%------------------------------------------------------------------------------
% File : ConnectPP---0.7.2
% Problem : SEU244+1 : TPTP v9.3.1. Released v3.3.0.
% 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 : n014.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 08:58:40 AM UTC 2026
% Result : Theorem 0.14s 0.39s
% Output : Proof 0.14s
% Verified :
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)
% Comments :
%------------------------------------------------------------------------------
fof(commutativity_k2_xboole_0,axiom,
! [A,B] : set_union2(A,B) = set_union2(B,A),
file('theBenchmark.p',commutativity_k2_xboole_0) ).
fof(d12_relat_2,axiom,
! [A] :
( relation(A)
=> ( antisymmetric(A)
<=> is_antisymmetric_in(A,relation_field(A)) ) ),
file('theBenchmark.p',d12_relat_2) ).
fof(d14_relat_2,axiom,
! [A] :
( relation(A)
=> ( connected(A)
<=> is_connected_in(A,relation_field(A)) ) ),
file('theBenchmark.p',d14_relat_2) ).
fof(d16_relat_2,axiom,
! [A] :
( relation(A)
=> ( transitive(A)
<=> is_transitive_in(A,relation_field(A)) ) ),
file('theBenchmark.p',d16_relat_2) ).
fof(d4_wellord1,axiom,
! [A] :
( relation(A)
=> ( well_ordering(A)
<=> ( well_founded_relation(A)
& connected(A)
& antisymmetric(A)
& transitive(A)
& reflexive(A) ) ) ),
file('theBenchmark.p',d4_wellord1) ).
fof(d5_wellord1,axiom,
! [A] :
( relation(A)
=> ! [B] :
( well_orders(A,B)
<=> ( is_well_founded_in(A,B)
& is_connected_in(A,B)
& is_antisymmetric_in(A,B)
& is_transitive_in(A,B)
& is_reflexive_in(A,B) ) ) ),
file('theBenchmark.p',d5_wellord1) ).
fof(d6_relat_1,axiom,
! [A] :
( relation(A)
=> relation_field(A) = set_union2(relation_dom(A),relation_rng(A)) ),
file('theBenchmark.p',d6_relat_1) ).
fof(d9_relat_2,axiom,
! [A] :
( relation(A)
=> ( reflexive(A)
<=> is_reflexive_in(A,relation_field(A)) ) ),
file('theBenchmark.p',d9_relat_2) ).
fof(dt_k1_relat_1,axiom,
$true,
file('theBenchmark.p',dt_k1_relat_1) ).
fof(dt_k2_relat_1,axiom,
$true,
file('theBenchmark.p',dt_k2_relat_1) ).
fof(dt_k2_xboole_0,axiom,
$true,
file('theBenchmark.p',dt_k2_xboole_0) ).
fof(dt_k3_relat_1,axiom,
$true,
file('theBenchmark.p',dt_k3_relat_1) ).
fof(idempotence_k2_xboole_0,axiom,
! [A,B] : set_union2(A,A) = A,
file('theBenchmark.p',idempotence_k2_xboole_0) ).
fof(t5_wellord1,axiom,
! [A] :
( relation(A)
=> ( well_founded_relation(A)
<=> is_well_founded_in(A,relation_field(A)) ) ),
file('theBenchmark.p',t5_wellord1) ).
fof(t8_wellord1,conjecture,
! [A] :
( relation(A)
=> ( well_orders(A,relation_field(A))
<=> well_ordering(A) ) ),
file('theBenchmark.p',t8_wellord1) ).
fof(f_1_1,plain,
! [A,B] : set_union2(A,B) = set_union2(B,A),
inference(fof_nnf,[status(thm)],[commutativity_k2_xboole_0]) ).
fof(f_1_2,plain,
! [U_1,U_0] : set_union2(U_1,U_0) = set_union2(U_0,U_1),
inference(variable_rename,[status(thm)],[f_1_1]) ).
cnf(f_1_3,plain,
set_union2(U_1,U_0) = set_union2(U_0,U_1),
inference(clausify,[status(thm)],[f_1_2]) ).
fof(f_2_1,plain,
! [A] :
( ( ( antisymmetric(A)
| ~ is_antisymmetric_in(A,relation_field(A)) )
& ( is_antisymmetric_in(A,relation_field(A))
| ~ antisymmetric(A) ) )
| ~ relation(A) ),
inference(fof_nnf,[status(thm)],[d12_relat_2]) ).
