%------------------------------------------------------------------------------
% File : ConnectPP---0.7.2
% Problem : SEU111+1 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/connect++ --verbosity 1 --no-colour --tptp-proof --schedule default --timeout 300 /export/starexec/sandbox2/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 08:58:03 AM UTC 2026
% Result : Theorem 273.54s 273.85s
% Output : Proof 275.35s
% 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(cc1_finset_1,axiom,
! [A] :
( empty(A)
=> finite(A) ),
file('theBenchmark.p',cc1_finset_1) ).
fof(cc1_finsub_1,axiom,
! [A] :
( preboolean(A)
=> ( diff_closed(A)
& cup_closed(A) ) ),
file('theBenchmark.p',cc1_finsub_1) ).
fof(cc2_finset_1,axiom,
! [A] :
( finite(A)
=> ! [B] :
( element(B,powerset(A))
=> finite(B) ) ),
file('theBenchmark.p',cc2_finset_1) ).
fof(cc2_finsub_1,axiom,
! [A] :
( ( diff_closed(A)
& cup_closed(A) )
=> preboolean(A) ),
file('theBenchmark.p',cc2_finsub_1) ).
fof(cc3_finsub_1,axiom,
! [A,B] :
( element(B,finite_subsets(A))
=> finite(B) ),
file('theBenchmark.p',cc3_finsub_1) ).
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(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(d5_finsub_1,axiom,
! [A,B] :
( preboolean(B)
=> ( B = finite_subsets(A)
<=> ! [C] :
( in(C,B)
<=> ( finite(C)
& subset(C,A) ) ) ) ),
file('theBenchmark.p',d5_finsub_1) ).
fof(dt_k5_finsub_1,axiom,
! [A] : preboolean(finite_subsets(A)),
file('theBenchmark.p',dt_k5_finsub_1) ).
fof(existence_m1_subset_1,axiom,
! [A] :
? [B] : element(B,A),
file('theBenchmark.p',existence_m1_subset_1) ).
fof(fc10_finset_1,axiom,
! [A,B] :
( finite(B)
=> finite(set_intersection2(A,B)) ),
file('theBenchmark.p',fc10_finset_1) ).
fof(fc11_finset_1,axiom,
! [A,B] :
( finite(A)
=> finite(set_intersection2(A,B)) ),
file('theBenchmark.p',fc11_finset_1) ).
fof(fc1_finsub_1,axiom,
! [A] :
( preboolean(powerset(A))
& diff_closed(powerset(A))
& cup_closed(powerset(A))
& ~ empty(powerset(A)) ),
file('theBenchmark.p',fc1_finsub_1) ).
fof(fc1_subset_1,axiom,
! [A] : ~ empty(powerset(A)),
file('theBenchmark.p',fc1_subset_1) ).
fof(fc1_xboole_0,axiom,
empty(empty_set),
file('theBenchmark.p',fc1_xboole_0) ).
fof(fc2_finsub_1,axiom,
! [A] :
( preboolean(finite_subsets(A))
& diff_closed(finite_subsets(A))
& cup_closed(finite_subsets(A))
& ~ empty(finite_subsets(A)) ),
file('theBenchmark.p',fc2_finsub_1) ).
fof(idempotence_k3_xboole_0,axiom,
! [A,B] : set_intersection2(A,A) = A,
file('theBenchmark.p',idempotence_k3_xboole_0) ).
fof(rc1_finset_1,axiom,
? [A] :
( finite(A)
& ~ empty(A) ),
file('theBenchmark.p',rc1_finset_1) ).
fof(rc1_finsub_1,axiom,
? [A] :
( preboolean(A)
& diff_closed(A)
& cap_closed(A)
& cup_closed(A)
& ~ empty(A) ),
file('theBenchmark.p',rc1_finsub_1) ).
fof(rc1_subset_1,axiom,
! [A] :
( ~ empty(A)
=> ? [B] :
( ~ empty(B)
& element(B,powerset(A)) ) ),
file('theBenchmark.p',rc1_subset_1) ).
fof(rc1_xboole_0,axiom,
? [A] : empty(A),
file('theBenchmark.p',rc1_xboole_0) ).
fof(rc2_finset_1,axiom,
! [A] :
? [B] :
( finite(B)
& natural(B)
& ordinal(B)
& epsilon_connected(B)
& epsilon_transitive(B)
& one_to_one(B)
& function(B)
& relation(B)
& empty(B)
& element(B,powerset(A)) ),
file('theBenchmark.p',rc2_finset_1) ).
fof(rc2_subset_1,axiom,
! [A] :
? [B] :
( empty(B)
& element(B,powerset(A)) ),
file('theBenchmark.p',rc2_subset_1) ).
fof(rc2_xboole_0,axiom,
? [A] : ~ empty(A),
file('theBenchmark.p',rc2_xboole_0) ).
fof(rc3_finset_1,axiom,
! [A] :
( ~ empty(A)
=> ? [B] :
( finite(B)
& ~ empty(B)
& element(B,powerset(A)) ) ),
file('theBenchmark.p',rc3_finset_1) ).
fof(rc4_finset_1,axiom,
! [A] :
( ~ empty(A)
=> ? [B] :
( finite(B)
& ~ empty(B)
& element(B,powerset(A)) ) ),
file('theBenchmark.p',rc4_finset_1) ).
fof(reflexivity_r1_tarski,axiom,
! [A,B] : subset(A,A),
file('theBenchmark.p',reflexivity_r1_tarski) ).
fof(t17_xboole_1,axiom,
! [A,B] : subset(set_intersection2(A,B),A),
file('theBenchmark.p',t17_xboole_1) ).
fof(t19_xboole_1,axiom,
! [A,B,C] :
( ( subset(A,C)
& subset(A,B) )
=> subset(A,set_intersection2(B,C)) ),
file('theBenchmark.p',t19_xboole_1) ).
fof(t1_subset,axiom,
! [A,B] :
( in(A,B)
=> element(A,B) ),
file('theBenchmark.p',t1_subset) ).
fof(t23_finsub_1,axiom,
! [A,B] :
( subset(A,B)
=> subset(finite_subsets(A),finite_subsets(B)) ),
file('theBenchmark.p',t23_finsub_1) ).
fof(t24_finsub_1,conjecture,
! [A,B] : finite_subsets(set_intersection2(A,B)) = set_intersection2(finite_subsets(A),finite_subsets(B)),
file('theBenchmark.p',t24_finsub_1) ).
fof(t2_boole,axiom,
! [A] : set_intersection2(A,empty_set) = empty_set,
file('theBenchmark.p',t2_boole) ).
fof(t2_subset,axiom,
! [A,B] :
( element(A,B)
=> ( in(A,B)
| empty(B) ) ),
file('theBenchmark.p',t2_subset) ).
fof(t3_subset,axiom,
! [A,B] :
( element(A,powerset(B))
<=> subset(A,B) ),
file('theBenchmark.p',t3_subset) ).
fof(t4_subset,axiom,
! [A,B,C] :
( ( element(B,powerset(C))
& in(A,B) )
=> element(A,C) ),
file('theBenchmark.p',t4_subset) ).
fof(t5_subset,axiom,
! [A,B,C] :
~ ( empty(C)
& element(B,powerset(C))
& in(A,B) ),
file('theBenchmark.p',t5_subset) ).
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(t8_boole,axiom,
! [A,B] :
~ ( empty(B)
& A != B
& empty(A) ),
file('theBenchmark.p',t8_boole) ).
fof(f_1_1,plain,
! [A,B] :
( ~ in(B,A)
| ~ in(A,B) ),
inference(fof_nnf,[status(thm)],[antisymmetry_r2_hidden]) ).
fof(f_1_2,plain,
! [U_1,U_0] :
( ~ in(U_0,U_1)
| ~ in(U_1,U_0) ),
inference(variable_rename,[status(thm)],[f_1_1]) ).
fof(f_1_3,plain,
! [U_1,U_0] :
( ~ in(U_0,U_1)
| ~ in(U_1,U_0) ),
inference(definitional_conversion,[status(esa)],[f_1_2]) ).
cnf(f_1_4,plain,
( ~ in(U_0,U_1)
| ~ in(U_1,U_0) ),
inference(clausify,[status(thm)],[f_1_3]) ).
fof(f_2_1,plain,
! [A] :
( finite(A)
| ~ empty(A) ),
inference(fof_nnf,[status(thm)],[cc1_finset_1]) ).
fof(f_2_2,plain,
! [U_2] :
( finite(U_2)
| ~ empty(U_2) ),
inference(variable_rename,[status(thm)],[f_2_1]) ).
fof(f_2_3,plain,
! [U_2] :
( finite(U_2)
| ~ empty(U_2) ),
inference(definitional_conversion,[status(esa)],[f_2_2]) ).
cnf(f_2_4,plain,
( finite(U_2)
| ~ empty(U_2) ),
inference(clausify,[status(thm)],[f_2_3]) ).
fof(f_3_1,plain,
! [A] :
( ( diff_closed(A)
& cup_closed(A) )
| ~ preboolean(A) ),
inference(fof_nnf,[status(thm)],[cc1_finsub_1]) ).
fof(f_3_2,plain,
! [U_3] :
( ( diff_closed(U_3)
& cup_closed(U_3) )
| ~ preboolean(U_3) ),
inference(variable_rename,[status(thm)],[f_3_1]) ).
