%------------------------------------------------------------------------------
% File : ConnectPP---0.7.2
% Problem : SEU101+1 : TPTP v9.3.1. Released v3.2.0.
% 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 : n003.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 08:58:02 AM UTC 2026
% Result : Theorem 30.54s 35.85s
% Output : Proof 30.54s
% 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(commutativity_k2_xboole_0,axiom,
! [A,B] : set_union2(A,B) = set_union2(B,A),
file('theBenchmark.p',commutativity_k2_xboole_0) ).
fof(d1_finsub_1,axiom,
! [A] :
( cup_closed(A)
<=> ! [B,C] :
( ( in(C,A)
& in(B,A) )
=> in(set_union2(B,C),A) ) ),
file('theBenchmark.p',d1_finsub_1) ).
fof(d3_finsub_1,axiom,
! [A] :
( diff_closed(A)
<=> ! [B,C] :
( ( in(C,A)
& in(B,A) )
=> in(set_difference(B,C),A) ) ),
file('theBenchmark.p',d3_finsub_1) ).
fof(d4_finsub_1,axiom,
! [A] :
( preboolean(A)
<=> ( diff_closed(A)
& cup_closed(A) ) ),
file('theBenchmark.p',d4_finsub_1) ).
fof(existence_m1_subset_1,axiom,
! [A] :
? [B] : element(B,A),
file('theBenchmark.p',existence_m1_subset_1) ).
fof(fc12_finset_1,axiom,
! [A,B] :
( finite(A)
=> finite(set_difference(A,B)) ),
file('theBenchmark.p',fc12_finset_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_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(fc9_finset_1,axiom,
! [A,B] :
( ( finite(B)
& finite(A) )
=> finite(set_union2(A,B)) ),
file('theBenchmark.p',fc9_finset_1) ).
fof(idempotence_k2_xboole_0,axiom,
! [A,B] : set_union2(A,A) = A,
file('theBenchmark.p',idempotence_k2_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(t10_finsub_1,conjecture,
! [A] :
( preboolean(A)
<=> ! [B,C] :
( ( in(C,A)
& in(B,A) )
=> ( in(set_difference(B,C),A)
& in(set_union2(B,C),A) ) ) ),
file('theBenchmark.p',t10_finsub_1) ).
fof(t1_boole,axiom,
! [A] : set_union2(A,empty_set) = A,
file('theBenchmark.p',t1_boole) ).
fof(t1_subset,axiom,
! [A,B] :
( in(A,B)
=> element(A,B) ),
file('theBenchmark.p',t1_subset) ).
fof(t2_subset,axiom,
! [A,B] :
( element(A,B)
=> ( in(A,B)
| empty(B) ) ),
file('theBenchmark.p',t2_subset) ).
fof(t3_boole,axiom,
! [A] : set_difference(A,empty_set) = A,
file('theBenchmark.p',t3_boole) ).
fof(t3_subset,axiom,
! [A,B] :
( element(A,powerset(B))
<=> subset(A,B) ),
file('theBenchmark.p',t3_subset) ).
fof(t4_boole,axiom,
! [A] : set_difference(empty_set,A) = empty_set,
file('theBenchmark.p',t4_boole) ).
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] : set_union2(A,B) = set_union2(B,A),
inference(fof_nnf,[status(thm)],[commutativity_k2_xboole_0]) ).
fof(f_6_2,plain,
! [U_8,U_7] : set_union2(U_8,U_7) = set_union2(U_7,U_8),
inference(variable_rename,[status(thm)],[f_6_1]) ).
fof(f_6_3,plain,
! [U_8,U_7] : set_union2(U_8,U_7) = set_union2(U_7,U_8),
inference(definitional_conversion,[status(esa)],[f_6_2]) ).
cnf(f_6_4,plain,
set_union2(U_8,U_7) = set_union2(U_7,U_8),
inference(clausify,[status(thm)],[f_6_3]) ).
fof(f_7_1,plain,
! [A] :
( ( cup_closed(A)
| ? [B,C] :
( ~ in(set_union2(B,C),A)
& in(C,A)
& in(B,A) ) )
& ( ! [B,C] :
( in(set_union2(B,C),A)
| ~ in(C,A)
| ~ in(B,A) )
| ~ cup_closed(A) ) ),
inference(fof_nnf,[status(thm)],[d1_finsub_1]) ).
fof(f_7_2,plain,
! [U_13] :
( ( cup_closed(U_13)
| ? [U_12,U_11] :
( ~ in(set_union2(U_12,U_11),U_13)
& in(U_11,U_13)
& in(U_12,U_13) ) )
& ( ! [U_10,U_9] :
( in(set_union2(U_10,U_9),U_13)
| ~ in(U_9,U_13)
| ~ in(U_10,U_13) )
| ~ cup_closed(U_13) ) ),
inference(variable_rename,[status(thm)],[f_7_1]) ).
fof(f_7_3,plain,
( ! [U_15] :
( cup_closed(U_15)
| ? [U_12,U_11] :
( ~ in(set_union2(U_12,U_11),U_15)
& in(U_11,U_15)
& in(U_12,U_15) ) )
& ! [U_14] :
( ! [U_10,U_9] :
( in(set_union2(U_10,U_9),U_14)
| ~ in(U_9,U_14)
| ~ in(U_10,U_14) )
| ~ cup_closed(U_14) ) ),
inference(miniscope,[status(thm)],[f_7_2]) ).
fof(f_7_4,plain,
( ! [U_15] :
( cup_closed(U_15)
| ? [U_11] :
( ~ in(set_union2(sK1(U_15),U_11),U_15)
& in(U_11,U_15)
& in(sK1(U_15),U_15) ) )
& ! [U_14] :
( ! [U_10,U_9] :
( in(set_union2(U_10,U_9),U_14)
| ~ in(U_9,U_14)
| ~ in(U_10,U_14) )
| ~ cup_closed(U_14) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(U_12,sK1(U_15))],[f_7_3]) ).
fof(f_7_5,plain,
( ! [U_15] :
( cup_closed(U_15)
| ( ~ in(set_union2(sK1(U_15),sK2(U_15)),U_15)
& in(sK2(U_15),U_15)
& in(sK1(U_15),U_15) ) )
& ! [U_14] :
( ! [U_10,U_9] :
( in(set_union2(U_10,U_9),U_14)
| ~ in(U_9,U_14)
| ~ in(U_10,U_14) )
| ~ cup_closed(U_14) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2]),skolemize(U_11,sK2(U_15))],[f_7_4]) ).
fof(f_7_6,plain,
( ! [U_15] :
( ~ in(set_union2(sK1(U_15),sK2(U_15)),U_15)
| ~ sP1(U_15) )
& ! [U_15] :
( in(sK2(U_15),U_15)
| ~ sP1(U_15) )
& ! [U_15] :
( in(sK1(U_15),U_15)
| ~ sP1(U_15) )
& ! [U_15] :
( cup_closed(U_15)
| sP1(U_15) )
& ! [U_10,U_14,U_9] :
( in(set_union2(U_10,U_9),U_14)
| ~ in(U_9,U_14)
| ~ in(U_10,U_14)
| ~ cup_closed(U_14) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP1])],[f_7_5]) ).
