%------------------------------------------------------------------------------
% File : ConnectPP---0.7.2
% Problem : SEU339+1 : TPTP v9.3.1. Released v3.3.0.
% 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 : n016.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 08:59:02 AM UTC 2026
% Result : Theorem 193.13s 198.41s
% Output : Proof 194.03s
% 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_relset_1,axiom,
! [A,B,C] :
( element(C,powerset(cartesian_product2(A,B)))
=> relation(C) ),
file('theBenchmark.p',cc1_relset_1) ).
fof(commutativity_k2_tarski,axiom,
! [A,B] : unordered_pair(A,B) = unordered_pair(B,A),
file('theBenchmark.p',commutativity_k2_tarski) ).
fof(d4_relat_2,axiom,
! [A] :
( relation(A)
=> ! [B] :
( is_antisymmetric_in(A,B)
<=> ! [C,D] :
( ( in(ordered_pair(D,C),A)
& in(ordered_pair(C,D),A)
& in(D,B)
& in(C,B) )
=> C = D ) ) ),
file('theBenchmark.p',d4_relat_2) ).
fof(d5_tarski,axiom,
! [A,B] : ordered_pair(A,B) = unordered_pair(unordered_pair(A,B),singleton(A)),
file('theBenchmark.p',d5_tarski) ).
fof(d6_orders_2,axiom,
! [A] :
( rel_str(A)
=> ( antisymmetric_relstr(A)
<=> is_antisymmetric_in(the_InternalRel(A),the_carrier(A)) ) ),
file('theBenchmark.p',d6_orders_2) ).
fof(d9_orders_2,axiom,
! [A] :
( rel_str(A)
=> ! [B] :
( element(B,the_carrier(A))
=> ! [C] :
( element(C,the_carrier(A))
=> ( related(A,B,C)
<=> in(ordered_pair(B,C),the_InternalRel(A)) ) ) ) ),
file('theBenchmark.p',d9_orders_2) ).
fof(dt_k1_tarski,axiom,
$true,
file('theBenchmark.p',dt_k1_tarski) ).
fof(dt_k1_xboole_0,axiom,
$true,
file('theBenchmark.p',dt_k1_xboole_0) ).
fof(dt_k1_zfmisc_1,axiom,
$true,
file('theBenchmark.p',dt_k1_zfmisc_1) ).
fof(dt_k2_tarski,axiom,
$true,
file('theBenchmark.p',dt_k2_tarski) ).
fof(dt_k2_zfmisc_1,axiom,
$true,
file('theBenchmark.p',dt_k2_zfmisc_1) ).
fof(dt_k4_tarski,axiom,
$true,
file('theBenchmark.p',dt_k4_tarski) ).
fof(dt_l1_orders_2,axiom,
! [A] :
( rel_str(A)
=> one_sorted_str(A) ),
file('theBenchmark.p',dt_l1_orders_2) ).
fof(dt_l1_struct_0,axiom,
$true,
file('theBenchmark.p',dt_l1_struct_0) ).
fof(dt_m1_relset_1,axiom,
$true,
file('theBenchmark.p',dt_m1_relset_1) ).
fof(dt_m1_subset_1,axiom,
$true,
file('theBenchmark.p',dt_m1_subset_1) ).
fof(dt_m2_relset_1,axiom,
! [A,B,C] :
( relation_of2_as_subset(C,A,B)
=> element(C,powerset(cartesian_product2(A,B))) ),
file('theBenchmark.p',dt_m2_relset_1) ).
fof(dt_u1_orders_2,axiom,
! [A] :
( rel_str(A)
=> relation_of2_as_subset(the_InternalRel(A),the_carrier(A),the_carrier(A)) ),
file('theBenchmark.p',dt_u1_orders_2) ).
fof(dt_u1_struct_0,axiom,
$true,
file('theBenchmark.p',dt_u1_struct_0) ).
fof(existence_l1_orders_2,axiom,
? [A] : rel_str(A),
file('theBenchmark.p',existence_l1_orders_2) ).
fof(existence_l1_struct_0,axiom,
? [A] : one_sorted_str(A),
file('theBenchmark.p',existence_l1_struct_0) ).
fof(existence_m1_relset_1,axiom,
! [A,B] :
? [C] : relation_of2(C,A,B),
file('theBenchmark.p',existence_m1_relset_1) ).
fof(existence_m1_subset_1,axiom,
! [A] :
? [B] : element(B,A),
file('theBenchmark.p',existence_m1_subset_1) ).
fof(existence_m2_relset_1,axiom,
! [A,B] :
? [C] : relation_of2_as_subset(C,A,B),
file('theBenchmark.p',existence_m2_relset_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_subset_1,axiom,
! [A] : ~ empty(singleton(A)),
file('theBenchmark.p',fc2_subset_1) ).
fof(fc3_subset_1,axiom,
! [A,B] : ~ empty(unordered_pair(A,B)),
file('theBenchmark.p',fc3_subset_1) ).
fof(fc4_subset_1,axiom,
! [A,B] :
( ( ~ empty(B)
& ~ empty(A) )
=> ~ empty(cartesian_product2(A,B)) ),
file('theBenchmark.p',fc4_subset_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_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(redefinition_m2_relset_1,axiom,
! [A,B,C] :
( relation_of2_as_subset(C,A,B)
<=> relation_of2(C,A,B) ),
file('theBenchmark.p',redefinition_m2_relset_1) ).
fof(reflexivity_r1_tarski,axiom,
! [A,B] : subset(A,A),
file('theBenchmark.p',reflexivity_r1_tarski) ).
fof(t106_zfmisc_1,axiom,
! [A,B,C,D] :
( in(ordered_pair(A,B),cartesian_product2(C,D))
<=> ( in(B,D)
& in(A,C) ) ),
file('theBenchmark.p',t106_zfmisc_1) ).
fof(t1_subset,axiom,
! [A,B] :
( in(A,B)
=> element(A,B) ),
file('theBenchmark.p',t1_subset) ).
fof(t25_orders_2,conjecture,
! [A] :
( ( rel_str(A)
& antisymmetric_relstr(A) )
=> ! [B] :
( element(B,the_carrier(A))
=> ! [C] :
( element(C,the_carrier(A))
=> ( ( related(A,C,B)
& related(A,B,C) )
=> B = C ) ) ) ),
file('theBenchmark.p',t25_orders_2) ).