fof(f_3_3,plain,
( ! [U_3] :
( diff_closed(U_3)
| ~ sP0(U_3) )
& ! [U_3] :
( cup_closed(U_3)
| ~ sP0(U_3) )
& ! [U_3] :
( sP0(U_3)
| ~ preboolean(U_3) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP0])],[f_3_2]) ).
cnf(f_3_4,plain,
( sP0(U_3)
| ~ preboolean(U_3) ),
inference(clausify,[status(thm)],[f_3_3]) ).
cnf(f_3_5,plain,
( cup_closed(U_3)
| ~ sP0(U_3) ),
inference(clausify,[status(thm)],[f_3_3]) ).
cnf(f_3_6,plain,
( diff_closed(U_3)
| ~ sP0(U_3) ),
inference(clausify,[status(thm)],[f_3_3]) ).
fof(f_4_1,plain,
! [A] :
( ! [B] :
( finite(B)
| ~ element(B,powerset(A)) )
| ~ finite(A) ),
inference(fof_nnf,[status(thm)],[cc2_finset_1]) ).
fof(f_4_2,plain,
! [U_5] :
( ! [U_4] :
( finite(U_4)
| ~ element(U_4,powerset(U_5)) )
| ~ finite(U_5) ),
inference(variable_rename,[status(thm)],[f_4_1]) ).
fof(f_4_3,plain,
! [U_5,U_4] :
( finite(U_4)
| ~ element(U_4,powerset(U_5))
| ~ finite(U_5) ),
inference(definitional_conversion,[status(esa)],[f_4_2]) ).
cnf(f_4_4,plain,
( finite(U_4)
| ~ element(U_4,powerset(U_5))
| ~ finite(U_5) ),
inference(clausify,[status(thm)],[f_4_3]) ).
fof(f_5_1,plain,
! [A] :
( preboolean(A)
| ~ diff_closed(A)
| ~ cup_closed(A) ),
inference(fof_nnf,[status(thm)],[cc2_finsub_1]) ).
fof(f_5_2,plain,
! [U_6] :
( preboolean(U_6)
| ~ diff_closed(U_6)
| ~ cup_closed(U_6) ),
inference(variable_rename,[status(thm)],[f_5_1]) ).
fof(f_5_3,plain,
! [U_6] :
( preboolean(U_6)
| ~ diff_closed(U_6)
| ~ cup_closed(U_6) ),
inference(definitional_conversion,[status(esa)],[f_5_2]) ).
cnf(f_5_4,plain,
( preboolean(U_6)
| ~ diff_closed(U_6)
| ~ cup_closed(U_6) ),
inference(clausify,[status(thm)],[f_5_3]) ).
fof(f_6_1,plain,
! [A,B] :
( finite(B)
| ~ element(B,finite_subsets(A)) ),
inference(fof_nnf,[status(thm)],[cc3_finsub_1]) ).
fof(f_6_2,plain,
! [U_8,U_7] :
( finite(U_7)
| ~ element(U_7,finite_subsets(U_8)) ),
inference(variable_rename,[status(thm)],[f_6_1]) ).
fof(f_6_3,plain,
! [U_8,U_7] :
( finite(U_7)
| ~ element(U_7,finite_subsets(U_8)) ),
inference(definitional_conversion,[status(esa)],[f_6_2]) ).
cnf(f_6_4,plain,
( finite(U_7)
| ~ element(U_7,finite_subsets(U_8)) ),
inference(clausify,[status(thm)],[f_6_3]) ).
fof(f_7_1,plain,
! [A,B] : set_intersection2(A,B) = set_intersection2(B,A),
inference(fof_nnf,[status(thm)],[commutativity_k3_xboole_0]) ).
fof(f_7_2,plain,
! [U_10,U_9] : set_intersection2(U_10,U_9) = set_intersection2(U_9,U_10),
inference(variable_rename,[status(thm)],[f_7_1]) ).
fof(f_7_3,plain,
! [U_10,U_9] : set_intersection2(U_10,U_9) = set_intersection2(U_9,U_10),
inference(definitional_conversion,[status(esa)],[f_7_2]) ).
cnf(f_7_4,plain,
set_intersection2(U_10,U_9) = set_intersection2(U_9,U_10),
inference(clausify,[status(thm)],[f_7_3]) ).
fof(f_8_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_8_2,plain,
! [U_12,U_11] :
( ( U_12 = U_11
| ~ subset(U_11,U_12)
| ~ subset(U_12,U_11) )
& ( ( subset(U_11,U_12)
& subset(U_12,U_11) )
| U_12 != U_11 ) ),
inference(variable_rename,[status(thm)],[f_8_1]) ).
fof(f_8_3,plain,
( ! [U_16,U_14] :
( U_16 = U_14
| ~ subset(U_14,U_16)
| ~ subset(U_16,U_14) )
& ! [U_15,U_13] :
( ( subset(U_13,U_15)
& subset(U_15,U_13) )
| U_15 != U_13 ) ),
inference(miniscope,[status(thm)],[f_8_2]) ).
fof(f_8_4,plain,
( ! [U_15,U_13] :
( subset(U_13,U_15)
| ~ sP1(U_15,U_13) )
& ! [U_15,U_13] :
( subset(U_15,U_13)
| ~ sP1(U_15,U_13) )
& ! [U_14,U_16] :
( U_16 = U_14
| ~ subset(U_14,U_16)
| ~ subset(U_16,U_14) )
& ! [U_15,U_13] :
( sP1(U_15,U_13)
| U_15 != U_13 ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP1])],[f_8_3]) ).
cnf(f_8_5,plain,
( sP1(U_15,U_13)
| U_15 != U_13 ),
inference(clausify,[status(thm)],[f_8_4]) ).
cnf(f_8_6,plain,
( U_16 = U_14
| ~ subset(U_14,U_16)
| ~ subset(U_16,U_14) ),
inference(clausify,[status(thm)],[f_8_4]) ).
cnf(f_8_7,plain,
( subset(U_15,U_13)
| ~ sP1(U_15,U_13) ),
inference(clausify,[status(thm)],[f_8_4]) ).
cnf(f_8_8,plain,
( subset(U_13,U_15)
| ~ sP1(U_15,U_13) ),
inference(clausify,[status(thm)],[f_8_4]) ).
fof(f_9_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_9_2,plain,
! [U_20,U_19] :
( ( subset(U_20,U_19)
| ? [U_18] :
( ~ in(U_18,U_19)
& in(U_18,U_20) ) )
& ( ! [U_17] :
( in(U_17,U_19)
| ~ in(U_17,U_20) )
| ~ subset(U_20,U_19) ) ),
inference(variable_rename,[status(thm)],[f_9_1]) ).
fof(f_9_3,plain,
( ! [U_24,U_22] :
( subset(U_24,U_22)
| ? [U_18] :
( ~ in(U_18,U_22)
& in(U_18,U_24) ) )
& ! [U_23,U_21] :
( ! [U_17] :
( in(U_17,U_21)
| ~ in(U_17,U_23) )
| ~ subset(U_23,U_21) ) ),
inference(miniscope,[status(thm)],[f_9_2]) ).
fof(f_9_4,plain,
( ! [U_24,U_22] :
( subset(U_24,U_22)
| ( ~ in(sK1(U_24,U_22),U_22)
& in(sK1(U_24,U_22),U_24) ) )
& ! [U_23,U_21] :
( ! [U_17] :
( in(U_17,U_21)
| ~ in(U_17,U_23) )
| ~ subset(U_23,U_21) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(U_18,sK1(U_24,U_22))],[f_9_3]) ).
fof(f_9_5,plain,
( ! [U_22,U_24] :
( ~ in(sK1(U_24,U_22),U_22)
| ~ sP2(U_22,U_24) )
& ! [U_22,U_24] :
( in(sK1(U_24,U_22),U_24)
| ~ sP2(U_22,U_24) )
& ! [U_22,U_24] :
( subset(U_24,U_22)
| sP2(U_22,U_24) )
& ! [U_17,U_23,U_21] :
( in(U_17,U_21)
| ~ in(U_17,U_23)
| ~ subset(U_23,U_21) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP2])],[f_9_4]) ).
cnf(f_9_6,plain,
( in(U_17,U_21)
| ~ in(U_17,U_23)
| ~ subset(U_23,U_21) ),
inference(clausify,[status(thm)],[f_9_5]) ).
cnf(f_9_7,plain,
( subset(U_24,U_22)
| sP2(U_22,U_24) ),
inference(clausify,[status(thm)],[f_9_5]) ).
cnf(f_9_8,plain,
( in(sK1(U_24,U_22),U_24)
| ~ sP2(U_22,U_24) ),
inference(clausify,[status(thm)],[f_9_5]) ).
cnf(f_9_9,plain,
( ~ in(sK1(U_24,U_22),U_22)
| ~ sP2(U_22,U_24) ),
inference(clausify,[status(thm)],[f_9_5]) ).
fof(f_10_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_10_2,plain,
! [U_29,U_28,U_27] :
( ( U_27 = set_intersection2(U_29,U_28)
| ? [U_26] :
( ( ~ in(U_26,U_27)
& in(U_26,U_28)
& in(U_26,U_29) )
| ( ( ~ in(U_26,U_28)
| ~ in(U_26,U_29) )
& in(U_26,U_27) ) ) )
& ( ! [U_25] :
( ( in(U_25,U_27)
| ~ in(U_25,U_28)
| ~ in(U_25,U_29) )
& ( ( in(U_25,U_28)
& in(U_25,U_29) )
| ~ in(U_25,U_27) ) )
| U_27 != set_intersection2(U_29,U_28) ) ),
inference(variable_rename,[status(thm)],[f_10_1]) ).
