%------------------------------------------------------------------------------
% File : ConnectPP---0.7.2
% Problem : SEU239+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 : n015.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 08:58:39 AM UTC 2026
% Result : Theorem 0.46s 0.75s
% Output : Proof 0.46s
% 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(d1_relat_2,axiom,
! [A] :
( relation(A)
=> ! [B] :
( is_reflexive_in(A,B)
<=> ! [C] :
( in(C,B)
=> in(ordered_pair(C,C),A) ) ) ),
file('theBenchmark.p',d1_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(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_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(l1_wellord1,conjecture,
! [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(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] :
( ! [B] :
( ( is_reflexive_in(A,B)
| ? [C] :
( ~ in(ordered_pair(C,C),A)
& in(C,B) ) )
& ( ! [C] :
( in(ordered_pair(C,C),A)
| ~ in(C,B) )
| ~ is_reflexive_in(A,B) ) )
| ~ relation(A) ),
inference(fof_nnf,[status(thm)],[d1_relat_2]) ).
fof(f_6_2,plain,
! [U_11] :
( ! [U_10] :
( ( is_reflexive_in(U_11,U_10)
| ? [U_9] :
( ~ in(ordered_pair(U_9,U_9),U_11)
& in(U_9,U_10) ) )
& ( ! [U_8] :
( in(ordered_pair(U_8,U_8),U_11)
| ~ in(U_8,U_10) )
| ~ is_reflexive_in(U_11,U_10) ) )
| ~ relation(U_11) ),
inference(variable_rename,[status(thm)],[f_6_1]) ).
fof(f_6_3,plain,
! [U_11] :
( ( ! [U_13] :
( is_reflexive_in(U_11,U_13)
| ? [U_9] :
( ~ in(ordered_pair(U_9,U_9),U_11)
& in(U_9,U_13) ) )
& ! [U_12] :
( ! [U_8] :
( in(ordered_pair(U_8,U_8),U_11)
| ~ in(U_8,U_12) )
| ~ is_reflexive_in(U_11,U_12) ) )
| ~ relation(U_11) ),
inference(miniscope,[status(thm)],[f_6_2]) ).
fof(f_6_4,plain,
! [U_11] :
( ( ! [U_13] :
( is_reflexive_in(U_11,U_13)
| ( ~ in(ordered_pair(sK1(U_11,U_13),sK1(U_11,U_13)),U_11)
& in(sK1(U_11,U_13),U_13) ) )
& ! [U_12] :
( ! [U_8] :
( in(ordered_pair(U_8,U_8),U_11)
| ~ in(U_8,U_12) )
| ~ is_reflexive_in(U_11,U_12) ) )
| ~ relation(U_11) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(U_9,sK1(U_11,U_13))],[f_6_3]) ).
cnf(f_6_5,plain,
( in(ordered_pair(U_8,U_8),U_11)
| ~ in(U_8,U_12)
| ~ is_reflexive_in(U_11,U_12)
| ~ relation(U_11) ),
inference(clausify,[status(thm)],[f_6_4]) ).
cnf(f_6_6,plain,
( in(sK1(U_11,U_13),U_13)
| is_reflexive_in(U_11,U_13)
| ~ relation(U_11) ),
inference(clausify,[status(thm)],[f_6_4]) ).
cnf(f_6_7,plain,
( ~ in(ordered_pair(sK1(U_11,U_13),sK1(U_11,U_13)),U_11)
| is_reflexive_in(U_11,U_13)
| ~ relation(U_11) ),
inference(clausify,[status(thm)],[f_6_4]) ).
