%------------------------------------------------------------------------------
% File : ConnectPP---0.7.2
% Problem : SEU252+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 : n010.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 08:58:43 AM UTC 2026
% Result : Theorem 0.21s 0.56s
% Output : Proof 0.31s
% 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(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(commutativity_k2_tarski,axiom,
! [A,B] : unordered_pair(A,B) = unordered_pair(B,A),
file('theBenchmark.p',commutativity_k2_tarski) ).
fof(commutativity_k2_xboole_0,axiom,
! [A,B] : set_union2(A,B) = set_union2(B,A),
file('theBenchmark.p',commutativity_k2_xboole_0) ).
fof(commutativity_k3_xboole_0,axiom,
! [A,B] : set_intersection2(A,B) = set_intersection2(B,A),
file('theBenchmark.p',commutativity_k3_xboole_0) ).
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_relat_1,axiom,
! [A] :
( relation(A)
=> relation_field(A) = set_union2(relation_dom(A),relation_rng(A)) ),
file('theBenchmark.p',d6_relat_1) ).
fof(d6_wellord1,axiom,
! [A] :
( relation(A)
=> ! [B] : relation_restriction(A,B) = set_intersection2(A,cartesian_product2(B,B)) ),
file('theBenchmark.p',d6_wellord1) ).
fof(dt_k1_relat_1,axiom,
$true,
file('theBenchmark.p',dt_k1_relat_1) ).
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_k2_relat_1,axiom,
$true,
file('theBenchmark.p',dt_k2_relat_1) ).
fof(dt_k2_tarski,axiom,
$true,
file('theBenchmark.p',dt_k2_tarski) ).
fof(dt_k2_wellord1,axiom,
! [A,B] :
( relation(A)
=> relation(relation_restriction(A,B)) ),
file('theBenchmark.p',dt_k2_wellord1) ).
fof(dt_k2_xboole_0,axiom,
$true,
file('theBenchmark.p',dt_k2_xboole_0) ).
fof(dt_k2_zfmisc_1,axiom,
$true,
file('theBenchmark.p',dt_k2_zfmisc_1) ).
fof(dt_k3_relat_1,axiom,
$true,
file('theBenchmark.p',dt_k3_relat_1) ).
fof(dt_k3_xboole_0,axiom,
$true,
file('theBenchmark.p',dt_k3_xboole_0) ).
fof(dt_k4_tarski,axiom,
$true,
file('theBenchmark.p',dt_k4_tarski) ).
fof(dt_m1_subset_1,axiom,
$true,
file('theBenchmark.p',dt_m1_subset_1) ).
fof(existence_m1_subset_1,axiom,
! [A] :
? [B] : element(B,A),
file('theBenchmark.p',existence_m1_subset_1) ).
fof(fc1_xboole_0,axiom,
empty(empty_set),
file('theBenchmark.p',fc1_xboole_0) ).
fof(fc1_zfmisc_1,axiom,
! [A,B] : ~ empty(ordered_pair(A,B)),
file('theBenchmark.p',fc1_zfmisc_1) ).
fof(fc2_xboole_0,axiom,
! [A,B] :
( ~ empty(A)
=> ~ empty(set_union2(A,B)) ),
file('theBenchmark.p',fc2_xboole_0) ).
fof(fc3_xboole_0,axiom,
! [A,B] :
( ~ empty(A)
=> ~ empty(set_union2(B,A)) ),
file('theBenchmark.p',fc3_xboole_0) ).
fof(idempotence_k2_xboole_0,axiom,
! [A,B] : set_union2(A,A) = A,
file('theBenchmark.p',idempotence_k2_xboole_0) ).
fof(idempotence_k3_xboole_0,axiom,
! [A,B] : set_intersection2(A,A) = A,
file('theBenchmark.p',idempotence_k3_xboole_0) ).
fof(l1_wellord1,axiom,
! [A] :
( relation(A)
=> ( reflexive(A)
<=> ! [B] :
( in(B,relation_field(A))
=> in(ordered_pair(B,B),A) ) ) ),
file('theBenchmark.p',l1_wellord1) ).
fof(rc1_funct_1,axiom,
? [A] :
( function(A)
& relation(A) ),
file('theBenchmark.p',rc1_funct_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_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(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(t16_wellord1,axiom,
! [A,B,C] :
( relation(C)
=> ( in(A,relation_restriction(C,B))
<=> ( in(A,cartesian_product2(B,B))
& in(A,C) ) ) ),
file('theBenchmark.p',t16_wellord1) ).
fof(t19_wellord1,axiom,
! [A,B,C] :
( relation(C)
=> ( in(A,relation_field(relation_restriction(C,B)))
=> ( in(A,B)
& in(A,relation_field(C)) ) ) ),
file('theBenchmark.p',t19_wellord1) ).