fof(f_10_3,plain,
( ! [U_39,U_37,U_35] :
( U_35 = set_intersection2(U_39,U_37)
| ? [U_33] :
( ~ in(U_33,U_35)
& in(U_33,U_37)
& in(U_33,U_39) )
| ? [U_32] :
( ( ~ in(U_32,U_37)
| ~ in(U_32,U_39) )
& in(U_32,U_35) ) )
& ! [U_38,U_36,U_34] :
( ( ! [U_31] :
( in(U_31,U_34)
| ~ in(U_31,U_36)
| ~ in(U_31,U_38) )
& ! [U_30] :
( ( in(U_30,U_36)
& in(U_30,U_38) )
| ~ in(U_30,U_34) ) )
| U_34 != set_intersection2(U_38,U_36) ) ),
inference(miniscope,[status(thm)],[f_10_2]) ).
fof(f_10_4,plain,
( ! [U_39,U_37,U_35] :
( U_35 = set_intersection2(U_39,U_37)
| ? [U_33] :
( ~ in(U_33,U_35)
& in(U_33,U_37)
& in(U_33,U_39) )
| ( ( ~ in(sK2(U_39,U_37,U_35),U_37)
| ~ in(sK2(U_39,U_37,U_35),U_39) )
& in(sK2(U_39,U_37,U_35),U_35) ) )
& ! [U_38,U_36,U_34] :
( ( ! [U_31] :
( in(U_31,U_34)
| ~ in(U_31,U_36)
| ~ in(U_31,U_38) )
& ! [U_30] :
( ( in(U_30,U_36)
& in(U_30,U_38) )
| ~ in(U_30,U_34) ) )
| U_34 != set_intersection2(U_38,U_36) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2]),skolemize(U_32,sK2(U_39,U_37,U_35))],[f_10_3]) ).
fof(f_10_5,plain,
( ! [U_39,U_37,U_35] :
( U_35 = set_intersection2(U_39,U_37)
| ( ~ in(sK3(U_39,U_37,U_35),U_35)
& in(sK3(U_39,U_37,U_35),U_37)
& in(sK3(U_39,U_37,U_35),U_39) )
| ( ( ~ in(sK2(U_39,U_37,U_35),U_37)
| ~ in(sK2(U_39,U_37,U_35),U_39) )
& in(sK2(U_39,U_37,U_35),U_35) ) )
& ! [U_38,U_36,U_34] :
( ( ! [U_31] :
( in(U_31,U_34)
| ~ in(U_31,U_36)
| ~ in(U_31,U_38) )
& ! [U_30] :
( ( in(U_30,U_36)
& in(U_30,U_38) )
| ~ in(U_30,U_34) ) )
| U_34 != set_intersection2(U_38,U_36) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3]),skolemize(U_33,sK3(U_39,U_37,U_35))],[f_10_4]) ).
fof(f_10_6,plain,
( ! [U_37,U_39,U_35] :
( ~ in(sK3(U_39,U_37,U_35),U_35)
| ~ sP6(U_37,U_39,U_35) )
& ! [U_37,U_39,U_35] :
( in(sK3(U_39,U_37,U_35),U_37)
| ~ sP6(U_37,U_39,U_35) )
& ! [U_37,U_39,U_35] :
( in(sK3(U_39,U_37,U_35),U_39)
| ~ sP6(U_37,U_39,U_35) )
& ! [U_37,U_39,U_35] :
( ~ in(sK2(U_39,U_37,U_35),U_37)
| ~ in(sK2(U_39,U_37,U_35),U_39)
| ~ sP5(U_37,U_39,U_35) )
& ! [U_37,U_39,U_35] :
( in(sK2(U_39,U_37,U_35),U_35)
| ~ sP5(U_37,U_39,U_35) )
& ! [U_30,U_38,U_36] :
( in(U_30,U_36)
| ~ sP3(U_30,U_38,U_36) )
& ! [U_30,U_38,U_36] :
( in(U_30,U_38)
| ~ sP3(U_30,U_38,U_36) )
& ! [U_30,U_38,U_34,U_36,U_31] :
( in(U_31,U_34)
| ~ in(U_31,U_36)
| ~ in(U_31,U_38)
| ~ sP4(U_30,U_38,U_34,U_36,U_31) )
& ! [U_30,U_38,U_34,U_36,U_31] :
( sP3(U_30,U_38,U_36)
| ~ in(U_30,U_34)
| ~ sP4(U_30,U_38,U_34,U_36,U_31) )
& ! [U_37,U_39,U_35] :
( U_35 = set_intersection2(U_39,U_37)
| sP6(U_37,U_39,U_35)
| sP5(U_37,U_39,U_35) )
& ! [U_30,U_38,U_34,U_36,U_31] :
( sP4(U_30,U_38,U_34,U_36,U_31)
| U_34 != set_intersection2(U_38,U_36) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP3,sP4,sP5,sP6])],[f_10_5]) ).
cnf(f_10_7,plain,
( sP4(U_30,U_38,U_34,U_36,U_31)
| U_34 != set_intersection2(U_38,U_36) ),
inference(clausify,[status(thm)],[f_10_6]) ).
cnf(f_10_8,plain,
( U_35 = set_intersection2(U_39,U_37)
| sP6(U_37,U_39,U_35)
| sP5(U_37,U_39,U_35) ),
inference(clausify,[status(thm)],[f_10_6]) ).
cnf(f_10_9,plain,
( sP3(U_30,U_38,U_36)
| ~ in(U_30,U_34)
| ~ sP4(U_30,U_38,U_34,U_36,U_31) ),
inference(clausify,[status(thm)],[f_10_6]) ).
cnf(f_10_10,plain,
( in(U_31,U_34)
| ~ in(U_31,U_36)
| ~ in(U_31,U_38)
| ~ sP4(U_30,U_38,U_34,U_36,U_31) ),
inference(clausify,[status(thm)],[f_10_6]) ).
cnf(f_10_11,plain,
( in(U_30,U_38)
| ~ sP3(U_30,U_38,U_36) ),
inference(clausify,[status(thm)],[f_10_6]) ).
cnf(f_10_12,plain,
( in(U_30,U_36)
| ~ sP3(U_30,U_38,U_36) ),
inference(clausify,[status(thm)],[f_10_6]) ).
cnf(f_10_13,plain,
( in(sK2(U_39,U_37,U_35),U_35)
| ~ sP5(U_37,U_39,U_35) ),
inference(clausify,[status(thm)],[f_10_6]) ).
cnf(f_10_14,plain,
( ~ in(sK2(U_39,U_37,U_35),U_37)
| ~ in(sK2(U_39,U_37,U_35),U_39)
| ~ sP5(U_37,U_39,U_35) ),
inference(clausify,[status(thm)],[f_10_6]) ).
cnf(f_10_15,plain,
( in(sK3(U_39,U_37,U_35),U_39)
| ~ sP6(U_37,U_39,U_35) ),
inference(clausify,[status(thm)],[f_10_6]) ).
cnf(f_10_16,plain,
( in(sK3(U_39,U_37,U_35),U_37)
| ~ sP6(U_37,U_39,U_35) ),
inference(clausify,[status(thm)],[f_10_6]) ).
cnf(f_10_17,plain,
( ~ in(sK3(U_39,U_37,U_35),U_35)
| ~ sP6(U_37,U_39,U_35) ),
inference(clausify,[status(thm)],[f_10_6]) ).
fof(f_11_1,plain,
! [A,B] :
( ( ( B = finite_subsets(A)
| ? [C] :
( ( ~ in(C,B)
& finite(C)
& subset(C,A) )
| ( ( ~ finite(C)
| ~ subset(C,A) )
& in(C,B) ) ) )
& ( ! [C] :
( ( in(C,B)
| ~ finite(C)
| ~ subset(C,A) )
& ( ( finite(C)
& subset(C,A) )
| ~ in(C,B) ) )
| B != finite_subsets(A) ) )
| ~ preboolean(B) ),
inference(fof_nnf,[status(thm)],[d5_finsub_1]) ).
fof(f_11_2,plain,
! [U_43,U_42] :
( ( ( U_42 = finite_subsets(U_43)
| ? [U_41] :
( ( ~ in(U_41,U_42)
& finite(U_41)
& subset(U_41,U_43) )
| ( ( ~ finite(U_41)
| ~ subset(U_41,U_43) )
& in(U_41,U_42) ) ) )
& ( ! [U_40] :
( ( in(U_40,U_42)
| ~ finite(U_40)
| ~ subset(U_40,U_43) )
& ( ( finite(U_40)
& subset(U_40,U_43) )
| ~ in(U_40,U_42) ) )
| U_42 != finite_subsets(U_43) ) )
| ~ preboolean(U_42) ),
inference(variable_rename,[status(thm)],[f_11_1]) ).
