%------------------------------------------------------------------------------
% File : ConnectPP---0.7.2
% Problem : SEU117+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 08:58:04 AM UTC 2026
% Result : Theorem 0.10s 0.45s
% Output : Proof 0.10s
% Verified :
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)
% Comments :
%------------------------------------------------------------------------------
fof(fc1_xboole_0,axiom,
empty(empty_set),
file('theBenchmark.p',fc1_xboole_0) ).
fof(cc2_finsub_1,axiom,
! [A] :
( ( diff_closed(A)
& cup_closed(A) )
=> preboolean(A) ),
file('theBenchmark.p',cc2_finsub_1) ).
fof(cc1_finset_1,axiom,
! [A] :
( empty(A)
=> finite(A) ),
file('theBenchmark.p',cc1_finset_1) ).
fof(t2_subset,axiom,
! [A,B] :
( element(A,B)
=> ( in(A,B)
| empty(B) ) ),
file('theBenchmark.p',t2_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(t8_boole,axiom,
! [A,B] :
~ ( empty(B)
& A != B
& empty(A) ),
file('theBenchmark.p',t8_boole) ).
fof(reflexivity_r1_tarski,axiom,
! [A,B] : subset(A,A),
file('theBenchmark.p',reflexivity_r1_tarski) ).
fof(antisymmetry_r2_hidden,axiom,
! [A,B] :
( in(A,B)
=> ~ in(B,A) ),
file('theBenchmark.p',antisymmetry_r2_hidden) ).
fof(existence_m1_subset_1,axiom,
! [A] :
? [B] : element(B,A),
file('theBenchmark.p',existence_m1_subset_1) ).
fof(dt_k5_finsub_1,axiom,
! [A] : preboolean(finite_subsets(A)),
file('theBenchmark.p',dt_k5_finsub_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(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(cc1_finsub_1,axiom,
! [A] :
( preboolean(A)
=> ( diff_closed(A)
& cup_closed(A) ) ),
file('theBenchmark.p',cc1_finsub_1) ).
fof(cc3_finsub_1,axiom,
! [A,B] :
( element(B,finite_subsets(A))
=> finite(B) ),
file('theBenchmark.p',cc3_finsub_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(cc2_finset_1,axiom,
! [A] :
( finite(A)
=> ! [B] :
( element(B,powerset(A))
=> finite(B) ) ),
file('theBenchmark.p',cc2_finset_1) ).
fof(rc1_finset_1,axiom,
? [A] :
( finite(A)
& ~ empty(A) ),
file('theBenchmark.p',rc1_finset_1) ).
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(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(fc1_subset_1,axiom,
! [A] : ~ empty(powerset(A)),
file('theBenchmark.p',fc1_subset_1) ).
fof(rc1_subset_1,axiom,
! [A] :
( ~ empty(A)
=> ? [B] :
( ~ empty(B)
& element(B,powerset(A)) ) ),
file('theBenchmark.p',rc1_subset_1) ).
fof(rc2_subset_1,axiom,
! [A] :
? [B] :
( empty(B)
& element(B,powerset(A)) ),
file('theBenchmark.p',rc2_subset_1) ).
fof(rc1_xboole_0,axiom,
? [A] : empty(A),
file('theBenchmark.p',rc1_xboole_0) ).
fof(rc2_xboole_0,axiom,
? [A] : ~ empty(A),
file('theBenchmark.p',rc2_xboole_0) ).
fof(t1_subset,axiom,
! [A,B] :
( in(A,B)
=> element(A,B) ),
file('theBenchmark.p',t1_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(t7_boole,axiom,
! [A,B] :
~ ( empty(B)
& in(A,B) ),
file('theBenchmark.p',t7_boole) ).
fof(t32_finsub_1,conjecture,
! [A,B] :
( element(B,finite_subsets(A))
=> element(B,powerset(A)) ),
file('theBenchmark.p',t32_finsub_1) ).
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(f_1_1,plain,
empty(empty_set),
inference(fof_nnf,[status(thm)],[fc1_xboole_0]) ).
cnf(f_1_2,plain,
empty(empty_set),
inference(clausify,[status(thm)],[f_1_1]) ).
fof(f_2_1,plain,
! [A] :
( preboolean(A)
| ~ diff_closed(A)
| ~ cup_closed(A) ),
inference(fof_nnf,[status(thm)],[cc2_finsub_1]) ).
fof(f_2_2,plain,
! [U_0] :
( preboolean(U_0)
| ~ diff_closed(U_0)
| ~ cup_closed(U_0) ),
inference(variable_rename,[status(thm)],[f_2_1]) ).