cnf(f_7_7,plain,
( in(set_union2(U_10,U_9),U_14)
| ~ in(U_9,U_14)
| ~ in(U_10,U_14)
| ~ cup_closed(U_14) ),
inference(clausify,[status(thm)],[f_7_6]) ).
cnf(f_7_8,plain,
( cup_closed(U_15)
| sP1(U_15) ),
inference(clausify,[status(thm)],[f_7_6]) ).
cnf(f_7_9,plain,
( in(sK1(U_15),U_15)
| ~ sP1(U_15) ),
inference(clausify,[status(thm)],[f_7_6]) ).
cnf(f_7_10,plain,
( in(sK2(U_15),U_15)
| ~ sP1(U_15) ),
inference(clausify,[status(thm)],[f_7_6]) ).
cnf(f_7_11,plain,
( ~ in(set_union2(sK1(U_15),sK2(U_15)),U_15)
| ~ sP1(U_15) ),
inference(clausify,[status(thm)],[f_7_6]) ).
fof(f_8_1,plain,
! [A] :
( ( diff_closed(A)
| ? [B,C] :
( ~ in(set_difference(B,C),A)
& in(C,A)
& in(B,A) ) )
& ( ! [B,C] :
( in(set_difference(B,C),A)
| ~ in(C,A)
| ~ in(B,A) )
| ~ diff_closed(A) ) ),
inference(fof_nnf,[status(thm)],[d3_finsub_1]) ).
fof(f_8_2,plain,
! [U_20] :
( ( diff_closed(U_20)
| ? [U_19,U_18] :
( ~ in(set_difference(U_19,U_18),U_20)
& in(U_18,U_20)
& in(U_19,U_20) ) )
& ( ! [U_17,U_16] :
( in(set_difference(U_17,U_16),U_20)
| ~ in(U_16,U_20)
| ~ in(U_17,U_20) )
| ~ diff_closed(U_20) ) ),
inference(variable_rename,[status(thm)],[f_8_1]) ).
fof(f_8_3,plain,
( ! [U_22] :
( diff_closed(U_22)
| ? [U_19,U_18] :
( ~ in(set_difference(U_19,U_18),U_22)
& in(U_18,U_22)
& in(U_19,U_22) ) )
& ! [U_21] :
( ! [U_17,U_16] :
( in(set_difference(U_17,U_16),U_21)
| ~ in(U_16,U_21)
| ~ in(U_17,U_21) )
| ~ diff_closed(U_21) ) ),
inference(miniscope,[status(thm)],[f_8_2]) ).
fof(f_8_4,plain,
( ! [U_22] :
( diff_closed(U_22)
| ? [U_18] :
( ~ in(set_difference(sK3(U_22),U_18),U_22)
& in(U_18,U_22)
& in(sK3(U_22),U_22) ) )
& ! [U_21] :
( ! [U_17,U_16] :
( in(set_difference(U_17,U_16),U_21)
| ~ in(U_16,U_21)
| ~ in(U_17,U_21) )
| ~ diff_closed(U_21) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3]),skolemize(U_19,sK3(U_22))],[f_8_3]) ).
fof(f_8_5,plain,
( ! [U_22] :
( diff_closed(U_22)
| ( ~ in(set_difference(sK3(U_22),sK4(U_22)),U_22)
& in(sK4(U_22),U_22)
& in(sK3(U_22),U_22) ) )
& ! [U_21] :
( ! [U_17,U_16] :
( in(set_difference(U_17,U_16),U_21)
| ~ in(U_16,U_21)
| ~ in(U_17,U_21) )
| ~ diff_closed(U_21) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4]),skolemize(U_18,sK4(U_22))],[f_8_4]) ).
fof(f_8_6,plain,
( ! [U_22] :
( ~ in(set_difference(sK3(U_22),sK4(U_22)),U_22)
| ~ sP2(U_22) )
& ! [U_22] :
( in(sK4(U_22),U_22)
| ~ sP2(U_22) )
& ! [U_22] :
( in(sK3(U_22),U_22)
| ~ sP2(U_22) )
& ! [U_22] :
( diff_closed(U_22)
| sP2(U_22) )
& ! [U_17,U_16,U_21] :
( in(set_difference(U_17,U_16),U_21)
| ~ in(U_16,U_21)
| ~ in(U_17,U_21)
| ~ diff_closed(U_21) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP2])],[f_8_5]) ).
cnf(f_8_7,plain,
( in(set_difference(U_17,U_16),U_21)
| ~ in(U_16,U_21)
| ~ in(U_17,U_21)
| ~ diff_closed(U_21) ),
inference(clausify,[status(thm)],[f_8_6]) ).
cnf(f_8_8,plain,
( diff_closed(U_22)
| sP2(U_22) ),
inference(clausify,[status(thm)],[f_8_6]) ).
cnf(f_8_9,plain,
( in(sK3(U_22),U_22)
| ~ sP2(U_22) ),
inference(clausify,[status(thm)],[f_8_6]) ).
cnf(f_8_10,plain,
( in(sK4(U_22),U_22)
| ~ sP2(U_22) ),
inference(clausify,[status(thm)],[f_8_6]) ).
cnf(f_8_11,plain,
( ~ in(set_difference(sK3(U_22),sK4(U_22)),U_22)
| ~ sP2(U_22) ),
inference(clausify,[status(thm)],[f_8_6]) ).
fof(f_9_1,plain,
! [A] :
( ( preboolean(A)
| ~ diff_closed(A)
| ~ cup_closed(A) )
& ( ( diff_closed(A)
& cup_closed(A) )
| ~ preboolean(A) ) ),
inference(fof_nnf,[status(thm)],[d4_finsub_1]) ).
fof(f_9_2,plain,
! [U_23] :
( ( preboolean(U_23)
| ~ diff_closed(U_23)
| ~ cup_closed(U_23) )
& ( ( diff_closed(U_23)
& cup_closed(U_23) )
| ~ preboolean(U_23) ) ),
inference(variable_rename,[status(thm)],[f_9_1]) ).
fof(f_9_3,plain,
( ! [U_25] :
( preboolean(U_25)
| ~ diff_closed(U_25)
| ~ cup_closed(U_25) )
& ! [U_24] :
( ( diff_closed(U_24)
& cup_closed(U_24) )
| ~ preboolean(U_24) ) ),
inference(miniscope,[status(thm)],[f_9_2]) ).
fof(f_9_4,plain,
( ! [U_24] :
( diff_closed(U_24)
| ~ sP3(U_24) )
& ! [U_24] :
( cup_closed(U_24)
| ~ sP3(U_24) )
& ! [U_25] :
( preboolean(U_25)
| ~ diff_closed(U_25)
| ~ cup_closed(U_25) )
& ! [U_24] :
( sP3(U_24)
| ~ preboolean(U_24) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP3])],[f_9_3]) ).
