%------------------------------------------------------------------------------
% File : ConnectPP---0.7.2
% Problem : NUM401+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 : n012.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 08:52:10 AM UTC 2026
% Result : Theorem 111.82s 122.17s
% Output : Proof 112.23s
% 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_funct_1,axiom,
! [A] :
( empty(A)
=> function(A) ),
file('theBenchmark.p',cc1_funct_1) ).
fof(cc1_ordinal1,axiom,
! [A] :
( ordinal(A)
=> ( epsilon_connected(A)
& epsilon_transitive(A) ) ),
file('theBenchmark.p',cc1_ordinal1) ).
fof(cc1_relat_1,axiom,
! [A] :
( empty(A)
=> relation(A) ),
file('theBenchmark.p',cc1_relat_1) ).
fof(cc2_funct_1,axiom,
! [A] :
( ( function(A)
& empty(A)
& relation(A) )
=> ( one_to_one(A)
& function(A)
& relation(A) ) ),
file('theBenchmark.p',cc2_funct_1) ).
fof(cc2_ordinal1,axiom,
! [A] :
( ( epsilon_connected(A)
& epsilon_transitive(A) )
=> ordinal(A) ),
file('theBenchmark.p',cc2_ordinal1) ).
fof(cc3_ordinal1,axiom,
! [A] :
( empty(A)
=> ( ordinal(A)
& epsilon_connected(A)
& epsilon_transitive(A) ) ),
file('theBenchmark.p',cc3_ordinal1) ).
fof(commutativity_k2_xboole_0,axiom,
! [A,B] : set_union2(A,B) = set_union2(B,A),
file('theBenchmark.p',commutativity_k2_xboole_0) ).
fof(connectedness_r1_ordinal1,axiom,
! [A,B] :
( ( ordinal(B)
& ordinal(A) )
=> ( ordinal_subset(B,A)
| ordinal_subset(A,B) ) ),
file('theBenchmark.p',connectedness_r1_ordinal1) ).
fof(d10_xboole_0,axiom,
! [A,B] :
( A = B
<=> ( subset(B,A)
& subset(A,B) ) ),
file('theBenchmark.p',d10_xboole_0) ).
fof(d1_ordinal1,axiom,
! [A] : succ(A) = set_union2(A,singleton(A)),
file('theBenchmark.p',d1_ordinal1) ).
fof(d1_tarski,axiom,
! [A,B] :
( B = singleton(A)
<=> ! [C] :
( in(C,B)
<=> C = A ) ),
file('theBenchmark.p',d1_tarski) ).
fof(d2_ordinal1,axiom,
! [A] :
( epsilon_transitive(A)
<=> ! [B] :
( in(B,A)
=> subset(B,A) ) ),
file('theBenchmark.p',d2_ordinal1) ).
fof(d2_xboole_0,axiom,
! [A,B,C] :
( C = set_union2(A,B)
<=> ! [D] :
( in(D,C)
<=> ( in(D,B)
| in(D,A) ) ) ),
file('theBenchmark.p',d2_xboole_0) ).
fof(existence_m1_subset_1,axiom,
! [A] :
? [B] : element(B,A),
file('theBenchmark.p',existence_m1_subset_1) ).
fof(fc12_relat_1,axiom,
( relation_empty_yielding(empty_set)
& relation(empty_set)
& empty(empty_set) ),
file('theBenchmark.p',fc12_relat_1) ).
fof(fc1_ordinal1,axiom,
! [A] : ~ empty(succ(A)),
file('theBenchmark.p',fc1_ordinal1) ).
fof(fc1_xboole_0,axiom,
empty(empty_set),
file('theBenchmark.p',fc1_xboole_0) ).
fof(fc2_ordinal1,axiom,
( ordinal(empty_set)
& epsilon_connected(empty_set)
& epsilon_transitive(empty_set)
& empty(empty_set)
& one_to_one(empty_set)
& function(empty_set)
& relation_empty_yielding(empty_set)
& relation(empty_set) ),
file('theBenchmark.p',fc2_ordinal1) ).
fof(fc2_relat_1,axiom,
! [A,B] :
( ( relation(B)
& relation(A) )
=> relation(set_union2(A,B)) ),
file('theBenchmark.p',fc2_relat_1) ).
fof(fc2_xboole_0,axiom,
! [A,B] :
( ~ empty(A)
=> ~ empty(set_union2(A,B)) ),
file('theBenchmark.p',fc2_xboole_0) ).
fof(fc3_ordinal1,axiom,
! [A] :
( ordinal(A)
=> ( ordinal(succ(A))
& epsilon_connected(succ(A))
& epsilon_transitive(succ(A))
& ~ empty(succ(A)) ) ),
file('theBenchmark.p',fc3_ordinal1) ).
fof(fc3_xboole_0,axiom,
! [A,B] :
( ~ empty(A)
=> ~ empty(set_union2(B,A)) ),
file('theBenchmark.p',fc3_xboole_0) ).
fof(fc4_relat_1,axiom,
( relation(empty_set)
& empty(empty_set) ),
file('theBenchmark.p',fc4_relat_1) ).
fof(idempotence_k2_xboole_0,axiom,
! [A,B] : set_union2(A,A) = A,
file('theBenchmark.p',idempotence_k2_xboole_0) ).
fof(rc1_funct_1,axiom,
? [A] :
( function(A)
& relation(A) ),
file('theBenchmark.p',rc1_funct_1) ).
fof(rc1_ordinal1,axiom,
? [A] :
( ordinal(A)
& epsilon_connected(A)
& epsilon_transitive(A) ),
file('theBenchmark.p',rc1_ordinal1) ).
fof(rc1_relat_1,axiom,
? [A] :
( relation(A)
& empty(A) ),
file('theBenchmark.p',rc1_relat_1) ).
fof(rc1_xboole_0,axiom,
? [A] : empty(A),
file('theBenchmark.p',rc1_xboole_0) ).
fof(rc2_funct_1,axiom,
? [A] :
( function(A)
& empty(A)
& relation(A) ),
file('theBenchmark.p',rc2_funct_1) ).
fof(rc2_ordinal1,axiom,
? [A] :
( ordinal(A)
& epsilon_connected(A)
& epsilon_transitive(A)
& empty(A)
& one_to_one(A)
& function(A)
& relation(A) ),
file('theBenchmark.p',rc2_ordinal1) ).
fof(rc2_relat_1,axiom,
? [A] :
( relation(A)
& ~ empty(A) ),
file('theBenchmark.p',rc2_relat_1) ).
fof(rc2_xboole_0,axiom,
? [A] : ~ empty(A),
file('theBenchmark.p',rc2_xboole_0) ).
fof(rc3_funct_1,axiom,
? [A] :
( one_to_one(A)
& function(A)
& relation(A) ),
file('theBenchmark.p',rc3_funct_1) ).
fof(rc3_ordinal1,axiom,
? [A] :
( ordinal(A)
& epsilon_connected(A)
& epsilon_transitive(A)
& ~ empty(A) ),
file('theBenchmark.p',rc3_ordinal1) ).
fof(rc3_relat_1,axiom,
? [A] :
( relation_empty_yielding(A)
& relation(A) ),
file('theBenchmark.p',rc3_relat_1) ).
fof(rc4_funct_1,axiom,
? [A] :
( function(A)
& relation_empty_yielding(A)
& relation(A) ),
file('theBenchmark.p',rc4_funct_1) ).
fof(rc5_funct_1,axiom,
? [A] :
( function(A)
& relation_non_empty(A)
& relation(A) ),
file('theBenchmark.p',rc5_funct_1) ).
fof(redefinition_r1_ordinal1,axiom,
! [A,B] :
( ( ordinal(B)
& ordinal(A) )
=> ( ordinal_subset(A,B)
<=> subset(A,B) ) ),
file('theBenchmark.p',redefinition_r1_ordinal1) ).
fof(reflexivity_r1_ordinal1,axiom,
! [A,B] :
( ( ordinal(B)
& ordinal(A) )
=> ordinal_subset(A,A) ),
file('theBenchmark.p',reflexivity_r1_ordinal1) ).
fof(reflexivity_r1_tarski,axiom,
! [A,B] : subset(A,A),
file('theBenchmark.p',reflexivity_r1_tarski) ).
fof(t10_ordinal1,axiom,
! [A] : in(A,succ(A)),
file('theBenchmark.p',t10_ordinal1) ).
fof(t14_ordinal1,axiom,
! [A] : A != succ(A),
file('theBenchmark.p',t14_ordinal1) ).