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(t22_wellord1,conjecture,
! [A,B] :
( relation(B)
=> ( reflexive(B)
=> reflexive(relation_restriction(B,A)) ) ),
file('theBenchmark.p',t22_wellord1) ).
fof(t2_boole,axiom,
! [A] : set_intersection2(A,empty_set) = empty_set,
file('theBenchmark.p',t2_boole) ).
fof(t2_subset,axiom,
! [A,B] :
( element(A,B)
=> ( in(A,B)
| empty(B) ) ),
file('theBenchmark.p',t2_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] :
( ( one_to_one(A)
& function(A)
& relation(A) )
| ~ function(A)
| ~ empty(A)
| ~ relation(A) ),
inference(fof_nnf,[status(thm)],[cc2_funct_1]) ).
fof(f_3_2,plain,
! [U_3] :
( ( one_to_one(U_3)
& function(U_3)
& relation(U_3) )
| ~ function(U_3)
| ~ empty(U_3)
| ~ relation(U_3) ),
inference(variable_rename,[status(thm)],[f_3_1]) ).
cnf(f_3_3,plain,
( relation(U_3)
| ~ function(U_3)
| ~ empty(U_3)
| ~ relation(U_3) ),
inference(clausify,[status(thm)],[f_3_2]) ).
cnf(f_3_4,plain,
( function(U_3)
| ~ function(U_3)
| ~ empty(U_3)
| ~ relation(U_3) ),
inference(clausify,[status(thm)],[f_3_2]) ).
cnf(f_3_5,plain,
( one_to_one(U_3)
| ~ function(U_3)
| ~ empty(U_3)
| ~ relation(U_3) ),
inference(clausify,[status(thm)],[f_3_2]) ).
fof(f_4_1,plain,
! [A,B] : unordered_pair(A,B) = unordered_pair(B,A),
inference(fof_nnf,[status(thm)],[commutativity_k2_tarski]) ).
fof(f_4_2,plain,
! [U_5,U_4] : unordered_pair(U_5,U_4) = unordered_pair(U_4,U_5),
inference(variable_rename,[status(thm)],[f_4_1]) ).
cnf(f_4_3,plain,
unordered_pair(U_5,U_4) = unordered_pair(U_4,U_5),
inference(clausify,[status(thm)],[f_4_2]) ).
fof(f_5_1,plain,
! [A,B] : set_union2(A,B) = set_union2(B,A),
inference(fof_nnf,[status(thm)],[commutativity_k2_xboole_0]) ).
fof(f_5_2,plain,
! [U_7,U_6] : set_union2(U_7,U_6) = set_union2(U_6,U_7),
inference(variable_rename,[status(thm)],[f_5_1]) ).
cnf(f_5_3,plain,
set_union2(U_7,U_6) = set_union2(U_6,U_7),
inference(clausify,[status(thm)],[f_5_2]) ).
fof(f_6_1,plain,
! [A,B] : set_intersection2(A,B) = set_intersection2(B,A),
inference(fof_nnf,[status(thm)],[commutativity_k3_xboole_0]) ).
fof(f_6_2,plain,
! [U_9,U_8] : set_intersection2(U_9,U_8) = set_intersection2(U_8,U_9),
inference(variable_rename,[status(thm)],[f_6_1]) ).
cnf(f_6_3,plain,
set_intersection2(U_9,U_8) = set_intersection2(U_8,U_9),
inference(clausify,[status(thm)],[f_6_2]) ).
fof(f_7_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_7_2,plain,
! [U_11,U_10] : ordered_pair(U_11,U_10) = unordered_pair(unordered_pair(U_11,U_10),singleton(U_11)),
inference(variable_rename,[status(thm)],[f_7_1]) ).
cnf(f_7_3,plain,
ordered_pair(U_11,U_10) = unordered_pair(unordered_pair(U_11,U_10),singleton(U_11)),
inference(clausify,[status(thm)],[f_7_2]) ).