fof(t2_subset,axiom,
! [A,B] :
( element(A,B)
=> ( in(A,B)
| empty(B) ) ),
file('theBenchmark.p',t2_subset) ).
fof(t3_subset,axiom,
! [A,B] :
( element(A,powerset(B))
<=> subset(A,B) ),
file('theBenchmark.p',t3_subset) ).
fof(t4_subset,axiom,
! [A,B,C] :
( ( element(B,powerset(C))
& in(A,B) )
=> element(A,C) ),
file('theBenchmark.p',t4_subset) ).
fof(t5_subset,axiom,
! [A,B,C] :
~ ( empty(C)
& element(B,powerset(C))
& in(A,B) ),
file('theBenchmark.p',t5_subset) ).
fof(t6_boole,axiom,
! [A] :
( empty(A)
=> A = empty_set ),
file('theBenchmark.p',t6_boole) ).
fof(t7_boole,axiom,
! [A,B] :
~ ( empty(B)
& in(A,B) ),
file('theBenchmark.p',t7_boole) ).
fof(t8_boole,axiom,
! [A,B] :
~ ( empty(B)
& A != B
& empty(A) ),
file('theBenchmark.p',t8_boole) ).
fof(f_1_1,plain,
! [A,B] :
( ~ in(B,A)
| ~ in(A,B) ),
inference(fof_nnf,[status(thm)],[antisymmetry_r2_hidden]) ).
fof(f_1_2,plain,
! [U_1,U_0] :
( ~ in(U_0,U_1)
| ~ in(U_1,U_0) ),
inference(variable_rename,[status(thm)],[f_1_1]) ).
cnf(f_1_3,plain,
( ~ in(U_0,U_1)
| ~ in(U_1,U_0) ),
inference(clausify,[status(thm)],[f_1_2]) ).
fof(f_2_1,plain,
! [A,B,C] :
( relation(C)
| ~ element(C,powerset(cartesian_product2(A,B))) ),
inference(fof_nnf,[status(thm)],[cc1_relset_1]) ).
fof(f_2_2,plain,
! [U_4,U_3,U_2] :
( relation(U_2)
| ~ element(U_2,powerset(cartesian_product2(U_4,U_3))) ),
inference(variable_rename,[status(thm)],[f_2_1]) ).
cnf(f_2_3,plain,
( relation(U_2)
| ~ element(U_2,powerset(cartesian_product2(U_4,U_3))) ),
inference(clausify,[status(thm)],[f_2_2]) ).
fof(f_3_1,plain,
! [A,B] : unordered_pair(A,B) = unordered_pair(B,A),
inference(fof_nnf,[status(thm)],[commutativity_k2_tarski]) ).
fof(f_3_2,plain,
! [U_6,U_5] : unordered_pair(U_6,U_5) = unordered_pair(U_5,U_6),
inference(variable_rename,[status(thm)],[f_3_1]) ).
cnf(f_3_3,plain,
unordered_pair(U_6,U_5) = unordered_pair(U_5,U_6),
inference(clausify,[status(thm)],[f_3_2]) ).
fof(f_4_1,plain,
! [A] :
( ! [B] :
( ( is_antisymmetric_in(A,B)
| ? [C,D] :
( C != D
& in(ordered_pair(D,C),A)
& in(ordered_pair(C,D),A)
& in(D,B)
& in(C,B) ) )
& ( ! [C,D] :
( C = D
| ~ in(ordered_pair(D,C),A)
| ~ in(ordered_pair(C,D),A)
| ~ in(D,B)
| ~ in(C,B) )
| ~ is_antisymmetric_in(A,B) ) )
| ~ relation(A) ),
inference(fof_nnf,[status(thm)],[d4_relat_2]) ).
fof(f_4_2,plain,
! [U_12] :
( ! [U_11] :
( ( is_antisymmetric_in(U_12,U_11)
| ? [U_10,U_9] :
( U_10 != U_9
& in(ordered_pair(U_9,U_10),U_12)
& in(ordered_pair(U_10,U_9),U_12)
& in(U_9,U_11)
& in(U_10,U_11) ) )
& ( ! [U_8,U_7] :
( U_8 = U_7
| ~ in(ordered_pair(U_7,U_8),U_12)
| ~ in(ordered_pair(U_8,U_7),U_12)
| ~ in(U_7,U_11)
| ~ in(U_8,U_11) )
| ~ is_antisymmetric_in(U_12,U_11) ) )
| ~ relation(U_12) ),
inference(variable_rename,[status(thm)],[f_4_1]) ).
fof(f_4_3,plain,
! [U_12] :
( ( ! [U_14] :
( is_antisymmetric_in(U_12,U_14)
| ? [U_10,U_9] :
( U_10 != U_9
& in(ordered_pair(U_9,U_10),U_12)
& in(ordered_pair(U_10,U_9),U_12)
& in(U_9,U_14)
& in(U_10,U_14) ) )
& ! [U_13] :
( ! [U_8,U_7] :
( U_8 = U_7
| ~ in(ordered_pair(U_7,U_8),U_12)
| ~ in(ordered_pair(U_8,U_7),U_12)
| ~ in(U_7,U_13)
| ~ in(U_8,U_13) )
| ~ is_antisymmetric_in(U_12,U_13) ) )
| ~ relation(U_12) ),
inference(miniscope,[status(thm)],[f_4_2]) ).
fof(f_4_4,plain,
! [U_12] :
( ( ! [U_14] :
( is_antisymmetric_in(U_12,U_14)
| ? [U_9] :
( sK1(U_12,U_14) != U_9
& in(ordered_pair(U_9,sK1(U_12,U_14)),U_12)
& in(ordered_pair(sK1(U_12,U_14),U_9),U_12)
& in(U_9,U_14)
& in(sK1(U_12,U_14),U_14) ) )
& ! [U_13] :
( ! [U_8,U_7] :
( U_8 = U_7
| ~ in(ordered_pair(U_7,U_8),U_12)
| ~ in(ordered_pair(U_8,U_7),U_12)
| ~ in(U_7,U_13)
| ~ in(U_8,U_13) )
| ~ is_antisymmetric_in(U_12,U_13) ) )
| ~ relation(U_12) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(U_10,sK1(U_12,U_14))],[f_4_3]) ).