cnf(f_9_5,plain,
( sP3(U_24)
| ~ preboolean(U_24) ),
inference(clausify,[status(thm)],[f_9_4]) ).
cnf(f_9_6,plain,
( preboolean(U_25)
| ~ diff_closed(U_25)
| ~ cup_closed(U_25) ),
inference(clausify,[status(thm)],[f_9_4]) ).
cnf(f_9_7,plain,
( cup_closed(U_24)
| ~ sP3(U_24) ),
inference(clausify,[status(thm)],[f_9_4]) ).
cnf(f_9_8,plain,
( diff_closed(U_24)
| ~ sP3(U_24) ),
inference(clausify,[status(thm)],[f_9_4]) ).
fof(f_10_1,plain,
! [A] :
? [B] : element(B,A),
inference(fof_nnf,[status(thm)],[existence_m1_subset_1]) ).
fof(f_10_2,plain,
! [U_27] :
? [U_26] : element(U_26,U_27),
inference(variable_rename,[status(thm)],[f_10_1]) ).
fof(f_10_3,plain,
! [U_27] : element(sK5(U_27),U_27),
inference(skolemize,[status(esa),new_symbols(skolem,[sK5]),skolemize(U_26,sK5(U_27))],[f_10_2]) ).
fof(f_10_4,plain,
! [U_27] : element(sK5(U_27),U_27),
inference(definitional_conversion,[status(esa)],[f_10_3]) ).
cnf(f_10_5,plain,
element(sK5(U_27),U_27),
inference(clausify,[status(thm)],[f_10_4]) ).
fof(f_11_1,plain,
! [A,B] :
( finite(set_difference(A,B))
| ~ finite(A) ),
inference(fof_nnf,[status(thm)],[fc12_finset_1]) ).
fof(f_11_2,plain,
! [U_29,U_28] :
( finite(set_difference(U_29,U_28))
| ~ finite(U_29) ),
inference(variable_rename,[status(thm)],[f_11_1]) ).
fof(f_11_3,plain,
! [U_29] :
( ! [U_28] : finite(set_difference(U_29,U_28))
| ~ finite(U_29) ),
inference(miniscope,[status(thm)],[f_11_2]) ).
fof(f_11_4,plain,
! [U_28,U_29] :
( finite(set_difference(U_29,U_28))
| ~ finite(U_29) ),
inference(definitional_conversion,[status(esa)],[f_11_3]) ).
cnf(f_11_5,plain,
( finite(set_difference(U_29,U_28))
| ~ finite(U_29) ),
inference(clausify,[status(thm)],[f_11_4]) ).
fof(f_12_1,plain,
! [A] : ~ empty(powerset(A)),
inference(fof_nnf,[status(thm)],[fc1_subset_1]) ).
fof(f_12_2,plain,
! [U_30] : ~ empty(powerset(U_30)),
inference(variable_rename,[status(thm)],[f_12_1]) ).
fof(f_12_3,plain,
! [U_30] : ~ empty(powerset(U_30)),
inference(definitional_conversion,[status(esa)],[f_12_2]) ).
cnf(f_12_4,plain,
~ empty(powerset(U_30)),
inference(clausify,[status(thm)],[f_12_3]) ).
fof(f_13_1,plain,
empty(empty_set),
inference(fof_nnf,[status(thm)],[fc1_xboole_0]) ).
fof(f_13_2,plain,
empty(empty_set),
inference(definitional_conversion,[status(esa)],[f_13_1]) ).
cnf(f_13_3,plain,
empty(empty_set),
inference(clausify,[status(thm)],[f_13_2]) ).
fof(f_14_1,plain,
! [A,B] :
( ~ empty(set_union2(A,B))
| empty(A) ),
inference(fof_nnf,[status(thm)],[fc2_xboole_0]) ).
fof(f_14_2,plain,
! [U_32,U_31] :
( ~ empty(set_union2(U_32,U_31))
| empty(U_32) ),
inference(variable_rename,[status(thm)],[f_14_1]) ).
fof(f_14_3,plain,
! [U_32] :
( ! [U_31] : ~ empty(set_union2(U_32,U_31))
| empty(U_32) ),
inference(miniscope,[status(thm)],[f_14_2]) ).
fof(f_14_4,plain,
! [U_32,U_31] :
( ~ empty(set_union2(U_32,U_31))
| empty(U_32) ),
inference(definitional_conversion,[status(esa)],[f_14_3]) ).
cnf(f_14_5,plain,
( ~ empty(set_union2(U_32,U_31))
| empty(U_32) ),
inference(clausify,[status(thm)],[f_14_4]) ).
fof(f_15_1,plain,
! [A,B] :
( ~ empty(set_union2(B,A))
| empty(A) ),
inference(fof_nnf,[status(thm)],[fc3_xboole_0]) ).
fof(f_15_2,plain,
! [U_34,U_33] :
( ~ empty(set_union2(U_33,U_34))
| empty(U_34) ),
inference(variable_rename,[status(thm)],[f_15_1]) ).
fof(f_15_3,plain,
! [U_34] :
( ! [U_33] : ~ empty(set_union2(U_33,U_34))
| empty(U_34) ),
inference(miniscope,[status(thm)],[f_15_2]) ).
fof(f_15_4,plain,
! [U_33,U_34] :
( ~ empty(set_union2(U_33,U_34))
| empty(U_34) ),
inference(definitional_conversion,[status(esa)],[f_15_3]) ).
cnf(f_15_5,plain,
( ~ empty(set_union2(U_33,U_34))
| empty(U_34) ),
inference(clausify,[status(thm)],[f_15_4]) ).
fof(f_16_1,plain,
! [A,B] :
( finite(set_union2(A,B))
| ~ finite(B)
| ~ finite(A) ),
inference(fof_nnf,[status(thm)],[fc9_finset_1]) ).
fof(f_16_2,plain,
! [U_36,U_35] :
( finite(set_union2(U_36,U_35))
| ~ finite(U_35)
| ~ finite(U_36) ),
inference(variable_rename,[status(thm)],[f_16_1]) ).
fof(f_16_3,plain,
! [U_35,U_36] :
( finite(set_union2(U_36,U_35))
| ~ finite(U_35)
| ~ finite(U_36) ),
inference(definitional_conversion,[status(esa)],[f_16_2]) ).
cnf(f_16_4,plain,
( finite(set_union2(U_36,U_35))
| ~ finite(U_35)
| ~ finite(U_36) ),
inference(clausify,[status(thm)],[f_16_3]) ).
fof(f_17_1,plain,
! [A,B] : set_union2(A,A) = A,
inference(fof_nnf,[status(thm)],[idempotence_k2_xboole_0]) ).
fof(f_17_2,plain,
! [U_38,U_37] : set_union2(U_38,U_38) = U_38,
inference(variable_rename,[status(thm)],[f_17_1]) ).