fof(f_11_3,plain,
! [U_43,U_42] :
( ( ( U_42 = finite_subsets(U_43)
| ? [U_47] :
( ~ in(U_47,U_42)
& finite(U_47)
& subset(U_47,U_43) )
| ? [U_46] :
( ( ~ finite(U_46)
| ~ subset(U_46,U_43) )
& in(U_46,U_42) ) )
& ( ( ! [U_45] :
( in(U_45,U_42)
| ~ finite(U_45)
| ~ subset(U_45,U_43) )
& ! [U_44] :
( ( finite(U_44)
& subset(U_44,U_43) )
| ~ in(U_44,U_42) ) )
| U_42 != finite_subsets(U_43) ) )
| ~ preboolean(U_42) ),
inference(miniscope,[status(thm)],[f_11_2]) ).
fof(f_11_4,plain,
! [U_43,U_42] :
( ( ( U_42 = finite_subsets(U_43)
| ? [U_47] :
( ~ in(U_47,U_42)
& finite(U_47)
& subset(U_47,U_43) )
| ( ( ~ finite(sK4(U_43,U_42))
| ~ subset(sK4(U_43,U_42),U_43) )
& in(sK4(U_43,U_42),U_42) ) )
& ( ( ! [U_45] :
( in(U_45,U_42)
| ~ finite(U_45)
| ~ subset(U_45,U_43) )
& ! [U_44] :
( ( finite(U_44)
& subset(U_44,U_43) )
| ~ in(U_44,U_42) ) )
| U_42 != finite_subsets(U_43) ) )
| ~ preboolean(U_42) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4]),skolemize(U_46,sK4(U_43,U_42))],[f_11_3]) ).
fof(f_11_5,plain,
! [U_43,U_42] :
( ( ( U_42 = finite_subsets(U_43)
| ( ~ in(sK5(U_43,U_42),U_42)
& finite(sK5(U_43,U_42))
& subset(sK5(U_43,U_42),U_43) )
| ( ( ~ finite(sK4(U_43,U_42))
| ~ subset(sK4(U_43,U_42),U_43) )
& in(sK4(U_43,U_42),U_42) ) )
& ( ( ! [U_45] :
( in(U_45,U_42)
| ~ finite(U_45)
| ~ subset(U_45,U_43) )
& ! [U_44] :
( ( finite(U_44)
& subset(U_44,U_43) )
| ~ in(U_44,U_42) ) )
| U_42 != finite_subsets(U_43) ) )
| ~ preboolean(U_42) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK5]),skolemize(U_47,sK5(U_43,U_42))],[f_11_4]) ).
fof(f_11_6,plain,
( ! [U_43,U_42] :
( ~ in(sK5(U_43,U_42),U_42)
| ~ sP10(U_43,U_42) )
& ! [U_43,U_42] :
( finite(sK5(U_43,U_42))
| ~ sP10(U_43,U_42) )
& ! [U_43,U_42] :
( subset(sK5(U_43,U_42),U_43)
| ~ sP10(U_43,U_42) )
& ! [U_43,U_42] :
( ~ finite(sK4(U_43,U_42))
| ~ subset(sK4(U_43,U_42),U_43)
| ~ sP9(U_43,U_42) )
& ! [U_43,U_42] :
( in(sK4(U_43,U_42),U_42)
| ~ sP9(U_43,U_42) )
& ! [U_43,U_44] :
( finite(U_44)
| ~ sP7(U_43,U_44) )
& ! [U_43,U_44] :
( subset(U_44,U_43)
| ~ sP7(U_43,U_44) )
& ! [U_43,U_42,U_44,U_45] :
( in(U_45,U_42)
| ~ finite(U_45)
| ~ subset(U_45,U_43)
| ~ sP8(U_43,U_42,U_44,U_45) )
& ! [U_43,U_42,U_44,U_45] :
( sP7(U_43,U_44)
| ~ in(U_44,U_42)
| ~ sP8(U_43,U_42,U_44,U_45) )
& ! [U_43,U_42,U_44,U_45] :
( U_42 = finite_subsets(U_43)
| sP10(U_43,U_42)
| sP9(U_43,U_42)
| ~ sP11(U_43,U_42,U_44,U_45) )
& ! [U_43,U_42,U_44,U_45] :
( sP8(U_43,U_42,U_44,U_45)
| U_42 != finite_subsets(U_43)
| ~ sP11(U_43,U_42,U_44,U_45) )
& ! [U_43,U_42,U_44,U_45] :
( sP11(U_43,U_42,U_44,U_45)
| ~ preboolean(U_42) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP7,sP8,sP9,sP10,sP11])],[f_11_5]) ).
cnf(f_11_7,plain,
( sP11(U_43,U_42,U_44,U_45)
| ~ preboolean(U_42) ),
inference(clausify,[status(thm)],[f_11_6]) ).
cnf(f_11_8,plain,
( sP8(U_43,U_42,U_44,U_45)
| U_42 != finite_subsets(U_43)
| ~ sP11(U_43,U_42,U_44,U_45) ),
inference(clausify,[status(thm)],[f_11_6]) ).
cnf(f_11_9,plain,
( U_42 = finite_subsets(U_43)
| sP10(U_43,U_42)
| sP9(U_43,U_42)
| ~ sP11(U_43,U_42,U_44,U_45) ),
inference(clausify,[status(thm)],[f_11_6]) ).
cnf(f_11_10,plain,
( sP7(U_43,U_44)
| ~ in(U_44,U_42)
| ~ sP8(U_43,U_42,U_44,U_45) ),
inference(clausify,[status(thm)],[f_11_6]) ).
cnf(f_11_11,plain,
( in(U_45,U_42)
| ~ finite(U_45)
| ~ subset(U_45,U_43)
| ~ sP8(U_43,U_42,U_44,U_45) ),
inference(clausify,[status(thm)],[f_11_6]) ).
cnf(f_11_12,plain,
( subset(U_44,U_43)
| ~ sP7(U_43,U_44) ),
inference(clausify,[status(thm)],[f_11_6]) ).
cnf(f_11_13,plain,
( finite(U_44)
| ~ sP7(U_43,U_44) ),
inference(clausify,[status(thm)],[f_11_6]) ).
cnf(f_11_14,plain,
( in(sK4(U_43,U_42),U_42)
| ~ sP9(U_43,U_42) ),
inference(clausify,[status(thm)],[f_11_6]) ).
cnf(f_11_15,plain,
( ~ finite(sK4(U_43,U_42))
| ~ subset(sK4(U_43,U_42),U_43)
| ~ sP9(U_43,U_42) ),
inference(clausify,[status(thm)],[f_11_6]) ).
cnf(f_11_16,plain,
( subset(sK5(U_43,U_42),U_43)
| ~ sP10(U_43,U_42) ),
inference(clausify,[status(thm)],[f_11_6]) ).
cnf(f_11_17,plain,
( finite(sK5(U_43,U_42))
| ~ sP10(U_43,U_42) ),
inference(clausify,[status(thm)],[f_11_6]) ).
cnf(f_11_18,plain,
( ~ in(sK5(U_43,U_42),U_42)
| ~ sP10(U_43,U_42) ),
inference(clausify,[status(thm)],[f_11_6]) ).
fof(f_12_1,plain,
! [A] : preboolean(finite_subsets(A)),
inference(fof_nnf,[status(thm)],[dt_k5_finsub_1]) ).
fof(f_12_2,plain,
! [U_48] : preboolean(finite_subsets(U_48)),
inference(variable_rename,[status(thm)],[f_12_1]) ).
fof(f_12_3,plain,
! [U_48] : preboolean(finite_subsets(U_48)),
inference(definitional_conversion,[status(esa)],[f_12_2]) ).
cnf(f_12_4,plain,
preboolean(finite_subsets(U_48)),
inference(clausify,[status(thm)],[f_12_3]) ).
fof(f_13_1,plain,
! [A] :
? [B] : element(B,A),
inference(fof_nnf,[status(thm)],[existence_m1_subset_1]) ).
fof(f_13_2,plain,
! [U_50] :
? [U_49] : element(U_49,U_50),
inference(variable_rename,[status(thm)],[f_13_1]) ).
fof(f_13_3,plain,
! [U_50] : element(sK6(U_50),U_50),
inference(skolemize,[status(esa),new_symbols(skolem,[sK6]),skolemize(U_49,sK6(U_50))],[f_13_2]) ).
fof(f_13_4,plain,
! [U_50] : element(sK6(U_50),U_50),
inference(definitional_conversion,[status(esa)],[f_13_3]) ).
cnf(f_13_5,plain,
element(sK6(U_50),U_50),
inference(clausify,[status(thm)],[f_13_4]) ).
fof(f_14_1,plain,
! [A,B] :
( finite(set_intersection2(A,B))
| ~ finite(B) ),
inference(fof_nnf,[status(thm)],[fc10_finset_1]) ).
fof(f_14_2,plain,
! [U_52,U_51] :
( finite(set_intersection2(U_52,U_51))
| ~ finite(U_51) ),
inference(variable_rename,[status(thm)],[f_14_1]) ).
fof(f_14_3,plain,
! [U_51,U_52] :
( finite(set_intersection2(U_52,U_51))
| ~ finite(U_51) ),
inference(definitional_conversion,[status(esa)],[f_14_2]) ).
cnf(f_14_4,plain,
( finite(set_intersection2(U_52,U_51))
| ~ finite(U_51) ),
inference(clausify,[status(thm)],[f_14_3]) ).
fof(f_15_1,plain,
! [A,B] :
( finite(set_intersection2(A,B))
| ~ finite(A) ),
inference(fof_nnf,[status(thm)],[fc11_finset_1]) ).