fof(f_4_5,plain,
! [U_12] :
( ( ! [U_14] :
( is_antisymmetric_in(U_12,U_14)
| ( sK1(U_12,U_14) != sK2(U_12,U_14)
& in(ordered_pair(sK2(U_12,U_14),sK1(U_12,U_14)),U_12)
& in(ordered_pair(sK1(U_12,U_14),sK2(U_12,U_14)),U_12)
& in(sK2(U_12,U_14),U_14)
& in(sK1(U_12,U_14),U_14) ) )
& ! [U_13] :
( ! [U_8,U_7] :
( U_8 = U_7
| ~ in(ordered_pair(U_7,U_8),U_12)
| ~ in(ordered_pair(U_8,U_7),U_12)
| ~ in(U_7,U_13)
| ~ in(U_8,U_13) )
| ~ is_antisymmetric_in(U_12,U_13) ) )
| ~ relation(U_12) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2]),skolemize(U_9,sK2(U_12,U_14))],[f_4_4]) ).
cnf(f_4_6,plain,
( U_8 = U_7
| ~ in(ordered_pair(U_7,U_8),U_12)
| ~ in(ordered_pair(U_8,U_7),U_12)
| ~ in(U_7,U_13)
| ~ in(U_8,U_13)
| ~ is_antisymmetric_in(U_12,U_13)
| ~ relation(U_12) ),
inference(clausify,[status(thm)],[f_4_5]) ).
cnf(f_4_7,plain,
( in(sK1(U_12,U_14),U_14)
| is_antisymmetric_in(U_12,U_14)
| ~ relation(U_12) ),
inference(clausify,[status(thm)],[f_4_5]) ).
cnf(f_4_8,plain,
( in(sK2(U_12,U_14),U_14)
| is_antisymmetric_in(U_12,U_14)
| ~ relation(U_12) ),
inference(clausify,[status(thm)],[f_4_5]) ).
cnf(f_4_9,plain,
( in(ordered_pair(sK1(U_12,U_14),sK2(U_12,U_14)),U_12)
| is_antisymmetric_in(U_12,U_14)
| ~ relation(U_12) ),
inference(clausify,[status(thm)],[f_4_5]) ).
cnf(f_4_10,plain,
( in(ordered_pair(sK2(U_12,U_14),sK1(U_12,U_14)),U_12)
| is_antisymmetric_in(U_12,U_14)
| ~ relation(U_12) ),
inference(clausify,[status(thm)],[f_4_5]) ).
cnf(f_4_11,plain,
( sK1(U_12,U_14) != sK2(U_12,U_14)
| is_antisymmetric_in(U_12,U_14)
| ~ relation(U_12) ),
inference(clausify,[status(thm)],[f_4_5]) ).
fof(f_5_1,plain,
! [A,B] : ordered_pair(A,B) = unordered_pair(unordered_pair(A,B),singleton(A)),
inference(fof_nnf,[status(thm)],[d5_tarski]) ).
fof(f_5_2,plain,
! [U_16,U_15] : ordered_pair(U_16,U_15) = unordered_pair(unordered_pair(U_16,U_15),singleton(U_16)),
inference(variable_rename,[status(thm)],[f_5_1]) ).
cnf(f_5_3,plain,
ordered_pair(U_16,U_15) = unordered_pair(unordered_pair(U_16,U_15),singleton(U_16)),
inference(clausify,[status(thm)],[f_5_2]) ).
fof(f_6_1,plain,
! [A] :
( ( ( antisymmetric_relstr(A)
| ~ is_antisymmetric_in(the_InternalRel(A),the_carrier(A)) )
& ( is_antisymmetric_in(the_InternalRel(A),the_carrier(A))
| ~ antisymmetric_relstr(A) ) )
| ~ rel_str(A) ),
inference(fof_nnf,[status(thm)],[d6_orders_2]) ).
fof(f_6_2,plain,
! [U_17] :
( ( ( antisymmetric_relstr(U_17)
| ~ is_antisymmetric_in(the_InternalRel(U_17),the_carrier(U_17)) )
& ( is_antisymmetric_in(the_InternalRel(U_17),the_carrier(U_17))
| ~ antisymmetric_relstr(U_17) ) )
| ~ rel_str(U_17) ),
inference(variable_rename,[status(thm)],[f_6_1]) ).
cnf(f_6_3,plain,
( is_antisymmetric_in(the_InternalRel(U_17),the_carrier(U_17))
| ~ antisymmetric_relstr(U_17)
| ~ rel_str(U_17) ),
inference(clausify,[status(thm)],[f_6_2]) ).
cnf(f_6_4,plain,
( antisymmetric_relstr(U_17)
| ~ is_antisymmetric_in(the_InternalRel(U_17),the_carrier(U_17))
| ~ rel_str(U_17) ),
inference(clausify,[status(thm)],[f_6_2]) ).
fof(f_7_1,plain,
! [A] :
( ! [B] :
( ! [C] :
( ( ( related(A,B,C)
| ~ in(ordered_pair(B,C),the_InternalRel(A)) )
& ( in(ordered_pair(B,C),the_InternalRel(A))
| ~ related(A,B,C) ) )
| ~ element(C,the_carrier(A)) )
| ~ element(B,the_carrier(A)) )
| ~ rel_str(A) ),
inference(fof_nnf,[status(thm)],[d9_orders_2]) ).
fof(f_7_2,plain,
! [U_20] :
( ! [U_19] :
( ! [U_18] :
( ( ( related(U_20,U_19,U_18)
| ~ in(ordered_pair(U_19,U_18),the_InternalRel(U_20)) )
& ( in(ordered_pair(U_19,U_18),the_InternalRel(U_20))
| ~ related(U_20,U_19,U_18) ) )
| ~ element(U_18,the_carrier(U_20)) )
| ~ element(U_19,the_carrier(U_20)) )
| ~ rel_str(U_20) ),
inference(variable_rename,[status(thm)],[f_7_1]) ).