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(t24_ordinal1,axiom,
! [A] :
( ordinal(A)
=> ! [B] :
( ordinal(B)
=> ~ ( ~ in(B,A)
& A != B
& ~ in(A,B) ) ) ),
file('theBenchmark.p',t24_ordinal1) ).
fof(t2_subset,axiom,
! [A,B] :
( element(A,B)
=> ( in(A,B)
| empty(B) ) ),
file('theBenchmark.p',t2_subset) ).
fof(t34_ordinal1,conjecture,
! [A] :
( ordinal(A)
=> ! [B] :
( ordinal(B)
=> ( in(A,succ(B))
<=> ordinal_subset(A,B) ) ) ),
file('theBenchmark.p',t34_ordinal1) ).
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]) ).
cnf(f_1_3,plain,
( ~ in(U_0,U_1)
| ~ in(U_1,U_0) ),
inference(clausify,[status(thm)],[f_1_2]) ).
fof(f_2_1,plain,
! [A] :
( function(A)
| ~ empty(A) ),
inference(fof_nnf,[status(thm)],[cc1_funct_1]) ).
fof(f_2_2,plain,
! [U_2] :
( function(U_2)
| ~ empty(U_2) ),
inference(variable_rename,[status(thm)],[f_2_1]) ).
cnf(f_2_3,plain,
( function(U_2)
| ~ empty(U_2) ),
inference(clausify,[status(thm)],[f_2_2]) ).
fof(f_3_1,plain,
! [A] :
( ( epsilon_connected(A)
& epsilon_transitive(A) )
| ~ ordinal(A) ),
inference(fof_nnf,[status(thm)],[cc1_ordinal1]) ).
fof(f_3_2,plain,
! [U_3] :
( ( epsilon_connected(U_3)
& epsilon_transitive(U_3) )
| ~ ordinal(U_3) ),
inference(variable_rename,[status(thm)],[f_3_1]) ).
cnf(f_3_3,plain,
( epsilon_transitive(U_3)
| ~ ordinal(U_3) ),
inference(clausify,[status(thm)],[f_3_2]) ).
cnf(f_3_4,plain,
( epsilon_connected(U_3)
| ~ ordinal(U_3) ),
inference(clausify,[status(thm)],[f_3_2]) ).
fof(f_4_1,plain,
! [A] :
( relation(A)
| ~ empty(A) ),
inference(fof_nnf,[status(thm)],[cc1_relat_1]) ).
fof(f_4_2,plain,
! [U_4] :
( relation(U_4)
| ~ empty(U_4) ),
inference(variable_rename,[status(thm)],[f_4_1]) ).
cnf(f_4_3,plain,
( relation(U_4)
| ~ empty(U_4) ),
inference(clausify,[status(thm)],[f_4_2]) ).
fof(f_5_1,plain,
! [A] :
( ( one_to_one(A)
& function(A)
& relation(A) )
| ~ function(A)
| ~ empty(A)
| ~ relation(A) ),
inference(fof_nnf,[status(thm)],[cc2_funct_1]) ).
fof(f_5_2,plain,
! [U_5] :
( ( one_to_one(U_5)
& function(U_5)
& relation(U_5) )
| ~ function(U_5)
| ~ empty(U_5)
| ~ relation(U_5) ),
inference(variable_rename,[status(thm)],[f_5_1]) ).
cnf(f_5_3,plain,
( relation(U_5)
| ~ function(U_5)
| ~ empty(U_5)
| ~ relation(U_5) ),
inference(clausify,[status(thm)],[f_5_2]) ).
cnf(f_5_4,plain,
( function(U_5)
| ~ function(U_5)
| ~ empty(U_5)
| ~ relation(U_5) ),
inference(clausify,[status(thm)],[f_5_2]) ).
cnf(f_5_5,plain,
( one_to_one(U_5)
| ~ function(U_5)
| ~ empty(U_5)
| ~ relation(U_5) ),
inference(clausify,[status(thm)],[f_5_2]) ).
fof(f_6_1,plain,
! [A] :
( ordinal(A)
| ~ epsilon_connected(A)
| ~ epsilon_transitive(A) ),
inference(fof_nnf,[status(thm)],[cc2_ordinal1]) ).
fof(f_6_2,plain,
! [U_6] :
( ordinal(U_6)
| ~ epsilon_connected(U_6)
| ~ epsilon_transitive(U_6) ),
inference(variable_rename,[status(thm)],[f_6_1]) ).
cnf(f_6_3,plain,
( ordinal(U_6)
| ~ epsilon_connected(U_6)
| ~ epsilon_transitive(U_6) ),
inference(clausify,[status(thm)],[f_6_2]) ).
fof(f_7_1,plain,
! [A] :
( ( ordinal(A)
& epsilon_connected(A)
& epsilon_transitive(A) )
| ~ empty(A) ),
inference(fof_nnf,[status(thm)],[cc3_ordinal1]) ).
fof(f_7_2,plain,
! [U_7] :
( ( ordinal(U_7)
& epsilon_connected(U_7)
& epsilon_transitive(U_7) )
| ~ empty(U_7) ),
inference(variable_rename,[status(thm)],[f_7_1]) ).
cnf(f_7_3,plain,
( epsilon_transitive(U_7)
| ~ empty(U_7) ),
inference(clausify,[status(thm)],[f_7_2]) ).
cnf(f_7_4,plain,
( epsilon_connected(U_7)
| ~ empty(U_7) ),
inference(clausify,[status(thm)],[f_7_2]) ).
cnf(f_7_5,plain,
( ordinal(U_7)
| ~ empty(U_7) ),
inference(clausify,[status(thm)],[f_7_2]) ).
fof(f_8_1,plain,
! [A,B] : set_union2(A,B) = set_union2(B,A),
inference(fof_nnf,[status(thm)],[commutativity_k2_xboole_0]) ).
fof(f_8_2,plain,
! [U_9,U_8] : set_union2(U_9,U_8) = set_union2(U_8,U_9),
inference(variable_rename,[status(thm)],[f_8_1]) ).
cnf(f_8_3,plain,
set_union2(U_9,U_8) = set_union2(U_8,U_9),
inference(clausify,[status(thm)],[f_8_2]) ).
fof(f_9_1,plain,
! [A,B] :
( ordinal_subset(B,A)
| ordinal_subset(A,B)
| ~ ordinal(B)
| ~ ordinal(A) ),
inference(fof_nnf,[status(thm)],[connectedness_r1_ordinal1]) ).
fof(f_9_2,plain,
! [U_11,U_10] :
( ordinal_subset(U_10,U_11)
| ordinal_subset(U_11,U_10)
| ~ ordinal(U_10)
| ~ ordinal(U_11) ),
inference(variable_rename,[status(thm)],[f_9_1]) ).
cnf(f_9_3,plain,
( ordinal_subset(U_10,U_11)
| ordinal_subset(U_11,U_10)
| ~ ordinal(U_10)
| ~ ordinal(U_11) ),
inference(clausify,[status(thm)],[f_9_2]) ).
fof(f_10_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_10_2,plain,
! [U_13,U_12] :
( ( U_13 = U_12
| ~ subset(U_12,U_13)
| ~ subset(U_13,U_12) )
& ( ( subset(U_12,U_13)
& subset(U_13,U_12) )
| U_13 != U_12 ) ),
inference(variable_rename,[status(thm)],[f_10_1]) ).
fof(f_10_3,plain,
( ! [U_17,U_15] :
( U_17 = U_15
| ~ subset(U_15,U_17)
| ~ subset(U_17,U_15) )
& ! [U_16,U_14] :
( ( subset(U_14,U_16)
& subset(U_16,U_14) )
| U_16 != U_14 ) ),
inference(miniscope,[status(thm)],[f_10_2]) ).
cnf(f_10_4,plain,
( subset(U_16,U_14)
| U_16 != U_14 ),
inference(clausify,[status(thm)],[f_10_3]) ).
cnf(f_10_5,plain,
( subset(U_14,U_16)
| U_16 != U_14 ),
inference(clausify,[status(thm)],[f_10_3]) ).
cnf(f_10_6,plain,
( U_17 = U_15
| ~ subset(U_15,U_17)
| ~ subset(U_17,U_15) ),
inference(clausify,[status(thm)],[f_10_3]) ).