cnf(f_2_3,plain,
( preboolean(U_0)
| ~ diff_closed(U_0)
| ~ cup_closed(U_0) ),
inference(clausify,[status(thm)],[f_2_2]) ).
fof(f_3_1,plain,
! [A] :
( finite(A)
| ~ empty(A) ),
inference(fof_nnf,[status(thm)],[cc1_finset_1]) ).
fof(f_3_2,plain,
! [U_1] :
( finite(U_1)
| ~ empty(U_1) ),
inference(variable_rename,[status(thm)],[f_3_1]) ).
cnf(f_3_3,plain,
( finite(U_1)
| ~ empty(U_1) ),
inference(clausify,[status(thm)],[f_3_2]) ).
fof(f_4_1,plain,
! [A,B] :
( in(A,B)
| empty(B)
| ~ element(A,B) ),
inference(fof_nnf,[status(thm)],[t2_subset]) ).
fof(f_4_2,plain,
! [U_3,U_2] :
( in(U_3,U_2)
| empty(U_2)
| ~ element(U_3,U_2) ),
inference(variable_rename,[status(thm)],[f_4_1]) ).
cnf(f_4_3,plain,
( in(U_3,U_2)
| empty(U_2)
| ~ element(U_3,U_2) ),
inference(clausify,[status(thm)],[f_4_2]) ).
fof(f_5_1,plain,
! [A,B,C] :
( ~ empty(C)
| ~ element(B,powerset(C))
| ~ in(A,B) ),
inference(fof_nnf,[status(thm)],[t5_subset]) ).
fof(f_5_2,plain,
! [U_6,U_5,U_4] :
( ~ empty(U_4)
| ~ element(U_5,powerset(U_4))
| ~ in(U_6,U_5) ),
inference(variable_rename,[status(thm)],[f_5_1]) ).
fof(f_5_3,plain,
! [U_6,U_5] :
( ! [U_4] :
( ~ empty(U_4)
| ~ element(U_5,powerset(U_4)) )
| ~ in(U_6,U_5) ),
inference(miniscope,[status(thm)],[f_5_2]) ).
cnf(f_5_4,plain,
( ~ empty(U_4)
| ~ element(U_5,powerset(U_4))
| ~ in(U_6,U_5) ),
inference(clausify,[status(thm)],[f_5_3]) ).
fof(f_6_1,plain,
! [A] :
( A = empty_set
| ~ empty(A) ),
inference(fof_nnf,[status(thm)],[t6_boole]) ).
fof(f_6_2,plain,
! [U_7] :
( U_7 = empty_set
| ~ empty(U_7) ),
inference(variable_rename,[status(thm)],[f_6_1]) ).
cnf(f_6_3,plain,
( U_7 = empty_set
| ~ empty(U_7) ),
inference(clausify,[status(thm)],[f_6_2]) ).
fof(f_7_1,plain,
! [A,B] :
( ~ empty(B)
| A = B
| ~ empty(A) ),
inference(fof_nnf,[status(thm)],[t8_boole]) ).
fof(f_7_2,plain,
! [U_9,U_8] :
( ~ empty(U_8)
| U_9 = U_8
| ~ empty(U_9) ),
inference(variable_rename,[status(thm)],[f_7_1]) ).
fof(f_7_3,plain,
! [U_9] :
( ! [U_8] :
( ~ empty(U_8)
| U_9 = U_8 )
| ~ empty(U_9) ),
inference(miniscope,[status(thm)],[f_7_2]) ).
cnf(f_7_4,plain,
( ~ empty(U_8)
| U_9 = U_8
| ~ empty(U_9) ),
inference(clausify,[status(thm)],[f_7_3]) ).
fof(f_8_1,plain,
! [A,B] : subset(A,A),
inference(fof_nnf,[status(thm)],[reflexivity_r1_tarski]) ).
fof(f_8_2,plain,
! [U_11,U_10] : subset(U_11,U_11),
inference(variable_rename,[status(thm)],[f_8_1]) ).
fof(f_8_3,plain,
! [U_11] : subset(U_11,U_11),
inference(miniscope,[status(thm)],[f_8_2]) ).
cnf(f_8_4,plain,
subset(U_11,U_11),
inference(clausify,[status(thm)],[f_8_3]) ).
fof(f_9_1,plain,
! [A,B] :
( ~ in(B,A)
| ~ in(A,B) ),
inference(fof_nnf,[status(thm)],[antisymmetry_r2_hidden]) ).
fof(f_9_2,plain,
! [U_13,U_12] :
( ~ in(U_12,U_13)
| ~ in(U_13,U_12) ),
inference(variable_rename,[status(thm)],[f_9_1]) ).
cnf(f_9_3,plain,
( ~ in(U_12,U_13)
| ~ in(U_13,U_12) ),
inference(clausify,[status(thm)],[f_9_2]) ).