fof(f_2_2,plain,
! [U_2] :
( ( ( antisymmetric(U_2)
| ~ is_antisymmetric_in(U_2,relation_field(U_2)) )
& ( is_antisymmetric_in(U_2,relation_field(U_2))
| ~ antisymmetric(U_2) ) )
| ~ relation(U_2) ),
inference(variable_rename,[status(thm)],[f_2_1]) ).
cnf(f_2_3,plain,
( is_antisymmetric_in(U_2,relation_field(U_2))
| ~ antisymmetric(U_2)
| ~ relation(U_2) ),
inference(clausify,[status(thm)],[f_2_2]) ).
cnf(f_2_4,plain,
( antisymmetric(U_2)
| ~ is_antisymmetric_in(U_2,relation_field(U_2))
| ~ relation(U_2) ),
inference(clausify,[status(thm)],[f_2_2]) ).
fof(f_3_1,plain,
! [A] :
( ( ( connected(A)
| ~ is_connected_in(A,relation_field(A)) )
& ( is_connected_in(A,relation_field(A))
| ~ connected(A) ) )
| ~ relation(A) ),
inference(fof_nnf,[status(thm)],[d14_relat_2]) ).
fof(f_3_2,plain,
! [U_3] :
( ( ( connected(U_3)
| ~ is_connected_in(U_3,relation_field(U_3)) )
& ( is_connected_in(U_3,relation_field(U_3))
| ~ connected(U_3) ) )
| ~ relation(U_3) ),
inference(variable_rename,[status(thm)],[f_3_1]) ).
cnf(f_3_3,plain,
( is_connected_in(U_3,relation_field(U_3))
| ~ connected(U_3)
| ~ relation(U_3) ),
inference(clausify,[status(thm)],[f_3_2]) ).
cnf(f_3_4,plain,
( connected(U_3)
| ~ is_connected_in(U_3,relation_field(U_3))
| ~ relation(U_3) ),
inference(clausify,[status(thm)],[f_3_2]) ).
fof(f_4_1,plain,
! [A] :
( ( ( transitive(A)
| ~ is_transitive_in(A,relation_field(A)) )
& ( is_transitive_in(A,relation_field(A))
| ~ transitive(A) ) )
| ~ relation(A) ),
inference(fof_nnf,[status(thm)],[d16_relat_2]) ).
fof(f_4_2,plain,
! [U_4] :
( ( ( transitive(U_4)
| ~ is_transitive_in(U_4,relation_field(U_4)) )
& ( is_transitive_in(U_4,relation_field(U_4))
| ~ transitive(U_4) ) )
| ~ relation(U_4) ),
inference(variable_rename,[status(thm)],[f_4_1]) ).
cnf(f_4_3,plain,
( is_transitive_in(U_4,relation_field(U_4))
| ~ transitive(U_4)
| ~ relation(U_4) ),
inference(clausify,[status(thm)],[f_4_2]) ).
cnf(f_4_4,plain,
( transitive(U_4)
| ~ is_transitive_in(U_4,relation_field(U_4))
| ~ relation(U_4) ),
inference(clausify,[status(thm)],[f_4_2]) ).
fof(f_5_1,plain,
! [A] :
( ( ( well_ordering(A)
| ~ well_founded_relation(A)
| ~ connected(A)
| ~ antisymmetric(A)
| ~ transitive(A)
| ~ reflexive(A) )
& ( ( well_founded_relation(A)
& connected(A)
& antisymmetric(A)
& transitive(A)
& reflexive(A) )
| ~ well_ordering(A) ) )
| ~ relation(A) ),
inference(fof_nnf,[status(thm)],[d4_wellord1]) ).
fof(f_5_2,plain,
! [U_5] :
( ( ( well_ordering(U_5)
| ~ well_founded_relation(U_5)
| ~ connected(U_5)
| ~ antisymmetric(U_5)
| ~ transitive(U_5)
| ~ reflexive(U_5) )
& ( ( well_founded_relation(U_5)
& connected(U_5)
& antisymmetric(U_5)
& transitive(U_5)
& reflexive(U_5) )
| ~ well_ordering(U_5) ) )
| ~ relation(U_5) ),
inference(variable_rename,[status(thm)],[f_5_1]) ).
cnf(f_5_3,plain,
( reflexive(U_5)
| ~ well_ordering(U_5)
| ~ relation(U_5) ),
inference(clausify,[status(thm)],[f_5_2]) ).
cnf(f_5_4,plain,
( transitive(U_5)
| ~ well_ordering(U_5)
| ~ relation(U_5) ),
inference(clausify,[status(thm)],[f_5_2]) ).
