%------------------------------------------------------------------------------
% File : ConnectPP---0.7.2
% Problem : SEU242+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 08:58:40 AM UTC 2026
% Result : Theorem 0.14s 5.86s
% Output : Proof 0.14s
% 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(d14_relat_2,axiom,
! [A] :
( relation(A)
=> ( connected(A)
<=> is_connected_in(A,relation_field(A)) ) ),
file('theBenchmark.p',d14_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_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_relat_2,axiom,
! [A] :
( relation(A)
=> ! [B] :
( is_connected_in(A,B)
<=> ! [C,D] :
~ ( ~ in(ordered_pair(D,C),A)
& ~ in(ordered_pair(C,D),A)
& C != D
& in(D,B)
& in(C,B) ) ) ),
file('theBenchmark.p',d6_relat_2) ).
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_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(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(l4_wellord1,conjecture,
! [A] :
( relation(A)
=> ( connected(A)
<=> ! [B,C] :
~ ( ~ in(ordered_pair(C,B),A)
& ~ in(ordered_pair(B,C),A)
& B != C
& in(C,relation_field(A))
& in(B,relation_field(A)) ) ) ),
file('theBenchmark.p',l4_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(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(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] :
( ( ( 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_6_2,plain,
! [U_8] :
( ( ( connected(U_8)
| ~ is_connected_in(U_8,relation_field(U_8)) )
& ( is_connected_in(U_8,relation_field(U_8))
| ~ connected(U_8) ) )
| ~ relation(U_8) ),
inference(variable_rename,[status(thm)],[f_6_1]) ).
cnf(f_6_3,plain,
( is_connected_in(U_8,relation_field(U_8))
| ~ connected(U_8)
| ~ relation(U_8) ),
inference(clausify,[status(thm)],[f_6_2]) ).
cnf(f_6_4,plain,
( connected(U_8)
| ~ is_connected_in(U_8,relation_field(U_8))
| ~ relation(U_8) ),
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_10,U_9] : ordered_pair(U_10,U_9) = unordered_pair(unordered_pair(U_10,U_9),singleton(U_10)),
inference(variable_rename,[status(thm)],[f_7_1]) ).
cnf(f_7_3,plain,
ordered_pair(U_10,U_9) = unordered_pair(unordered_pair(U_10,U_9),singleton(U_10)),
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_11] :
( relation_field(U_11) = set_union2(relation_dom(U_11),relation_rng(U_11))
| ~ relation(U_11) ),
inference(variable_rename,[status(thm)],[f_8_1]) ).
cnf(f_8_3,plain,
( relation_field(U_11) = set_union2(relation_dom(U_11),relation_rng(U_11))
| ~ relation(U_11) ),
inference(clausify,[status(thm)],[f_8_2]) ).
fof(f_9_1,plain,
! [A] :
( ! [B] :
( ( is_connected_in(A,B)
| ? [C,D] :
( ~ in(ordered_pair(D,C),A)
& ~ in(ordered_pair(C,D),A)
& C != D
& in(D,B)
& in(C,B) ) )
& ( ! [C,D] :
( in(ordered_pair(D,C),A)
| in(ordered_pair(C,D),A)
| C = D
| ~ in(D,B)
| ~ in(C,B) )
| ~ is_connected_in(A,B) ) )
| ~ relation(A) ),
inference(fof_nnf,[status(thm)],[d6_relat_2]) ).
fof(f_9_2,plain,
! [U_17] :
( ! [U_16] :
( ( is_connected_in(U_17,U_16)
| ? [U_15,U_14] :
( ~ in(ordered_pair(U_14,U_15),U_17)
& ~ in(ordered_pair(U_15,U_14),U_17)
& U_15 != U_14
& in(U_14,U_16)
& in(U_15,U_16) ) )
& ( ! [U_13,U_12] :
( in(ordered_pair(U_12,U_13),U_17)
| in(ordered_pair(U_13,U_12),U_17)
| U_13 = U_12
| ~ in(U_12,U_16)
| ~ in(U_13,U_16) )
| ~ is_connected_in(U_17,U_16) ) )
| ~ relation(U_17) ),
inference(variable_rename,[status(thm)],[f_9_1]) ).