fof(f_11_1,plain,
! [A] : succ(A) = set_union2(A,singleton(A)),
inference(fof_nnf,[status(thm)],[d1_ordinal1]) ).
fof(f_11_2,plain,
! [U_18] : succ(U_18) = set_union2(U_18,singleton(U_18)),
inference(variable_rename,[status(thm)],[f_11_1]) ).
cnf(f_11_3,plain,
succ(U_18) = set_union2(U_18,singleton(U_18)),
inference(clausify,[status(thm)],[f_11_2]) ).
fof(f_12_1,plain,
! [A,B] :
( ( B = singleton(A)
| ? [C] :
( ( ~ in(C,B)
& C = A )
| ( C != A
& in(C,B) ) ) )
& ( ! [C] :
( ( in(C,B)
| C != A )
& ( C = A
| ~ in(C,B) ) )
| B != singleton(A) ) ),
inference(fof_nnf,[status(thm)],[d1_tarski]) ).
fof(f_12_2,plain,
! [U_22,U_21] :
( ( U_21 = singleton(U_22)
| ? [U_20] :
( ( ~ in(U_20,U_21)
& U_20 = U_22 )
| ( U_20 != U_22
& in(U_20,U_21) ) ) )
& ( ! [U_19] :
( ( in(U_19,U_21)
| U_19 != U_22 )
& ( U_19 = U_22
| ~ in(U_19,U_21) ) )
| U_21 != singleton(U_22) ) ),
inference(variable_rename,[status(thm)],[f_12_1]) ).
fof(f_12_3,plain,
( ! [U_30,U_28] :
( U_28 = singleton(U_30)
| ? [U_26] :
( ~ in(U_26,U_28)
& U_26 = U_30 )
| ? [U_25] :
( U_25 != U_30
& in(U_25,U_28) ) )
& ! [U_29,U_27] :
( ( ! [U_24] :
( in(U_24,U_27)
| U_24 != U_29 )
& ! [U_23] :
( U_23 = U_29
| ~ in(U_23,U_27) ) )
| U_27 != singleton(U_29) ) ),
inference(miniscope,[status(thm)],[f_12_2]) ).
fof(f_12_4,plain,
( ! [U_30,U_28] :
( U_28 = singleton(U_30)
| ? [U_26] :
( ~ in(U_26,U_28)
& U_26 = U_30 )
| ( sK1(U_30,U_28) != U_30
& in(sK1(U_30,U_28),U_28) ) )
& ! [U_29,U_27] :
( ( ! [U_24] :
( in(U_24,U_27)
| U_24 != U_29 )
& ! [U_23] :
( U_23 = U_29
| ~ in(U_23,U_27) ) )
| U_27 != singleton(U_29) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(U_25,sK1(U_30,U_28))],[f_12_3]) ).
fof(f_12_5,plain,
( ! [U_30,U_28] :
( U_28 = singleton(U_30)
| ( ~ in(sK2(U_30,U_28),U_28)
& sK2(U_30,U_28) = U_30 )
| ( sK1(U_30,U_28) != U_30
& in(sK1(U_30,U_28),U_28) ) )
& ! [U_29,U_27] :
( ( ! [U_24] :
( in(U_24,U_27)
| U_24 != U_29 )
& ! [U_23] :
( U_23 = U_29
| ~ in(U_23,U_27) ) )
| U_27 != singleton(U_29) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2]),skolemize(U_26,sK2(U_30,U_28))],[f_12_4]) ).
cnf(f_12_6,plain,
( U_23 = U_29
| ~ in(U_23,U_27)
| U_27 != singleton(U_29) ),
inference(clausify,[status(thm)],[f_12_5]) ).
cnf(f_12_7,plain,
( in(U_24,U_27)
| U_24 != U_29
| U_27 != singleton(U_29) ),
inference(clausify,[status(thm)],[f_12_5]) ).
cnf(f_12_8,plain,
( sK2(U_30,U_28) = U_30
| in(sK1(U_30,U_28),U_28)
| U_28 = singleton(U_30) ),
inference(clausify,[status(thm)],[f_12_5]) ).
cnf(f_12_9,plain,
( ~ in(sK2(U_30,U_28),U_28)
| in(sK1(U_30,U_28),U_28)
| U_28 = singleton(U_30) ),
inference(clausify,[status(thm)],[f_12_5]) ).
cnf(f_12_10,plain,
( sK2(U_30,U_28) = U_30
| sK1(U_30,U_28) != U_30
| U_28 = singleton(U_30) ),
inference(clausify,[status(thm)],[f_12_5]) ).
cnf(f_12_11,plain,
( ~ in(sK2(U_30,U_28),U_28)
| sK1(U_30,U_28) != U_30
| U_28 = singleton(U_30) ),
inference(clausify,[status(thm)],[f_12_5]) ).
fof(f_13_1,plain,
! [A] :
( ( epsilon_transitive(A)
| ? [B] :
( ~ subset(B,A)
& in(B,A) ) )
& ( ! [B] :
( subset(B,A)
| ~ in(B,A) )
| ~ epsilon_transitive(A) ) ),
inference(fof_nnf,[status(thm)],[d2_ordinal1]) ).
fof(f_13_2,plain,
! [U_33] :
( ( epsilon_transitive(U_33)
| ? [U_32] :
( ~ subset(U_32,U_33)
& in(U_32,U_33) ) )
& ( ! [U_31] :
( subset(U_31,U_33)
| ~ in(U_31,U_33) )
| ~ epsilon_transitive(U_33) ) ),
inference(variable_rename,[status(thm)],[f_13_1]) ).
fof(f_13_3,plain,
( ! [U_35] :
( epsilon_transitive(U_35)
| ? [U_32] :
( ~ subset(U_32,U_35)
& in(U_32,U_35) ) )
& ! [U_34] :
( ! [U_31] :
( subset(U_31,U_34)
| ~ in(U_31,U_34) )
| ~ epsilon_transitive(U_34) ) ),
inference(miniscope,[status(thm)],[f_13_2]) ).
fof(f_13_4,plain,
( ! [U_35] :
( epsilon_transitive(U_35)
| ( ~ subset(sK3(U_35),U_35)
& in(sK3(U_35),U_35) ) )
& ! [U_34] :
( ! [U_31] :
( subset(U_31,U_34)
| ~ in(U_31,U_34) )
| ~ epsilon_transitive(U_34) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3]),skolemize(U_32,sK3(U_35))],[f_13_3]) ).
cnf(f_13_5,plain,
( subset(U_31,U_34)
| ~ in(U_31,U_34)
| ~ epsilon_transitive(U_34) ),
inference(clausify,[status(thm)],[f_13_4]) ).
cnf(f_13_6,plain,
( in(sK3(U_35),U_35)
| epsilon_transitive(U_35) ),
inference(clausify,[status(thm)],[f_13_4]) ).
cnf(f_13_7,plain,
( ~ subset(sK3(U_35),U_35)
| epsilon_transitive(U_35) ),
inference(clausify,[status(thm)],[f_13_4]) ).
fof(f_14_1,plain,
! [A,B,C] :
( ( C = set_union2(A,B)
| ? [D] :
( ( ~ in(D,C)
& ( in(D,B)
| in(D,A) ) )
| ( ~ in(D,B)
& ~ in(D,A)
& in(D,C) ) ) )
& ( ! [D] :
( ( in(D,C)
| ( ~ in(D,B)
& ~ in(D,A) ) )
& ( in(D,B)
| in(D,A)
| ~ in(D,C) ) )
| C != set_union2(A,B) ) ),
inference(fof_nnf,[status(thm)],[d2_xboole_0]) ).
fof(f_14_2,plain,
! [U_40,U_39,U_38] :
( ( U_38 = set_union2(U_40,U_39)
| ? [U_37] :
( ( ~ in(U_37,U_38)
& ( in(U_37,U_39)
| in(U_37,U_40) ) )
| ( ~ in(U_37,U_39)
& ~ in(U_37,U_40)
& in(U_37,U_38) ) ) )
& ( ! [U_36] :
( ( in(U_36,U_38)
| ( ~ in(U_36,U_39)
& ~ in(U_36,U_40) ) )
& ( in(U_36,U_39)
| in(U_36,U_40)
| ~ in(U_36,U_38) ) )
| U_38 != set_union2(U_40,U_39) ) ),
inference(variable_rename,[status(thm)],[f_14_1]) ).