cnf(f_7_3,plain,
( in(ordered_pair(U_19,U_18),the_InternalRel(U_20))
| ~ related(U_20,U_19,U_18)
| ~ element(U_18,the_carrier(U_20))
| ~ element(U_19,the_carrier(U_20))
| ~ rel_str(U_20) ),
inference(clausify,[status(thm)],[f_7_2]) ).
cnf(f_7_4,plain,
( related(U_20,U_19,U_18)
| ~ in(ordered_pair(U_19,U_18),the_InternalRel(U_20))
| ~ element(U_18,the_carrier(U_20))
| ~ element(U_19,the_carrier(U_20))
| ~ rel_str(U_20) ),
inference(clausify,[status(thm)],[f_7_2]) ).
fof(f_8_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_k1_tarski]) ).
cnf(f_8_2,plain,
$true,
inference(clausify,[status(thm)],[f_8_1]) ).
fof(f_9_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_k1_xboole_0]) ).
cnf(f_9_2,plain,
$true,
inference(clausify,[status(thm)],[f_9_1]) ).
fof(f_10_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_k1_zfmisc_1]) ).
cnf(f_10_2,plain,
$true,
inference(clausify,[status(thm)],[f_10_1]) ).
fof(f_11_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_k2_tarski]) ).
cnf(f_11_2,plain,
$true,
inference(clausify,[status(thm)],[f_11_1]) ).
fof(f_12_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_k2_zfmisc_1]) ).
cnf(f_12_2,plain,
$true,
inference(clausify,[status(thm)],[f_12_1]) ).
fof(f_13_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_k4_tarski]) ).
cnf(f_13_2,plain,
$true,
inference(clausify,[status(thm)],[f_13_1]) ).
fof(f_14_1,plain,
! [A] :
( one_sorted_str(A)
| ~ rel_str(A) ),
inference(fof_nnf,[status(thm)],[dt_l1_orders_2]) ).
fof(f_14_2,plain,
! [U_21] :
( one_sorted_str(U_21)
| ~ rel_str(U_21) ),
inference(variable_rename,[status(thm)],[f_14_1]) ).
cnf(f_14_3,plain,
( one_sorted_str(U_21)
| ~ rel_str(U_21) ),
inference(clausify,[status(thm)],[f_14_2]) ).
fof(f_15_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_l1_struct_0]) ).
cnf(f_15_2,plain,
$true,
inference(clausify,[status(thm)],[f_15_1]) ).
fof(f_16_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_m1_relset_1]) ).
cnf(f_16_2,plain,
$true,
inference(clausify,[status(thm)],[f_16_1]) ).
fof(f_17_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_m1_subset_1]) ).
cnf(f_17_2,plain,
$true,
inference(clausify,[status(thm)],[f_17_1]) ).
fof(f_18_1,plain,
! [A,B,C] :
( element(C,powerset(cartesian_product2(A,B)))
| ~ relation_of2_as_subset(C,A,B) ),
inference(fof_nnf,[status(thm)],[dt_m2_relset_1]) ).
fof(f_18_2,plain,
! [U_24,U_23,U_22] :
( element(U_22,powerset(cartesian_product2(U_24,U_23)))
| ~ relation_of2_as_subset(U_22,U_24,U_23) ),
inference(variable_rename,[status(thm)],[f_18_1]) ).
cnf(f_18_3,plain,
( element(U_22,powerset(cartesian_product2(U_24,U_23)))
| ~ relation_of2_as_subset(U_22,U_24,U_23) ),
inference(clausify,[status(thm)],[f_18_2]) ).
fof(f_19_1,plain,
! [A] :
( relation_of2_as_subset(the_InternalRel(A),the_carrier(A),the_carrier(A))
| ~ rel_str(A) ),
inference(fof_nnf,[status(thm)],[dt_u1_orders_2]) ).
fof(f_19_2,plain,
! [U_25] :
( relation_of2_as_subset(the_InternalRel(U_25),the_carrier(U_25),the_carrier(U_25))
| ~ rel_str(U_25) ),
inference(variable_rename,[status(thm)],[f_19_1]) ).
cnf(f_19_3,plain,
( relation_of2_as_subset(the_InternalRel(U_25),the_carrier(U_25),the_carrier(U_25))
| ~ rel_str(U_25) ),
inference(clausify,[status(thm)],[f_19_2]) ).
fof(f_20_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_u1_struct_0]) ).
cnf(f_20_2,plain,
$true,
inference(clausify,[status(thm)],[f_20_1]) ).
fof(f_21_1,plain,
? [A] : rel_str(A),
inference(fof_nnf,[status(thm)],[existence_l1_orders_2]) ).
fof(f_21_2,plain,
? [U_26] : rel_str(U_26),
inference(variable_rename,[status(thm)],[f_21_1]) ).
fof(f_21_3,plain,
rel_str(sK3),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3]),skolemize(U_26,sK3)],[f_21_2]) ).
cnf(f_21_4,plain,
rel_str(sK3),
inference(clausify,[status(thm)],[f_21_3]) ).
fof(f_22_1,plain,
? [A] : one_sorted_str(A),
inference(fof_nnf,[status(thm)],[existence_l1_struct_0]) ).
fof(f_22_2,plain,
? [U_27] : one_sorted_str(U_27),
inference(variable_rename,[status(thm)],[f_22_1]) ).
fof(f_22_3,plain,
one_sorted_str(sK4),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4]),skolemize(U_27,sK4)],[f_22_2]) ).
cnf(f_22_4,plain,
one_sorted_str(sK4),
inference(clausify,[status(thm)],[f_22_3]) ).
fof(f_23_1,plain,
! [A,B] :
? [C] : relation_of2(C,A,B),
inference(fof_nnf,[status(thm)],[existence_m1_relset_1]) ).
fof(f_23_2,plain,
! [U_30,U_29] :
? [U_28] : relation_of2(U_28,U_30,U_29),
inference(variable_rename,[status(thm)],[f_23_1]) ).
fof(f_23_3,plain,
! [U_30,U_29] : relation_of2(sK5(U_30,U_29),U_30,U_29),
inference(skolemize,[status(esa),new_symbols(skolem,[sK5]),skolemize(U_28,sK5(U_30,U_29))],[f_23_2]) ).