fof(f_9_3,plain,
! [U_17] :
( ( ! [U_19] :
( is_connected_in(U_17,U_19)
| ? [U_15] :
( ? [U_14] :
( ~ in(ordered_pair(U_14,U_15),U_17)
& ~ in(ordered_pair(U_15,U_14),U_17)
& U_15 != U_14
& in(U_14,U_19) )
& in(U_15,U_19) ) )
& ! [U_18] :
( ! [U_13] :
( ! [U_12] :
( in(ordered_pair(U_12,U_13),U_17)
| in(ordered_pair(U_13,U_12),U_17)
| U_13 = U_12
| ~ in(U_12,U_18) )
| ~ in(U_13,U_18) )
| ~ is_connected_in(U_17,U_18) ) )
| ~ relation(U_17) ),
inference(miniscope,[status(thm)],[f_9_2]) ).
fof(f_9_4,plain,
! [U_17] :
( ( ! [U_19] :
( is_connected_in(U_17,U_19)
| ( ? [U_14] :
( ~ in(ordered_pair(U_14,sK1(U_17,U_19)),U_17)
& ~ in(ordered_pair(sK1(U_17,U_19),U_14),U_17)
& sK1(U_17,U_19) != U_14
& in(U_14,U_19) )
& in(sK1(U_17,U_19),U_19) ) )
& ! [U_18] :
( ! [U_13] :
( ! [U_12] :
( in(ordered_pair(U_12,U_13),U_17)
| in(ordered_pair(U_13,U_12),U_17)
| U_13 = U_12
| ~ in(U_12,U_18) )
| ~ in(U_13,U_18) )
| ~ is_connected_in(U_17,U_18) ) )
| ~ relation(U_17) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(U_15,sK1(U_17,U_19))],[f_9_3]) ).
fof(f_9_5,plain,
! [U_17] :
( ( ! [U_19] :
( is_connected_in(U_17,U_19)
| ( ~ in(ordered_pair(sK2(U_17,U_19),sK1(U_17,U_19)),U_17)
& ~ in(ordered_pair(sK1(U_17,U_19),sK2(U_17,U_19)),U_17)
& sK1(U_17,U_19) != sK2(U_17,U_19)
& in(sK2(U_17,U_19),U_19)
& in(sK1(U_17,U_19),U_19) ) )
& ! [U_18] :
( ! [U_13] :
( ! [U_12] :
( in(ordered_pair(U_12,U_13),U_17)
| in(ordered_pair(U_13,U_12),U_17)
| U_13 = U_12
| ~ in(U_12,U_18) )
| ~ in(U_13,U_18) )
| ~ is_connected_in(U_17,U_18) ) )
| ~ relation(U_17) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2]),skolemize(U_14,sK2(U_17,U_19))],[f_9_4]) ).
cnf(f_9_6,plain,
( in(ordered_pair(U_12,U_13),U_17)
| in(ordered_pair(U_13,U_12),U_17)
| U_13 = U_12
| ~ in(U_12,U_18)
| ~ in(U_13,U_18)
| ~ is_connected_in(U_17,U_18)
| ~ relation(U_17) ),
inference(clausify,[status(thm)],[f_9_5]) ).
cnf(f_9_7,plain,
( in(sK1(U_17,U_19),U_19)
| is_connected_in(U_17,U_19)
| ~ relation(U_17) ),
inference(clausify,[status(thm)],[f_9_5]) ).
cnf(f_9_8,plain,
( in(sK2(U_17,U_19),U_19)
| is_connected_in(U_17,U_19)
| ~ relation(U_17) ),
inference(clausify,[status(thm)],[f_9_5]) ).
cnf(f_9_9,plain,
( sK1(U_17,U_19) != sK2(U_17,U_19)
| is_connected_in(U_17,U_19)
| ~ relation(U_17) ),
inference(clausify,[status(thm)],[f_9_5]) ).
cnf(f_9_10,plain,
( ~ in(ordered_pair(sK1(U_17,U_19),sK2(U_17,U_19)),U_17)
| is_connected_in(U_17,U_19)
| ~ relation(U_17) ),
inference(clausify,[status(thm)],[f_9_5]) ).
cnf(f_9_11,plain,
( ~ in(ordered_pair(sK2(U_17,U_19),sK1(U_17,U_19)),U_17)
| is_connected_in(U_17,U_19)
| ~ relation(U_17) ),
inference(clausify,[status(thm)],[f_9_5]) ).