fof(f_14_3,plain,
( ! [U_50,U_48,U_46] :
( U_46 = set_union2(U_50,U_48)
| ? [U_44] :
( ~ in(U_44,U_46)
& ( in(U_44,U_48)
| in(U_44,U_50) ) )
| ? [U_43] :
( ~ in(U_43,U_48)
& ~ in(U_43,U_50)
& in(U_43,U_46) ) )
& ! [U_49,U_47,U_45] :
( ( ! [U_42] :
( in(U_42,U_45)
| ( ~ in(U_42,U_47)
& ~ in(U_42,U_49) ) )
& ! [U_41] :
( in(U_41,U_47)
| in(U_41,U_49)
| ~ in(U_41,U_45) ) )
| U_45 != set_union2(U_49,U_47) ) ),
inference(miniscope,[status(thm)],[f_14_2]) ).
fof(f_14_4,plain,
( ! [U_50,U_48,U_46] :
( U_46 = set_union2(U_50,U_48)
| ? [U_44] :
( ~ in(U_44,U_46)
& ( in(U_44,U_48)
| in(U_44,U_50) ) )
| ( ~ in(sK4(U_50,U_48,U_46),U_48)
& ~ in(sK4(U_50,U_48,U_46),U_50)
& in(sK4(U_50,U_48,U_46),U_46) ) )
& ! [U_49,U_47,U_45] :
( ( ! [U_42] :
( in(U_42,U_45)
| ( ~ in(U_42,U_47)
& ~ in(U_42,U_49) ) )
& ! [U_41] :
( in(U_41,U_47)
| in(U_41,U_49)
| ~ in(U_41,U_45) ) )
| U_45 != set_union2(U_49,U_47) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4]),skolemize(U_43,sK4(U_50,U_48,U_46))],[f_14_3]) ).
fof(f_14_5,plain,
( ! [U_50,U_48,U_46] :
( U_46 = set_union2(U_50,U_48)
| ( ~ in(sK5(U_50,U_48,U_46),U_46)
& ( in(sK5(U_50,U_48,U_46),U_48)
| in(sK5(U_50,U_48,U_46),U_50) ) )
| ( ~ in(sK4(U_50,U_48,U_46),U_48)
& ~ in(sK4(U_50,U_48,U_46),U_50)
& in(sK4(U_50,U_48,U_46),U_46) ) )
& ! [U_49,U_47,U_45] :
( ( ! [U_42] :
( in(U_42,U_45)
| ( ~ in(U_42,U_47)
& ~ in(U_42,U_49) ) )
& ! [U_41] :
( in(U_41,U_47)
| in(U_41,U_49)
| ~ in(U_41,U_45) ) )
| U_45 != set_union2(U_49,U_47) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK5]),skolemize(U_44,sK5(U_50,U_48,U_46))],[f_14_4]) ).
cnf(f_14_6,plain,
( in(U_41,U_47)
| in(U_41,U_49)
| ~ in(U_41,U_45)
| U_45 != set_union2(U_49,U_47) ),
inference(clausify,[status(thm)],[f_14_5]) ).
cnf(f_14_7,plain,
( ~ in(U_42,U_49)
| in(U_42,U_45)
| U_45 != set_union2(U_49,U_47) ),
inference(clausify,[status(thm)],[f_14_5]) ).
cnf(f_14_8,plain,
( ~ in(U_42,U_47)
| in(U_42,U_45)
| U_45 != set_union2(U_49,U_47) ),
inference(clausify,[status(thm)],[f_14_5]) ).
cnf(f_14_9,plain,
( in(sK5(U_50,U_48,U_46),U_48)
| in(sK5(U_50,U_48,U_46),U_50)
| in(sK4(U_50,U_48,U_46),U_46)
| U_46 = set_union2(U_50,U_48) ),
inference(clausify,[status(thm)],[f_14_5]) ).
cnf(f_14_10,plain,
( ~ in(sK5(U_50,U_48,U_46),U_46)
| in(sK4(U_50,U_48,U_46),U_46)
| U_46 = set_union2(U_50,U_48) ),
inference(clausify,[status(thm)],[f_14_5]) ).
cnf(f_14_11,plain,
( ~ in(sK4(U_50,U_48,U_46),U_50)
| in(sK5(U_50,U_48,U_46),U_48)
| in(sK5(U_50,U_48,U_46),U_50)
| U_46 = set_union2(U_50,U_48) ),
inference(clausify,[status(thm)],[f_14_5]) ).
cnf(f_14_12,plain,
( ~ in(sK4(U_50,U_48,U_46),U_48)
| in(sK5(U_50,U_48,U_46),U_48)
| in(sK5(U_50,U_48,U_46),U_50)
| U_46 = set_union2(U_50,U_48) ),
inference(clausify,[status(thm)],[f_14_5]) ).
cnf(f_14_13,plain,
( ~ in(sK4(U_50,U_48,U_46),U_50)
| ~ in(sK5(U_50,U_48,U_46),U_46)
| U_46 = set_union2(U_50,U_48) ),
inference(clausify,[status(thm)],[f_14_5]) ).
cnf(f_14_14,plain,
( ~ in(sK4(U_50,U_48,U_46),U_48)
| ~ in(sK5(U_50,U_48,U_46),U_46)
| U_46 = set_union2(U_50,U_48) ),
inference(clausify,[status(thm)],[f_14_5]) ).
fof(f_15_1,plain,
! [A] :
? [B] : element(B,A),
inference(fof_nnf,[status(thm)],[existence_m1_subset_1]) ).
fof(f_15_2,plain,
! [U_52] :
? [U_51] : element(U_51,U_52),
inference(variable_rename,[status(thm)],[f_15_1]) ).
fof(f_15_3,plain,
! [U_52] : element(sK6(U_52),U_52),
inference(skolemize,[status(esa),new_symbols(skolem,[sK6]),skolemize(U_51,sK6(U_52))],[f_15_2]) ).
cnf(f_15_4,plain,
element(sK6(U_52),U_52),
inference(clausify,[status(thm)],[f_15_3]) ).
fof(f_16_1,plain,
( relation_empty_yielding(empty_set)
& relation(empty_set)
& empty(empty_set) ),
inference(fof_nnf,[status(thm)],[fc12_relat_1]) ).
cnf(f_16_2,plain,
empty(empty_set),
inference(clausify,[status(thm)],[f_16_1]) ).
cnf(f_16_3,plain,
relation(empty_set),
inference(clausify,[status(thm)],[f_16_1]) ).
cnf(f_16_4,plain,
relation_empty_yielding(empty_set),
inference(clausify,[status(thm)],[f_16_1]) ).
fof(f_17_1,plain,
! [A] : ~ empty(succ(A)),
inference(fof_nnf,[status(thm)],[fc1_ordinal1]) ).
fof(f_17_2,plain,
! [U_53] : ~ empty(succ(U_53)),
inference(variable_rename,[status(thm)],[f_17_1]) ).
cnf(f_17_3,plain,
~ empty(succ(U_53)),
inference(clausify,[status(thm)],[f_17_2]) ).
fof(f_18_1,plain,
empty(empty_set),
inference(fof_nnf,[status(thm)],[fc1_xboole_0]) ).
cnf(f_18_2,plain,
empty(empty_set),
inference(clausify,[status(thm)],[f_18_1]) ).
fof(f_19_1,plain,
( ordinal(empty_set)
& epsilon_connected(empty_set)
& epsilon_transitive(empty_set)
& empty(empty_set)
& one_to_one(empty_set)
& function(empty_set)
& relation_empty_yielding(empty_set)
& relation(empty_set) ),
inference(fof_nnf,[status(thm)],[fc2_ordinal1]) ).
cnf(f_19_2,plain,
relation(empty_set),
inference(clausify,[status(thm)],[f_19_1]) ).
cnf(f_19_3,plain,
relation_empty_yielding(empty_set),
inference(clausify,[status(thm)],[f_19_1]) ).
cnf(f_19_4,plain,
function(empty_set),
inference(clausify,[status(thm)],[f_19_1]) ).
cnf(f_19_5,plain,
one_to_one(empty_set),
inference(clausify,[status(thm)],[f_19_1]) ).
cnf(f_19_6,plain,
empty(empty_set),
inference(clausify,[status(thm)],[f_19_1]) ).
cnf(f_19_7,plain,
epsilon_transitive(empty_set),
inference(clausify,[status(thm)],[f_19_1]) ).
cnf(f_19_8,plain,
epsilon_connected(empty_set),
inference(clausify,[status(thm)],[f_19_1]) ).