fof(f_15_2,plain,
! [U_54,U_53] :
( finite(set_intersection2(U_54,U_53))
| ~ finite(U_54) ),
inference(variable_rename,[status(thm)],[f_15_1]) ).
fof(f_15_3,plain,
! [U_54] :
( ! [U_53] : finite(set_intersection2(U_54,U_53))
| ~ finite(U_54) ),
inference(miniscope,[status(thm)],[f_15_2]) ).
fof(f_15_4,plain,
! [U_54,U_53] :
( finite(set_intersection2(U_54,U_53))
| ~ finite(U_54) ),
inference(definitional_conversion,[status(esa)],[f_15_3]) ).
cnf(f_15_5,plain,
( finite(set_intersection2(U_54,U_53))
| ~ finite(U_54) ),
inference(clausify,[status(thm)],[f_15_4]) ).
fof(f_16_1,plain,
! [A] :
( preboolean(powerset(A))
& diff_closed(powerset(A))
& cup_closed(powerset(A))
& ~ empty(powerset(A)) ),
inference(fof_nnf,[status(thm)],[fc1_finsub_1]) ).
fof(f_16_2,plain,
! [U_55] :
( preboolean(powerset(U_55))
& diff_closed(powerset(U_55))
& cup_closed(powerset(U_55))
& ~ empty(powerset(U_55)) ),
inference(variable_rename,[status(thm)],[f_16_1]) ).
fof(f_16_3,plain,
( ! [U_59] : preboolean(powerset(U_59))
& ! [U_58] : diff_closed(powerset(U_58))
& ! [U_57] : cup_closed(powerset(U_57))
& ! [U_56] : ~ empty(powerset(U_56)) ),
inference(miniscope,[status(thm)],[f_16_2]) ).
fof(f_16_4,plain,
( ! [U_59] : preboolean(powerset(U_59))
& ! [U_58] : diff_closed(powerset(U_58))
& ! [U_57] : cup_closed(powerset(U_57))
& ! [U_56] : ~ empty(powerset(U_56)) ),
inference(definitional_conversion,[status(esa)],[f_16_3]) ).
cnf(f_16_5,plain,
~ empty(powerset(U_56)),
inference(clausify,[status(thm)],[f_16_4]) ).
cnf(f_16_6,plain,
cup_closed(powerset(U_57)),
inference(clausify,[status(thm)],[f_16_4]) ).
cnf(f_16_7,plain,
diff_closed(powerset(U_58)),
inference(clausify,[status(thm)],[f_16_4]) ).
cnf(f_16_8,plain,
preboolean(powerset(U_59)),
inference(clausify,[status(thm)],[f_16_4]) ).
fof(f_17_1,plain,
! [A] : ~ empty(powerset(A)),
inference(fof_nnf,[status(thm)],[fc1_subset_1]) ).
fof(f_17_2,plain,
! [U_60] : ~ empty(powerset(U_60)),
inference(variable_rename,[status(thm)],[f_17_1]) ).
fof(f_17_3,plain,
! [U_60] : ~ empty(powerset(U_60)),
inference(definitional_conversion,[status(esa)],[f_17_2]) ).
cnf(f_17_4,plain,
~ empty(powerset(U_60)),
inference(clausify,[status(thm)],[f_17_3]) ).
fof(f_18_1,plain,
empty(empty_set),
inference(fof_nnf,[status(thm)],[fc1_xboole_0]) ).
fof(f_18_2,plain,
empty(empty_set),
inference(definitional_conversion,[status(esa)],[f_18_1]) ).
cnf(f_18_3,plain,
empty(empty_set),
inference(clausify,[status(thm)],[f_18_2]) ).
fof(f_19_1,plain,
! [A] :
( preboolean(finite_subsets(A))
& diff_closed(finite_subsets(A))
& cup_closed(finite_subsets(A))
& ~ empty(finite_subsets(A)) ),
inference(fof_nnf,[status(thm)],[fc2_finsub_1]) ).
fof(f_19_2,plain,
! [U_61] :
( preboolean(finite_subsets(U_61))
& diff_closed(finite_subsets(U_61))
& cup_closed(finite_subsets(U_61))
& ~ empty(finite_subsets(U_61)) ),
inference(variable_rename,[status(thm)],[f_19_1]) ).
fof(f_19_3,plain,
( ! [U_65] : preboolean(finite_subsets(U_65))
& ! [U_64] : diff_closed(finite_subsets(U_64))
& ! [U_63] : cup_closed(finite_subsets(U_63))
& ! [U_62] : ~ empty(finite_subsets(U_62)) ),
inference(miniscope,[status(thm)],[f_19_2]) ).
fof(f_19_4,plain,
( ! [U_65] : preboolean(finite_subsets(U_65))
& ! [U_64] : diff_closed(finite_subsets(U_64))
& ! [U_63] : cup_closed(finite_subsets(U_63))
& ! [U_62] : ~ empty(finite_subsets(U_62)) ),
inference(definitional_conversion,[status(esa)],[f_19_3]) ).
cnf(f_19_5,plain,
~ empty(finite_subsets(U_62)),
inference(clausify,[status(thm)],[f_19_4]) ).
cnf(f_19_6,plain,
cup_closed(finite_subsets(U_63)),
inference(clausify,[status(thm)],[f_19_4]) ).
cnf(f_19_7,plain,
diff_closed(finite_subsets(U_64)),
inference(clausify,[status(thm)],[f_19_4]) ).
cnf(f_19_8,plain,
preboolean(finite_subsets(U_65)),
inference(clausify,[status(thm)],[f_19_4]) ).
fof(f_20_1,plain,
! [A,B] : set_intersection2(A,A) = A,
inference(fof_nnf,[status(thm)],[idempotence_k3_xboole_0]) ).
fof(f_20_2,plain,
! [U_67,U_66] : set_intersection2(U_67,U_67) = U_67,
inference(variable_rename,[status(thm)],[f_20_1]) ).
fof(f_20_3,plain,
! [U_67] : set_intersection2(U_67,U_67) = U_67,
inference(miniscope,[status(thm)],[f_20_2]) ).
fof(f_20_4,plain,
! [U_67] : set_intersection2(U_67,U_67) = U_67,
inference(definitional_conversion,[status(esa)],[f_20_3]) ).
cnf(f_20_5,plain,
set_intersection2(U_67,U_67) = U_67,
inference(clausify,[status(thm)],[f_20_4]) ).
fof(f_21_1,plain,
? [A] :
( finite(A)
& ~ empty(A) ),
inference(fof_nnf,[status(thm)],[rc1_finset_1]) ).
fof(f_21_2,plain,
? [U_68] :
( finite(U_68)
& ~ empty(U_68) ),
inference(variable_rename,[status(thm)],[f_21_1]) ).
fof(f_21_3,plain,
( finite(sK7)
& ~ empty(sK7) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK7]),skolemize(U_68,sK7)],[f_21_2]) ).
fof(f_21_4,plain,
( finite(sK7)
& ~ empty(sK7) ),
inference(definitional_conversion,[status(esa)],[f_21_3]) ).
cnf(f_21_5,plain,
~ empty(sK7),
inference(clausify,[status(thm)],[f_21_4]) ).
cnf(f_21_6,plain,
finite(sK7),
inference(clausify,[status(thm)],[f_21_4]) ).
fof(f_22_1,plain,
? [A] :
( preboolean(A)
& diff_closed(A)
& cap_closed(A)
& cup_closed(A)
& ~ empty(A) ),
inference(fof_nnf,[status(thm)],[rc1_finsub_1]) ).
fof(f_22_2,plain,
? [U_69] :
( preboolean(U_69)
& diff_closed(U_69)
& cap_closed(U_69)
& cup_closed(U_69)
& ~ empty(U_69) ),
inference(variable_rename,[status(thm)],[f_22_1]) ).
fof(f_22_3,plain,
( preboolean(sK8)
& diff_closed(sK8)
& cap_closed(sK8)
& cup_closed(sK8)
& ~ empty(sK8) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK8]),skolemize(U_69,sK8)],[f_22_2]) ).
fof(f_22_4,plain,
( preboolean(sK8)
& diff_closed(sK8)
& cap_closed(sK8)
& cup_closed(sK8)
& ~ empty(sK8) ),
inference(definitional_conversion,[status(esa)],[f_22_3]) ).
cnf(f_22_5,plain,
~ empty(sK8),
inference(clausify,[status(thm)],[f_22_4]) ).
cnf(f_22_6,plain,
cup_closed(sK8),
inference(clausify,[status(thm)],[f_22_4]) ).
cnf(f_22_7,plain,
cap_closed(sK8),
inference(clausify,[status(thm)],[f_22_4]) ).
cnf(f_22_8,plain,
diff_closed(sK8),
inference(clausify,[status(thm)],[f_22_4]) ).
cnf(f_22_9,plain,
preboolean(sK8),
inference(clausify,[status(thm)],[f_22_4]) ).
fof(f_23_1,plain,
! [A] :
( ? [B] :
( ~ empty(B)
& element(B,powerset(A)) )
| empty(A) ),
inference(fof_nnf,[status(thm)],[rc1_subset_1]) ).
fof(f_23_2,plain,
! [U_71] :
( ? [U_70] :
( ~ empty(U_70)
& element(U_70,powerset(U_71)) )
| empty(U_71) ),
inference(variable_rename,[status(thm)],[f_23_1]) ).