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,
$true,
inference(fof_nnf,[status(thm)],[dt_k2_xboole_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_k3_relat_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_k4_tarski]) ).
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_m1_subset_1]) ).
cnf(f_18_2,plain,
$true,
inference(clausify,[status(thm)],[f_18_1]) ).
fof(f_19_1,plain,
! [A] :
? [B] : element(B,A),
inference(fof_nnf,[status(thm)],[existence_m1_subset_1]) ).
fof(f_19_2,plain,
! [U_21] :
? [U_20] : element(U_20,U_21),
inference(variable_rename,[status(thm)],[f_19_1]) ).
fof(f_19_3,plain,
! [U_21] : element(sK3(U_21),U_21),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3]),skolemize(U_20,sK3(U_21))],[f_19_2]) ).
cnf(f_19_4,plain,
element(sK3(U_21),U_21),
inference(clausify,[status(thm)],[f_19_3]) ).
fof(f_20_1,plain,
empty(empty_set),
inference(fof_nnf,[status(thm)],[fc1_xboole_0]) ).
cnf(f_20_2,plain,
empty(empty_set),
inference(clausify,[status(thm)],[f_20_1]) ).
fof(f_21_1,plain,
! [A,B] : ~ empty(ordered_pair(A,B)),
inference(fof_nnf,[status(thm)],[fc1_zfmisc_1]) ).
fof(f_21_2,plain,
! [U_23,U_22] : ~ empty(ordered_pair(U_23,U_22)),
inference(variable_rename,[status(thm)],[f_21_1]) ).
cnf(f_21_3,plain,
~ empty(ordered_pair(U_23,U_22)),
inference(clausify,[status(thm)],[f_21_2]) ).
fof(f_22_1,plain,
! [A,B] :
( ~ empty(set_union2(A,B))
| empty(A) ),
inference(fof_nnf,[status(thm)],[fc2_xboole_0]) ).
fof(f_22_2,plain,
! [U_25,U_24] :
( ~ empty(set_union2(U_25,U_24))
| empty(U_25) ),
inference(variable_rename,[status(thm)],[f_22_1]) ).
fof(f_22_3,plain,
! [U_25] :
( ! [U_24] : ~ empty(set_union2(U_25,U_24))
| empty(U_25) ),
inference(miniscope,[status(thm)],[f_22_2]) ).
cnf(f_22_4,plain,
( ~ empty(set_union2(U_25,U_24))
| empty(U_25) ),
inference(clausify,[status(thm)],[f_22_3]) ).
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_27,U_26] :
( ~ empty(set_union2(U_26,U_27))
| empty(U_27) ),
inference(variable_rename,[status(thm)],[f_23_1]) ).
fof(f_23_3,plain,
! [U_27] :
( ! [U_26] : ~ empty(set_union2(U_26,U_27))
| empty(U_27) ),
inference(miniscope,[status(thm)],[f_23_2]) ).
cnf(f_23_4,plain,
( ~ empty(set_union2(U_26,U_27))
| empty(U_27) ),
inference(clausify,[status(thm)],[f_23_3]) ).
fof(f_24_1,plain,
! [A,B] : set_union2(A,A) = A,
inference(fof_nnf,[status(thm)],[idempotence_k2_xboole_0]) ).
fof(f_24_2,plain,
! [U_29,U_28] : set_union2(U_29,U_29) = U_29,
inference(variable_rename,[status(thm)],[f_24_1]) ).
fof(f_24_3,plain,
! [U_29] : set_union2(U_29,U_29) = U_29,
inference(miniscope,[status(thm)],[f_24_2]) ).