fof(f_17_3,plain,
! [U_38] : set_union2(U_38,U_38) = U_38,
inference(miniscope,[status(thm)],[f_17_2]) ).
fof(f_17_4,plain,
! [U_38] : set_union2(U_38,U_38) = U_38,
inference(definitional_conversion,[status(esa)],[f_17_3]) ).
cnf(f_17_5,plain,
set_union2(U_38,U_38) = U_38,
inference(clausify,[status(thm)],[f_17_4]) ).
fof(f_18_1,plain,
? [A] :
( finite(A)
& ~ empty(A) ),
inference(fof_nnf,[status(thm)],[rc1_finset_1]) ).
fof(f_18_2,plain,
? [U_39] :
( finite(U_39)
& ~ empty(U_39) ),
inference(variable_rename,[status(thm)],[f_18_1]) ).
fof(f_18_3,plain,
( finite(sK6)
& ~ empty(sK6) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK6]),skolemize(U_39,sK6)],[f_18_2]) ).
fof(f_18_4,plain,
( finite(sK6)
& ~ empty(sK6) ),
inference(definitional_conversion,[status(esa)],[f_18_3]) ).
cnf(f_18_5,plain,
~ empty(sK6),
inference(clausify,[status(thm)],[f_18_4]) ).
cnf(f_18_6,plain,
finite(sK6),
inference(clausify,[status(thm)],[f_18_4]) ).
fof(f_19_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_19_2,plain,
? [U_40] :
( preboolean(U_40)
& diff_closed(U_40)
& cap_closed(U_40)
& cup_closed(U_40)
& ~ empty(U_40) ),
inference(variable_rename,[status(thm)],[f_19_1]) ).
fof(f_19_3,plain,
( preboolean(sK7)
& diff_closed(sK7)
& cap_closed(sK7)
& cup_closed(sK7)
& ~ empty(sK7) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK7]),skolemize(U_40,sK7)],[f_19_2]) ).
fof(f_19_4,plain,
( preboolean(sK7)
& diff_closed(sK7)
& cap_closed(sK7)
& cup_closed(sK7)
& ~ empty(sK7) ),
inference(definitional_conversion,[status(esa)],[f_19_3]) ).
cnf(f_19_5,plain,
~ empty(sK7),
inference(clausify,[status(thm)],[f_19_4]) ).
cnf(f_19_6,plain,
cup_closed(sK7),
inference(clausify,[status(thm)],[f_19_4]) ).
cnf(f_19_7,plain,
cap_closed(sK7),
inference(clausify,[status(thm)],[f_19_4]) ).
cnf(f_19_8,plain,
diff_closed(sK7),
inference(clausify,[status(thm)],[f_19_4]) ).
cnf(f_19_9,plain,
preboolean(sK7),
inference(clausify,[status(thm)],[f_19_4]) ).
fof(f_20_1,plain,
! [A] :
( ? [B] :
( ~ empty(B)
& element(B,powerset(A)) )
| empty(A) ),
inference(fof_nnf,[status(thm)],[rc1_subset_1]) ).
fof(f_20_2,plain,
! [U_42] :
( ? [U_41] :
( ~ empty(U_41)
& element(U_41,powerset(U_42)) )
| empty(U_42) ),
inference(variable_rename,[status(thm)],[f_20_1]) ).
fof(f_20_3,plain,
! [U_42] :
( ( ~ empty(sK8(U_42))
& element(sK8(U_42),powerset(U_42)) )
| empty(U_42) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK8]),skolemize(U_41,sK8(U_42))],[f_20_2]) ).
fof(f_20_4,plain,
( ! [U_42] :
( ~ empty(sK8(U_42))
| ~ sP4(U_42) )
& ! [U_42] :
( element(sK8(U_42),powerset(U_42))
| ~ sP4(U_42) )
& ! [U_42] :
( sP4(U_42)
| empty(U_42) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP4])],[f_20_3]) ).
cnf(f_20_5,plain,
( sP4(U_42)
| empty(U_42) ),
inference(clausify,[status(thm)],[f_20_4]) ).
cnf(f_20_6,plain,
( element(sK8(U_42),powerset(U_42))
| ~ sP4(U_42) ),
inference(clausify,[status(thm)],[f_20_4]) ).
cnf(f_20_7,plain,
( ~ empty(sK8(U_42))
| ~ sP4(U_42) ),
inference(clausify,[status(thm)],[f_20_4]) ).
fof(f_21_1,plain,
? [A] : empty(A),
inference(fof_nnf,[status(thm)],[rc1_xboole_0]) ).
fof(f_21_2,plain,
? [U_43] : empty(U_43),
inference(variable_rename,[status(thm)],[f_21_1]) ).
fof(f_21_3,plain,
empty(sK9),
inference(skolemize,[status(esa),new_symbols(skolem,[sK9]),skolemize(U_43,sK9)],[f_21_2]) ).
fof(f_21_4,plain,
empty(sK9),
inference(definitional_conversion,[status(esa)],[f_21_3]) ).
cnf(f_21_5,plain,
empty(sK9),
inference(clausify,[status(thm)],[f_21_4]) ).
fof(f_22_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_22_2,plain,
! [U_45] :
? [U_44] :
( finite(U_44)
& natural(U_44)
& ordinal(U_44)
& epsilon_connected(U_44)
& epsilon_transitive(U_44)
& one_to_one(U_44)
& function(U_44)
& relation(U_44)
& empty(U_44)
& element(U_44,powerset(U_45)) ),
inference(variable_rename,[status(thm)],[f_22_1]) ).
fof(f_22_3,plain,
! [U_45] :
( finite(sK10(U_45))
& natural(sK10(U_45))
& ordinal(sK10(U_45))
& epsilon_connected(sK10(U_45))
& epsilon_transitive(sK10(U_45))
& one_to_one(sK10(U_45))
& function(sK10(U_45))
& relation(sK10(U_45))
& empty(sK10(U_45))
& element(sK10(U_45),powerset(U_45)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK10]),skolemize(U_44,sK10(U_45))],[f_22_2]) ).
fof(f_22_4,plain,
( ! [U_45] : finite(sK10(U_45))
& ! [U_45] : natural(sK10(U_45))
& ! [U_45] : ordinal(sK10(U_45))
& ! [U_45] : epsilon_connected(sK10(U_45))
& ! [U_45] : epsilon_transitive(sK10(U_45))
& ! [U_45] : one_to_one(sK10(U_45))
& ! [U_45] : function(sK10(U_45))
& ! [U_45] : relation(sK10(U_45))
& ! [U_45] : empty(sK10(U_45))
& ! [U_45] : element(sK10(U_45),powerset(U_45)) ),
inference(definitional_conversion,[status(esa)],[f_22_3]) ).
cnf(f_22_5,plain,
element(sK10(U_45),powerset(U_45)),
inference(clausify,[status(thm)],[f_22_4]) ).
cnf(f_22_6,plain,
empty(sK10(U_45)),
inference(clausify,[status(thm)],[f_22_4]) ).