fof(f_8_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_8_2,plain,
! [U_12] :
( relation_field(U_12) = set_union2(relation_dom(U_12),relation_rng(U_12))
| ~ relation(U_12) ),
inference(variable_rename,[status(thm)],[f_8_1]) ).
cnf(f_8_3,plain,
( relation_field(U_12) = set_union2(relation_dom(U_12),relation_rng(U_12))
| ~ relation(U_12) ),
inference(clausify,[status(thm)],[f_8_2]) ).
fof(f_9_1,plain,
! [A] :
( ! [B] : relation_restriction(A,B) = set_intersection2(A,cartesian_product2(B,B))
| ~ relation(A) ),
inference(fof_nnf,[status(thm)],[d6_wellord1]) ).
fof(f_9_2,plain,
! [U_14] :
( ! [U_13] : relation_restriction(U_14,U_13) = set_intersection2(U_14,cartesian_product2(U_13,U_13))
| ~ relation(U_14) ),
inference(variable_rename,[status(thm)],[f_9_1]) ).
cnf(f_9_3,plain,
( relation_restriction(U_14,U_13) = set_intersection2(U_14,cartesian_product2(U_13,U_13))
| ~ relation(U_14) ),
inference(clausify,[status(thm)],[f_9_2]) ).
fof(f_10_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_k1_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_k1_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_k1_xboole_0]) ).
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_k2_relat_1]) ).
cnf(f_13_2,plain,
$true,
inference(clausify,[status(thm)],[f_13_1]) ).
fof(f_14_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_k2_tarski]) ).
cnf(f_14_2,plain,
$true,
inference(clausify,[status(thm)],[f_14_1]) ).
fof(f_15_1,plain,
! [A,B] :
( relation(relation_restriction(A,B))
| ~ relation(A) ),
inference(fof_nnf,[status(thm)],[dt_k2_wellord1]) ).
fof(f_15_2,plain,
! [U_16,U_15] :
( relation(relation_restriction(U_16,U_15))
| ~ relation(U_16) ),
inference(variable_rename,[status(thm)],[f_15_1]) ).
fof(f_15_3,plain,
! [U_16] :
( ! [U_15] : relation(relation_restriction(U_16,U_15))
| ~ relation(U_16) ),
inference(miniscope,[status(thm)],[f_15_2]) ).
cnf(f_15_4,plain,
( relation(relation_restriction(U_16,U_15))
| ~ relation(U_16) ),
inference(clausify,[status(thm)],[f_15_3]) ).
fof(f_16_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_k2_xboole_0]) ).
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_k2_zfmisc_1]) ).
cnf(f_17_2,plain,
$true,
inference(clausify,[status(thm)],[f_17_1]) ).
fof(f_18_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_k3_relat_1]) ).
cnf(f_18_2,plain,
$true,
inference(clausify,[status(thm)],[f_18_1]) ).
fof(f_19_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_k3_xboole_0]) ).
cnf(f_19_2,plain,
$true,
inference(clausify,[status(thm)],[f_19_1]) ).
fof(f_20_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_k4_tarski]) ).
cnf(f_20_2,plain,
$true,
inference(clausify,[status(thm)],[f_20_1]) ).
fof(f_21_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_m1_subset_1]) ).
cnf(f_21_2,plain,
$true,
inference(clausify,[status(thm)],[f_21_1]) ).
fof(f_22_1,plain,
! [A] :
? [B] : element(B,A),
inference(fof_nnf,[status(thm)],[existence_m1_subset_1]) ).
fof(f_22_2,plain,
! [U_18] :
? [U_17] : element(U_17,U_18),
inference(variable_rename,[status(thm)],[f_22_1]) ).
fof(f_22_3,plain,
! [U_18] : element(sK1(U_18),U_18),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(U_17,sK1(U_18))],[f_22_2]) ).
cnf(f_22_4,plain,
element(sK1(U_18),U_18),
inference(clausify,[status(thm)],[f_22_3]) ).
fof(f_23_1,plain,
empty(empty_set),
inference(fof_nnf,[status(thm)],[fc1_xboole_0]) ).
cnf(f_23_2,plain,
empty(empty_set),
inference(clausify,[status(thm)],[f_23_1]) ).