cnf(f_24_4,plain,
set_union2(U_29,U_29) = U_29,
inference(clausify,[status(thm)],[f_24_3]) ).
fof(f_25_1,negated_conjecture,
~ ! [A] :
( relation(A)
=> ( connected(A)
<=> ! [B,C] :
~ ( ~ in(ordered_pair(C,B),A)
& ~ in(ordered_pair(B,C),A)
& B != C
& in(C,relation_field(A))
& in(B,relation_field(A)) ) ) ),
inference(negate,[status(cth)],[l4_wellord1]) ).
fof(f_25_2,negated_conjecture,
? [A] :
( ( ( ~ connected(A)
& ! [B,C] :
( in(ordered_pair(C,B),A)
| in(ordered_pair(B,C),A)
| B = C
| ~ in(C,relation_field(A))
| ~ in(B,relation_field(A)) ) )
| ( ? [B,C] :
( ~ in(ordered_pair(C,B),A)
& ~ in(ordered_pair(B,C),A)
& B != C
& in(C,relation_field(A))
& in(B,relation_field(A)) )
& connected(A) ) )
& relation(A) ),
inference(fof_nnf,[status(thm)],[f_25_1]) ).
fof(f_25_3,negated_conjecture,
? [U_34] :
( ( ( ~ connected(U_34)
& ! [U_33,U_32] :
( in(ordered_pair(U_32,U_33),U_34)
| in(ordered_pair(U_33,U_32),U_34)
| U_33 = U_32
| ~ in(U_32,relation_field(U_34))
| ~ in(U_33,relation_field(U_34)) ) )
| ( ? [U_31,U_30] :
( ~ in(ordered_pair(U_30,U_31),U_34)
& ~ in(ordered_pair(U_31,U_30),U_34)
& U_31 != U_30
& in(U_30,relation_field(U_34))
& in(U_31,relation_field(U_34)) )
& connected(U_34) ) )
& relation(U_34) ),
inference(variable_rename,[status(thm)],[f_25_2]) ).
fof(f_25_4,negated_conjecture,
? [U_34] :
( ( ( ~ connected(U_34)
& ! [U_33] :
( ! [U_32] :
( in(ordered_pair(U_32,U_33),U_34)
| in(ordered_pair(U_33,U_32),U_34)
| U_33 = U_32
| ~ in(U_32,relation_field(U_34)) )
| ~ in(U_33,relation_field(U_34)) ) )
| ( ? [U_31] :
( ? [U_30] :
( ~ in(ordered_pair(U_30,U_31),U_34)
& ~ in(ordered_pair(U_31,U_30),U_34)
& U_31 != U_30
& in(U_30,relation_field(U_34)) )
& in(U_31,relation_field(U_34)) )
& connected(U_34) ) )
& relation(U_34) ),
inference(miniscope,[status(thm)],[f_25_3]) ).
fof(f_25_5,negated_conjecture,
( ( ( ~ connected(sK4)
& ! [U_33] :
( ! [U_32] :
( in(ordered_pair(U_32,U_33),sK4)
| in(ordered_pair(U_33,U_32),sK4)
| U_33 = U_32
| ~ in(U_32,relation_field(sK4)) )
| ~ in(U_33,relation_field(sK4)) ) )
| ( ? [U_31] :
( ? [U_30] :
( ~ in(ordered_pair(U_30,U_31),sK4)
& ~ in(ordered_pair(U_31,U_30),sK4)
& U_31 != U_30
& in(U_30,relation_field(sK4)) )
& in(U_31,relation_field(sK4)) )
& connected(sK4) ) )
& relation(sK4) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4]),skolemize(U_34,sK4)],[f_25_4]) ).