cnf(f_23_4,plain,
relation_of2(sK5(U_30,U_29),U_30,U_29),
inference(clausify,[status(thm)],[f_23_3]) ).
fof(f_24_1,plain,
! [A] :
? [B] : element(B,A),
inference(fof_nnf,[status(thm)],[existence_m1_subset_1]) ).
fof(f_24_2,plain,
! [U_32] :
? [U_31] : element(U_31,U_32),
inference(variable_rename,[status(thm)],[f_24_1]) ).
fof(f_24_3,plain,
! [U_32] : element(sK6(U_32),U_32),
inference(skolemize,[status(esa),new_symbols(skolem,[sK6]),skolemize(U_31,sK6(U_32))],[f_24_2]) ).
cnf(f_24_4,plain,
element(sK6(U_32),U_32),
inference(clausify,[status(thm)],[f_24_3]) ).
fof(f_25_1,plain,
! [A,B] :
? [C] : relation_of2_as_subset(C,A,B),
inference(fof_nnf,[status(thm)],[existence_m2_relset_1]) ).
fof(f_25_2,plain,
! [U_35,U_34] :
? [U_33] : relation_of2_as_subset(U_33,U_35,U_34),
inference(variable_rename,[status(thm)],[f_25_1]) ).
fof(f_25_3,plain,
! [U_35,U_34] : relation_of2_as_subset(sK7(U_35,U_34),U_35,U_34),
inference(skolemize,[status(esa),new_symbols(skolem,[sK7]),skolemize(U_33,sK7(U_35,U_34))],[f_25_2]) ).
cnf(f_25_4,plain,
relation_of2_as_subset(sK7(U_35,U_34),U_35,U_34),
inference(clausify,[status(thm)],[f_25_3]) ).
fof(f_26_1,plain,
! [A] : ~ empty(powerset(A)),
inference(fof_nnf,[status(thm)],[fc1_subset_1]) ).
fof(f_26_2,plain,
! [U_36] : ~ empty(powerset(U_36)),
inference(variable_rename,[status(thm)],[f_26_1]) ).
cnf(f_26_3,plain,
~ empty(powerset(U_36)),
inference(clausify,[status(thm)],[f_26_2]) ).
fof(f_27_1,plain,
empty(empty_set),
inference(fof_nnf,[status(thm)],[fc1_xboole_0]) ).
cnf(f_27_2,plain,
empty(empty_set),
inference(clausify,[status(thm)],[f_27_1]) ).
fof(f_28_1,plain,
! [A] : ~ empty(singleton(A)),
inference(fof_nnf,[status(thm)],[fc2_subset_1]) ).
fof(f_28_2,plain,
! [U_37] : ~ empty(singleton(U_37)),
inference(variable_rename,[status(thm)],[f_28_1]) ).
cnf(f_28_3,plain,
~ empty(singleton(U_37)),
inference(clausify,[status(thm)],[f_28_2]) ).
fof(f_29_1,plain,
! [A,B] : ~ empty(unordered_pair(A,B)),
inference(fof_nnf,[status(thm)],[fc3_subset_1]) ).
fof(f_29_2,plain,
! [U_39,U_38] : ~ empty(unordered_pair(U_39,U_38)),
inference(variable_rename,[status(thm)],[f_29_1]) ).
cnf(f_29_3,plain,
~ empty(unordered_pair(U_39,U_38)),
inference(clausify,[status(thm)],[f_29_2]) ).
fof(f_30_1,plain,
! [A,B] :
( ~ empty(cartesian_product2(A,B))
| empty(B)
| empty(A) ),
inference(fof_nnf,[status(thm)],[fc4_subset_1]) ).
fof(f_30_2,plain,
! [U_41,U_40] :
( ~ empty(cartesian_product2(U_41,U_40))
| empty(U_40)
| empty(U_41) ),
inference(variable_rename,[status(thm)],[f_30_1]) ).
cnf(f_30_3,plain,
( ~ empty(cartesian_product2(U_41,U_40))
| empty(U_40)
| empty(U_41) ),
inference(clausify,[status(thm)],[f_30_2]) ).
fof(f_31_1,plain,
! [A] :
( ? [B] :
( ~ empty(B)
& element(B,powerset(A)) )
| empty(A) ),
inference(fof_nnf,[status(thm)],[rc1_subset_1]) ).
fof(f_31_2,plain,
! [U_43] :
( ? [U_42] :
( ~ empty(U_42)
& element(U_42,powerset(U_43)) )
| empty(U_43) ),
inference(variable_rename,[status(thm)],[f_31_1]) ).
fof(f_31_3,plain,
! [U_43] :
( ( ~ empty(sK8(U_43))
& element(sK8(U_43),powerset(U_43)) )
| empty(U_43) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK8]),skolemize(U_42,sK8(U_43))],[f_31_2]) ).
cnf(f_31_4,plain,
( element(sK8(U_43),powerset(U_43))
| empty(U_43) ),
inference(clausify,[status(thm)],[f_31_3]) ).
cnf(f_31_5,plain,
( ~ empty(sK8(U_43))
| empty(U_43) ),
inference(clausify,[status(thm)],[f_31_3]) ).
fof(f_32_1,plain,
? [A] : empty(A),
inference(fof_nnf,[status(thm)],[rc1_xboole_0]) ).
fof(f_32_2,plain,
? [U_44] : empty(U_44),
inference(variable_rename,[status(thm)],[f_32_1]) ).
fof(f_32_3,plain,
empty(sK9),
inference(skolemize,[status(esa),new_symbols(skolem,[sK9]),skolemize(U_44,sK9)],[f_32_2]) ).
cnf(f_32_4,plain,
empty(sK9),
inference(clausify,[status(thm)],[f_32_3]) ).
fof(f_33_1,plain,
! [A] :
? [B] :
( empty(B)
& element(B,powerset(A)) ),
inference(fof_nnf,[status(thm)],[rc2_subset_1]) ).
fof(f_33_2,plain,
! [U_46] :
? [U_45] :
( empty(U_45)
& element(U_45,powerset(U_46)) ),
inference(variable_rename,[status(thm)],[f_33_1]) ).