fof(f_24_1,plain,
! [A,B] : ~ empty(ordered_pair(A,B)),
inference(fof_nnf,[status(thm)],[fc1_zfmisc_1]) ).
fof(f_24_2,plain,
! [U_20,U_19] : ~ empty(ordered_pair(U_20,U_19)),
inference(variable_rename,[status(thm)],[f_24_1]) ).
cnf(f_24_3,plain,
~ empty(ordered_pair(U_20,U_19)),
inference(clausify,[status(thm)],[f_24_2]) ).
fof(f_25_1,plain,
! [A,B] :
( ~ empty(set_union2(A,B))
| empty(A) ),
inference(fof_nnf,[status(thm)],[fc2_xboole_0]) ).
fof(f_25_2,plain,
! [U_22,U_21] :
( ~ empty(set_union2(U_22,U_21))
| empty(U_22) ),
inference(variable_rename,[status(thm)],[f_25_1]) ).
fof(f_25_3,plain,
! [U_22] :
( ! [U_21] : ~ empty(set_union2(U_22,U_21))
| empty(U_22) ),
inference(miniscope,[status(thm)],[f_25_2]) ).
cnf(f_25_4,plain,
( ~ empty(set_union2(U_22,U_21))
| empty(U_22) ),
inference(clausify,[status(thm)],[f_25_3]) ).
fof(f_26_1,plain,
! [A,B] :
( ~ empty(set_union2(B,A))
| empty(A) ),
inference(fof_nnf,[status(thm)],[fc3_xboole_0]) ).
fof(f_26_2,plain,
! [U_24,U_23] :
( ~ empty(set_union2(U_23,U_24))
| empty(U_24) ),
inference(variable_rename,[status(thm)],[f_26_1]) ).
fof(f_26_3,plain,
! [U_24] :
( ! [U_23] : ~ empty(set_union2(U_23,U_24))
| empty(U_24) ),
inference(miniscope,[status(thm)],[f_26_2]) ).
cnf(f_26_4,plain,
( ~ empty(set_union2(U_23,U_24))
| empty(U_24) ),
inference(clausify,[status(thm)],[f_26_3]) ).
fof(f_27_1,plain,
! [A,B] : set_union2(A,A) = A,
inference(fof_nnf,[status(thm)],[idempotence_k2_xboole_0]) ).
fof(f_27_2,plain,
! [U_26,U_25] : set_union2(U_26,U_26) = U_26,
inference(variable_rename,[status(thm)],[f_27_1]) ).
fof(f_27_3,plain,
! [U_26] : set_union2(U_26,U_26) = U_26,
inference(miniscope,[status(thm)],[f_27_2]) ).
cnf(f_27_4,plain,
set_union2(U_26,U_26) = U_26,
inference(clausify,[status(thm)],[f_27_3]) ).
fof(f_28_1,plain,
! [A,B] : set_intersection2(A,A) = A,
inference(fof_nnf,[status(thm)],[idempotence_k3_xboole_0]) ).
fof(f_28_2,plain,
! [U_28,U_27] : set_intersection2(U_28,U_28) = U_28,
inference(variable_rename,[status(thm)],[f_28_1]) ).
fof(f_28_3,plain,
! [U_28] : set_intersection2(U_28,U_28) = U_28,
inference(miniscope,[status(thm)],[f_28_2]) ).
cnf(f_28_4,plain,
set_intersection2(U_28,U_28) = U_28,
inference(clausify,[status(thm)],[f_28_3]) ).
fof(f_29_1,plain,
! [A] :
( ( ( reflexive(A)
| ? [B] :
( ~ in(ordered_pair(B,B),A)
& in(B,relation_field(A)) ) )
& ( ! [B] :
( in(ordered_pair(B,B),A)
| ~ in(B,relation_field(A)) )
| ~ reflexive(A) ) )
| ~ relation(A) ),
inference(fof_nnf,[status(thm)],[l1_wellord1]) ).
fof(f_29_2,plain,
! [U_31] :
( ( ( reflexive(U_31)
| ? [U_30] :
( ~ in(ordered_pair(U_30,U_30),U_31)
& in(U_30,relation_field(U_31)) ) )
& ( ! [U_29] :
( in(ordered_pair(U_29,U_29),U_31)
| ~ in(U_29,relation_field(U_31)) )
| ~ reflexive(U_31) ) )
| ~ relation(U_31) ),
inference(variable_rename,[status(thm)],[f_29_1]) ).