fof(f_25_6,negated_conjecture,
( ( ( ~ connected(sK4)
& ! [U_33] :
( ! [U_32] :
( in(ordered_pair(U_32,U_33),sK4)
| in(ordered_pair(U_33,U_32),sK4)
| U_33 = U_32
| ~ in(U_32,relation_field(sK4)) )
| ~ in(U_33,relation_field(sK4)) ) )
| ( ? [U_30] :
( ~ in(ordered_pair(U_30,sK5),sK4)
& ~ in(ordered_pair(sK5,U_30),sK4)
& sK5 != U_30
& in(U_30,relation_field(sK4)) )
& in(sK5,relation_field(sK4))
& connected(sK4) ) )
& relation(sK4) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK5]),skolemize(U_31,sK5)],[f_25_5]) ).
fof(f_25_7,negated_conjecture,
( ( ( ~ connected(sK4)
& ! [U_33] :
( ! [U_32] :
( in(ordered_pair(U_32,U_33),sK4)
| in(ordered_pair(U_33,U_32),sK4)
| U_33 = U_32
| ~ in(U_32,relation_field(sK4)) )
| ~ in(U_33,relation_field(sK4)) ) )
| ( ~ in(ordered_pair(sK6,sK5),sK4)
& ~ in(ordered_pair(sK5,sK6),sK4)
& sK5 != sK6
& in(sK6,relation_field(sK4))
& in(sK5,relation_field(sK4))
& connected(sK4) ) )
& relation(sK4) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK6]),skolemize(U_30,sK6)],[f_25_6]) ).
fof(f_25_8,negated_conjecture,
( ! [U_32,U_33] :
( ~ connected(sK4)
| ~ sP1(U_32,U_33) )
& ! [U_32,U_33] :
( in(ordered_pair(U_32,U_33),sK4)
| in(ordered_pair(U_33,U_32),sK4)
| U_33 = U_32
| ~ in(U_32,relation_field(sK4))
| ~ in(U_33,relation_field(sK4))
| ~ sP1(U_32,U_33) )
& ( ~ in(ordered_pair(sK6,sK5),sK4)
| ~ sP0 )
& ( ~ in(ordered_pair(sK5,sK6),sK4)
| ~ sP0 )
& ( sK5 != sK6
| ~ sP0 )
& ( in(sK6,relation_field(sK4))
| ~ sP0 )
& ( in(sK5,relation_field(sK4))
| ~ sP0 )
& ( connected(sK4)
| ~ sP0 )
& ! [U_32,U_33] :
( sP1(U_32,U_33)
| sP0 )
& relation(sK4) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP0,sP1])],[f_25_7]) ).
cnf(f_25_9,negated_conjecture,
relation(sK4),
inference(clausify,[status(thm)],[f_25_8]) ).
cnf(f_25_10,negated_conjecture,
( sP1(U_32,U_33)
| sP0 ),
inference(clausify,[status(thm)],[f_25_8]) ).
cnf(f_25_11,negated_conjecture,
( connected(sK4)
| ~ sP0 ),
inference(clausify,[status(thm)],[f_25_8]) ).
cnf(f_25_12,negated_conjecture,
( in(sK5,relation_field(sK4))
| ~ sP0 ),
inference(clausify,[status(thm)],[f_25_8]) ).
cnf(f_25_13,negated_conjecture,
( in(sK6,relation_field(sK4))
| ~ sP0 ),
inference(clausify,[status(thm)],[f_25_8]) ).
cnf(f_25_14,negated_conjecture,
( sK5 != sK6
| ~ sP0 ),
inference(clausify,[status(thm)],[f_25_8]) ).
cnf(f_25_15,negated_conjecture,
( ~ in(ordered_pair(sK5,sK6),sK4)
| ~ sP0 ),
inference(clausify,[status(thm)],[f_25_8]) ).
cnf(f_25_16,negated_conjecture,
( ~ in(ordered_pair(sK6,sK5),sK4)
| ~ sP0 ),
inference(clausify,[status(thm)],[f_25_8]) ).
cnf(f_25_17,negated_conjecture,
( in(ordered_pair(U_32,U_33),sK4)
| in(ordered_pair(U_33,U_32),sK4)
| U_33 = U_32
| ~ in(U_32,relation_field(sK4))
| ~ in(U_33,relation_field(sK4))
| ~ sP1(U_32,U_33) ),
inference(clausify,[status(thm)],[f_25_8]) ).