fof(f_33_3,plain,
! [U_46] :
( empty(sK10(U_46))
& element(sK10(U_46),powerset(U_46)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK10]),skolemize(U_45,sK10(U_46))],[f_33_2]) ).
cnf(f_33_4,plain,
element(sK10(U_46),powerset(U_46)),
inference(clausify,[status(thm)],[f_33_3]) ).
cnf(f_33_5,plain,
empty(sK10(U_46)),
inference(clausify,[status(thm)],[f_33_3]) ).
fof(f_34_1,plain,
? [A] : ~ empty(A),
inference(fof_nnf,[status(thm)],[rc2_xboole_0]) ).
fof(f_34_2,plain,
? [U_47] : ~ empty(U_47),
inference(variable_rename,[status(thm)],[f_34_1]) ).
fof(f_34_3,plain,
~ empty(sK11),
inference(skolemize,[status(esa),new_symbols(skolem,[sK11]),skolemize(U_47,sK11)],[f_34_2]) ).
cnf(f_34_4,plain,
~ empty(sK11),
inference(clausify,[status(thm)],[f_34_3]) ).
fof(f_35_1,plain,
! [A,B,C] :
( ( relation_of2_as_subset(C,A,B)
| ~ relation_of2(C,A,B) )
& ( relation_of2(C,A,B)
| ~ relation_of2_as_subset(C,A,B) ) ),
inference(fof_nnf,[status(thm)],[redefinition_m2_relset_1]) ).
fof(f_35_2,plain,
! [U_50,U_49,U_48] :
( ( relation_of2_as_subset(U_48,U_50,U_49)
| ~ relation_of2(U_48,U_50,U_49) )
& ( relation_of2(U_48,U_50,U_49)
| ~ relation_of2_as_subset(U_48,U_50,U_49) ) ),
inference(variable_rename,[status(thm)],[f_35_1]) ).
fof(f_35_3,plain,
( ! [U_56,U_54,U_52] :
( relation_of2_as_subset(U_52,U_56,U_54)
| ~ relation_of2(U_52,U_56,U_54) )
& ! [U_55,U_53,U_51] :
( relation_of2(U_51,U_55,U_53)
| ~ relation_of2_as_subset(U_51,U_55,U_53) ) ),
inference(miniscope,[status(thm)],[f_35_2]) ).
cnf(f_35_4,plain,
( relation_of2(U_51,U_55,U_53)
| ~ relation_of2_as_subset(U_51,U_55,U_53) ),
inference(clausify,[status(thm)],[f_35_3]) ).
cnf(f_35_5,plain,
( relation_of2_as_subset(U_52,U_56,U_54)
| ~ relation_of2(U_52,U_56,U_54) ),
inference(clausify,[status(thm)],[f_35_3]) ).
fof(f_36_1,plain,
! [A,B] : subset(A,A),
inference(fof_nnf,[status(thm)],[reflexivity_r1_tarski]) ).
fof(f_36_2,plain,
! [U_58,U_57] : subset(U_58,U_58),
inference(variable_rename,[status(thm)],[f_36_1]) ).
fof(f_36_3,plain,
! [U_58] : subset(U_58,U_58),
inference(miniscope,[status(thm)],[f_36_2]) ).
cnf(f_36_4,plain,
subset(U_58,U_58),
inference(clausify,[status(thm)],[f_36_3]) ).
fof(f_37_1,plain,
! [A,B,C,D] :
( ( in(ordered_pair(A,B),cartesian_product2(C,D))
| ~ in(B,D)
| ~ in(A,C) )
& ( ( in(B,D)
& in(A,C) )
| ~ in(ordered_pair(A,B),cartesian_product2(C,D)) ) ),
inference(fof_nnf,[status(thm)],[t106_zfmisc_1]) ).
fof(f_37_2,plain,
! [U_62,U_61,U_60,U_59] :
( ( in(ordered_pair(U_62,U_61),cartesian_product2(U_60,U_59))
| ~ in(U_61,U_59)
| ~ in(U_62,U_60) )
& ( ( in(U_61,U_59)
& in(U_62,U_60) )
| ~ in(ordered_pair(U_62,U_61),cartesian_product2(U_60,U_59)) ) ),
inference(variable_rename,[status(thm)],[f_37_1]) ).
fof(f_37_3,plain,
( ! [U_70,U_68,U_66,U_64] :
( in(ordered_pair(U_70,U_68),cartesian_product2(U_66,U_64))
| ~ in(U_68,U_64)
| ~ in(U_70,U_66) )
& ! [U_69,U_67,U_65,U_63] :
( ( in(U_67,U_63)
& in(U_69,U_65) )
| ~ in(ordered_pair(U_69,U_67),cartesian_product2(U_65,U_63)) ) ),
inference(miniscope,[status(thm)],[f_37_2]) ).
cnf(f_37_4,plain,
( in(U_69,U_65)
| ~ in(ordered_pair(U_69,U_67),cartesian_product2(U_65,U_63)) ),
inference(clausify,[status(thm)],[f_37_3]) ).
cnf(f_37_5,plain,
( in(U_67,U_63)
| ~ in(ordered_pair(U_69,U_67),cartesian_product2(U_65,U_63)) ),
inference(clausify,[status(thm)],[f_37_3]) ).
cnf(f_37_6,plain,
( in(ordered_pair(U_70,U_68),cartesian_product2(U_66,U_64))
| ~ in(U_68,U_64)
| ~ in(U_70,U_66) ),
inference(clausify,[status(thm)],[f_37_3]) ).
fof(f_38_1,plain,
! [A,B] :
( element(A,B)
| ~ in(A,B) ),
inference(fof_nnf,[status(thm)],[t1_subset]) ).
fof(f_38_2,plain,
! [U_72,U_71] :
( element(U_72,U_71)
| ~ in(U_72,U_71) ),
inference(variable_rename,[status(thm)],[f_38_1]) ).
cnf(f_38_3,plain,
( element(U_72,U_71)
| ~ in(U_72,U_71) ),
inference(clausify,[status(thm)],[f_38_2]) ).