cnf(f_22_7,plain,
relation(sK10(U_45)),
inference(clausify,[status(thm)],[f_22_4]) ).
cnf(f_22_8,plain,
function(sK10(U_45)),
inference(clausify,[status(thm)],[f_22_4]) ).
cnf(f_22_9,plain,
one_to_one(sK10(U_45)),
inference(clausify,[status(thm)],[f_22_4]) ).
cnf(f_22_10,plain,
epsilon_transitive(sK10(U_45)),
inference(clausify,[status(thm)],[f_22_4]) ).
cnf(f_22_11,plain,
epsilon_connected(sK10(U_45)),
inference(clausify,[status(thm)],[f_22_4]) ).
cnf(f_22_12,plain,
ordinal(sK10(U_45)),
inference(clausify,[status(thm)],[f_22_4]) ).
cnf(f_22_13,plain,
natural(sK10(U_45)),
inference(clausify,[status(thm)],[f_22_4]) ).
cnf(f_22_14,plain,
finite(sK10(U_45)),
inference(clausify,[status(thm)],[f_22_4]) ).
fof(f_23_1,plain,
! [A] :
? [B] :
( empty(B)
& element(B,powerset(A)) ),
inference(fof_nnf,[status(thm)],[rc2_subset_1]) ).
fof(f_23_2,plain,
! [U_47] :
? [U_46] :
( empty(U_46)
& element(U_46,powerset(U_47)) ),
inference(variable_rename,[status(thm)],[f_23_1]) ).
fof(f_23_3,plain,
! [U_47] :
( empty(sK11(U_47))
& element(sK11(U_47),powerset(U_47)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK11]),skolemize(U_46,sK11(U_47))],[f_23_2]) ).
fof(f_23_4,plain,
( ! [U_47] : empty(sK11(U_47))
& ! [U_47] : element(sK11(U_47),powerset(U_47)) ),
inference(definitional_conversion,[status(esa)],[f_23_3]) ).
cnf(f_23_5,plain,
element(sK11(U_47),powerset(U_47)),
inference(clausify,[status(thm)],[f_23_4]) ).
cnf(f_23_6,plain,
empty(sK11(U_47)),
inference(clausify,[status(thm)],[f_23_4]) ).
fof(f_24_1,plain,
? [A] : ~ empty(A),
inference(fof_nnf,[status(thm)],[rc2_xboole_0]) ).
fof(f_24_2,plain,
? [U_48] : ~ empty(U_48),
inference(variable_rename,[status(thm)],[f_24_1]) ).
fof(f_24_3,plain,
~ empty(sK12),
inference(skolemize,[status(esa),new_symbols(skolem,[sK12]),skolemize(U_48,sK12)],[f_24_2]) ).
fof(f_24_4,plain,
~ empty(sK12),
inference(definitional_conversion,[status(esa)],[f_24_3]) ).
cnf(f_24_5,plain,
~ empty(sK12),
inference(clausify,[status(thm)],[f_24_4]) ).
fof(f_25_1,plain,
! [A] :
( ? [B] :
( finite(B)
& ~ empty(B)
& element(B,powerset(A)) )
| empty(A) ),
inference(fof_nnf,[status(thm)],[rc3_finset_1]) ).
fof(f_25_2,plain,
! [U_50] :
( ? [U_49] :
( finite(U_49)
& ~ empty(U_49)
& element(U_49,powerset(U_50)) )
| empty(U_50) ),
inference(variable_rename,[status(thm)],[f_25_1]) ).
fof(f_25_3,plain,
! [U_50] :
( ( finite(sK13(U_50))
& ~ empty(sK13(U_50))
& element(sK13(U_50),powerset(U_50)) )
| empty(U_50) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK13]),skolemize(U_49,sK13(U_50))],[f_25_2]) ).
fof(f_25_4,plain,
( ! [U_50] :
( finite(sK13(U_50))
| ~ sP5(U_50) )
& ! [U_50] :
( ~ empty(sK13(U_50))
| ~ sP5(U_50) )
& ! [U_50] :
( element(sK13(U_50),powerset(U_50))
| ~ sP5(U_50) )
& ! [U_50] :
( sP5(U_50)
| empty(U_50) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP5])],[f_25_3]) ).
cnf(f_25_5,plain,
( sP5(U_50)
| empty(U_50) ),
inference(clausify,[status(thm)],[f_25_4]) ).
cnf(f_25_6,plain,
( element(sK13(U_50),powerset(U_50))
| ~ sP5(U_50) ),
inference(clausify,[status(thm)],[f_25_4]) ).
cnf(f_25_7,plain,
( ~ empty(sK13(U_50))
| ~ sP5(U_50) ),
inference(clausify,[status(thm)],[f_25_4]) ).
cnf(f_25_8,plain,
( finite(sK13(U_50))
| ~ sP5(U_50) ),
inference(clausify,[status(thm)],[f_25_4]) ).
fof(f_26_1,plain,
! [A] :
( ? [B] :
( finite(B)
& ~ empty(B)
& element(B,powerset(A)) )
| empty(A) ),
inference(fof_nnf,[status(thm)],[rc4_finset_1]) ).
fof(f_26_2,plain,
! [U_52] :
( ? [U_51] :
( finite(U_51)
& ~ empty(U_51)
& element(U_51,powerset(U_52)) )
| empty(U_52) ),
inference(variable_rename,[status(thm)],[f_26_1]) ).
fof(f_26_3,plain,
! [U_52] :
( ( finite(sK14(U_52))
& ~ empty(sK14(U_52))
& element(sK14(U_52),powerset(U_52)) )
| empty(U_52) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK14]),skolemize(U_51,sK14(U_52))],[f_26_2]) ).
fof(f_26_4,plain,
( ! [U_52] :
( finite(sK14(U_52))
| ~ sP6(U_52) )
& ! [U_52] :
( ~ empty(sK14(U_52))
| ~ sP6(U_52) )
& ! [U_52] :
( element(sK14(U_52),powerset(U_52))
| ~ sP6(U_52) )
& ! [U_52] :
( sP6(U_52)
| empty(U_52) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP6])],[f_26_3]) ).
cnf(f_26_5,plain,
( sP6(U_52)
| empty(U_52) ),
inference(clausify,[status(thm)],[f_26_4]) ).
cnf(f_26_6,plain,
( element(sK14(U_52),powerset(U_52))
| ~ sP6(U_52) ),
inference(clausify,[status(thm)],[f_26_4]) ).
cnf(f_26_7,plain,
( ~ empty(sK14(U_52))
| ~ sP6(U_52) ),
inference(clausify,[status(thm)],[f_26_4]) ).
cnf(f_26_8,plain,
( finite(sK14(U_52))
| ~ sP6(U_52) ),
inference(clausify,[status(thm)],[f_26_4]) ).
fof(f_27_1,plain,
! [A,B] : subset(A,A),
inference(fof_nnf,[status(thm)],[reflexivity_r1_tarski]) ).