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_15] :
? [U_14] : element(U_14,U_15),
inference(variable_rename,[status(thm)],[f_10_1]) ).
fof(f_10_3,plain,
! [U_15] : element(sK1(U_15),U_15),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(U_14,sK1(U_15))],[f_10_2]) ).
cnf(f_10_4,plain,
element(sK1(U_15),U_15),
inference(clausify,[status(thm)],[f_10_3]) ).
fof(f_11_1,plain,
! [A] : preboolean(finite_subsets(A)),
inference(fof_nnf,[status(thm)],[dt_k5_finsub_1]) ).
fof(f_11_2,plain,
! [U_16] : preboolean(finite_subsets(U_16)),
inference(variable_rename,[status(thm)],[f_11_1]) ).
cnf(f_11_3,plain,
preboolean(finite_subsets(U_16)),
inference(clausify,[status(thm)],[f_11_2]) ).
fof(f_12_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_12_2,plain,
! [U_17] :
( preboolean(powerset(U_17))
& diff_closed(powerset(U_17))
& cup_closed(powerset(U_17))
& ~ empty(powerset(U_17)) ),
inference(variable_rename,[status(thm)],[f_12_1]) ).
fof(f_12_3,plain,
( ! [U_21] : preboolean(powerset(U_21))
& ! [U_20] : diff_closed(powerset(U_20))
& ! [U_19] : cup_closed(powerset(U_19))
& ! [U_18] : ~ empty(powerset(U_18)) ),
inference(miniscope,[status(thm)],[f_12_2]) ).
cnf(f_12_4,plain,
~ empty(powerset(U_18)),
inference(clausify,[status(thm)],[f_12_3]) ).
cnf(f_12_5,plain,
cup_closed(powerset(U_19)),
inference(clausify,[status(thm)],[f_12_3]) ).
cnf(f_12_6,plain,
diff_closed(powerset(U_20)),
inference(clausify,[status(thm)],[f_12_3]) ).
cnf(f_12_7,plain,
preboolean(powerset(U_21)),
inference(clausify,[status(thm)],[f_12_3]) ).
fof(f_13_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_13_2,plain,
! [U_22] :
( preboolean(finite_subsets(U_22))
& diff_closed(finite_subsets(U_22))
& cup_closed(finite_subsets(U_22))
& ~ empty(finite_subsets(U_22)) ),
inference(variable_rename,[status(thm)],[f_13_1]) ).
fof(f_13_3,plain,
( ! [U_26] : preboolean(finite_subsets(U_26))
& ! [U_25] : diff_closed(finite_subsets(U_25))
& ! [U_24] : cup_closed(finite_subsets(U_24))
& ! [U_23] : ~ empty(finite_subsets(U_23)) ),
inference(miniscope,[status(thm)],[f_13_2]) ).
cnf(f_13_4,plain,
~ empty(finite_subsets(U_23)),
inference(clausify,[status(thm)],[f_13_3]) ).
cnf(f_13_5,plain,
cup_closed(finite_subsets(U_24)),
inference(clausify,[status(thm)],[f_13_3]) ).
cnf(f_13_6,plain,
diff_closed(finite_subsets(U_25)),
inference(clausify,[status(thm)],[f_13_3]) ).
cnf(f_13_7,plain,
preboolean(finite_subsets(U_26)),
inference(clausify,[status(thm)],[f_13_3]) ).
fof(f_14_1,plain,
! [A] :
( ( diff_closed(A)
& cup_closed(A) )
| ~ preboolean(A) ),
inference(fof_nnf,[status(thm)],[cc1_finsub_1]) ).
fof(f_14_2,plain,
! [U_27] :
( ( diff_closed(U_27)
& cup_closed(U_27) )
| ~ preboolean(U_27) ),
inference(variable_rename,[status(thm)],[f_14_1]) ).
cnf(f_14_3,plain,
( cup_closed(U_27)
| ~ preboolean(U_27) ),
inference(clausify,[status(thm)],[f_14_2]) ).
cnf(f_14_4,plain,
( diff_closed(U_27)
| ~ preboolean(U_27) ),
inference(clausify,[status(thm)],[f_14_2]) ).
fof(f_15_1,plain,
! [A,B] :
( finite(B)
| ~ element(B,finite_subsets(A)) ),
inference(fof_nnf,[status(thm)],[cc3_finsub_1]) ).
fof(f_15_2,plain,
! [U_29,U_28] :
( finite(U_28)
| ~ element(U_28,finite_subsets(U_29)) ),
inference(variable_rename,[status(thm)],[f_15_1]) ).