cnf(f_19_9,plain,
ordinal(empty_set),
inference(clausify,[status(thm)],[f_19_1]) ).
fof(f_20_1,plain,
! [A,B] :
( relation(set_union2(A,B))
| ~ relation(B)
| ~ relation(A) ),
inference(fof_nnf,[status(thm)],[fc2_relat_1]) ).
fof(f_20_2,plain,
! [U_55,U_54] :
( relation(set_union2(U_55,U_54))
| ~ relation(U_54)
| ~ relation(U_55) ),
inference(variable_rename,[status(thm)],[f_20_1]) ).
cnf(f_20_3,plain,
( relation(set_union2(U_55,U_54))
| ~ relation(U_54)
| ~ relation(U_55) ),
inference(clausify,[status(thm)],[f_20_2]) ).
fof(f_21_1,plain,
! [A,B] :
( ~ empty(set_union2(A,B))
| empty(A) ),
inference(fof_nnf,[status(thm)],[fc2_xboole_0]) ).
fof(f_21_2,plain,
! [U_57,U_56] :
( ~ empty(set_union2(U_57,U_56))
| empty(U_57) ),
inference(variable_rename,[status(thm)],[f_21_1]) ).
fof(f_21_3,plain,
! [U_57] :
( ! [U_56] : ~ empty(set_union2(U_57,U_56))
| empty(U_57) ),
inference(miniscope,[status(thm)],[f_21_2]) ).
cnf(f_21_4,plain,
( ~ empty(set_union2(U_57,U_56))
| empty(U_57) ),
inference(clausify,[status(thm)],[f_21_3]) ).
fof(f_22_1,plain,
! [A] :
( ( ordinal(succ(A))
& epsilon_connected(succ(A))
& epsilon_transitive(succ(A))
& ~ empty(succ(A)) )
| ~ ordinal(A) ),
inference(fof_nnf,[status(thm)],[fc3_ordinal1]) ).
fof(f_22_2,plain,
! [U_58] :
( ( ordinal(succ(U_58))
& epsilon_connected(succ(U_58))
& epsilon_transitive(succ(U_58))
& ~ empty(succ(U_58)) )
| ~ ordinal(U_58) ),
inference(variable_rename,[status(thm)],[f_22_1]) ).
cnf(f_22_3,plain,
( ~ empty(succ(U_58))
| ~ ordinal(U_58) ),
inference(clausify,[status(thm)],[f_22_2]) ).
cnf(f_22_4,plain,
( epsilon_transitive(succ(U_58))
| ~ ordinal(U_58) ),
inference(clausify,[status(thm)],[f_22_2]) ).
cnf(f_22_5,plain,
( epsilon_connected(succ(U_58))
| ~ ordinal(U_58) ),
inference(clausify,[status(thm)],[f_22_2]) ).
cnf(f_22_6,plain,
( ordinal(succ(U_58))
| ~ ordinal(U_58) ),
inference(clausify,[status(thm)],[f_22_2]) ).
fof(f_23_1,plain,
! [A,B] :
( ~ empty(set_union2(B,A))
| empty(A) ),
inference(fof_nnf,[status(thm)],[fc3_xboole_0]) ).
fof(f_23_2,plain,
! [U_60,U_59] :
( ~ empty(set_union2(U_59,U_60))
| empty(U_60) ),
inference(variable_rename,[status(thm)],[f_23_1]) ).
fof(f_23_3,plain,
! [U_60] :
( ! [U_59] : ~ empty(set_union2(U_59,U_60))
| empty(U_60) ),
inference(miniscope,[status(thm)],[f_23_2]) ).
cnf(f_23_4,plain,
( ~ empty(set_union2(U_59,U_60))
| empty(U_60) ),
inference(clausify,[status(thm)],[f_23_3]) ).
fof(f_24_1,plain,
( relation(empty_set)
& empty(empty_set) ),
inference(fof_nnf,[status(thm)],[fc4_relat_1]) ).
cnf(f_24_2,plain,
empty(empty_set),
inference(clausify,[status(thm)],[f_24_1]) ).
cnf(f_24_3,plain,
relation(empty_set),
inference(clausify,[status(thm)],[f_24_1]) ).
fof(f_25_1,plain,
! [A,B] : set_union2(A,A) = A,
inference(fof_nnf,[status(thm)],[idempotence_k2_xboole_0]) ).
fof(f_25_2,plain,
! [U_62,U_61] : set_union2(U_62,U_62) = U_62,
inference(variable_rename,[status(thm)],[f_25_1]) ).
fof(f_25_3,plain,
! [U_62] : set_union2(U_62,U_62) = U_62,
inference(miniscope,[status(thm)],[f_25_2]) ).
cnf(f_25_4,plain,
set_union2(U_62,U_62) = U_62,
inference(clausify,[status(thm)],[f_25_3]) ).
fof(f_26_1,plain,
? [A] :
( function(A)
& relation(A) ),
inference(fof_nnf,[status(thm)],[rc1_funct_1]) ).
fof(f_26_2,plain,
? [U_63] :
( function(U_63)
& relation(U_63) ),
inference(variable_rename,[status(thm)],[f_26_1]) ).
fof(f_26_3,plain,
( function(sK7)
& relation(sK7) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK7]),skolemize(U_63,sK7)],[f_26_2]) ).
cnf(f_26_4,plain,
relation(sK7),
inference(clausify,[status(thm)],[f_26_3]) ).
cnf(f_26_5,plain,
function(sK7),
inference(clausify,[status(thm)],[f_26_3]) ).
fof(f_27_1,plain,
? [A] :
( ordinal(A)
& epsilon_connected(A)
& epsilon_transitive(A) ),
inference(fof_nnf,[status(thm)],[rc1_ordinal1]) ).
fof(f_27_2,plain,
? [U_64] :
( ordinal(U_64)
& epsilon_connected(U_64)
& epsilon_transitive(U_64) ),
inference(variable_rename,[status(thm)],[f_27_1]) ).
fof(f_27_3,plain,
( ordinal(sK8)
& epsilon_connected(sK8)
& epsilon_transitive(sK8) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK8]),skolemize(U_64,sK8)],[f_27_2]) ).
cnf(f_27_4,plain,
epsilon_transitive(sK8),
inference(clausify,[status(thm)],[f_27_3]) ).
cnf(f_27_5,plain,
epsilon_connected(sK8),
inference(clausify,[status(thm)],[f_27_3]) ).
cnf(f_27_6,plain,
ordinal(sK8),
inference(clausify,[status(thm)],[f_27_3]) ).
fof(f_28_1,plain,
? [A] :
( relation(A)
& empty(A) ),
inference(fof_nnf,[status(thm)],[rc1_relat_1]) ).
fof(f_28_2,plain,
? [U_65] :
( relation(U_65)
& empty(U_65) ),
inference(variable_rename,[status(thm)],[f_28_1]) ).
fof(f_28_3,plain,
( relation(sK9)
& empty(sK9) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK9]),skolemize(U_65,sK9)],[f_28_2]) ).
cnf(f_28_4,plain,
empty(sK9),
inference(clausify,[status(thm)],[f_28_3]) ).
cnf(f_28_5,plain,
relation(sK9),
inference(clausify,[status(thm)],[f_28_3]) ).
fof(f_29_1,plain,
? [A] : empty(A),
inference(fof_nnf,[status(thm)],[rc1_xboole_0]) ).
fof(f_29_2,plain,
? [U_66] : empty(U_66),
inference(variable_rename,[status(thm)],[f_29_1]) ).
fof(f_29_3,plain,
empty(sK10),
inference(skolemize,[status(esa),new_symbols(skolem,[sK10]),skolemize(U_66,sK10)],[f_29_2]) ).
cnf(f_29_4,plain,
empty(sK10),
inference(clausify,[status(thm)],[f_29_3]) ).
fof(f_30_1,plain,
? [A] :
( function(A)
& empty(A)
& relation(A) ),
inference(fof_nnf,[status(thm)],[rc2_funct_1]) ).
fof(f_30_2,plain,
? [U_67] :
( function(U_67)
& empty(U_67)
& relation(U_67) ),
inference(variable_rename,[status(thm)],[f_30_1]) ).
fof(f_30_3,plain,
( function(sK11)
& empty(sK11)
& relation(sK11) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK11]),skolemize(U_67,sK11)],[f_30_2]) ).
cnf(f_30_4,plain,
relation(sK11),
inference(clausify,[status(thm)],[f_30_3]) ).