fof(f_23_3,plain,
! [U_71] :
( ( ~ empty(sK9(U_71))
& element(sK9(U_71),powerset(U_71)) )
| empty(U_71) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK9]),skolemize(U_70,sK9(U_71))],[f_23_2]) ).
fof(f_23_4,plain,
( ! [U_71] :
( ~ empty(sK9(U_71))
| ~ sP12(U_71) )
& ! [U_71] :
( element(sK9(U_71),powerset(U_71))
| ~ sP12(U_71) )
& ! [U_71] :
( sP12(U_71)
| empty(U_71) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP12])],[f_23_3]) ).
cnf(f_23_5,plain,
( sP12(U_71)
| empty(U_71) ),
inference(clausify,[status(thm)],[f_23_4]) ).
cnf(f_23_6,plain,
( element(sK9(U_71),powerset(U_71))
| ~ sP12(U_71) ),
inference(clausify,[status(thm)],[f_23_4]) ).
cnf(f_23_7,plain,
( ~ empty(sK9(U_71))
| ~ sP12(U_71) ),
inference(clausify,[status(thm)],[f_23_4]) ).
fof(f_24_1,plain,
? [A] : empty(A),
inference(fof_nnf,[status(thm)],[rc1_xboole_0]) ).
fof(f_24_2,plain,
? [U_72] : empty(U_72),
inference(variable_rename,[status(thm)],[f_24_1]) ).
fof(f_24_3,plain,
empty(sK10),
inference(skolemize,[status(esa),new_symbols(skolem,[sK10]),skolemize(U_72,sK10)],[f_24_2]) ).
fof(f_24_4,plain,
empty(sK10),
inference(definitional_conversion,[status(esa)],[f_24_3]) ).
cnf(f_24_5,plain,
empty(sK10),
inference(clausify,[status(thm)],[f_24_4]) ).
fof(f_25_1,plain,
! [A] :
? [B] :
( finite(B)
& natural(B)
& ordinal(B)
& epsilon_connected(B)
& epsilon_transitive(B)
& one_to_one(B)
& function(B)
& relation(B)
& empty(B)
& element(B,powerset(A)) ),
inference(fof_nnf,[status(thm)],[rc2_finset_1]) ).
fof(f_25_2,plain,
! [U_74] :
? [U_73] :
( finite(U_73)
& natural(U_73)
& ordinal(U_73)
& epsilon_connected(U_73)
& epsilon_transitive(U_73)
& one_to_one(U_73)
& function(U_73)
& relation(U_73)
& empty(U_73)
& element(U_73,powerset(U_74)) ),
inference(variable_rename,[status(thm)],[f_25_1]) ).
fof(f_25_3,plain,
! [U_74] :
( finite(sK11(U_74))
& natural(sK11(U_74))
& ordinal(sK11(U_74))
& epsilon_connected(sK11(U_74))
& epsilon_transitive(sK11(U_74))
& one_to_one(sK11(U_74))
& function(sK11(U_74))
& relation(sK11(U_74))
& empty(sK11(U_74))
& element(sK11(U_74),powerset(U_74)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK11]),skolemize(U_73,sK11(U_74))],[f_25_2]) ).
fof(f_25_4,plain,
( ! [U_74] : finite(sK11(U_74))
& ! [U_74] : natural(sK11(U_74))
& ! [U_74] : ordinal(sK11(U_74))
& ! [U_74] : epsilon_connected(sK11(U_74))
& ! [U_74] : epsilon_transitive(sK11(U_74))
& ! [U_74] : one_to_one(sK11(U_74))
& ! [U_74] : function(sK11(U_74))
& ! [U_74] : relation(sK11(U_74))
& ! [U_74] : empty(sK11(U_74))
& ! [U_74] : element(sK11(U_74),powerset(U_74)) ),
inference(definitional_conversion,[status(esa)],[f_25_3]) ).
cnf(f_25_5,plain,
element(sK11(U_74),powerset(U_74)),
inference(clausify,[status(thm)],[f_25_4]) ).
cnf(f_25_6,plain,
empty(sK11(U_74)),
inference(clausify,[status(thm)],[f_25_4]) ).
cnf(f_25_7,plain,
relation(sK11(U_74)),
inference(clausify,[status(thm)],[f_25_4]) ).
cnf(f_25_8,plain,
function(sK11(U_74)),
inference(clausify,[status(thm)],[f_25_4]) ).
cnf(f_25_9,plain,
one_to_one(sK11(U_74)),
inference(clausify,[status(thm)],[f_25_4]) ).
cnf(f_25_10,plain,
epsilon_transitive(sK11(U_74)),
inference(clausify,[status(thm)],[f_25_4]) ).
cnf(f_25_11,plain,
epsilon_connected(sK11(U_74)),
inference(clausify,[status(thm)],[f_25_4]) ).
cnf(f_25_12,plain,
ordinal(sK11(U_74)),
inference(clausify,[status(thm)],[f_25_4]) ).
cnf(f_25_13,plain,
natural(sK11(U_74)),
inference(clausify,[status(thm)],[f_25_4]) ).
cnf(f_25_14,plain,
finite(sK11(U_74)),
inference(clausify,[status(thm)],[f_25_4]) ).
fof(f_26_1,plain,
! [A] :
? [B] :
( empty(B)
& element(B,powerset(A)) ),
inference(fof_nnf,[status(thm)],[rc2_subset_1]) ).
fof(f_26_2,plain,
! [U_76] :
? [U_75] :
( empty(U_75)
& element(U_75,powerset(U_76)) ),
inference(variable_rename,[status(thm)],[f_26_1]) ).
fof(f_26_3,plain,
! [U_76] :
( empty(sK12(U_76))
& element(sK12(U_76),powerset(U_76)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK12]),skolemize(U_75,sK12(U_76))],[f_26_2]) ).
fof(f_26_4,plain,
( ! [U_76] : empty(sK12(U_76))
& ! [U_76] : element(sK12(U_76),powerset(U_76)) ),
inference(definitional_conversion,[status(esa)],[f_26_3]) ).
cnf(f_26_5,plain,
element(sK12(U_76),powerset(U_76)),
inference(clausify,[status(thm)],[f_26_4]) ).
cnf(f_26_6,plain,
empty(sK12(U_76)),
inference(clausify,[status(thm)],[f_26_4]) ).
fof(f_27_1,plain,
? [A] : ~ empty(A),
inference(fof_nnf,[status(thm)],[rc2_xboole_0]) ).
fof(f_27_2,plain,
? [U_77] : ~ empty(U_77),
inference(variable_rename,[status(thm)],[f_27_1]) ).
fof(f_27_3,plain,
~ empty(sK13),
inference(skolemize,[status(esa),new_symbols(skolem,[sK13]),skolemize(U_77,sK13)],[f_27_2]) ).
fof(f_27_4,plain,
~ empty(sK13),
inference(definitional_conversion,[status(esa)],[f_27_3]) ).
cnf(f_27_5,plain,
~ empty(sK13),
inference(clausify,[status(thm)],[f_27_4]) ).
fof(f_28_1,plain,
! [A] :
( ? [B] :
( finite(B)
& ~ empty(B)
& element(B,powerset(A)) )
| empty(A) ),
inference(fof_nnf,[status(thm)],[rc3_finset_1]) ).
fof(f_28_2,plain,
! [U_79] :
( ? [U_78] :
( finite(U_78)
& ~ empty(U_78)
& element(U_78,powerset(U_79)) )
| empty(U_79) ),
inference(variable_rename,[status(thm)],[f_28_1]) ).
fof(f_28_3,plain,
! [U_79] :
( ( finite(sK14(U_79))
& ~ empty(sK14(U_79))
& element(sK14(U_79),powerset(U_79)) )
| empty(U_79) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK14]),skolemize(U_78,sK14(U_79))],[f_28_2]) ).
fof(f_28_4,plain,
( ! [U_79] :
( finite(sK14(U_79))
| ~ sP13(U_79) )
& ! [U_79] :
( ~ empty(sK14(U_79))
| ~ sP13(U_79) )
& ! [U_79] :
( element(sK14(U_79),powerset(U_79))
| ~ sP13(U_79) )
& ! [U_79] :
( sP13(U_79)
| empty(U_79) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP13])],[f_28_3]) ).
cnf(f_28_5,plain,
( sP13(U_79)
| empty(U_79) ),
inference(clausify,[status(thm)],[f_28_4]) ).
cnf(f_28_6,plain,
( element(sK14(U_79),powerset(U_79))
| ~ sP13(U_79) ),
inference(clausify,[status(thm)],[f_28_4]) ).
cnf(f_28_7,plain,
( ~ empty(sK14(U_79))
| ~ sP13(U_79) ),
inference(clausify,[status(thm)],[f_28_4]) ).
cnf(f_28_8,plain,
( finite(sK14(U_79))
| ~ sP13(U_79) ),
inference(clausify,[status(thm)],[f_28_4]) ).
fof(f_29_1,plain,
! [A] :
( ? [B] :
( finite(B)
& ~ empty(B)
& element(B,powerset(A)) )
| empty(A) ),
inference(fof_nnf,[status(thm)],[rc4_finset_1]) ).