cnf(f_5_5,plain,
( antisymmetric(U_5)
| ~ well_ordering(U_5)
| ~ relation(U_5) ),
inference(clausify,[status(thm)],[f_5_2]) ).
cnf(f_5_6,plain,
( connected(U_5)
| ~ well_ordering(U_5)
| ~ relation(U_5) ),
inference(clausify,[status(thm)],[f_5_2]) ).
cnf(f_5_7,plain,
( well_founded_relation(U_5)
| ~ well_ordering(U_5)
| ~ relation(U_5) ),
inference(clausify,[status(thm)],[f_5_2]) ).
cnf(f_5_8,plain,
( well_ordering(U_5)
| ~ well_founded_relation(U_5)
| ~ connected(U_5)
| ~ antisymmetric(U_5)
| ~ transitive(U_5)
| ~ reflexive(U_5)
| ~ relation(U_5) ),
inference(clausify,[status(thm)],[f_5_2]) ).
fof(f_6_1,plain,
! [A] :
( ! [B] :
( ( well_orders(A,B)
| ~ is_well_founded_in(A,B)
| ~ is_connected_in(A,B)
| ~ is_antisymmetric_in(A,B)
| ~ is_transitive_in(A,B)
| ~ is_reflexive_in(A,B) )
& ( ( is_well_founded_in(A,B)
& is_connected_in(A,B)
& is_antisymmetric_in(A,B)
& is_transitive_in(A,B)
& is_reflexive_in(A,B) )
| ~ well_orders(A,B) ) )
| ~ relation(A) ),
inference(fof_nnf,[status(thm)],[d5_wellord1]) ).
fof(f_6_2,plain,
! [U_7] :
( ! [U_6] :
( ( well_orders(U_7,U_6)
| ~ is_well_founded_in(U_7,U_6)
| ~ is_connected_in(U_7,U_6)
| ~ is_antisymmetric_in(U_7,U_6)
| ~ is_transitive_in(U_7,U_6)
| ~ is_reflexive_in(U_7,U_6) )
& ( ( is_well_founded_in(U_7,U_6)
& is_connected_in(U_7,U_6)
& is_antisymmetric_in(U_7,U_6)
& is_transitive_in(U_7,U_6)
& is_reflexive_in(U_7,U_6) )
| ~ well_orders(U_7,U_6) ) )
| ~ relation(U_7) ),
inference(variable_rename,[status(thm)],[f_6_1]) ).
fof(f_6_3,plain,
! [U_7] :
( ( ! [U_9] :
( well_orders(U_7,U_9)
| ~ is_well_founded_in(U_7,U_9)
| ~ is_connected_in(U_7,U_9)
| ~ is_antisymmetric_in(U_7,U_9)
| ~ is_transitive_in(U_7,U_9)
| ~ is_reflexive_in(U_7,U_9) )
& ! [U_8] :
( ( is_well_founded_in(U_7,U_8)
& is_connected_in(U_7,U_8)
& is_antisymmetric_in(U_7,U_8)
& is_transitive_in(U_7,U_8)
& is_reflexive_in(U_7,U_8) )
| ~ well_orders(U_7,U_8) ) )
| ~ relation(U_7) ),
inference(miniscope,[status(thm)],[f_6_2]) ).
cnf(f_6_4,plain,
( is_reflexive_in(U_7,U_8)
| ~ well_orders(U_7,U_8)
| ~ relation(U_7) ),
inference(clausify,[status(thm)],[f_6_3]) ).
cnf(f_6_5,plain,
( is_transitive_in(U_7,U_8)
| ~ well_orders(U_7,U_8)
| ~ relation(U_7) ),
inference(clausify,[status(thm)],[f_6_3]) ).
cnf(f_6_6,plain,
( is_antisymmetric_in(U_7,U_8)
| ~ well_orders(U_7,U_8)
| ~ relation(U_7) ),
inference(clausify,[status(thm)],[f_6_3]) ).
cnf(f_6_7,plain,
( is_connected_in(U_7,U_8)
| ~ well_orders(U_7,U_8)
| ~ relation(U_7) ),
inference(clausify,[status(thm)],[f_6_3]) ).
cnf(f_6_8,plain,
( is_well_founded_in(U_7,U_8)
| ~ well_orders(U_7,U_8)
| ~ relation(U_7) ),
inference(clausify,[status(thm)],[f_6_3]) ).
cnf(f_6_9,plain,
( well_orders(U_7,U_9)
| ~ is_well_founded_in(U_7,U_9)
| ~ is_connected_in(U_7,U_9)
| ~ is_antisymmetric_in(U_7,U_9)
| ~ is_transitive_in(U_7,U_9)
| ~ is_reflexive_in(U_7,U_9)
| ~ relation(U_7) ),
inference(clausify,[status(thm)],[f_6_3]) ).