cnf(f_30_5,plain,
empty(sK11),
inference(clausify,[status(thm)],[f_30_3]) ).
cnf(f_30_6,plain,
function(sK11),
inference(clausify,[status(thm)],[f_30_3]) ).
fof(f_31_1,plain,
? [A] :
( ordinal(A)
& epsilon_connected(A)
& epsilon_transitive(A)
& empty(A)
& one_to_one(A)
& function(A)
& relation(A) ),
inference(fof_nnf,[status(thm)],[rc2_ordinal1]) ).
fof(f_31_2,plain,
? [U_68] :
( ordinal(U_68)
& epsilon_connected(U_68)
& epsilon_transitive(U_68)
& empty(U_68)
& one_to_one(U_68)
& function(U_68)
& relation(U_68) ),
inference(variable_rename,[status(thm)],[f_31_1]) ).
fof(f_31_3,plain,
( ordinal(sK12)
& epsilon_connected(sK12)
& epsilon_transitive(sK12)
& empty(sK12)
& one_to_one(sK12)
& function(sK12)
& relation(sK12) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK12]),skolemize(U_68,sK12)],[f_31_2]) ).
cnf(f_31_4,plain,
relation(sK12),
inference(clausify,[status(thm)],[f_31_3]) ).
cnf(f_31_5,plain,
function(sK12),
inference(clausify,[status(thm)],[f_31_3]) ).
cnf(f_31_6,plain,
one_to_one(sK12),
inference(clausify,[status(thm)],[f_31_3]) ).
cnf(f_31_7,plain,
empty(sK12),
inference(clausify,[status(thm)],[f_31_3]) ).
cnf(f_31_8,plain,
epsilon_transitive(sK12),
inference(clausify,[status(thm)],[f_31_3]) ).
cnf(f_31_9,plain,
epsilon_connected(sK12),
inference(clausify,[status(thm)],[f_31_3]) ).
cnf(f_31_10,plain,
ordinal(sK12),
inference(clausify,[status(thm)],[f_31_3]) ).
fof(f_32_1,plain,
? [A] :
( relation(A)
& ~ empty(A) ),
inference(fof_nnf,[status(thm)],[rc2_relat_1]) ).
fof(f_32_2,plain,
? [U_69] :
( relation(U_69)
& ~ empty(U_69) ),
inference(variable_rename,[status(thm)],[f_32_1]) ).
fof(f_32_3,plain,
( relation(sK13)
& ~ empty(sK13) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK13]),skolemize(U_69,sK13)],[f_32_2]) ).
cnf(f_32_4,plain,
~ empty(sK13),
inference(clausify,[status(thm)],[f_32_3]) ).
cnf(f_32_5,plain,
relation(sK13),
inference(clausify,[status(thm)],[f_32_3]) ).
fof(f_33_1,plain,
? [A] : ~ empty(A),
inference(fof_nnf,[status(thm)],[rc2_xboole_0]) ).
fof(f_33_2,plain,
? [U_70] : ~ empty(U_70),
inference(variable_rename,[status(thm)],[f_33_1]) ).
fof(f_33_3,plain,
~ empty(sK14),
inference(skolemize,[status(esa),new_symbols(skolem,[sK14]),skolemize(U_70,sK14)],[f_33_2]) ).
cnf(f_33_4,plain,
~ empty(sK14),
inference(clausify,[status(thm)],[f_33_3]) ).
fof(f_34_1,plain,
? [A] :
( one_to_one(A)
& function(A)
& relation(A) ),
inference(fof_nnf,[status(thm)],[rc3_funct_1]) ).
fof(f_34_2,plain,
? [U_71] :
( one_to_one(U_71)
& function(U_71)
& relation(U_71) ),
inference(variable_rename,[status(thm)],[f_34_1]) ).
fof(f_34_3,plain,
( one_to_one(sK15)
& function(sK15)
& relation(sK15) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK15]),skolemize(U_71,sK15)],[f_34_2]) ).
cnf(f_34_4,plain,
relation(sK15),
inference(clausify,[status(thm)],[f_34_3]) ).
cnf(f_34_5,plain,
function(sK15),
inference(clausify,[status(thm)],[f_34_3]) ).
cnf(f_34_6,plain,
one_to_one(sK15),
inference(clausify,[status(thm)],[f_34_3]) ).
fof(f_35_1,plain,
? [A] :
( ordinal(A)
& epsilon_connected(A)
& epsilon_transitive(A)
& ~ empty(A) ),
inference(fof_nnf,[status(thm)],[rc3_ordinal1]) ).
fof(f_35_2,plain,
? [U_72] :
( ordinal(U_72)
& epsilon_connected(U_72)
& epsilon_transitive(U_72)
& ~ empty(U_72) ),
inference(variable_rename,[status(thm)],[f_35_1]) ).
fof(f_35_3,plain,
( ordinal(sK16)
& epsilon_connected(sK16)
& epsilon_transitive(sK16)
& ~ empty(sK16) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK16]),skolemize(U_72,sK16)],[f_35_2]) ).
cnf(f_35_4,plain,
~ empty(sK16),
inference(clausify,[status(thm)],[f_35_3]) ).
cnf(f_35_5,plain,
epsilon_transitive(sK16),
inference(clausify,[status(thm)],[f_35_3]) ).
cnf(f_35_6,plain,
epsilon_connected(sK16),
inference(clausify,[status(thm)],[f_35_3]) ).
cnf(f_35_7,plain,
ordinal(sK16),
inference(clausify,[status(thm)],[f_35_3]) ).
fof(f_36_1,plain,
? [A] :
( relation_empty_yielding(A)
& relation(A) ),
inference(fof_nnf,[status(thm)],[rc3_relat_1]) ).
fof(f_36_2,plain,
? [U_73] :
( relation_empty_yielding(U_73)
& relation(U_73) ),
inference(variable_rename,[status(thm)],[f_36_1]) ).
fof(f_36_3,plain,
( relation_empty_yielding(sK17)
& relation(sK17) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK17]),skolemize(U_73,sK17)],[f_36_2]) ).
cnf(f_36_4,plain,
relation(sK17),
inference(clausify,[status(thm)],[f_36_3]) ).
cnf(f_36_5,plain,
relation_empty_yielding(sK17),
inference(clausify,[status(thm)],[f_36_3]) ).
fof(f_37_1,plain,
? [A] :
( function(A)
& relation_empty_yielding(A)
& relation(A) ),
inference(fof_nnf,[status(thm)],[rc4_funct_1]) ).
fof(f_37_2,plain,
? [U_74] :
( function(U_74)
& relation_empty_yielding(U_74)
& relation(U_74) ),
inference(variable_rename,[status(thm)],[f_37_1]) ).
fof(f_37_3,plain,
( function(sK18)
& relation_empty_yielding(sK18)
& relation(sK18) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK18]),skolemize(U_74,sK18)],[f_37_2]) ).
cnf(f_37_4,plain,
relation(sK18),
inference(clausify,[status(thm)],[f_37_3]) ).
cnf(f_37_5,plain,
relation_empty_yielding(sK18),
inference(clausify,[status(thm)],[f_37_3]) ).
cnf(f_37_6,plain,
function(sK18),
inference(clausify,[status(thm)],[f_37_3]) ).
fof(f_38_1,plain,
? [A] :
( function(A)
& relation_non_empty(A)
& relation(A) ),
inference(fof_nnf,[status(thm)],[rc5_funct_1]) ).
fof(f_38_2,plain,
? [U_75] :
( function(U_75)
& relation_non_empty(U_75)
& relation(U_75) ),
inference(variable_rename,[status(thm)],[f_38_1]) ).
fof(f_38_3,plain,
( function(sK19)
& relation_non_empty(sK19)
& relation(sK19) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK19]),skolemize(U_75,sK19)],[f_38_2]) ).
cnf(f_38_4,plain,
relation(sK19),
inference(clausify,[status(thm)],[f_38_3]) ).
cnf(f_38_5,plain,
relation_non_empty(sK19),
inference(clausify,[status(thm)],[f_38_3]) ).
cnf(f_38_6,plain,
function(sK19),
inference(clausify,[status(thm)],[f_38_3]) ).
fof(f_39_1,plain,
! [A,B] :
( ( ( ordinal_subset(A,B)
| ~ subset(A,B) )
& ( subset(A,B)
| ~ ordinal_subset(A,B) ) )
| ~ ordinal(B)
| ~ ordinal(A) ),
inference(fof_nnf,[status(thm)],[redefinition_r1_ordinal1]) ).