cnf(f_15_3,plain,
( finite(U_28)
| ~ element(U_28,finite_subsets(U_29)) ),
inference(clausify,[status(thm)],[f_15_2]) ).
fof(f_16_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_16_2,plain,
? [U_30] :
( preboolean(U_30)
& diff_closed(U_30)
& cap_closed(U_30)
& cup_closed(U_30)
& ~ empty(U_30) ),
inference(variable_rename,[status(thm)],[f_16_1]) ).
fof(f_16_3,plain,
( preboolean(sK2)
& diff_closed(sK2)
& cap_closed(sK2)
& cup_closed(sK2)
& ~ empty(sK2) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2]),skolemize(U_30,sK2)],[f_16_2]) ).
cnf(f_16_4,plain,
~ empty(sK2),
inference(clausify,[status(thm)],[f_16_3]) ).
cnf(f_16_5,plain,
cup_closed(sK2),
inference(clausify,[status(thm)],[f_16_3]) ).
cnf(f_16_6,plain,
cap_closed(sK2),
inference(clausify,[status(thm)],[f_16_3]) ).
cnf(f_16_7,plain,
diff_closed(sK2),
inference(clausify,[status(thm)],[f_16_3]) ).
cnf(f_16_8,plain,
preboolean(sK2),
inference(clausify,[status(thm)],[f_16_3]) ).
fof(f_17_1,plain,
! [A] :
( ! [B] :
( finite(B)
| ~ element(B,powerset(A)) )
| ~ finite(A) ),
inference(fof_nnf,[status(thm)],[cc2_finset_1]) ).
fof(f_17_2,plain,
! [U_32] :
( ! [U_31] :
( finite(U_31)
| ~ element(U_31,powerset(U_32)) )
| ~ finite(U_32) ),
inference(variable_rename,[status(thm)],[f_17_1]) ).
cnf(f_17_3,plain,
( finite(U_31)
| ~ element(U_31,powerset(U_32))
| ~ finite(U_32) ),
inference(clausify,[status(thm)],[f_17_2]) ).
fof(f_18_1,plain,
? [A] :
( finite(A)
& ~ empty(A) ),
inference(fof_nnf,[status(thm)],[rc1_finset_1]) ).
fof(f_18_2,plain,
? [U_33] :
( finite(U_33)
& ~ empty(U_33) ),
inference(variable_rename,[status(thm)],[f_18_1]) ).
fof(f_18_3,plain,
( finite(sK3)
& ~ empty(sK3) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3]),skolemize(U_33,sK3)],[f_18_2]) ).
cnf(f_18_4,plain,
~ empty(sK3),
inference(clausify,[status(thm)],[f_18_3]) ).
cnf(f_18_5,plain,
finite(sK3),
inference(clausify,[status(thm)],[f_18_3]) ).
fof(f_19_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_19_2,plain,
! [U_35] :
? [U_34] :
( finite(U_34)
& natural(U_34)
& ordinal(U_34)
& epsilon_connected(U_34)
& epsilon_transitive(U_34)
& one_to_one(U_34)
& function(U_34)
& relation(U_34)
& empty(U_34)
& element(U_34,powerset(U_35)) ),
inference(variable_rename,[status(thm)],[f_19_1]) ).
fof(f_19_3,plain,
! [U_35] :
( finite(sK4(U_35))
& natural(sK4(U_35))
& ordinal(sK4(U_35))
& epsilon_connected(sK4(U_35))
& epsilon_transitive(sK4(U_35))
& one_to_one(sK4(U_35))
& function(sK4(U_35))
& relation(sK4(U_35))
& empty(sK4(U_35))
& element(sK4(U_35),powerset(U_35)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4]),skolemize(U_34,sK4(U_35))],[f_19_2]) ).
cnf(f_19_4,plain,
element(sK4(U_35),powerset(U_35)),
inference(clausify,[status(thm)],[f_19_3]) ).
cnf(f_19_5,plain,
empty(sK4(U_35)),
inference(clausify,[status(thm)],[f_19_3]) ).
cnf(f_19_6,plain,
relation(sK4(U_35)),
inference(clausify,[status(thm)],[f_19_3]) ).
cnf(f_19_7,plain,
function(sK4(U_35)),
inference(clausify,[status(thm)],[f_19_3]) ).
cnf(f_19_8,plain,
one_to_one(sK4(U_35)),
inference(clausify,[status(thm)],[f_19_3]) ).
cnf(f_19_9,plain,
epsilon_transitive(sK4(U_35)),
inference(clausify,[status(thm)],[f_19_3]) ).
cnf(f_19_10,plain,
epsilon_connected(sK4(U_35)),
inference(clausify,[status(thm)],[f_19_3]) ).