fof(f_7_1,plain,
! [A] :
( relation_field(A) = set_union2(relation_dom(A),relation_rng(A))
| ~ relation(A) ),
inference(fof_nnf,[status(thm)],[d6_relat_1]) ).
fof(f_7_2,plain,
! [U_10] :
( relation_field(U_10) = set_union2(relation_dom(U_10),relation_rng(U_10))
| ~ relation(U_10) ),
inference(variable_rename,[status(thm)],[f_7_1]) ).
cnf(f_7_3,plain,
( relation_field(U_10) = set_union2(relation_dom(U_10),relation_rng(U_10))
| ~ relation(U_10) ),
inference(clausify,[status(thm)],[f_7_2]) ).
fof(f_8_1,plain,
! [A] :
( ( ( reflexive(A)
| ~ is_reflexive_in(A,relation_field(A)) )
& ( is_reflexive_in(A,relation_field(A))
| ~ reflexive(A) ) )
| ~ relation(A) ),
inference(fof_nnf,[status(thm)],[d9_relat_2]) ).
fof(f_8_2,plain,
! [U_11] :
( ( ( reflexive(U_11)
| ~ is_reflexive_in(U_11,relation_field(U_11)) )
& ( is_reflexive_in(U_11,relation_field(U_11))
| ~ reflexive(U_11) ) )
| ~ relation(U_11) ),
inference(variable_rename,[status(thm)],[f_8_1]) ).
cnf(f_8_3,plain,
( is_reflexive_in(U_11,relation_field(U_11))
| ~ reflexive(U_11)
| ~ relation(U_11) ),
inference(clausify,[status(thm)],[f_8_2]) ).
cnf(f_8_4,plain,
( reflexive(U_11)
| ~ is_reflexive_in(U_11,relation_field(U_11))
| ~ relation(U_11) ),
inference(clausify,[status(thm)],[f_8_2]) ).
fof(f_9_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_k1_relat_1]) ).
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_k2_relat_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_xboole_0]) ).
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_k3_relat_1]) ).
cnf(f_12_2,plain,
$true,
inference(clausify,[status(thm)],[f_12_1]) ).
fof(f_13_1,plain,
! [A,B] : set_union2(A,A) = A,
inference(fof_nnf,[status(thm)],[idempotence_k2_xboole_0]) ).
fof(f_13_2,plain,
! [U_13,U_12] : set_union2(U_13,U_13) = U_13,
inference(variable_rename,[status(thm)],[f_13_1]) ).
fof(f_13_3,plain,
! [U_13] : set_union2(U_13,U_13) = U_13,
inference(miniscope,[status(thm)],[f_13_2]) ).
cnf(f_13_4,plain,
set_union2(U_13,U_13) = U_13,
inference(clausify,[status(thm)],[f_13_3]) ).
fof(f_14_1,plain,
! [A] :
( ( ( well_founded_relation(A)
| ~ is_well_founded_in(A,relation_field(A)) )
& ( is_well_founded_in(A,relation_field(A))
| ~ well_founded_relation(A) ) )
| ~ relation(A) ),
inference(fof_nnf,[status(thm)],[t5_wellord1]) ).
fof(f_14_2,plain,
! [U_14] :
( ( ( well_founded_relation(U_14)
| ~ is_well_founded_in(U_14,relation_field(U_14)) )
& ( is_well_founded_in(U_14,relation_field(U_14))
| ~ well_founded_relation(U_14) ) )
| ~ relation(U_14) ),
inference(variable_rename,[status(thm)],[f_14_1]) ).
cnf(f_14_3,plain,
( is_well_founded_in(U_14,relation_field(U_14))
| ~ well_founded_relation(U_14)
| ~ relation(U_14) ),
inference(clausify,[status(thm)],[f_14_2]) ).
cnf(f_14_4,plain,
( well_founded_relation(U_14)
| ~ is_well_founded_in(U_14,relation_field(U_14))
| ~ relation(U_14) ),
inference(clausify,[status(thm)],[f_14_2]) ).
fof(f_15_1,negated_conjecture,
~ ! [A] :
( relation(A)
=> ( well_orders(A,relation_field(A))
<=> well_ordering(A) ) ),
inference(negate,[status(cth)],[t8_wellord1]) ).