fof(f_27_2,plain,
! [U_54,U_53] : subset(U_54,U_54),
inference(variable_rename,[status(thm)],[f_27_1]) ).
fof(f_27_3,plain,
! [U_54] : subset(U_54,U_54),
inference(miniscope,[status(thm)],[f_27_2]) ).
fof(f_27_4,plain,
! [U_54] : subset(U_54,U_54),
inference(definitional_conversion,[status(esa)],[f_27_3]) ).
cnf(f_27_5,plain,
subset(U_54,U_54),
inference(clausify,[status(thm)],[f_27_4]) ).
fof(f_28_1,negated_conjecture,
~ ! [A] :
( preboolean(A)
<=> ! [B,C] :
( ( in(C,A)
& in(B,A) )
=> ( in(set_difference(B,C),A)
& in(set_union2(B,C),A) ) ) ),
inference(negate,[status(cth)],[t10_finsub_1]) ).
fof(f_28_2,negated_conjecture,
? [A] :
( ( ~ preboolean(A)
& ! [B,C] :
( ( in(set_difference(B,C),A)
& in(set_union2(B,C),A) )
| ~ in(C,A)
| ~ in(B,A) ) )
| ( ? [B,C] :
( ( ~ in(set_difference(B,C),A)
| ~ in(set_union2(B,C),A) )
& in(C,A)
& in(B,A) )
& preboolean(A) ) ),
inference(fof_nnf,[status(thm)],[f_28_1]) ).
fof(f_28_3,negated_conjecture,
? [U_59] :
( ( ~ preboolean(U_59)
& ! [U_58,U_57] :
( ( in(set_difference(U_58,U_57),U_59)
& in(set_union2(U_58,U_57),U_59) )
| ~ in(U_57,U_59)
| ~ in(U_58,U_59) ) )
| ( ? [U_56,U_55] :
( ( ~ in(set_difference(U_56,U_55),U_59)
| ~ in(set_union2(U_56,U_55),U_59) )
& in(U_55,U_59)
& in(U_56,U_59) )
& preboolean(U_59) ) ),
inference(variable_rename,[status(thm)],[f_28_2]) ).
fof(f_28_4,negated_conjecture,
( ? [U_61] :
( ~ preboolean(U_61)
& ! [U_58,U_57] :
( ( in(set_difference(U_58,U_57),U_61)
& in(set_union2(U_58,U_57),U_61) )
| ~ in(U_57,U_61)
| ~ in(U_58,U_61) ) )
| ? [U_60] :
( ? [U_56,U_55] :
( ( ~ in(set_difference(U_56,U_55),U_60)
| ~ in(set_union2(U_56,U_55),U_60) )
& in(U_55,U_60)
& in(U_56,U_60) )
& preboolean(U_60) ) ),
inference(miniscope,[status(thm)],[f_28_3]) ).
fof(f_28_5,negated_conjecture,
( ? [U_61] :
( ~ preboolean(U_61)
& ! [U_58,U_57] :
( ( in(set_difference(U_58,U_57),U_61)
& in(set_union2(U_58,U_57),U_61) )
| ~ in(U_57,U_61)
| ~ in(U_58,U_61) ) )
| ( ? [U_56,U_55] :
( ( ~ in(set_difference(U_56,U_55),sK15)
| ~ in(set_union2(U_56,U_55),sK15) )
& in(U_55,sK15)
& in(U_56,sK15) )
& preboolean(sK15) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK15]),skolemize(U_60,sK15)],[f_28_4]) ).
fof(f_28_6,negated_conjecture,
( ? [U_61] :
( ~ preboolean(U_61)
& ! [U_58,U_57] :
( ( in(set_difference(U_58,U_57),U_61)
& in(set_union2(U_58,U_57),U_61) )
| ~ in(U_57,U_61)
| ~ in(U_58,U_61) ) )
| ( ? [U_55] :
( ( ~ in(set_difference(sK16,U_55),sK15)
| ~ in(set_union2(sK16,U_55),sK15) )
& in(U_55,sK15)
& in(sK16,sK15) )
& preboolean(sK15) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK16]),skolemize(U_56,sK16)],[f_28_5]) ).
fof(f_28_7,negated_conjecture,
( ? [U_61] :
( ~ preboolean(U_61)
& ! [U_58,U_57] :
( ( in(set_difference(U_58,U_57),U_61)
& in(set_union2(U_58,U_57),U_61) )
| ~ in(U_57,U_61)
| ~ in(U_58,U_61) ) )
| ( ( ~ in(set_difference(sK16,sK17),sK15)
| ~ in(set_union2(sK16,sK17),sK15) )
& in(sK17,sK15)
& in(sK16,sK15)
& preboolean(sK15) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK17]),skolemize(U_55,sK17)],[f_28_6]) ).
fof(f_28_8,negated_conjecture,
( ( ~ preboolean(sK18)
& ! [U_58,U_57] :
( ( in(set_difference(U_58,U_57),sK18)
& in(set_union2(U_58,U_57),sK18) )
| ~ in(U_57,sK18)
| ~ in(U_58,sK18) ) )
| ( ( ~ in(set_difference(sK16,sK17),sK15)
| ~ in(set_union2(sK16,sK17),sK15) )
& in(sK17,sK15)
& in(sK16,sK15)
& preboolean(sK15) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK18]),skolemize(U_61,sK18)],[f_28_7]) ).
fof(f_28_9,negated_conjecture,
( ! [U_57,U_58] :
( in(set_difference(U_58,U_57),sK18)
| ~ sP8(U_57,U_58) )
& ! [U_57,U_58] :
( in(set_union2(U_58,U_57),sK18)
| ~ sP8(U_57,U_58) )
& ! [U_57,U_58] :
( ~ preboolean(sK18)
| ~ sP9(U_57,U_58) )
& ! [U_57,U_58] :
( sP8(U_57,U_58)
| ~ in(U_57,sK18)
| ~ in(U_58,sK18)
| ~ sP9(U_57,U_58) )
& ( ~ in(set_difference(sK16,sK17),sK15)
| ~ in(set_union2(sK16,sK17),sK15)
| ~ sP7 )
& ( in(sK17,sK15)
| ~ sP7 )
& ( in(sK16,sK15)
| ~ sP7 )
& ( preboolean(sK15)
| ~ sP7 )
& ! [U_57,U_58] :
( sP9(U_57,U_58)
| sP7 ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP7,sP8,sP9])],[f_28_8]) ).
cnf(f_28_10,negated_conjecture,
( sP9(U_57,U_58)
| sP7 ),
inference(clausify,[status(thm)],[f_28_9]) ).
cnf(f_28_11,negated_conjecture,
( preboolean(sK15)
| ~ sP7 ),
inference(clausify,[status(thm)],[f_28_9]) ).
cnf(f_28_12,negated_conjecture,
( in(sK16,sK15)
| ~ sP7 ),
inference(clausify,[status(thm)],[f_28_9]) ).