cnf(f_19_11,plain,
ordinal(sK4(U_35)),
inference(clausify,[status(thm)],[f_19_3]) ).
cnf(f_19_12,plain,
natural(sK4(U_35)),
inference(clausify,[status(thm)],[f_19_3]) ).
cnf(f_19_13,plain,
finite(sK4(U_35)),
inference(clausify,[status(thm)],[f_19_3]) ).
fof(f_20_1,plain,
! [A] :
( ? [B] :
( finite(B)
& ~ empty(B)
& element(B,powerset(A)) )
| empty(A) ),
inference(fof_nnf,[status(thm)],[rc3_finset_1]) ).
fof(f_20_2,plain,
! [U_37] :
( ? [U_36] :
( finite(U_36)
& ~ empty(U_36)
& element(U_36,powerset(U_37)) )
| empty(U_37) ),
inference(variable_rename,[status(thm)],[f_20_1]) ).
fof(f_20_3,plain,
! [U_37] :
( ( finite(sK5(U_37))
& ~ empty(sK5(U_37))
& element(sK5(U_37),powerset(U_37)) )
| empty(U_37) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK5]),skolemize(U_36,sK5(U_37))],[f_20_2]) ).
cnf(f_20_4,plain,
( element(sK5(U_37),powerset(U_37))
| empty(U_37) ),
inference(clausify,[status(thm)],[f_20_3]) ).
cnf(f_20_5,plain,
( ~ empty(sK5(U_37))
| empty(U_37) ),
inference(clausify,[status(thm)],[f_20_3]) ).
cnf(f_20_6,plain,
( finite(sK5(U_37))
| empty(U_37) ),
inference(clausify,[status(thm)],[f_20_3]) ).
fof(f_21_1,plain,
! [A] :
( ? [B] :
( finite(B)
& ~ empty(B)
& element(B,powerset(A)) )
| empty(A) ),
inference(fof_nnf,[status(thm)],[rc4_finset_1]) ).
fof(f_21_2,plain,
! [U_39] :
( ? [U_38] :
( finite(U_38)
& ~ empty(U_38)
& element(U_38,powerset(U_39)) )
| empty(U_39) ),
inference(variable_rename,[status(thm)],[f_21_1]) ).
fof(f_21_3,plain,
! [U_39] :
( ( finite(sK6(U_39))
& ~ empty(sK6(U_39))
& element(sK6(U_39),powerset(U_39)) )
| empty(U_39) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK6]),skolemize(U_38,sK6(U_39))],[f_21_2]) ).
cnf(f_21_4,plain,
( element(sK6(U_39),powerset(U_39))
| empty(U_39) ),
inference(clausify,[status(thm)],[f_21_3]) ).
cnf(f_21_5,plain,
( ~ empty(sK6(U_39))
| empty(U_39) ),
inference(clausify,[status(thm)],[f_21_3]) ).
cnf(f_21_6,plain,
( finite(sK6(U_39))
| empty(U_39) ),
inference(clausify,[status(thm)],[f_21_3]) ).
fof(f_22_1,plain,
! [A] : ~ empty(powerset(A)),
inference(fof_nnf,[status(thm)],[fc1_subset_1]) ).
fof(f_22_2,plain,
! [U_40] : ~ empty(powerset(U_40)),
inference(variable_rename,[status(thm)],[f_22_1]) ).
cnf(f_22_3,plain,
~ empty(powerset(U_40)),
inference(clausify,[status(thm)],[f_22_2]) ).
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_42] :
( ? [U_41] :
( ~ empty(U_41)
& element(U_41,powerset(U_42)) )
| empty(U_42) ),
inference(variable_rename,[status(thm)],[f_23_1]) ).
fof(f_23_3,plain,
! [U_42] :
( ( ~ empty(sK7(U_42))
& element(sK7(U_42),powerset(U_42)) )
| empty(U_42) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK7]),skolemize(U_41,sK7(U_42))],[f_23_2]) ).
cnf(f_23_4,plain,
( element(sK7(U_42),powerset(U_42))
| empty(U_42) ),
inference(clausify,[status(thm)],[f_23_3]) ).
cnf(f_23_5,plain,
( ~ empty(sK7(U_42))
| empty(U_42) ),
inference(clausify,[status(thm)],[f_23_3]) ).
fof(f_24_1,plain,
! [A] :
? [B] :
( empty(B)
& element(B,powerset(A)) ),
inference(fof_nnf,[status(thm)],[rc2_subset_1]) ).
fof(f_24_2,plain,
! [U_44] :
? [U_43] :
( empty(U_43)
& element(U_43,powerset(U_44)) ),
inference(variable_rename,[status(thm)],[f_24_1]) ).