fof(f_29_2,plain,
! [U_81] :
( ? [U_80] :
( finite(U_80)
& ~ empty(U_80)
& element(U_80,powerset(U_81)) )
| empty(U_81) ),
inference(variable_rename,[status(thm)],[f_29_1]) ).
fof(f_29_3,plain,
! [U_81] :
( ( finite(sK15(U_81))
& ~ empty(sK15(U_81))
& element(sK15(U_81),powerset(U_81)) )
| empty(U_81) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK15]),skolemize(U_80,sK15(U_81))],[f_29_2]) ).
fof(f_29_4,plain,
( ! [U_81] :
( finite(sK15(U_81))
| ~ sP14(U_81) )
& ! [U_81] :
( ~ empty(sK15(U_81))
| ~ sP14(U_81) )
& ! [U_81] :
( element(sK15(U_81),powerset(U_81))
| ~ sP14(U_81) )
& ! [U_81] :
( sP14(U_81)
| empty(U_81) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP14])],[f_29_3]) ).
cnf(f_29_5,plain,
( sP14(U_81)
| empty(U_81) ),
inference(clausify,[status(thm)],[f_29_4]) ).
cnf(f_29_6,plain,
( element(sK15(U_81),powerset(U_81))
| ~ sP14(U_81) ),
inference(clausify,[status(thm)],[f_29_4]) ).
cnf(f_29_7,plain,
( ~ empty(sK15(U_81))
| ~ sP14(U_81) ),
inference(clausify,[status(thm)],[f_29_4]) ).
cnf(f_29_8,plain,
( finite(sK15(U_81))
| ~ sP14(U_81) ),
inference(clausify,[status(thm)],[f_29_4]) ).
fof(f_30_1,plain,
! [A,B] : subset(A,A),
inference(fof_nnf,[status(thm)],[reflexivity_r1_tarski]) ).
fof(f_30_2,plain,
! [U_83,U_82] : subset(U_83,U_83),
inference(variable_rename,[status(thm)],[f_30_1]) ).
fof(f_30_3,plain,
! [U_83] : subset(U_83,U_83),
inference(miniscope,[status(thm)],[f_30_2]) ).
fof(f_30_4,plain,
! [U_83] : subset(U_83,U_83),
inference(definitional_conversion,[status(esa)],[f_30_3]) ).
cnf(f_30_5,plain,
subset(U_83,U_83),
inference(clausify,[status(thm)],[f_30_4]) ).
fof(f_31_1,plain,
! [A,B] : subset(set_intersection2(A,B),A),
inference(fof_nnf,[status(thm)],[t17_xboole_1]) ).
fof(f_31_2,plain,
! [U_85,U_84] : subset(set_intersection2(U_85,U_84),U_85),
inference(variable_rename,[status(thm)],[f_31_1]) ).
fof(f_31_3,plain,
! [U_84,U_85] : subset(set_intersection2(U_85,U_84),U_85),
inference(definitional_conversion,[status(esa)],[f_31_2]) ).
cnf(f_31_4,plain,
subset(set_intersection2(U_85,U_84),U_85),
inference(clausify,[status(thm)],[f_31_3]) ).
fof(f_32_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_32_2,plain,
! [U_88,U_87,U_86] :
( subset(U_88,set_intersection2(U_87,U_86))
| ~ subset(U_88,U_86)
| ~ subset(U_88,U_87) ),
inference(variable_rename,[status(thm)],[f_32_1]) ).
fof(f_32_3,plain,
! [U_86,U_87,U_88] :
( subset(U_88,set_intersection2(U_87,U_86))
| ~ subset(U_88,U_86)
| ~ subset(U_88,U_87) ),
inference(definitional_conversion,[status(esa)],[f_32_2]) ).
cnf(f_32_4,plain,
( subset(U_88,set_intersection2(U_87,U_86))
| ~ subset(U_88,U_86)
| ~ subset(U_88,U_87) ),
inference(clausify,[status(thm)],[f_32_3]) ).
fof(f_33_1,plain,
! [A,B] :
( element(A,B)
| ~ in(A,B) ),
inference(fof_nnf,[status(thm)],[t1_subset]) ).
fof(f_33_2,plain,
! [U_90,U_89] :
( element(U_90,U_89)
| ~ in(U_90,U_89) ),
inference(variable_rename,[status(thm)],[f_33_1]) ).
fof(f_33_3,plain,
! [U_89,U_90] :
( element(U_90,U_89)
| ~ in(U_90,U_89) ),
inference(definitional_conversion,[status(esa)],[f_33_2]) ).
cnf(f_33_4,plain,
( element(U_90,U_89)
| ~ in(U_90,U_89) ),
inference(clausify,[status(thm)],[f_33_3]) ).
fof(f_34_1,plain,
! [A,B] :
( subset(finite_subsets(A),finite_subsets(B))
| ~ subset(A,B) ),
inference(fof_nnf,[status(thm)],[t23_finsub_1]) ).
fof(f_34_2,plain,
! [U_92,U_91] :
( subset(finite_subsets(U_92),finite_subsets(U_91))
| ~ subset(U_92,U_91) ),
inference(variable_rename,[status(thm)],[f_34_1]) ).
fof(f_34_3,plain,
! [U_91,U_92] :
( subset(finite_subsets(U_92),finite_subsets(U_91))
| ~ subset(U_92,U_91) ),
inference(definitional_conversion,[status(esa)],[f_34_2]) ).
cnf(f_34_4,plain,
( subset(finite_subsets(U_92),finite_subsets(U_91))
| ~ subset(U_92,U_91) ),
inference(clausify,[status(thm)],[f_34_3]) ).
fof(f_35_1,negated_conjecture,
~ ! [A,B] : finite_subsets(set_intersection2(A,B)) = set_intersection2(finite_subsets(A),finite_subsets(B)),
inference(negate,[status(cth)],[t24_finsub_1]) ).
fof(f_35_2,negated_conjecture,
? [A,B] : finite_subsets(set_intersection2(A,B)) != set_intersection2(finite_subsets(A),finite_subsets(B)),
inference(fof_nnf,[status(thm)],[f_35_1]) ).
fof(f_35_3,negated_conjecture,
? [U_94,U_93] : finite_subsets(set_intersection2(U_94,U_93)) != set_intersection2(finite_subsets(U_94),finite_subsets(U_93)),
inference(variable_rename,[status(thm)],[f_35_2]) ).
fof(f_35_4,negated_conjecture,
? [U_93] : finite_subsets(set_intersection2(sK16,U_93)) != set_intersection2(finite_subsets(sK16),finite_subsets(U_93)),
inference(skolemize,[status(esa),new_symbols(skolem,[sK16]),skolemize(U_94,sK16)],[f_35_3]) ).
fof(f_35_5,negated_conjecture,
finite_subsets(set_intersection2(sK16,sK17)) != set_intersection2(finite_subsets(sK16),finite_subsets(sK17)),
inference(skolemize,[status(esa),new_symbols(skolem,[sK17]),skolemize(U_93,sK17)],[f_35_4]) ).
fof(f_35_6,negated_conjecture,
finite_subsets(set_intersection2(sK16,sK17)) != set_intersection2(finite_subsets(sK16),finite_subsets(sK17)),
inference(definitional_conversion,[status(esa)],[f_35_5]) ).
cnf(f_35_7,negated_conjecture,
finite_subsets(set_intersection2(sK16,sK17)) != set_intersection2(finite_subsets(sK16),finite_subsets(sK17)),
inference(clausify,[status(thm)],[f_35_6]) ).
fof(f_36_1,plain,
! [A] : set_intersection2(A,empty_set) = empty_set,
inference(fof_nnf,[status(thm)],[t2_boole]) ).
fof(f_36_2,plain,
! [U_95] : set_intersection2(U_95,empty_set) = empty_set,
inference(variable_rename,[status(thm)],[f_36_1]) ).
fof(f_36_3,plain,
! [U_95] : set_intersection2(U_95,empty_set) = empty_set,
inference(definitional_conversion,[status(esa)],[f_36_2]) ).
cnf(f_36_4,plain,
set_intersection2(U_95,empty_set) = empty_set,
inference(clausify,[status(thm)],[f_36_3]) ).
fof(f_37_1,plain,
! [A,B] :
( in(A,B)
| empty(B)
| ~ element(A,B) ),
inference(fof_nnf,[status(thm)],[t2_subset]) ).
fof(f_37_2,plain,
! [U_97,U_96] :
( in(U_97,U_96)
| empty(U_96)
| ~ element(U_97,U_96) ),
inference(variable_rename,[status(thm)],[f_37_1]) ).
fof(f_37_3,plain,
! [U_97,U_96] :
( in(U_97,U_96)
| empty(U_96)
| ~ element(U_97,U_96) ),
inference(definitional_conversion,[status(esa)],[f_37_2]) ).
cnf(f_37_4,plain,
( in(U_97,U_96)
| empty(U_96)
| ~ element(U_97,U_96) ),
inference(clausify,[status(thm)],[f_37_3]) ).
fof(f_38_1,plain,
! [A,B] :
( ( element(A,powerset(B))
| ~ subset(A,B) )
& ( subset(A,B)
| ~ element(A,powerset(B)) ) ),
inference(fof_nnf,[status(thm)],[t3_subset]) ).
fof(f_38_2,plain,
! [U_99,U_98] :
( ( element(U_99,powerset(U_98))
| ~ subset(U_99,U_98) )
& ( subset(U_99,U_98)
| ~ element(U_99,powerset(U_98)) ) ),
inference(variable_rename,[status(thm)],[f_38_1]) ).