cnf(f_25_18,negated_conjecture,
( ~ connected(sK4)
| ~ sP1(U_32,U_33) ),
inference(clausify,[status(thm)],[f_25_8]) ).
fof(f_26_1,plain,
? [A] :
( function(A)
& relation(A) ),
inference(fof_nnf,[status(thm)],[rc1_funct_1]) ).
fof(f_26_2,plain,
? [U_35] :
( function(U_35)
& relation(U_35) ),
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_35,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] : empty(A),
inference(fof_nnf,[status(thm)],[rc1_xboole_0]) ).
fof(f_27_2,plain,
? [U_36] : empty(U_36),
inference(variable_rename,[status(thm)],[f_27_1]) ).
fof(f_27_3,plain,
empty(sK8),
inference(skolemize,[status(esa),new_symbols(skolem,[sK8]),skolemize(U_36,sK8)],[f_27_2]) ).
cnf(f_27_4,plain,
empty(sK8),
inference(clausify,[status(thm)],[f_27_3]) ).
fof(f_28_1,plain,
? [A] :
( function(A)
& empty(A)
& relation(A) ),
inference(fof_nnf,[status(thm)],[rc2_funct_1]) ).
fof(f_28_2,plain,
? [U_37] :
( function(U_37)
& empty(U_37)
& relation(U_37) ),
inference(variable_rename,[status(thm)],[f_28_1]) ).
fof(f_28_3,plain,
( function(sK9)
& empty(sK9)
& relation(sK9) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK9]),skolemize(U_37,sK9)],[f_28_2]) ).
cnf(f_28_4,plain,
relation(sK9),
inference(clausify,[status(thm)],[f_28_3]) ).
cnf(f_28_5,plain,
empty(sK9),
inference(clausify,[status(thm)],[f_28_3]) ).
cnf(f_28_6,plain,
function(sK9),
inference(clausify,[status(thm)],[f_28_3]) ).
fof(f_29_1,plain,
? [A] : ~ empty(A),
inference(fof_nnf,[status(thm)],[rc2_xboole_0]) ).
fof(f_29_2,plain,
? [U_38] : ~ empty(U_38),
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_38,sK10)],[f_29_2]) ).
cnf(f_29_4,plain,
~ empty(sK10),
inference(clausify,[status(thm)],[f_29_3]) ).
fof(f_30_1,plain,
? [A] :
( one_to_one(A)
& function(A)
& relation(A) ),
inference(fof_nnf,[status(thm)],[rc3_funct_1]) ).
fof(f_30_2,plain,
? [U_39] :
( one_to_one(U_39)
& function(U_39)
& relation(U_39) ),
inference(variable_rename,[status(thm)],[f_30_1]) ).
fof(f_30_3,plain,
( one_to_one(sK11)
& function(sK11)
& relation(sK11) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK11]),skolemize(U_39,sK11)],[f_30_2]) ).
cnf(f_30_4,plain,
relation(sK11),
inference(clausify,[status(thm)],[f_30_3]) ).
cnf(f_30_5,plain,
function(sK11),
inference(clausify,[status(thm)],[f_30_3]) ).
cnf(f_30_6,plain,
one_to_one(sK11),
inference(clausify,[status(thm)],[f_30_3]) ).
fof(f_31_1,plain,
! [A] : set_union2(A,empty_set) = A,
inference(fof_nnf,[status(thm)],[t1_boole]) ).
fof(f_31_2,plain,
! [U_40] : set_union2(U_40,empty_set) = U_40,
inference(variable_rename,[status(thm)],[f_31_1]) ).
cnf(f_31_3,plain,
set_union2(U_40,empty_set) = U_40,
inference(clausify,[status(thm)],[f_31_2]) ).
fof(f_32_1,plain,
! [A,B] :
( element(A,B)
| ~ in(A,B) ),
inference(fof_nnf,[status(thm)],[t1_subset]) ).