fof(f_24_3,plain,
! [U_44] :
( empty(sK8(U_44))
& element(sK8(U_44),powerset(U_44)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK8]),skolemize(U_43,sK8(U_44))],[f_24_2]) ).
cnf(f_24_4,plain,
element(sK8(U_44),powerset(U_44)),
inference(clausify,[status(thm)],[f_24_3]) ).
cnf(f_24_5,plain,
empty(sK8(U_44)),
inference(clausify,[status(thm)],[f_24_3]) ).
fof(f_25_1,plain,
? [A] : empty(A),
inference(fof_nnf,[status(thm)],[rc1_xboole_0]) ).
fof(f_25_2,plain,
? [U_45] : empty(U_45),
inference(variable_rename,[status(thm)],[f_25_1]) ).
fof(f_25_3,plain,
empty(sK9),
inference(skolemize,[status(esa),new_symbols(skolem,[sK9]),skolemize(U_45,sK9)],[f_25_2]) ).
cnf(f_25_4,plain,
empty(sK9),
inference(clausify,[status(thm)],[f_25_3]) ).
fof(f_26_1,plain,
? [A] : ~ empty(A),
inference(fof_nnf,[status(thm)],[rc2_xboole_0]) ).
fof(f_26_2,plain,
? [U_46] : ~ empty(U_46),
inference(variable_rename,[status(thm)],[f_26_1]) ).
fof(f_26_3,plain,
~ empty(sK10),
inference(skolemize,[status(esa),new_symbols(skolem,[sK10]),skolemize(U_46,sK10)],[f_26_2]) ).
cnf(f_26_4,plain,
~ empty(sK10),
inference(clausify,[status(thm)],[f_26_3]) ).
fof(f_27_1,plain,
! [A,B] :
( element(A,B)
| ~ in(A,B) ),
inference(fof_nnf,[status(thm)],[t1_subset]) ).
fof(f_27_2,plain,
! [U_48,U_47] :
( element(U_48,U_47)
| ~ in(U_48,U_47) ),
inference(variable_rename,[status(thm)],[f_27_1]) ).
cnf(f_27_3,plain,
( element(U_48,U_47)
| ~ in(U_48,U_47) ),
inference(clausify,[status(thm)],[f_27_2]) ).
fof(f_28_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_28_2,plain,
! [U_50,U_49] :
( ( element(U_50,powerset(U_49))
| ~ subset(U_50,U_49) )
& ( subset(U_50,U_49)
| ~ element(U_50,powerset(U_49)) ) ),
inference(variable_rename,[status(thm)],[f_28_1]) ).
fof(f_28_3,plain,
( ! [U_54,U_52] :
( element(U_54,powerset(U_52))
| ~ subset(U_54,U_52) )
& ! [U_53,U_51] :
( subset(U_53,U_51)
| ~ element(U_53,powerset(U_51)) ) ),
inference(miniscope,[status(thm)],[f_28_2]) ).
cnf(f_28_4,plain,
( subset(U_53,U_51)
| ~ element(U_53,powerset(U_51)) ),
inference(clausify,[status(thm)],[f_28_3]) ).
cnf(f_28_5,plain,
( element(U_54,powerset(U_52))
| ~ subset(U_54,U_52) ),
inference(clausify,[status(thm)],[f_28_3]) ).
fof(f_29_1,plain,
! [A,B,C] :
( element(A,C)
| ~ element(B,powerset(C))
| ~ in(A,B) ),
inference(fof_nnf,[status(thm)],[t4_subset]) ).
fof(f_29_2,plain,
! [U_57,U_56,U_55] :
( element(U_57,U_55)
| ~ element(U_56,powerset(U_55))
| ~ in(U_57,U_56) ),
inference(variable_rename,[status(thm)],[f_29_1]) ).
cnf(f_29_3,plain,
( element(U_57,U_55)
| ~ element(U_56,powerset(U_55))
| ~ in(U_57,U_56) ),
inference(clausify,[status(thm)],[f_29_2]) ).
fof(f_30_1,plain,
! [A,B] :
( ~ empty(B)
| ~ in(A,B) ),
inference(fof_nnf,[status(thm)],[t7_boole]) ).
fof(f_30_2,plain,
! [U_59,U_58] :
( ~ empty(U_58)
| ~ in(U_59,U_58) ),
inference(variable_rename,[status(thm)],[f_30_1]) ).
cnf(f_30_3,plain,
( ~ empty(U_58)
| ~ in(U_59,U_58) ),
inference(clausify,[status(thm)],[f_30_2]) ).
fof(f_31_1,negated_conjecture,
~ ! [A,B] :
( element(B,finite_subsets(A))
=> element(B,powerset(A)) ),
inference(negate,[status(cth)],[t32_finsub_1]) ).