fof(f_38_3,plain,
( ! [U_103,U_101] :
( element(U_103,powerset(U_101))
| ~ subset(U_103,U_101) )
& ! [U_102,U_100] :
( subset(U_102,U_100)
| ~ element(U_102,powerset(U_100)) ) ),
inference(miniscope,[status(thm)],[f_38_2]) ).
fof(f_38_4,plain,
( ! [U_103,U_101] :
( element(U_103,powerset(U_101))
| ~ subset(U_103,U_101) )
& ! [U_102,U_100] :
( subset(U_102,U_100)
| ~ element(U_102,powerset(U_100)) ) ),
inference(definitional_conversion,[status(esa)],[f_38_3]) ).
cnf(f_38_5,plain,
( subset(U_102,U_100)
| ~ element(U_102,powerset(U_100)) ),
inference(clausify,[status(thm)],[f_38_4]) ).
cnf(f_38_6,plain,
( element(U_103,powerset(U_101))
| ~ subset(U_103,U_101) ),
inference(clausify,[status(thm)],[f_38_4]) ).
fof(f_39_1,plain,
! [A,B,C] :
( element(A,C)
| ~ element(B,powerset(C))
| ~ in(A,B) ),
inference(fof_nnf,[status(thm)],[t4_subset]) ).
fof(f_39_2,plain,
! [U_106,U_105,U_104] :
( element(U_106,U_104)
| ~ element(U_105,powerset(U_104))
| ~ in(U_106,U_105) ),
inference(variable_rename,[status(thm)],[f_39_1]) ).
fof(f_39_3,plain,
! [U_105,U_104,U_106] :
( element(U_106,U_104)
| ~ element(U_105,powerset(U_104))
| ~ in(U_106,U_105) ),
inference(definitional_conversion,[status(esa)],[f_39_2]) ).
cnf(f_39_4,plain,
( element(U_106,U_104)
| ~ element(U_105,powerset(U_104))
| ~ in(U_106,U_105) ),
inference(clausify,[status(thm)],[f_39_3]) ).
fof(f_40_1,plain,
! [A,B,C] :
( ~ empty(C)
| ~ element(B,powerset(C))
| ~ in(A,B) ),
inference(fof_nnf,[status(thm)],[t5_subset]) ).
fof(f_40_2,plain,
! [U_109,U_108,U_107] :
( ~ empty(U_107)
| ~ element(U_108,powerset(U_107))
| ~ in(U_109,U_108) ),
inference(variable_rename,[status(thm)],[f_40_1]) ).
fof(f_40_3,plain,
! [U_109,U_108] :
( ! [U_107] :
( ~ empty(U_107)
| ~ element(U_108,powerset(U_107)) )
| ~ in(U_109,U_108) ),
inference(miniscope,[status(thm)],[f_40_2]) ).
fof(f_40_4,plain,
! [U_109,U_107,U_108] :
( ~ empty(U_107)
| ~ element(U_108,powerset(U_107))
| ~ in(U_109,U_108) ),
inference(definitional_conversion,[status(esa)],[f_40_3]) ).
cnf(f_40_5,plain,
( ~ empty(U_107)
| ~ element(U_108,powerset(U_107))
| ~ in(U_109,U_108) ),
inference(clausify,[status(thm)],[f_40_4]) ).
fof(f_41_1,plain,
! [A] :
( A = empty_set
| ~ empty(A) ),
inference(fof_nnf,[status(thm)],[t6_boole]) ).
fof(f_41_2,plain,
! [U_110] :
( U_110 = empty_set
| ~ empty(U_110) ),
inference(variable_rename,[status(thm)],[f_41_1]) ).
fof(f_41_3,plain,
! [U_110] :
( U_110 = empty_set
| ~ empty(U_110) ),
inference(definitional_conversion,[status(esa)],[f_41_2]) ).
cnf(f_41_4,plain,
( U_110 = empty_set
| ~ empty(U_110) ),
inference(clausify,[status(thm)],[f_41_3]) ).
fof(f_42_1,plain,
! [A,B] :
( ~ empty(B)
| ~ in(A,B) ),
inference(fof_nnf,[status(thm)],[t7_boole]) ).
fof(f_42_2,plain,
! [U_112,U_111] :
( ~ empty(U_111)
| ~ in(U_112,U_111) ),
inference(variable_rename,[status(thm)],[f_42_1]) ).
fof(f_42_3,plain,
! [U_111,U_112] :
( ~ empty(U_111)
| ~ in(U_112,U_111) ),
inference(definitional_conversion,[status(esa)],[f_42_2]) ).
cnf(f_42_4,plain,
( ~ empty(U_111)
| ~ in(U_112,U_111) ),
inference(clausify,[status(thm)],[f_42_3]) ).
fof(f_43_1,plain,
! [A,B] :
( ~ empty(B)
| A = B
| ~ empty(A) ),
inference(fof_nnf,[status(thm)],[t8_boole]) ).
fof(f_43_2,plain,
! [U_114,U_113] :
( ~ empty(U_113)
| U_114 = U_113
| ~ empty(U_114) ),
inference(variable_rename,[status(thm)],[f_43_1]) ).
fof(f_43_3,plain,
! [U_114] :
( ! [U_113] :
( ~ empty(U_113)
| U_114 = U_113 )
| ~ empty(U_114) ),
inference(miniscope,[status(thm)],[f_43_2]) ).
fof(f_43_4,plain,
! [U_113,U_114] :
( ~ empty(U_113)
| U_114 = U_113
| ~ empty(U_114) ),
inference(definitional_conversion,[status(esa)],[f_43_3]) ).
cnf(f_43_5,plain,
( ~ empty(U_113)
| U_114 = U_113
| ~ empty(U_114) ),
inference(clausify,[status(thm)],[f_43_4]) ).
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,
( powerset(Eq_x_0) = powerset(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_5,axiom,
( finite_subsets(Eq_x_0) = finite_subsets(Eq_y_0)
| 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,
( 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_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) = sK5(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_12,axiom,
( sK6(Eq_x_0) = sK6(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_13,axiom,
( sK9(Eq_x_0) = sK9(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_14,axiom,
( sK11(Eq_x_0) = sK11(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_15,axiom,
( sK12(Eq_x_0) = sK12(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_16,axiom,
( sK14(Eq_x_0) = sK14(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_17,axiom,
( sK15(Eq_x_0) = sK15(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_18,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_19,axiom,
( empty(Eq_y_0)
| ~ empty(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_20,axiom,
( finite(Eq_y_0)
| ~ finite(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_21,axiom,
( preboolean(Eq_y_0)
| ~ preboolean(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_22,axiom,
( cup_closed(Eq_y_0)
| ~ cup_closed(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_23,axiom,
( diff_closed(Eq_y_0)
| ~ diff_closed(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_24,axiom,
( element(Eq_y_0,Eq_y_1)
| ~ element(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_25,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_26,axiom,
( cap_closed(Eq_y_0)
| ~ cap_closed(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_27,axiom,
( relation(Eq_y_0)
| ~ relation(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_28,axiom,
( function(Eq_y_0)
| ~ function(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_29,axiom,
( one_to_one(Eq_y_0)
| ~ one_to_one(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_30,axiom,
( epsilon_transitive(Eq_y_0)
| ~ epsilon_transitive(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_31,axiom,
( epsilon_connected(Eq_y_0)
| ~ epsilon_connected(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_32,axiom,
( ordinal(Eq_y_0)
| ~ ordinal(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_33,axiom,
( natural(Eq_y_0)
| ~ natural(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_34,axiom,
( sP0(Eq_y_0)
| ~ sP0(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_35,axiom,
( sP1(Eq_y_0,Eq_y_1)
| ~ sP1(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_36,axiom,
( sP2(Eq_y_0,Eq_y_1)
| ~ sP2(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_37,axiom,
( sP3(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP3(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_38,axiom,
( sP4(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
| ~ sP4(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4)
| Eq_x_4 != Eq_y_4
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_39,axiom,
( sP5(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP5(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_40,axiom,
( sP6(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP6(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_41,axiom,
( sP7(Eq_y_0,Eq_y_1)
| ~ sP7(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_42,axiom,
( sP8(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| ~ sP8(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_43,axiom,
( sP9(Eq_y_0,Eq_y_1)
| ~ sP9(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_44,axiom,
( sP10(Eq_y_0,Eq_y_1)
| ~ sP10(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_45,axiom,
( sP11(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| ~ sP11(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_46,axiom,
( sP12(Eq_y_0)
| ~ sP12(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_47,axiom,
( sP13(Eq_y_0)
| ~ sP13(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_48,axiom,
( sP14(Eq_y_0)
| ~ sP14(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 : SEU111+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.03 This is a FOF_THM_RFO_SEQ problem
% 0.00/0.04 % Command : /export/starexec/sandbox2/solver/bin/connect++ --verbosity 1 --no-colour --tptp-proof --schedule default --timeout 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.36 % Computer : n008.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Sat Sep 19 23:20:38 UTC 2026
% 0.10/0.36 % CPUTime :
% 273.54/273.85 % SZS status Theorem for theBenchmark
% 273.54/273.85 % SZS output start Proof for theBenchmark
% See solution above
%------------------------------------------------------------------------------