fof(f_29_3,plain,
! [U_31] :
( ( ( reflexive(U_31)
| ( ~ in(ordered_pair(sK2(U_31),sK2(U_31)),U_31)
& in(sK2(U_31),relation_field(U_31)) ) )
& ( ! [U_29] :
( in(ordered_pair(U_29,U_29),U_31)
| ~ in(U_29,relation_field(U_31)) )
| ~ reflexive(U_31) ) )
| ~ relation(U_31) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2]),skolemize(U_30,sK2(U_31))],[f_29_2]) ).
cnf(f_29_4,plain,
( in(ordered_pair(U_29,U_29),U_31)
| ~ in(U_29,relation_field(U_31))
| ~ reflexive(U_31)
| ~ relation(U_31) ),
inference(clausify,[status(thm)],[f_29_3]) ).
cnf(f_29_5,plain,
( in(sK2(U_31),relation_field(U_31))
| reflexive(U_31)
| ~ relation(U_31) ),
inference(clausify,[status(thm)],[f_29_3]) ).
cnf(f_29_6,plain,
( ~ in(ordered_pair(sK2(U_31),sK2(U_31)),U_31)
| reflexive(U_31)
| ~ relation(U_31) ),
inference(clausify,[status(thm)],[f_29_3]) ).
fof(f_30_1,plain,
? [A] :
( function(A)
& relation(A) ),
inference(fof_nnf,[status(thm)],[rc1_funct_1]) ).
fof(f_30_2,plain,
? [U_32] :
( function(U_32)
& relation(U_32) ),
inference(variable_rename,[status(thm)],[f_30_1]) ).
fof(f_30_3,plain,
( function(sK3)
& relation(sK3) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3]),skolemize(U_32,sK3)],[f_30_2]) ).
cnf(f_30_4,plain,
relation(sK3),
inference(clausify,[status(thm)],[f_30_3]) ).
cnf(f_30_5,plain,
function(sK3),
inference(clausify,[status(thm)],[f_30_3]) ).
fof(f_31_1,plain,
? [A] : empty(A),
inference(fof_nnf,[status(thm)],[rc1_xboole_0]) ).
fof(f_31_2,plain,
? [U_33] : empty(U_33),
inference(variable_rename,[status(thm)],[f_31_1]) ).
fof(f_31_3,plain,
empty(sK4),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4]),skolemize(U_33,sK4)],[f_31_2]) ).
cnf(f_31_4,plain,
empty(sK4),
inference(clausify,[status(thm)],[f_31_3]) ).
fof(f_32_1,plain,
? [A] :
( function(A)
& empty(A)
& relation(A) ),
inference(fof_nnf,[status(thm)],[rc2_funct_1]) ).
fof(f_32_2,plain,
? [U_34] :
( function(U_34)
& empty(U_34)
& relation(U_34) ),
inference(variable_rename,[status(thm)],[f_32_1]) ).
fof(f_32_3,plain,
( function(sK5)
& empty(sK5)
& relation(sK5) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK5]),skolemize(U_34,sK5)],[f_32_2]) ).
cnf(f_32_4,plain,
relation(sK5),
inference(clausify,[status(thm)],[f_32_3]) ).
cnf(f_32_5,plain,
empty(sK5),
inference(clausify,[status(thm)],[f_32_3]) ).
cnf(f_32_6,plain,
function(sK5),
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_35] : ~ empty(U_35),
inference(variable_rename,[status(thm)],[f_33_1]) ).
fof(f_33_3,plain,
~ empty(sK6),
inference(skolemize,[status(esa),new_symbols(skolem,[sK6]),skolemize(U_35,sK6)],[f_33_2]) ).
cnf(f_33_4,plain,
~ empty(sK6),
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_36] :
( one_to_one(U_36)
& function(U_36)
& relation(U_36) ),
inference(variable_rename,[status(thm)],[f_34_1]) ).
fof(f_34_3,plain,
( one_to_one(sK7)
& function(sK7)
& relation(sK7) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK7]),skolemize(U_36,sK7)],[f_34_2]) ).
cnf(f_34_4,plain,
relation(sK7),
inference(clausify,[status(thm)],[f_34_3]) ).