fof(f_39_1,negated_conjecture,
~ ! [A] :
( ( rel_str(A)
& antisymmetric_relstr(A) )
=> ! [B] :
( element(B,the_carrier(A))
=> ! [C] :
( element(C,the_carrier(A))
=> ( ( related(A,C,B)
& related(A,B,C) )
=> B = C ) ) ) ),
inference(negate,[status(cth)],[t25_orders_2]) ).
fof(f_39_2,negated_conjecture,
? [A] :
( ? [B] :
( ? [C] :
( B != C
& related(A,C,B)
& related(A,B,C)
& element(C,the_carrier(A)) )
& element(B,the_carrier(A)) )
& rel_str(A)
& antisymmetric_relstr(A) ),
inference(fof_nnf,[status(thm)],[f_39_1]) ).
fof(f_39_3,negated_conjecture,
? [U_75] :
( ? [U_74] :
( ? [U_73] :
( U_74 != U_73
& related(U_75,U_73,U_74)
& related(U_75,U_74,U_73)
& element(U_73,the_carrier(U_75)) )
& element(U_74,the_carrier(U_75)) )
& rel_str(U_75)
& antisymmetric_relstr(U_75) ),
inference(variable_rename,[status(thm)],[f_39_2]) ).
fof(f_39_4,negated_conjecture,
( ? [U_74] :
( ? [U_73] :
( U_74 != U_73
& related(sK12,U_73,U_74)
& related(sK12,U_74,U_73)
& element(U_73,the_carrier(sK12)) )
& element(U_74,the_carrier(sK12)) )
& rel_str(sK12)
& antisymmetric_relstr(sK12) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK12]),skolemize(U_75,sK12)],[f_39_3]) ).
fof(f_39_5,negated_conjecture,
( ? [U_73] :
( sK13 != U_73
& related(sK12,U_73,sK13)
& related(sK12,sK13,U_73)
& element(U_73,the_carrier(sK12)) )
& element(sK13,the_carrier(sK12))
& rel_str(sK12)
& antisymmetric_relstr(sK12) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK13]),skolemize(U_74,sK13)],[f_39_4]) ).
fof(f_39_6,negated_conjecture,
( sK13 != sK14
& related(sK12,sK14,sK13)
& related(sK12,sK13,sK14)
& element(sK14,the_carrier(sK12))
& element(sK13,the_carrier(sK12))
& rel_str(sK12)
& antisymmetric_relstr(sK12) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK14]),skolemize(U_73,sK14)],[f_39_5]) ).
cnf(f_39_7,negated_conjecture,
antisymmetric_relstr(sK12),
inference(clausify,[status(thm)],[f_39_6]) ).
cnf(f_39_8,negated_conjecture,
rel_str(sK12),
inference(clausify,[status(thm)],[f_39_6]) ).
cnf(f_39_9,negated_conjecture,
element(sK13,the_carrier(sK12)),
inference(clausify,[status(thm)],[f_39_6]) ).
cnf(f_39_10,negated_conjecture,
element(sK14,the_carrier(sK12)),
inference(clausify,[status(thm)],[f_39_6]) ).
cnf(f_39_11,negated_conjecture,
related(sK12,sK13,sK14),
inference(clausify,[status(thm)],[f_39_6]) ).
cnf(f_39_12,negated_conjecture,
related(sK12,sK14,sK13),
inference(clausify,[status(thm)],[f_39_6]) ).
cnf(f_39_13,negated_conjecture,
sK13 != sK14,
inference(clausify,[status(thm)],[f_39_6]) ).
fof(f_40_1,plain,
! [A,B] :
( in(A,B)
| empty(B)
| ~ element(A,B) ),
inference(fof_nnf,[status(thm)],[t2_subset]) ).
fof(f_40_2,plain,
! [U_77,U_76] :
( in(U_77,U_76)
| empty(U_76)
| ~ element(U_77,U_76) ),
inference(variable_rename,[status(thm)],[f_40_1]) ).
cnf(f_40_3,plain,
( in(U_77,U_76)
| empty(U_76)
| ~ element(U_77,U_76) ),
inference(clausify,[status(thm)],[f_40_2]) ).
fof(f_41_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_41_2,plain,
! [U_79,U_78] :
( ( element(U_79,powerset(U_78))
| ~ subset(U_79,U_78) )
& ( subset(U_79,U_78)
| ~ element(U_79,powerset(U_78)) ) ),
inference(variable_rename,[status(thm)],[f_41_1]) ).
fof(f_41_3,plain,
( ! [U_83,U_81] :
( element(U_83,powerset(U_81))
| ~ subset(U_83,U_81) )
& ! [U_82,U_80] :
( subset(U_82,U_80)
| ~ element(U_82,powerset(U_80)) ) ),
inference(miniscope,[status(thm)],[f_41_2]) ).
cnf(f_41_4,plain,
( subset(U_82,U_80)
| ~ element(U_82,powerset(U_80)) ),
inference(clausify,[status(thm)],[f_41_3]) ).
cnf(f_41_5,plain,
( element(U_83,powerset(U_81))
| ~ subset(U_83,U_81) ),
inference(clausify,[status(thm)],[f_41_3]) ).
fof(f_42_1,plain,
! [A,B,C] :
( element(A,C)
| ~ element(B,powerset(C))
| ~ in(A,B) ),
inference(fof_nnf,[status(thm)],[t4_subset]) ).
fof(f_42_2,plain,
! [U_86,U_85,U_84] :
( element(U_86,U_84)
| ~ element(U_85,powerset(U_84))
| ~ in(U_86,U_85) ),
inference(variable_rename,[status(thm)],[f_42_1]) ).
cnf(f_42_3,plain,
( element(U_86,U_84)
| ~ element(U_85,powerset(U_84))
| ~ in(U_86,U_85) ),
inference(clausify,[status(thm)],[f_42_2]) ).
fof(f_43_1,plain,
! [A,B,C] :
( ~ empty(C)
| ~ element(B,powerset(C))
| ~ in(A,B) ),
inference(fof_nnf,[status(thm)],[t5_subset]) ).
fof(f_43_2,plain,
! [U_89,U_88,U_87] :
( ~ empty(U_87)
| ~ element(U_88,powerset(U_87))
| ~ in(U_89,U_88) ),
inference(variable_rename,[status(thm)],[f_43_1]) ).