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_15,U_14] : ordered_pair(U_15,U_14) = unordered_pair(unordered_pair(U_15,U_14),singleton(U_15)),
inference(variable_rename,[status(thm)],[f_7_1]) ).
cnf(f_7_3,plain,
ordered_pair(U_15,U_14) = unordered_pair(unordered_pair(U_15,U_14),singleton(U_15)),
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_16] :
( relation_field(U_16) = set_union2(relation_dom(U_16),relation_rng(U_16))
| ~ relation(U_16) ),
inference(variable_rename,[status(thm)],[f_8_1]) ).
cnf(f_8_3,plain,
( relation_field(U_16) = set_union2(relation_dom(U_16),relation_rng(U_16))
| ~ relation(U_16) ),
inference(clausify,[status(thm)],[f_8_2]) ).
fof(f_9_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_9_2,plain,
! [U_17] :
( ( ( reflexive(U_17)
| ~ is_reflexive_in(U_17,relation_field(U_17)) )
& ( is_reflexive_in(U_17,relation_field(U_17))
| ~ reflexive(U_17) ) )
| ~ relation(U_17) ),
inference(variable_rename,[status(thm)],[f_9_1]) ).
cnf(f_9_3,plain,
( is_reflexive_in(U_17,relation_field(U_17))
| ~ reflexive(U_17)
| ~ relation(U_17) ),
inference(clausify,[status(thm)],[f_9_2]) ).
cnf(f_9_4,plain,
( reflexive(U_17)
| ~ is_reflexive_in(U_17,relation_field(U_17))
| ~ relation(U_17) ),
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,
$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_19] :
? [U_18] : element(U_18,U_19),
inference(variable_rename,[status(thm)],[f_19_1]) ).
fof(f_19_3,plain,
! [U_19] : element(sK2(U_19),U_19),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2]),skolemize(U_18,sK2(U_19))],[f_19_2]) ).
cnf(f_19_4,plain,
element(sK2(U_19),U_19),
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_21,U_20] : ~ empty(ordered_pair(U_21,U_20)),
inference(variable_rename,[status(thm)],[f_21_1]) ).
cnf(f_21_3,plain,
~ empty(ordered_pair(U_21,U_20)),
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_23,U_22] :
( ~ empty(set_union2(U_23,U_22))
| empty(U_23) ),
inference(variable_rename,[status(thm)],[f_22_1]) ).
fof(f_22_3,plain,
! [U_23] :
( ! [U_22] : ~ empty(set_union2(U_23,U_22))
| empty(U_23) ),
inference(miniscope,[status(thm)],[f_22_2]) ).
cnf(f_22_4,plain,
( ~ empty(set_union2(U_23,U_22))
| empty(U_23) ),
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_25,U_24] :
( ~ empty(set_union2(U_24,U_25))
| empty(U_25) ),
inference(variable_rename,[status(thm)],[f_23_1]) ).
fof(f_23_3,plain,
! [U_25] :
( ! [U_24] : ~ empty(set_union2(U_24,U_25))
| empty(U_25) ),
inference(miniscope,[status(thm)],[f_23_2]) ).
cnf(f_23_4,plain,
( ~ empty(set_union2(U_24,U_25))
| empty(U_25) ),
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_27,U_26] : set_union2(U_27,U_27) = U_27,
inference(variable_rename,[status(thm)],[f_24_1]) ).
fof(f_24_3,plain,
! [U_27] : set_union2(U_27,U_27) = U_27,
inference(miniscope,[status(thm)],[f_24_2]) ).
cnf(f_24_4,plain,
set_union2(U_27,U_27) = U_27,
inference(clausify,[status(thm)],[f_24_3]) ).
fof(f_25_1,negated_conjecture,
~ ! [A] :
( relation(A)
=> ( reflexive(A)
<=> ! [B] :
( in(B,relation_field(A))
=> in(ordered_pair(B,B),A) ) ) ),
inference(negate,[status(cth)],[l1_wellord1]) ).
fof(f_25_2,negated_conjecture,
? [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)],[f_25_1]) ).
fof(f_25_3,negated_conjecture,
? [U_30] :
( ( ( ~ reflexive(U_30)
& ! [U_29] :
( in(ordered_pair(U_29,U_29),U_30)
| ~ in(U_29,relation_field(U_30)) ) )
| ( ? [U_28] :
( ~ in(ordered_pair(U_28,U_28),U_30)
& in(U_28,relation_field(U_30)) )
& reflexive(U_30) ) )
& relation(U_30) ),
inference(variable_rename,[status(thm)],[f_25_2]) ).