cnf(f_34_5,plain,
function(sK7),
inference(clausify,[status(thm)],[f_34_3]) ).
cnf(f_34_6,plain,
one_to_one(sK7),
inference(clausify,[status(thm)],[f_34_3]) ).
fof(f_35_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_35_2,plain,
! [U_40,U_39,U_38,U_37] :
( ( in(ordered_pair(U_40,U_39),cartesian_product2(U_38,U_37))
| ~ in(U_39,U_37)
| ~ in(U_40,U_38) )
& ( ( in(U_39,U_37)
& in(U_40,U_38) )
| ~ in(ordered_pair(U_40,U_39),cartesian_product2(U_38,U_37)) ) ),
inference(variable_rename,[status(thm)],[f_35_1]) ).
fof(f_35_3,plain,
( ! [U_48,U_46,U_44,U_42] :
( in(ordered_pair(U_48,U_46),cartesian_product2(U_44,U_42))
| ~ in(U_46,U_42)
| ~ in(U_48,U_44) )
& ! [U_47,U_45,U_43,U_41] :
( ( in(U_45,U_41)
& in(U_47,U_43) )
| ~ in(ordered_pair(U_47,U_45),cartesian_product2(U_43,U_41)) ) ),
inference(miniscope,[status(thm)],[f_35_2]) ).
cnf(f_35_4,plain,
( in(U_47,U_43)
| ~ in(ordered_pair(U_47,U_45),cartesian_product2(U_43,U_41)) ),
inference(clausify,[status(thm)],[f_35_3]) ).
cnf(f_35_5,plain,
( in(U_45,U_41)
| ~ in(ordered_pair(U_47,U_45),cartesian_product2(U_43,U_41)) ),
inference(clausify,[status(thm)],[f_35_3]) ).
cnf(f_35_6,plain,
( in(ordered_pair(U_48,U_46),cartesian_product2(U_44,U_42))
| ~ in(U_46,U_42)
| ~ in(U_48,U_44) ),
inference(clausify,[status(thm)],[f_35_3]) ).
fof(f_36_1,plain,
! [A,B,C] :
( ( ( in(A,relation_restriction(C,B))
| ~ in(A,cartesian_product2(B,B))
| ~ in(A,C) )
& ( ( in(A,cartesian_product2(B,B))
& in(A,C) )
| ~ in(A,relation_restriction(C,B)) ) )
| ~ relation(C) ),
inference(fof_nnf,[status(thm)],[t16_wellord1]) ).
fof(f_36_2,plain,
! [U_51,U_50,U_49] :
( ( ( in(U_51,relation_restriction(U_49,U_50))
| ~ in(U_51,cartesian_product2(U_50,U_50))
| ~ in(U_51,U_49) )
& ( ( in(U_51,cartesian_product2(U_50,U_50))
& in(U_51,U_49) )
| ~ in(U_51,relation_restriction(U_49,U_50)) ) )
| ~ relation(U_49) ),
inference(variable_rename,[status(thm)],[f_36_1]) ).
cnf(f_36_3,plain,
( in(U_51,U_49)
| ~ in(U_51,relation_restriction(U_49,U_50))
| ~ relation(U_49) ),
inference(clausify,[status(thm)],[f_36_2]) ).
cnf(f_36_4,plain,
( in(U_51,cartesian_product2(U_50,U_50))
| ~ in(U_51,relation_restriction(U_49,U_50))
| ~ relation(U_49) ),
inference(clausify,[status(thm)],[f_36_2]) ).
cnf(f_36_5,plain,
( in(U_51,relation_restriction(U_49,U_50))
| ~ in(U_51,cartesian_product2(U_50,U_50))
| ~ in(U_51,U_49)
| ~ relation(U_49) ),
inference(clausify,[status(thm)],[f_36_2]) ).
fof(f_37_1,plain,
! [A,B,C] :
( ( in(A,B)
& in(A,relation_field(C)) )
| ~ in(A,relation_field(relation_restriction(C,B)))
| ~ relation(C) ),
inference(fof_nnf,[status(thm)],[t19_wellord1]) ).
fof(f_37_2,plain,
! [U_54,U_53,U_52] :
( ( in(U_54,U_53)
& in(U_54,relation_field(U_52)) )
| ~ in(U_54,relation_field(relation_restriction(U_52,U_53)))
| ~ relation(U_52) ),
inference(variable_rename,[status(thm)],[f_37_1]) ).
