboole_1]) ).
fof(f_53_2,plain,
! [U_173,U_172] : subset(U_173,set_union2(U_173,U_172)),
inference(variable_rename,[status(thm)],[f_53_1]) ).
cnf(f_53_3,plain,
subset(U_173,set_union2(U_173,U_172)),
inference(clausify,[status(thm)],[f_53_2]) ).
fof(f_54_1,plain,
! [A,B] :
( ~ empty(B)
| A = B
| ~ empty(A) ),
inference(fof_nnf,[status(thm)],[t8_boole]) ).
fof(f_54_2,plain,
! [U_175,U_174] :
( ~ empty(U_174)
| U_175 = U_174
| ~ empty(U_175) ),
inference(variable_rename,[status(thm)],[f_54_1]) ).
fof(f_54_3,plain,
! [U_175] :
( ! [U_174] :
( ~ empty(U_174)
| U_175 = U_174 )
| ~ empty(U_175) ),
inference(miniscope,[status(thm)],[f_54_2]) ).
cnf(f_54_4,plain,
( ~ empty(U_174)
| U_175 = U_174
| ~ empty(U_175) ),
inference(clausify,[status(thm)],[f_54_3]) ).
fof(f_55_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_55_2,plain,
! [U_178,U_177,U_176] :
( subset(set_union2(U_178,U_176),U_177)
| ~ subset(U_176,U_177)
| ~ subset(U_178,U_177) ),
inference(variable_rename,[status(thm)],[f_55_1]) ).
cnf(f_55_3,plain,
( subset(set_union2(U_178,U_176),U_177)
| ~ subset(U_176,U_177)
| ~ subset(U_178,U_177) ),
inference(clausify,[status(thm)],[f_55_2]) ).
cnf(f_13_2_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_13_2]) ).
cnf(f_14_2_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_14_2]) ).
cnf(f_15_2_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_15_2]) ).
cnf(f_16_2_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_16_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,
( 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_5,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_6,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_7,axiom,
( sK1(Eq_x_0) = sK1(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_8,axiom,
( sK2(Eq_x_0,Eq_x_1,Eq_x_2) = sK2(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_9,axiom,
( sK3(Eq_x_0,Eq_x_1,Eq_x_2) = sK3(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_10,axiom,
( sK4(Eq_x_0,Eq_x_1) = sK4(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,
( 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_12,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_13,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_14,axiom,
( sK8(Eq_x_0,Eq_x_1,Eq_x_2) = sK8(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,
( sK11(Eq_x_0,Eq_x_1) = sK11(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_16,axiom,
( sK12(Eq_x_0,Eq_x_1) = sK12(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,
( sK13(Eq_x_0,Eq_x_1) = sK13(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_18,axiom,
( sK14(Eq_x_0,Eq_x_1) = sK14(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_19,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_20,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_21,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_22,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_23,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
% 0.00/0.02 % Problem : SEU139+2 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.03 This is a FOF_THM_RFO_SEQ problem
% 0.00/0.03 % Command : /export/starexec/sandbox/solver/bin/connect++ --verbosity 1 --no-colour --tptp-proof --schedule default --timeout 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/15.37 % Computer : n008.cluster.edu
% 0.08/15.37 % Model : x86_64 x86_64
% 0.08/15.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/15.37 % Memory : 8046.5625MB
% 0.08/15.37 % OS : Linux 6.8.0-71-generic
% 0.08/15.37 % CPULimit : 300
% 0.08/15.37 % WCLimit : 300
% 0.08/15.37 % DateTime : Sat Sep 19 23:22:43 UTC 2026
% 0.08/15.38 % CPUTime :
% 0.13/15.68 % SZS status Theorem for theBenchmark
% 0.13/15.68 % SZS output start Proof for theBenchmark
% See solution above
%------------------------------------------------------------------------------