fof(f_25_4,negated_conjecture,
( ( ( ~ reflexive(sK3)
& ! [U_29] :
( in(ordered_pair(U_29,U_29),sK3)
| ~ in(U_29,relation_field(sK3)) ) )
| ( ? [U_28] :
( ~ in(ordered_pair(U_28,U_28),sK3)
& in(U_28,relation_field(sK3)) )
& reflexive(sK3) ) )
& relation(sK3) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3]),skolemize(U_30,sK3)],[f_25_3]) ).
fof(f_25_5,negated_conjecture,
( ( ( ~ reflexive(sK3)
& ! [U_29] :
( in(ordered_pair(U_29,U_29),sK3)
| ~ in(U_29,relation_field(sK3)) ) )
| ( ~ in(ordered_pair(sK4,sK4),sK3)
& in(sK4,relation_field(sK3))
& reflexive(sK3) ) )
& relation(sK3) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4]),skolemize(U_28,sK4)],[f_25_4]) ).
fof(f_25_6,negated_conjecture,
( ! [U_29] :
( ~ reflexive(sK3)
| ~ sP1(U_29) )
& ! [U_29] :
( in(ordered_pair(U_29,U_29),sK3)
| ~ in(U_29,relation_field(sK3))
| ~ sP1(U_29) )
& ( ~ in(ordered_pair(sK4,sK4),sK3)
| ~ sP0 )
& ( in(sK4,relation_field(sK3))
| ~ sP0 )
& ( reflexive(sK3)
| ~ sP0 )
& ! [U_29] :
( sP1(U_29)
| sP0 )
& relation(sK3) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP0,sP1])],[f_25_5]) ).
cnf(f_25_7,negated_conjecture,
relation(sK3),
inference(clausify,[status(thm)],[f_25_6]) ).
cnf(f_25_8,negated_conjecture,
( sP1(U_29)
| sP0 ),
inference(clausify,[status(thm)],[f_25_6]) ).
cnf(f_25_9,negated_conjecture,
( reflexive(sK3)
| ~ sP0 ),
inference(clausify,[status(thm)],[f_25_6]) ).
cnf(f_25_10,negated_conjecture,
( in(sK4,relation_field(sK3))
| ~ sP0 ),
inference(clausify,[status(thm)],[f_25_6]) ).
cnf(f_25_11,negated_conjecture,
( ~ in(ordered_pair(sK4,sK4),sK3)
| ~ sP0 ),
inference(clausify,[status(thm)],[f_25_6]) ).
cnf(f_25_12,negated_conjecture,
( in(ordered_pair(U_29,U_29),sK3)
| ~ in(U_29,relation_field(sK3))
| ~ sP1(U_29) ),
inference(clausify,[status(thm)],[f_25_6]) ).
cnf(f_25_13,negated_conjecture,
( ~ reflexive(sK3)
| ~ sP1(U_29) ),
inference(clausify,[status(thm)],[f_25_6]) ).
fof(f_26_1,plain,
? [A] :
( function(A)
& relation(A) ),
inference(fof_nnf,[status(thm)],[rc1_funct_1]) ).
fof(f_26_2,plain,
? [U_31] :
( function(U_31)
& relation(U_31) ),
inference(variable_rename,[status(thm)],[f_26_1]) ).
fof(f_26_3,plain,
( function(sK5)
& relation(sK5) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK5]),skolemize(U_31,sK5)],[f_26_2]) ).
cnf(f_26_4,plain,
relation(sK5),
inference(clausify,[status(thm)],[f_26_3]) ).
cnf(f_26_5,plain,
function(sK5),
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_32] : empty(U_32),
inference(variable_rename,[status(thm)],[f_27_1]) ).
fof(f_27_3,plain,
empty(sK6),
inference(skolemize,[status(esa),new_symbols(skolem,[sK6]),skolemize(U_32,sK6)],[f_27_2]) ).
cnf(f_27_4,plain,
empty(sK6),
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_33] :
( function(U_33)
& empty(U_33)
& relation(U_33) ),
inference(variable_rename,[status(thm)],[f_28_1]) ).