fof(f_31_2,negated_conjecture,
? [A,B] :
( ~ element(B,powerset(A))
& element(B,finite_subsets(A)) ),
inference(fof_nnf,[status(thm)],[f_31_1]) ).
fof(f_31_3,negated_conjecture,
? [U_61,U_60] :
( ~ element(U_60,powerset(U_61))
& element(U_60,finite_subsets(U_61)) ),
inference(variable_rename,[status(thm)],[f_31_2]) ).
fof(f_31_4,negated_conjecture,
? [U_60] :
( ~ element(U_60,powerset(sK11))
& element(U_60,finite_subsets(sK11)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK11]),skolemize(U_61,sK11)],[f_31_3]) ).
fof(f_31_5,negated_conjecture,
( ~ element(sK12,powerset(sK11))
& element(sK12,finite_subsets(sK11)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK12]),skolemize(U_60,sK12)],[f_31_4]) ).
fof(f_31_6,negated_conjecture,
( ~ element(sK12,powerset(sK11))
& element(sK12,finite_subsets(sK11)) ),
inference(definitional_conversion,[status(esa)],[f_31_5]) ).
cnf(f_31_7,negated_conjecture,
element(sK12,finite_subsets(sK11)),
inference(clausify,[status(thm)],[f_31_6]) ).
cnf(f_31_8,negated_conjecture,
~ element(sK12,powerset(sK11)),
inference(clausify,[status(thm)],[f_31_6]) ).
fof(f_32_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_32_2,plain,
! [U_65,U_64] :
( ( ( U_64 = finite_subsets(U_65)
| ? [U_63] :
( ( ~ in(U_63,U_64)
& finite(U_63)
& subset(U_63,U_65) )
| ( ( ~ finite(U_63)
| ~ subset(U_63,U_65) )
& in(U_63,U_64) ) ) )
& ( ! [U_62] :
( ( in(U_62,U_64)
| ~ finite(U_62)
| ~ subset(U_62,U_65) )
& ( ( finite(U_62)
& subset(U_62,U_65) )
| ~ in(U_62,U_64) ) )
| U_64 != finite_subsets(U_65) ) )
| ~ preboolean(U_64) ),
inference(variable_rename,[status(thm)],[f_32_1]) ).
fof(f_32_3,plain,
! [U_65,U_64] :
( ( ( U_64 = finite_subsets(U_65)
| ? [U_69] :
( ~ in(U_69,U_64)
& finite(U_69)
& subset(U_69,U_65) )
| ? [U_68] :
( ( ~ finite(U_68)
| ~ subset(U_68,U_65) )
& in(U_68,U_64) ) )
& ( ( ! [U_67] :
( in(U_67,U_64)
| ~ finite(U_67)
| ~ subset(U_67,U_65) )
& ! [U_66] :
( ( finite(U_66)
& subset(U_66,U_65) )
| ~ in(U_66,U_64) ) )
| U_64 != finite_subsets(U_65) ) )
| ~ preboolean(U_64) ),
inference(miniscope,[status(thm)],[f_32_2]) ).
fof(f_32_4,plain,
! [U_65,U_64] :
( ( ( U_64 = finite_subsets(U_65)
| ? [U_69] :
( ~ in(U_69,U_64)
& finite(U_69)
& subset(U_69,U_65) )
| ( ( ~ finite(sK13(U_65,U_64))
| ~ subset(sK13(U_65,U_64),U_65) )
& in(sK13(U_65,U_64),U_64) ) )
& ( ( ! [U_67] :
( in(U_67,U_64)
| ~ finite(U_67)
| ~ subset(U_67,U_65) )
& ! [U_66] :
( ( finite(U_66)
& subset(U_66,U_65) )
| ~ in(U_66,U_64) ) )
| U_64 != finite_subsets(U_65) ) )
| ~ preboolean(U_64) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK13]),skolemize(U_68,sK13(U_65,U_64))],[f_32_3]) ).
fof(f_32_5,plain,
! [U_65,U_64] :
( ( ( U_64 = finite_subsets(U_65)
| ( ~ in(sK14(U_65,U_64),U_64)
& finite(sK14(U_65,U_64))
& subset(sK14(U_65,U_64),U_65) )
| ( ( ~ finite(sK13(U_65,U_64))
| ~ subset(sK13(U_65,U_64),U_65) )
& in(sK13(U_65,U_64),U_64) ) )
& ( ( ! [U_67] :
( in(U_67,U_64)
| ~ finite(U_67)
| ~ subset(U_67,U_65) )
& ! [U_66] :
( ( finite(U_66)
& subset(U_66,U_65) )
| ~ in(U_66,U_64) ) )
| U_64 != finite_subsets(U_65) ) )
| ~ preboolean(U_64) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK14]),skolemize(U_69,sK14(U_65,U_64))],[f_32_4]) ).