cnf(f_37_3,plain,
( in(U_54,relation_field(U_52))
| ~ in(U_54,relation_field(relation_restriction(U_52,U_53)))
| ~ relation(U_52) ),
inference(clausify,[status(thm)],[f_37_2]) ).
cnf(f_37_4,plain,
( in(U_54,U_53)
| ~ in(U_54,relation_field(relation_restriction(U_52,U_53)))
| ~ relation(U_52) ),
inference(clausify,[status(thm)],[f_37_2]) ).
fof(f_38_1,plain,
! [A] : set_union2(A,empty_set) = A,
inference(fof_nnf,[status(thm)],[t1_boole]) ).
fof(f_38_2,plain,
! [U_55] : set_union2(U_55,empty_set) = U_55,
inference(variable_rename,[status(thm)],[f_38_1]) ).
cnf(f_38_3,plain,
set_union2(U_55,empty_set) = U_55,
inference(clausify,[status(thm)],[f_38_2]) ).
fof(f_39_1,plain,
! [A,B] :
( element(A,B)
| ~ in(A,B) ),
inference(fof_nnf,[status(thm)],[t1_subset]) ).
fof(f_39_2,plain,
! [U_57,U_56] :
( element(U_57,U_56)
| ~ in(U_57,U_56) ),
inference(variable_rename,[status(thm)],[f_39_1]) ).
cnf(f_39_3,plain,
( element(U_57,U_56)
| ~ in(U_57,U_56) ),
inference(clausify,[status(thm)],[f_39_2]) ).
fof(f_40_1,negated_conjecture,
~ ! [A,B] :
( relation(B)
=> ( reflexive(B)
=> reflexive(relation_restriction(B,A)) ) ),
inference(negate,[status(cth)],[t22_wellord1]) ).
fof(f_40_2,negated_conjecture,
? [A,B] :
( ~ reflexive(relation_restriction(B,A))
& reflexive(B)
& relation(B) ),
inference(fof_nnf,[status(thm)],[f_40_1]) ).
fof(f_40_3,negated_conjecture,
? [U_59,U_58] :
( ~ reflexive(relation_restriction(U_58,U_59))
& reflexive(U_58)
& relation(U_58) ),
inference(variable_rename,[status(thm)],[f_40_2]) ).
fof(f_40_4,negated_conjecture,
? [U_58] :
( ~ reflexive(relation_restriction(U_58,sK8))
& reflexive(U_58)
& relation(U_58) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK8]),skolemize(U_59,sK8)],[f_40_3]) ).
fof(f_40_5,negated_conjecture,
( ~ reflexive(relation_restriction(sK9,sK8))
& reflexive(sK9)
& relation(sK9) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK9]),skolemize(U_58,sK9)],[f_40_4]) ).
fof(f_40_6,negated_conjecture,
( ~ reflexive(relation_restriction(sK9,sK8))
& reflexive(sK9)
& relation(sK9) ),
inference(definitional_conversion,[status(esa)],[f_40_5]) ).
cnf(f_40_7,negated_conjecture,
relation(sK9),
inference(clausify,[status(thm)],[f_40_6]) ).
cnf(f_40_8,negated_conjecture,
reflexive(sK9),
inference(clausify,[status(thm)],[f_40_6]) ).
cnf(f_40_9,negated_conjecture,
~ reflexive(relation_restriction(sK9,sK8)),
inference(clausify,[status(thm)],[f_40_6]) ).
fof(f_41_1,plain,
! [A] : set_intersection2(A,empty_set) = empty_set,
inference(fof_nnf,[status(thm)],[t2_boole]) ).
fof(f_41_2,plain,
! [U_60] : set_intersection2(U_60,empty_set) = empty_set,
inference(variable_rename,[status(thm)],[f_41_1]) ).
cnf(f_41_3,plain,
set_intersection2(U_60,empty_set) = empty_set,
inference(clausify,[status(thm)],[f_41_2]) ).
fof(f_42_1,plain,
! [A,B] :
( in(A,B)
| empty(B)
| ~ element(A,B) ),
inference(fof_nnf,[status(thm)],[t2_subset]) ).