cnf(f_28_13,negated_conjecture,
( in(sK17,sK15)
| ~ sP7 ),
inference(clausify,[status(thm)],[f_28_9]) ).
cnf(f_28_14,negated_conjecture,
( ~ in(set_difference(sK16,sK17),sK15)
| ~ in(set_union2(sK16,sK17),sK15)
| ~ sP7 ),
inference(clausify,[status(thm)],[f_28_9]) ).
cnf(f_28_15,negated_conjecture,
( sP8(U_57,U_58)
| ~ in(U_57,sK18)
| ~ in(U_58,sK18)
| ~ sP9(U_57,U_58) ),
inference(clausify,[status(thm)],[f_28_9]) ).
cnf(f_28_16,negated_conjecture,
( ~ preboolean(sK18)
| ~ sP9(U_57,U_58) ),
inference(clausify,[status(thm)],[f_28_9]) ).
cnf(f_28_17,negated_conjecture,
( in(set_union2(U_58,U_57),sK18)
| ~ sP8(U_57,U_58) ),
inference(clausify,[status(thm)],[f_28_9]) ).
cnf(f_28_18,negated_conjecture,
( in(set_difference(U_58,U_57),sK18)
| ~ sP8(U_57,U_58) ),
inference(clausify,[status(thm)],[f_28_9]) ).
fof(f_29_1,plain,
! [A] : set_union2(A,empty_set) = A,
inference(fof_nnf,[status(thm)],[t1_boole]) ).
fof(f_29_2,plain,
! [U_62] : set_union2(U_62,empty_set) = U_62,
inference(variable_rename,[status(thm)],[f_29_1]) ).
fof(f_29_3,plain,
! [U_62] : set_union2(U_62,empty_set) = U_62,
inference(definitional_conversion,[status(esa)],[f_29_2]) ).
cnf(f_29_4,plain,
set_union2(U_62,empty_set) = U_62,
inference(clausify,[status(thm)],[f_29_3]) ).
fof(f_30_1,plain,
! [A,B] :
( element(A,B)
| ~ in(A,B) ),
inference(fof_nnf,[status(thm)],[t1_subset]) ).
fof(f_30_2,plain,
! [U_64,U_63] :
( element(U_64,U_63)
| ~ in(U_64,U_63) ),
inference(variable_rename,[status(thm)],[f_30_1]) ).
fof(f_30_3,plain,
! [U_63,U_64] :
( element(U_64,U_63)
| ~ in(U_64,U_63) ),
inference(definitional_conversion,[status(esa)],[f_30_2]) ).
cnf(f_30_4,plain,
( element(U_64,U_63)
| ~ in(U_64,U_63) ),
inference(clausify,[status(thm)],[f_30_3]) ).
fof(f_31_1,plain,
! [A,B] :
( in(A,B)
| empty(B)
| ~ element(A,B) ),
inference(fof_nnf,[status(thm)],[t2_subset]) ).
fof(f_31_2,plain,
! [U_66,U_65] :
( in(U_66,U_65)
| empty(U_65)
| ~ element(U_66,U_65) ),
inference(variable_rename,[status(thm)],[f_31_1]) ).
fof(f_31_3,plain,
! [U_66,U_65] :
( in(U_66,U_65)
| empty(U_65)
| ~ element(U_66,U_65) ),
inference(definitional_conversion,[status(esa)],[f_31_2]) ).
cnf(f_31_4,plain,
( in(U_66,U_65)
| empty(U_65)
| ~ element(U_66,U_65) ),
inference(clausify,[status(thm)],[f_31_3]) ).
fof(f_32_1,plain,
! [A] : set_difference(A,empty_set) = A,
inference(fof_nnf,[status(thm)],[t3_boole]) ).
fof(f_32_2,plain,
! [U_67] : set_difference(U_67,empty_set) = U_67,
inference(variable_rename,[status(thm)],[f_32_1]) ).
fof(f_32_3,plain,
! [U_67] : set_difference(U_67,empty_set) = U_67,
inference(definitional_conversion,[status(esa)],[f_32_2]) ).
cnf(f_32_4,plain,
set_difference(U_67,empty_set) = U_67,
inference(clausify,[status(thm)],[f_32_3]) ).
fof(f_33_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_33_2,plain,
! [U_69,U_68] :
( ( element(U_69,powerset(U_68))
| ~ subset(U_69,U_68) )
& ( subset(U_69,U_68)
| ~ element(U_69,powerset(U_68)) ) ),
inference(variable_rename,[status(thm)],[f_33_1]) ).
fof(f_33_3,plain,
( ! [U_73,U_71] :
( element(U_73,powerset(U_71))
| ~ subset(U_73,U_71) )
& ! [U_72,U_70] :
( subset(U_72,U_70)
| ~ element(U_72,powerset(U_70)) ) ),
inference(miniscope,[status(thm)],[f_33_2]) ).
fof(f_33_4,plain,
( ! [U_73,U_71] :
( element(U_73,powerset(U_71))
| ~ subset(U_73,U_71) )
& ! [U_72,U_70] :
( subset(U_72,U_70)
| ~ element(U_72,powerset(U_70)) ) ),
inference(definitional_conversion,[status(esa)],[f_33_3]) ).
cnf(f_33_5,plain,
( subset(U_72,U_70)
| ~ element(U_72,powerset(U_70)) ),
inference(clausify,[status(thm)],[f_33_4]) ).
cnf(f_33_6,plain,
( element(U_73,powerset(U_71))
| ~ subset(U_73,U_71) ),
inference(clausify,[status(thm)],[f_33_4]) ).
fof(f_34_1,plain,
! [A] : set_difference(empty_set,A) = empty_set,
inference(fof_nnf,[status(thm)],[t4_boole]) ).
fof(f_34_2,plain,
! [U_74] : set_difference(empty_set,U_74) = empty_set,
inference(variable_rename,[status(thm)],[f_34_1]) ).
fof(f_34_3,plain,
! [U_74] : set_difference(empty_set,U_74) = empty_set,
inference(definitional_conversion,[status(esa)],[f_34_2]) ).
cnf(f_34_4,plain,
set_difference(empty_set,U_74) = empty_set,
inference(clausify,[status(thm)],[f_34_3]) ).
fof(f_35_1,plain,
! [A,B,C] :
( element(A,C)
| ~ element(B,powerset(C))
| ~ in(A,B) ),
inference(fof_nnf,[status(thm)],[t4_subset]) ).
fof(f_35_2,plain,
! [U_77,U_76,U_75] :
( element(U_77,U_75)
| ~ element(U_76,powerset(U_75))
| ~ in(U_77,U_76) ),
inference(variable_rename,[status(thm)],[f_35_1]) ).
fof(f_35_3,plain,
! [U_75,U_77,U_76] :
( element(U_77,U_75)
| ~ element(U_76,powerset(U_75))
| ~ in(U_77,U_76) ),
inference(definitional_conversion,[status(esa)],[f_35_2]) ).