fof(f_43_3,plain,
! [U_89,U_88] :
( ! [U_87] :
( ~ empty(U_87)
| ~ element(U_88,powerset(U_87)) )
| ~ in(U_89,U_88) ),
inference(miniscope,[status(thm)],[f_43_2]) ).
cnf(f_43_4,plain,
( ~ empty(U_87)
| ~ element(U_88,powerset(U_87))
| ~ in(U_89,U_88) ),
inference(clausify,[status(thm)],[f_43_3]) ).
fof(f_44_1,plain,
! [A] :
( A = empty_set
| ~ empty(A) ),
inference(fof_nnf,[status(thm)],[t6_boole]) ).
fof(f_44_2,plain,
! [U_90] :
( U_90 = empty_set
| ~ empty(U_90) ),
inference(variable_rename,[status(thm)],[f_44_1]) ).
cnf(f_44_3,plain,
( U_90 = empty_set
| ~ empty(U_90) ),
inference(clausify,[status(thm)],[f_44_2]) ).
fof(f_45_1,plain,
! [A,B] :
( ~ empty(B)
| ~ in(A,B) ),
inference(fof_nnf,[status(thm)],[t7_boole]) ).
fof(f_45_2,plain,
! [U_92,U_91] :
( ~ empty(U_91)
| ~ in(U_92,U_91) ),
inference(variable_rename,[status(thm)],[f_45_1]) ).
cnf(f_45_3,plain,
( ~ empty(U_91)
| ~ in(U_92,U_91) ),
inference(clausify,[status(thm)],[f_45_2]) ).
fof(f_46_1,plain,
! [A,B] :
( ~ empty(B)
| A = B
| ~ empty(A) ),
inference(fof_nnf,[status(thm)],[t8_boole]) ).
fof(f_46_2,plain,
! [U_94,U_93] :
( ~ empty(U_93)
| U_94 = U_93
| ~ empty(U_94) ),
inference(variable_rename,[status(thm)],[f_46_1]) ).
fof(f_46_3,plain,
! [U_94] :
( ! [U_93] :
( ~ empty(U_93)
| U_94 = U_93 )
| ~ empty(U_94) ),
inference(miniscope,[status(thm)],[f_46_2]) ).
cnf(f_46_4,plain,
( ~ empty(U_93)
| U_94 = U_93
| ~ empty(U_94) ),
inference(clausify,[status(thm)],[f_46_3]) ).
cnf(f_8_2_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_8_2]) ).
cnf(f_9_2_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_9_2]) ).
cnf(f_10_2_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_10_2]) ).
cnf(f_11_2_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_11_2]) ).
cnf(f_12_2_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_12_2]) ).
cnf(f_13_2_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_13_2]) ).
cnf(f_15_2_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_15_2]) ).
cnf(f_16_2_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_16_2]) ).
cnf(f_17_2_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_17_2]) ).
cnf(f_20_2_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_20_2]) ).
cnf(equality_1,axiom,
Eq_x_0 = Eq_x_0,
theory(equality,[reflexivity]) ).
cnf(equality_2,axiom,
( Eq_x_1 = Eq_x_0
| Eq_x_0 != Eq_x_1 ),
theory(equality,[symmetry]) ).
cnf(equality_3,axiom,
( Eq_x_0 = Eq_x_2
| Eq_x_1 != Eq_x_2
| Eq_x_0 != Eq_x_1 ),
theory(equality,[transitivity]) ).
cnf(equality_4,axiom,
( cartesian_product2(Eq_x_0,Eq_x_1) = cartesian_product2(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,
( powerset(Eq_x_0) = powerset(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_6,axiom,
( unordered_pair(Eq_x_0,Eq_x_1) = unordered_pair(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,
( ordered_pair(Eq_x_0,Eq_x_1) = ordered_pair(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_8,axiom,
( singleton(Eq_x_0) = singleton(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_9,axiom,
( the_InternalRel(Eq_x_0) = the_InternalRel(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_10,axiom,
( the_carrier(Eq_x_0) = the_carrier(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_11,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_12,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_13,axiom,
( sK5(Eq_x_0,Eq_x_1) = sK5(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_14,axiom,
( sK6(Eq_x_0) = sK6(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_15,axiom,
( sK7(Eq_x_0,Eq_x_1) = sK7(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_16,axiom,
( sK8(Eq_x_0) = sK8(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_17,axiom,
( sK10(Eq_x_0) = sK10(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_18,axiom,
( in(Eq_y_0,Eq_y_1)
| ~ in(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_19,axiom,
( 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,
( relation(Eq_y_0)
| ~ relation(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_21,axiom,
( is_antisymmetric_in(Eq_y_0,Eq_y_1)
| ~ is_antisymmetric_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_22,axiom,
( rel_str(Eq_y_0)
| ~ rel_str(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_23,axiom,
( antisymmetric_relstr(Eq_y_0)
| ~ antisymmetric_relstr(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_24,axiom,
( related(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ related(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_25,axiom,
( one_sorted_str(Eq_y_0)
| ~ one_sorted_str(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_26,axiom,
( relation_of2_as_subset(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ relation_of2_as_subset(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_27,axiom,
( relation_of2(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ relation_of2(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_28,axiom,
( empty(Eq_y_0)
| ~ empty(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_29,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(sat_proved,plain,
$false,
inference(cadical,[status(thm)],[]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU339+1 : TPTP v9.3.1. Released v3.3.0.
% 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
% 0.08/5.37 % Computer : n016.cluster.edu
% 0.08/5.37 % Model : x86_64 x86_64
% 0.08/5.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/5.37 % Memory : 8046.5625MB
% 0.08/5.37 % OS : Linux 6.8.0-71-generic
% 0.08/5.37 % CPULimit : 300
% 0.08/5.37 % WCLimit : 300
% 0.08/5.37 % DateTime : Sun Sep 20 00:02:57 UTC 2026
% 0.08/5.38 % CPUTime :
% 193.13/198.41 % SZS status Theorem for theBenchmark
% 193.13/198.41 % SZS output start Proof for theBenchmark
% See solution above
%------------------------------------------------------------------------------