cnf(f_32_6,plain,
( subset(U_66,U_65)
| ~ in(U_66,U_64)
| U_64 != finite_subsets(U_65)
| ~ preboolean(U_64) ),
inference(clausify,[status(thm)],[f_32_5]) ).
cnf(f_32_7,plain,
( finite(U_66)
| ~ in(U_66,U_64)
| U_64 != finite_subsets(U_65)
| ~ preboolean(U_64) ),
inference(clausify,[status(thm)],[f_32_5]) ).
cnf(f_32_8,plain,
( in(U_67,U_64)
| ~ finite(U_67)
| ~ subset(U_67,U_65)
| U_64 != finite_subsets(U_65)
| ~ preboolean(U_64) ),
inference(clausify,[status(thm)],[f_32_5]) ).
cnf(f_32_9,plain,
( subset(sK14(U_65,U_64),U_65)
| in(sK13(U_65,U_64),U_64)
| U_64 = finite_subsets(U_65)
| ~ preboolean(U_64) ),
inference(clausify,[status(thm)],[f_32_5]) ).
cnf(f_32_10,plain,
( finite(sK14(U_65,U_64))
| in(sK13(U_65,U_64),U_64)
| U_64 = finite_subsets(U_65)
| ~ preboolean(U_64) ),
inference(clausify,[status(thm)],[f_32_5]) ).
cnf(f_32_11,plain,
( ~ in(sK14(U_65,U_64),U_64)
| in(sK13(U_65,U_64),U_64)
| U_64 = finite_subsets(U_65)
| ~ preboolean(U_64) ),
inference(clausify,[status(thm)],[f_32_5]) ).
cnf(f_32_12,plain,
( subset(sK14(U_65,U_64),U_65)
| ~ finite(sK13(U_65,U_64))
| ~ subset(sK13(U_65,U_64),U_65)
| U_64 = finite_subsets(U_65)
| ~ preboolean(U_64) ),
inference(clausify,[status(thm)],[f_32_5]) ).
cnf(f_32_13,plain,
( finite(sK14(U_65,U_64))
| ~ finite(sK13(U_65,U_64))
| ~ subset(sK13(U_65,U_64),U_65)
| U_64 = finite_subsets(U_65)
| ~ preboolean(U_64) ),
inference(clausify,[status(thm)],[f_32_5]) ).
cnf(f_32_14,plain,
( ~ in(sK14(U_65,U_64),U_64)
| ~ finite(sK13(U_65,U_64))
| ~ subset(sK13(U_65,U_64),U_65)
| U_64 = finite_subsets(U_65)
| ~ preboolean(U_64) ),
inference(clausify,[status(thm)],[f_32_5]) ).
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,
( sK1(Eq_x_0) = sK1(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_7,axiom,
( sK4(Eq_x_0) = sK4(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_8,axiom,
( sK5(Eq_x_0) = sK5(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_9,axiom,
( sK6(Eq_x_0) = sK6(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_10,axiom,
( sK7(Eq_x_0) = sK7(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_11,axiom,
( sK8(Eq_x_0) = sK8(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_12,axiom,
( sK13(Eq_x_0,Eq_x_1) = sK13(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_13,axiom,
( sK14(Eq_x_0,Eq_x_1) = sK14(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_14,axiom,
( empty(Eq_y_0)
| ~ empty(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_15,axiom,
( cup_closed(Eq_y_0)
| ~ cup_closed(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_16,axiom,
( diff_closed(Eq_y_0)
| ~ diff_closed(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_17,axiom,
( preboolean(Eq_y_0)
| ~ preboolean(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_18,axiom,
( finite(Eq_y_0)
| ~ finite(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_19,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_20,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_21,axiom,
( subset(Eq_y_0,Eq_y_1)
| ~ subset(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_22,axiom,
( cap_closed(Eq_y_0)
| ~ cap_closed(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_23,axiom,
( relation(Eq_y_0)
| ~ relation(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_24,axiom,
( function(Eq_y_0)
| ~ function(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_25,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_26,axiom,
( epsilon_transitive(Eq_y_0)
| ~ epsilon_transitive(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_27,axiom,
( epsilon_connected(Eq_y_0)
| ~ epsilon_connected(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_28,axiom,
( ordinal(Eq_y_0)
| ~ ordinal(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_29,axiom,
( natural(Eq_y_0)
| ~ natural(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 : SEU117+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 23:20:24 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.45 % SZS status Theorem for theBenchmark
% 0.10/0.45 % SZS output start Proof for theBenchmark
% See solution above
%------------------------------------------------------------------------------