fof(f_39_2,plain,
! [U_77,U_76] :
( ( ( ordinal_subset(U_77,U_76)
| ~ subset(U_77,U_76) )
& ( subset(U_77,U_76)
| ~ ordinal_subset(U_77,U_76) ) )
| ~ ordinal(U_76)
| ~ ordinal(U_77) ),
inference(variable_rename,[status(thm)],[f_39_1]) ).
cnf(f_39_3,plain,
( subset(U_77,U_76)
| ~ ordinal_subset(U_77,U_76)
| ~ ordinal(U_76)
| ~ ordinal(U_77) ),
inference(clausify,[status(thm)],[f_39_2]) ).
cnf(f_39_4,plain,
( ordinal_subset(U_77,U_76)
| ~ subset(U_77,U_76)
| ~ ordinal(U_76)
| ~ ordinal(U_77) ),
inference(clausify,[status(thm)],[f_39_2]) ).
fof(f_40_1,plain,
! [A,B] :
( ordinal_subset(A,A)
| ~ ordinal(B)
| ~ ordinal(A) ),
inference(fof_nnf,[status(thm)],[reflexivity_r1_ordinal1]) ).
fof(f_40_2,plain,
! [U_79,U_78] :
( ordinal_subset(U_79,U_79)
| ~ ordinal(U_78)
| ~ ordinal(U_79) ),
inference(variable_rename,[status(thm)],[f_40_1]) ).
fof(f_40_3,plain,
! [U_79] :
( ! [U_78] : ~ ordinal(U_78)
| ~ ordinal(U_79)
| ordinal_subset(U_79,U_79) ),
inference(miniscope,[status(thm)],[f_40_2]) ).
cnf(f_40_4,plain,
( ~ ordinal(U_78)
| ~ ordinal(U_79)
| ordinal_subset(U_79,U_79) ),
inference(clausify,[status(thm)],[f_40_3]) ).
fof(f_41_1,plain,
! [A,B] : subset(A,A),
inference(fof_nnf,[status(thm)],[reflexivity_r1_tarski]) ).
fof(f_41_2,plain,
! [U_81,U_80] : subset(U_81,U_81),
inference(variable_rename,[status(thm)],[f_41_1]) ).
fof(f_41_3,plain,
! [U_81] : subset(U_81,U_81),
inference(miniscope,[status(thm)],[f_41_2]) ).
cnf(f_41_4,plain,
subset(U_81,U_81),
inference(clausify,[status(thm)],[f_41_3]) ).
fof(f_42_1,plain,
! [A] : in(A,succ(A)),
inference(fof_nnf,[status(thm)],[t10_ordinal1]) ).
fof(f_42_2,plain,
! [U_82] : in(U_82,succ(U_82)),
inference(variable_rename,[status(thm)],[f_42_1]) ).
cnf(f_42_3,plain,
in(U_82,succ(U_82)),
inference(clausify,[status(thm)],[f_42_2]) ).
fof(f_43_1,plain,
! [A] : A != succ(A),
inference(fof_nnf,[status(thm)],[t14_ordinal1]) ).
fof(f_43_2,plain,
! [U_83] : U_83 != succ(U_83),
inference(variable_rename,[status(thm)],[f_43_1]) ).
cnf(f_43_3,plain,
U_83 != succ(U_83),
inference(clausify,[status(thm)],[f_43_2]) ).
fof(f_44_1,plain,
! [A] : set_union2(A,empty_set) = A,
inference(fof_nnf,[status(thm)],[t1_boole]) ).
fof(f_44_2,plain,
! [U_84] : set_union2(U_84,empty_set) = U_84,
inference(variable_rename,[status(thm)],[f_44_1]) ).
cnf(f_44_3,plain,
set_union2(U_84,empty_set) = U_84,
inference(clausify,[status(thm)],[f_44_2]) ).
fof(f_45_1,plain,
! [A,B] :
( element(A,B)
| ~ in(A,B) ),
inference(fof_nnf,[status(thm)],[t1_subset]) ).
fof(f_45_2,plain,
! [U_86,U_85] :
( element(U_86,U_85)
| ~ in(U_86,U_85) ),
inference(variable_rename,[status(thm)],[f_45_1]) ).
cnf(f_45_3,plain,
( element(U_86,U_85)
| ~ in(U_86,U_85) ),
inference(clausify,[status(thm)],[f_45_2]) ).
fof(f_46_1,plain,
! [A] :
( ! [B] :
( in(B,A)
| A = B
| in(A,B)
| ~ ordinal(B) )
| ~ ordinal(A) ),
inference(fof_nnf,[status(thm)],[t24_ordinal1]) ).
fof(f_46_2,plain,
! [U_88] :
( ! [U_87] :
( in(U_87,U_88)
| U_88 = U_87
| in(U_88,U_87)
| ~ ordinal(U_87) )
| ~ ordinal(U_88) ),
inference(variable_rename,[status(thm)],[f_46_1]) ).
cnf(f_46_3,plain,
( in(U_87,U_88)
| U_88 = U_87
| in(U_88,U_87)
| ~ ordinal(U_87)
| ~ ordinal(U_88) ),
inference(clausify,[status(thm)],[f_46_2]) ).
fof(f_47_1,plain,
! [A,B] :
( in(A,B)
| empty(B)
| ~ element(A,B) ),
inference(fof_nnf,[status(thm)],[t2_subset]) ).
fof(f_47_2,plain,
! [U_90,U_89] :
( in(U_90,U_89)
| empty(U_89)
| ~ element(U_90,U_89) ),
inference(variable_rename,[status(thm)],[f_47_1]) ).
cnf(f_47_3,plain,
( in(U_90,U_89)
| empty(U_89)
| ~ element(U_90,U_89) ),
inference(clausify,[status(thm)],[f_47_2]) ).
fof(f_48_1,negated_conjecture,
~ ! [A] :
( ordinal(A)
=> ! [B] :
( ordinal(B)
=> ( in(A,succ(B))
<=> ordinal_subset(A,B) ) ) ),
inference(negate,[status(cth)],[t34_ordinal1]) ).
fof(f_48_2,negated_conjecture,
? [A] :
( ? [B] :
( ( ( ~ in(A,succ(B))
& ordinal_subset(A,B) )
| ( ~ ordinal_subset(A,B)
& in(A,succ(B)) ) )
& ordinal(B) )
& ordinal(A) ),
inference(fof_nnf,[status(thm)],[f_48_1]) ).
fof(f_48_3,negated_conjecture,
? [U_92] :
( ? [U_91] :
( ( ( ~ in(U_92,succ(U_91))
& ordinal_subset(U_92,U_91) )
| ( ~ ordinal_subset(U_92,U_91)
& in(U_92,succ(U_91)) ) )
& ordinal(U_91) )
& ordinal(U_92) ),
inference(variable_rename,[status(thm)],[f_48_2]) ).
fof(f_48_4,negated_conjecture,
( ? [U_91] :
( ( ( ~ in(sK20,succ(U_91))
& ordinal_subset(sK20,U_91) )
| ( ~ ordinal_subset(sK20,U_91)
& in(sK20,succ(U_91)) ) )
& ordinal(U_91) )
& ordinal(sK20) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK20]),skolemize(U_92,sK20)],[f_48_3]) ).
fof(f_48_5,negated_conjecture,
( ( ( ~ in(sK20,succ(sK21))
& ordinal_subset(sK20,sK21) )
| ( ~ ordinal_subset(sK20,sK21)
& in(sK20,succ(sK21)) ) )
& ordinal(sK21)
& ordinal(sK20) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK21]),skolemize(U_91,sK21)],[f_48_4]) ).
cnf(f_48_6,negated_conjecture,
ordinal(sK20),
inference(clausify,[status(thm)],[f_48_5]) ).
cnf(f_48_7,negated_conjecture,
ordinal(sK21),
inference(clausify,[status(thm)],[f_48_5]) ).
cnf(f_48_8,negated_conjecture,
( ordinal_subset(sK20,sK21)
| in(sK20,succ(sK21)) ),
inference(clausify,[status(thm)],[f_48_5]) ).
cnf(f_48_9,negated_conjecture,
( ~ in(sK20,succ(sK21))
| in(sK20,succ(sK21)) ),
inference(clausify,[status(thm)],[f_48_5]) ).