fof(f_42_2,plain,
! [U_62,U_61] :
( in(U_62,U_61)
| empty(U_61)
| ~ element(U_62,U_61) ),
inference(variable_rename,[status(thm)],[f_42_1]) ).
cnf(f_42_3,plain,
( in(U_62,U_61)
| empty(U_61)
| ~ element(U_62,U_61) ),
inference(clausify,[status(thm)],[f_42_2]) ).
fof(f_43_1,plain,
! [A] :
( A = empty_set
| ~ empty(A) ),
inference(fof_nnf,[status(thm)],[t6_boole]) ).
fof(f_43_2,plain,
! [U_63] :
( U_63 = empty_set
| ~ empty(U_63) ),
inference(variable_rename,[status(thm)],[f_43_1]) ).
cnf(f_43_3,plain,
( U_63 = empty_set
| ~ empty(U_63) ),
inference(clausify,[status(thm)],[f_43_2]) ).
fof(f_44_1,plain,
! [A,B] :
( ~ empty(B)
| ~ in(A,B) ),
inference(fof_nnf,[status(thm)],[t7_boole]) ).
fof(f_44_2,plain,
! [U_65,U_64] :
( ~ empty(U_64)
| ~ in(U_65,U_64) ),
inference(variable_rename,[status(thm)],[f_44_1]) ).
cnf(f_44_3,plain,
( ~ empty(U_64)
| ~ in(U_65,U_64) ),
inference(clausify,[status(thm)],[f_44_2]) ).
fof(f_45_1,plain,
! [A,B] :
( ~ empty(B)
| A = B
| ~ empty(A) ),
inference(fof_nnf,[status(thm)],[t8_boole]) ).
fof(f_45_2,plain,
! [U_67,U_66] :
( ~ empty(U_66)
| U_67 = U_66
| ~ empty(U_67) ),
inference(variable_rename,[status(thm)],[f_45_1]) ).
fof(f_45_3,plain,
! [U_67] :
( ! [U_66] :
( ~ empty(U_66)
| U_67 = U_66 )
| ~ empty(U_67) ),
inference(miniscope,[status(thm)],[f_45_2]) ).
cnf(f_45_4,plain,
( ~ empty(U_66)
| U_67 = U_66
| ~ empty(U_67) ),
inference(clausify,[status(thm)],[f_45_3]) ).
cnf(f_3_3_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_3_3]) ).
cnf(f_3_4_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_3_4]) ).
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_14_2_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_14_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_18_2_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_18_2]) ).
cnf(f_19_2_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_19_2]) ).
cnf(f_20_2_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_20_2]) ).
cnf(f_21_2_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_21_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,
( 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_5,axiom,
( set_union2(Eq_x_0,Eq_x_1) = set_union2(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_6,axiom,
( set_intersection2(Eq_x_0,Eq_x_1) = set_intersection2(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,
( relation_field(Eq_x_0) = relation_field(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_10,axiom,
( relation_dom(Eq_x_0) = relation_dom(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_11,axiom,
( relation_rng(Eq_x_0) = relation_rng(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_12,axiom,
( relation_restriction(Eq_x_0,Eq_x_1) = relation_restriction(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,
( 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_14,axiom,
( sK1(Eq_x_0) = sK1(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_15,axiom,
( sK2(Eq_x_0) = sK2(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_16,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_17,axiom,
( empty(Eq_y_0)
| ~ empty(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_18,axiom,
( function(Eq_y_0)
| ~ function(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_19,axiom,
( relation(Eq_y_0)
| ~ relation(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_20,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_21,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_22,axiom,
( reflexive(Eq_y_0)
| ~ reflexive(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(sat_proved,plain,
$false,
inference(cadical,[status(thm)],[]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU252+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
% 0.08/0.35 % Computer : n010.cluster.edu
% 0.08/0.35 % Model : x86_64 x86_64
% 0.08/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.35 % Memory : 8046.5625MB
% 0.08/0.35 % OS : Linux 6.8.0-71-generic
% 0.08/0.35 % CPULimit : 300
% 0.08/0.35 % WCLimit : 300
% 0.08/0.35 % DateTime : Sat Sep 19 23:41:23 UTC 2026
% 0.12/0.36 % CPUTime :
% 0.21/0.56 % SZS status Theorem for theBenchmark
% 0.21/0.56 % SZS output start Proof for theBenchmark
% See solution above
%------------------------------------------------------------------------------