cnf(f_35_4,plain,
( element(U_77,U_75)
| ~ element(U_76,powerset(U_75))
| ~ in(U_77,U_76) ),
inference(clausify,[status(thm)],[f_35_3]) ).
fof(f_36_1,plain,
! [A,B,C] :
( ~ empty(C)
| ~ element(B,powerset(C))
| ~ in(A,B) ),
inference(fof_nnf,[status(thm)],[t5_subset]) ).
fof(f_36_2,plain,
! [U_80,U_79,U_78] :
( ~ empty(U_78)
| ~ element(U_79,powerset(U_78))
| ~ in(U_80,U_79) ),
inference(variable_rename,[status(thm)],[f_36_1]) ).
fof(f_36_3,plain,
! [U_80,U_79] :
( ! [U_78] :
( ~ empty(U_78)
| ~ element(U_79,powerset(U_78)) )
| ~ in(U_80,U_79) ),
inference(miniscope,[status(thm)],[f_36_2]) ).
fof(f_36_4,plain,
! [U_79,U_78,U_80] :
( ~ empty(U_78)
| ~ element(U_79,powerset(U_78))
| ~ in(U_80,U_79) ),
inference(definitional_conversion,[status(esa)],[f_36_3]) ).
cnf(f_36_5,plain,
( ~ empty(U_78)
| ~ element(U_79,powerset(U_78))
| ~ in(U_80,U_79) ),
inference(clausify,[status(thm)],[f_36_4]) ).
fof(f_37_1,plain,
! [A] :
( A = empty_set
| ~ empty(A) ),
inference(fof_nnf,[status(thm)],[t6_boole]) ).
fof(f_37_2,plain,
! [U_81] :
( U_81 = empty_set
| ~ empty(U_81) ),
inference(variable_rename,[status(thm)],[f_37_1]) ).
fof(f_37_3,plain,
! [U_81] :
( U_81 = empty_set
| ~ empty(U_81) ),
inference(definitional_conversion,[status(esa)],[f_37_2]) ).
cnf(f_37_4,plain,
( U_81 = empty_set
| ~ empty(U_81) ),
inference(clausify,[status(thm)],[f_37_3]) ).
fof(f_38_1,plain,
! [A,B] :
( ~ empty(B)
| ~ in(A,B) ),
inference(fof_nnf,[status(thm)],[t7_boole]) ).
fof(f_38_2,plain,
! [U_83,U_82] :
( ~ empty(U_82)
| ~ in(U_83,U_82) ),
inference(variable_rename,[status(thm)],[f_38_1]) ).
fof(f_38_3,plain,
! [U_82,U_83] :
( ~ empty(U_82)
| ~ in(U_83,U_82) ),
inference(definitional_conversion,[status(esa)],[f_38_2]) ).
cnf(f_38_4,plain,
( ~ empty(U_82)
| ~ in(U_83,U_82) ),
inference(clausify,[status(thm)],[f_38_3]) ).
fof(f_39_1,plain,
! [A,B] :
( ~ empty(B)
| A = B
| ~ empty(A) ),
inference(fof_nnf,[status(thm)],[t8_boole]) ).
fof(f_39_2,plain,
! [U_85,U_84] :
( ~ empty(U_84)
| U_85 = U_84
| ~ empty(U_85) ),
inference(variable_rename,[status(thm)],[f_39_1]) ).
fof(f_39_3,plain,
! [U_85] :
( ! [U_84] :
( ~ empty(U_84)
| U_85 = U_84 )
| ~ empty(U_85) ),
inference(miniscope,[status(thm)],[f_39_2]) ).
fof(f_39_4,plain,
! [U_85,U_84] :
( ~ empty(U_84)
| U_85 = U_84
| ~ empty(U_85) ),
inference(definitional_conversion,[status(esa)],[f_39_3]) ).
cnf(f_39_5,plain,
( ~ empty(U_84)
| U_85 = U_84
| ~ empty(U_85) ),
inference(clausify,[status(thm)],[f_39_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,
( set_union2(Eq_x_0,Eq_x_1) = set_union2(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_6,axiom,
( set_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) = sK2(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_9,axiom,
( sK3(Eq_x_0) = sK3(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_10,axiom,
( sK4(Eq_x_0) = sK4(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_11,axiom,
( sK5(Eq_x_0) = sK5(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_12,axiom,
( sK8(Eq_x_0) = sK8(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_13,axiom,
( sK10(Eq_x_0) = sK10(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,
( sK13(Eq_x_0) = sK13(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,
( 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_18,axiom,
( empty(Eq_y_0)
| ~ empty(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_19,axiom,
( finite(Eq_y_0)
| ~ finite(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_20,axiom,
( preboolean(Eq_y_0)
| ~ preboolean(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_21,axiom,
( cup_closed(Eq_y_0)
| ~ cup_closed(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_22,axiom,
( diff_closed(Eq_y_0)
| ~ diff_closed(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_23,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_24,axiom,
( cap_closed(Eq_y_0)
| ~ cap_closed(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_25,axiom,
( relation(Eq_y_0)
| ~ relation(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_26,axiom,
( function(Eq_y_0)
| ~ function(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_27,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_28,axiom,
( epsilon_transitive(Eq_y_0)
| ~ epsilon_transitive(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_29,axiom,
( epsilon_connected(Eq_y_0)
| ~ epsilon_connected(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_30,axiom,
( ordinal(Eq_y_0)
| ~ ordinal(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_31,axiom,
( natural(Eq_y_0)
| ~ natural(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_32,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_33,axiom,
( sP0(Eq_y_0)
| ~ sP0(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_34,axiom,
( sP1(Eq_y_0)
| ~ sP1(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_35,axiom,
( sP2(Eq_y_0)
| ~ sP2(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_36,axiom,
( sP3(Eq_y_0)
| ~ sP3(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_37,axiom,
( sP4(Eq_y_0)
| ~ sP4(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_38,axiom,
( sP5(Eq_y_0)
| ~ sP5(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_39,axiom,
( sP6(Eq_y_0)
| ~ sP6(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_40,axiom,
( sP8(Eq_y_0,Eq_y_1)
| ~ sP8(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_41,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(sat_proved,plain,
$false,
inference(cadical,[status(thm)],[]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU101+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/sandbox/solver/bin/connect++ --verbosity 1 --no-colour --tptp-proof --schedule default --timeout 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/5.37 % Computer : n003.cluster.edu
% 0.09/5.37 % Model : x86_64 x86_64
% 0.09/5.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/5.37 % Memory : 8046.5625MB
% 0.09/5.37 % OS : Linux 6.8.0-71-generic
% 0.09/5.37 % CPULimit : 300
% 0.09/5.37 % WCLimit : 300
% 0.09/5.37 % DateTime : Sat Sep 19 23:20:49 UTC 2026
% 0.09/5.37 % CPUTime :
% 30.54/35.85 % SZS status Theorem for theBenchmark
% 30.54/35.85 % SZS output start Proof for theBenchmark
% See solution above
%------------------------------------------------------------------------------