cnf(f_48_10,negated_conjecture,
( ordinal_subset(sK20,sK21)
| ~ ordinal_subset(sK20,sK21) ),
inference(clausify,[status(thm)],[f_48_5]) ).
cnf(f_48_11,negated_conjecture,
( ~ in(sK20,succ(sK21))
| ~ ordinal_subset(sK20,sK21) ),
inference(clausify,[status(thm)],[f_48_5]) ).
fof(f_49_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_49_2,plain,
! [U_94,U_93] :
( ( element(U_94,powerset(U_93))
| ~ subset(U_94,U_93) )
& ( subset(U_94,U_93)
| ~ element(U_94,powerset(U_93)) ) ),
inference(variable_rename,[status(thm)],[f_49_1]) ).
fof(f_49_3,plain,
( ! [U_98,U_96] :
( element(U_98,powerset(U_96))
| ~ subset(U_98,U_96) )
& ! [U_97,U_95] :
( subset(U_97,U_95)
| ~ element(U_97,powerset(U_95)) ) ),
inference(miniscope,[status(thm)],[f_49_2]) ).
cnf(f_49_4,plain,
( subset(U_97,U_95)
| ~ element(U_97,powerset(U_95)) ),
inference(clausify,[status(thm)],[f_49_3]) ).
cnf(f_49_5,plain,
( element(U_98,powerset(U_96))
| ~ subset(U_98,U_96) ),
inference(clausify,[status(thm)],[f_49_3]) ).
fof(f_50_1,plain,
! [A,B,C] :
( element(A,C)
| ~ element(B,powerset(C))
| ~ in(A,B) ),
inference(fof_nnf,[status(thm)],[t4_subset]) ).
fof(f_50_2,plain,
! [U_101,U_100,U_99] :
( element(U_101,U_99)
| ~ element(U_100,powerset(U_99))
| ~ in(U_101,U_100) ),
inference(variable_rename,[status(thm)],[f_50_1]) ).
cnf(f_50_3,plain,
( element(U_101,U_99)
| ~ element(U_100,powerset(U_99))
| ~ in(U_101,U_100) ),
inference(clausify,[status(thm)],[f_50_2]) ).
fof(f_51_1,plain,
! [A,B,C] :
( ~ empty(C)
| ~ element(B,powerset(C))
| ~ in(A,B) ),
inference(fof_nnf,[status(thm)],[t5_subset]) ).
fof(f_51_2,plain,
! [U_104,U_103,U_102] :
( ~ empty(U_102)
| ~ element(U_103,powerset(U_102))
| ~ in(U_104,U_103) ),
inference(variable_rename,[status(thm)],[f_51_1]) ).
fof(f_51_3,plain,
! [U_104,U_103] :
( ! [U_102] :
( ~ empty(U_102)
| ~ element(U_103,powerset(U_102)) )
| ~ in(U_104,U_103) ),
inference(miniscope,[status(thm)],[f_51_2]) ).
cnf(f_51_4,plain,
( ~ empty(U_102)
| ~ element(U_103,powerset(U_102))
| ~ in(U_104,U_103) ),
inference(clausify,[status(thm)],[f_51_3]) ).
fof(f_52_1,plain,
! [A] :
( A = empty_set
| ~ empty(A) ),
inference(fof_nnf,[status(thm)],[t6_boole]) ).
fof(f_52_2,plain,
! [U_105] :
( U_105 = empty_set
| ~ empty(U_105) ),
inference(variable_rename,[status(thm)],[f_52_1]) ).
cnf(f_52_3,plain,
( U_105 = empty_set
| ~ empty(U_105) ),
inference(clausify,[status(thm)],[f_52_2]) ).
fof(f_53_1,plain,
! [A,B] :
( ~ empty(B)
| ~ in(A,B) ),
inference(fof_nnf,[status(thm)],[t7_boole]) ).
fof(f_53_2,plain,
! [U_107,U_106] :
( ~ empty(U_106)
| ~ in(U_107,U_106) ),
inference(variable_rename,[status(thm)],[f_53_1]) ).
cnf(f_53_3,plain,
( ~ empty(U_106)
| ~ in(U_107,U_106) ),
inference(clausify,[status(thm)],[f_53_2]) ).
fof(f_54_1,plain,
! [A,B] :
( ~ empty(B)
| A = B
| ~ empty(A) ),
inference(fof_nnf,[status(thm)],[t8_boole]) ).
fof(f_54_2,plain,
! [U_109,U_108] :
( ~ empty(U_108)
| U_109 = U_108
| ~ empty(U_109) ),
inference(variable_rename,[status(thm)],[f_54_1]) ).
fof(f_54_3,plain,
! [U_109] :
( ! [U_108] :
( ~ empty(U_108)
| U_109 = U_108 )
| ~ empty(U_109) ),
inference(miniscope,[status(thm)],[f_54_2]) ).
cnf(f_54_4,plain,
( ~ empty(U_108)
| U_109 = U_108
| ~ empty(U_109) ),
inference(clausify,[status(thm)],[f_54_3]) ).
cnf(f_5_3_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_5_3]) ).
cnf(f_5_4_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_5_4]) ).
cnf(f_48_9_true,negated_conjecture,
$true,
inference(clause_is_true,[status(thm)],[f_48_9]) ).
cnf(f_48_10_true,negated_conjecture,
$true,
inference(clause_is_true,[status(thm)],[f_48_10]) ).
cnf(equality_1,axiom,
Eq_x_0 = Eq_x_0,
theory(equality,[reflexivity]) ).
cnf(equality_2,axiom,
( Eq_x_1 = Eq_x_0
| Eq_x_0 != Eq_x_1 ),
theory(equality,[symmetry]) ).
cnf(equality_3,axiom,
( Eq_x_0 = Eq_x_2
| Eq_x_1 != Eq_x_2
| Eq_x_0 != Eq_x_1 ),
theory(equality,[transitivity]) ).
cnf(equality_4,axiom,
( set_union2(Eq_x_0,Eq_x_1) = set_union2(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_5,axiom,
( succ(Eq_x_0) = succ(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_6,axiom,
( singleton(Eq_x_0) = singleton(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_7,axiom,
( powerset(Eq_x_0) = powerset(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_8,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_9,axiom,
( sK2(Eq_x_0,Eq_x_1) = sK2(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_10,axiom,
( sK3(Eq_x_0) = sK3(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_11,axiom,
( sK4(Eq_x_0,Eq_x_1,Eq_x_2) = sK4(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_12,axiom,
( sK5(Eq_x_0,Eq_x_1,Eq_x_2) = sK5(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_13,axiom,
( sK6(Eq_x_0) = sK6(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_14,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_15,axiom,
( empty(Eq_y_0)
| ~ empty(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_16,axiom,
( function(Eq_y_0)
| ~ function(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_17,axiom,
( ordinal(Eq_y_0)
| ~ ordinal(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_18,axiom,
( epsilon_transitive(Eq_y_0)
| ~ epsilon_transitive(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_19,axiom,
( epsilon_connected(Eq_y_0)
| ~ epsilon_connected(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_20,axiom,
( relation(Eq_y_0)
| ~ relation(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_21,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_22,axiom,
( ordinal_subset(Eq_y_0,Eq_y_1)
| ~ ordinal_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_23,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_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,
( relation_empty_yielding(Eq_y_0)
| ~ relation_empty_yielding(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_26,axiom,
( relation_non_empty(Eq_y_0)
| ~ relation_non_empty(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(sat_proved,plain,
$false,
inference(cadical,[status(thm)],[]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : NUM401+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.01 This is a FOF_THM_RFO_SEQ problem
% 0.00/0.02 % Command : /export/starexec/sandbox/solver/bin/connect++ --verbosity 1 --no-colour --tptp-proof --schedule default --timeout 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.03/10.31 % Computer : n012.cluster.edu
% 0.03/10.31 % Model : x86_64 x86_64
% 0.03/10.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.03/10.31 % Memory : 8046.5625MB
% 0.03/10.31 % OS : Linux 6.8.0-71-generic
% 0.03/10.31 % CPULimit : 300
% 0.03/10.31 % WCLimit : 300
% 0.03/10.31 % DateTime : Sat Sep 19 18:21:51 UTC 2026
% 0.03/10.31 % CPUTime :
% 111.82/122.17 % SZS status Theorem for theBenchmark
% 111.82/122.17 % SZS output start Proof for theBenchmark
% See solution above
%------------------------------------------------------------------------------