fof(f_15_2,negated_conjecture,
? [A] :
( ( ( ~ well_orders(A,relation_field(A))
& well_ordering(A) )
| ( ~ well_ordering(A)
& well_orders(A,relation_field(A)) ) )
& relation(A) ),
inference(fof_nnf,[status(thm)],[f_15_1]) ).
fof(f_15_3,negated_conjecture,
? [U_15] :
( ( ( ~ well_orders(U_15,relation_field(U_15))
& well_ordering(U_15) )
| ( ~ well_ordering(U_15)
& well_orders(U_15,relation_field(U_15)) ) )
& relation(U_15) ),
inference(variable_rename,[status(thm)],[f_15_2]) ).
fof(f_15_4,negated_conjecture,
( ( ( ~ well_orders(sK1,relation_field(sK1))
& well_ordering(sK1) )
| ( ~ well_ordering(sK1)
& well_orders(sK1,relation_field(sK1)) ) )
& relation(sK1) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(U_15,sK1)],[f_15_3]) ).
fof(f_15_5,negated_conjecture,
( ( ~ well_orders(sK1,relation_field(sK1))
| ~ sP1 )
& ( well_ordering(sK1)
| ~ sP1 )
& ( ~ well_ordering(sK1)
| ~ sP0 )
& ( well_orders(sK1,relation_field(sK1))
| ~ sP0 )
& ( sP1
| sP0 )
& relation(sK1) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP0,sP1])],[f_15_4]) ).
cnf(f_15_6,negated_conjecture,
relation(sK1),
inference(clausify,[status(thm)],[f_15_5]) ).
cnf(f_15_7,negated_conjecture,
( sP1
| sP0 ),
inference(clausify,[status(thm)],[f_15_5]) ).
cnf(f_15_8,negated_conjecture,
( well_orders(sK1,relation_field(sK1))
| ~ sP0 ),
inference(clausify,[status(thm)],[f_15_5]) ).
cnf(f_15_9,negated_conjecture,
( ~ well_ordering(sK1)
| ~ sP0 ),
inference(clausify,[status(thm)],[f_15_5]) ).
cnf(f_15_10,negated_conjecture,
( well_ordering(sK1)
| ~ sP1 ),
inference(clausify,[status(thm)],[f_15_5]) ).
cnf(f_15_11,negated_conjecture,
( ~ well_orders(sK1,relation_field(sK1))
| ~ sP1 ),
inference(clausify,[status(thm)],[f_15_5]) ).
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(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,
( relation_field(Eq_x_0) = relation_field(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_6,axiom,
( relation_dom(Eq_x_0) = relation_dom(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_7,axiom,
( relation_rng(Eq_x_0) = relation_rng(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_8,axiom,
( relation(Eq_y_0)
| ~ relation(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_9,axiom,
( antisymmetric(Eq_y_0)
| ~ antisymmetric(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_10,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_11,axiom,
( connected(Eq_y_0)
| ~ connected(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_12,axiom,
( is_connected_in(Eq_y_0,Eq_y_1)
| ~ is_connected_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_13,axiom,
( transitive(Eq_y_0)
| ~ transitive(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_14,axiom,
( is_transitive_in(Eq_y_0,Eq_y_1)
| ~ is_transitive_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,
( well_ordering(Eq_y_0)
| ~ well_ordering(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_16,axiom,
( reflexive(Eq_y_0)
| ~ reflexive(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_17,axiom,
( well_founded_relation(Eq_y_0)
| ~ well_founded_relation(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_18,axiom,
( well_orders(Eq_y_0,Eq_y_1)
| ~ well_orders(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,
( is_reflexive_in(Eq_y_0,Eq_y_1)
| ~ is_reflexive_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_20,axiom,
( is_well_founded_in(Eq_y_0,Eq_y_1)
| ~ is_well_founded_in(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
% 0.00/0.02 % Problem : SEU244+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/sandbox/solver/bin/connect++ --verbosity 1 --no-colour --tptp-proof --schedule default --timeout 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.35 % Computer : n014.cluster.edu
% 0.09/0.35 % Model : x86_64 x86_64
% 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.35 % Memory : 8046.5625MB
% 0.09/0.35 % OS : Linux 6.8.0-71-generic
% 0.09/0.35 % CPULimit : 300
% 0.09/0.35 % WCLimit : 300
% 0.09/0.35 % DateTime : Sat Sep 19 23:39:19 UTC 2026
% 0.09/0.35 % CPUTime :
% 0.14/0.39 % SZS status Theorem for theBenchmark
% 0.14/0.39 % SZS output start Proof for theBenchmark
% See solution above
%------------------------------------------------------------------------------