fof(f_32_2,plain,
! [U_42,U_41] :
( element(U_42,U_41)
| ~ in(U_42,U_41) ),
inference(variable_rename,[status(thm)],[f_32_1]) ).
cnf(f_32_3,plain,
( element(U_42,U_41)
| ~ in(U_42,U_41) ),
inference(clausify,[status(thm)],[f_32_2]) ).
fof(f_33_1,plain,
! [A,B] :
( in(A,B)
| empty(B)
| ~ element(A,B) ),
inference(fof_nnf,[status(thm)],[t2_subset]) ).
fof(f_33_2,plain,
! [U_44,U_43] :
( in(U_44,U_43)
| empty(U_43)
| ~ element(U_44,U_43) ),
inference(variable_rename,[status(thm)],[f_33_1]) ).
cnf(f_33_3,plain,
( in(U_44,U_43)
| empty(U_43)
| ~ element(U_44,U_43) ),
inference(clausify,[status(thm)],[f_33_2]) ).
fof(f_34_1,plain,
! [A] :
( A = empty_set
| ~ empty(A) ),
inference(fof_nnf,[status(thm)],[t6_boole]) ).
fof(f_34_2,plain,
! [U_45] :
( U_45 = empty_set
| ~ empty(U_45) ),
inference(variable_rename,[status(thm)],[f_34_1]) ).
cnf(f_34_3,plain,
( U_45 = empty_set
| ~ empty(U_45) ),
inference(clausify,[status(thm)],[f_34_2]) ).
fof(f_35_1,plain,
! [A,B] :
( ~ empty(B)
| ~ in(A,B) ),
inference(fof_nnf,[status(thm)],[t7_boole]) ).
fof(f_35_2,plain,
! [U_47,U_46] :
( ~ empty(U_46)
| ~ in(U_47,U_46) ),
inference(variable_rename,[status(thm)],[f_35_1]) ).
cnf(f_35_3,plain,
( ~ empty(U_46)
| ~ in(U_47,U_46) ),
inference(clausify,[status(thm)],[f_35_2]) ).
fof(f_36_1,plain,
! [A,B] :
( ~ empty(B)
| A = B
| ~ empty(A) ),
inference(fof_nnf,[status(thm)],[t8_boole]) ).
fof(f_36_2,plain,
! [U_49,U_48] :
( ~ empty(U_48)
| U_49 = U_48
| ~ empty(U_49) ),
inference(variable_rename,[status(thm)],[f_36_1]) ).
fof(f_36_3,plain,
! [U_49] :
( ! [U_48] :
( ~ empty(U_48)
| U_49 = U_48 )
| ~ empty(U_49) ),
inference(miniscope,[status(thm)],[f_36_2]) ).
cnf(f_36_4,plain,
( ~ empty(U_48)
| U_49 = U_48
| ~ empty(U_49) ),
inference(clausify,[status(thm)],[f_36_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_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_18_2_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_18_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,
( relation_field(Eq_x_0) = relation_field(Eq_y_0)
| 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_dom(Eq_x_0) = relation_dom(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_10,axiom,
( relation_rng(Eq_x_0) = relation_rng(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,
( sK3(Eq_x_0) = sK3(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,
( relation(Eq_y_0)
| ~ relation(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_18,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_19,axiom,
( connected(Eq_y_0)
| ~ connected(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_20,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_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,
( sP1(Eq_y_0,Eq_y_1)
| ~ sP1(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 : SEU242+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
% 0.10/5.58 % Computer : n016.cluster.edu
% 0.10/5.58 % Model : x86_64 x86_64
% 0.10/5.58 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/5.58 % Memory : 8046.5625MB
% 0.10/5.58 % OS : Linux 6.8.0-71-generic
% 0.10/5.58 % CPULimit : 300
% 0.10/5.58 % WCLimit : 300
% 0.10/5.58 % DateTime : Sat Sep 19 23:42:57 UTC 2026
% 0.10/5.59 % CPUTime :
% 0.14/5.86 % SZS status Theorem for theBenchmark
% 0.14/5.86 % SZS output start Proof for theBenchmark
% See solution above
%------------------------------------------------------------------------------