fof(f_28_3,plain,
( function(sK7)
& empty(sK7)
& relation(sK7) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK7]),skolemize(U_33,sK7)],[f_28_2]) ).
cnf(f_28_4,plain,
relation(sK7),
inference(clausify,[status(thm)],[f_28_3]) ).
cnf(f_28_5,plain,
empty(sK7),
inference(clausify,[status(thm)],[f_28_3]) ).
cnf(f_28_6,plain,
function(sK7),
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_34] : ~ empty(U_34),
inference(variable_rename,[status(thm)],[f_29_1]) ).
fof(f_29_3,plain,
~ empty(sK8),
inference(skolemize,[status(esa),new_symbols(skolem,[sK8]),skolemize(U_34,sK8)],[f_29_2]) ).
cnf(f_29_4,plain,
~ empty(sK8),
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_35] :
( one_to_one(U_35)
& function(U_35)
& relation(U_35) ),
inference(variable_rename,[status(thm)],[f_30_1]) ).
fof(f_30_3,plain,
( one_to_one(sK9)
& function(sK9)
& relation(sK9) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK9]),skolemize(U_35,sK9)],[f_30_2]) ).
cnf(f_30_4,plain,
relation(sK9),
inference(clausify,[status(thm)],[f_30_3]) ).
cnf(f_30_5,plain,
function(sK9),
inference(clausify,[status(thm)],[f_30_3]) ).
cnf(f_30_6,plain,
one_to_one(sK9),
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_36] : set_union2(U_36,empty_set) = U_36,
inference(variable_rename,[status(thm)],[f_31_1]) ).
cnf(f_31_3,plain,
set_union2(U_36,empty_set) = U_36,
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_38,U_37] :
( element(U_38,U_37)
| ~ in(U_38,U_37) ),
inference(variable_rename,[status(thm)],[f_32_1]) ).
cnf(f_32_3,plain,
( element(U_38,U_37)
| ~ in(U_38,U_37) ),
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_40,U_39] :
( in(U_40,U_39)
| empty(U_39)
| ~ element(U_40,U_39) ),
inference(variable_rename,[status(thm)],[f_33_1]) ).
cnf(f_33_3,plain,
( in(U_40,U_39)
| empty(U_39)
| ~ element(U_40,U_39) ),
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_41] :
( U_41 = empty_set
| ~ empty(U_41) ),
inference(variable_rename,[status(thm)],[f_34_1]) ).
cnf(f_34_3,plain,
( U_41 = empty_set
| ~ empty(U_41) ),
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_43,U_42] :
( ~ empty(U_42)
| ~ in(U_43,U_42) ),
inference(variable_rename,[status(thm)],[f_35_1]) ).
cnf(f_35_3,plain,
( ~ empty(U_42)
| ~ in(U_43,U_42) ),
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_45,U_44] :
( ~ empty(U_44)
| U_45 = U_44
| ~ empty(U_45) ),
inference(variable_rename,[status(thm)],[f_36_1]) ).
fof(f_36_3,plain,
! [U_45] :
( ! [U_44] :
( ~ empty(U_44)
| U_45 = U_44 )
| ~ empty(U_45) ),
inference(miniscope,[status(thm)],[f_36_2]) ).
cnf(f_36_4,plain,
( ~ empty(U_44)
| U_45 = U_44
| ~ empty(U_45) ),
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,
( 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_7,axiom,
( singleton(Eq_x_0) = singleton(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_8,axiom,
( relation_field(Eq_x_0) = relation_field(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) = sK2(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_13,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_14,axiom,
( empty(Eq_y_0)
| ~ empty(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_15,axiom,
( function(Eq_y_0)
| ~ function(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_16,axiom,
( relation(Eq_y_0)
| ~ relation(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_17,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_18,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_19,axiom,
( reflexive(Eq_y_0)
| ~ reflexive(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_20,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_21,axiom,
( sP1(Eq_y_0)
| ~ sP1(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 : SEU239+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
% 0.10/0.36 % Computer : n015.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Sat Sep 19 23:40:50 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.46/0.75 % SZS status Theorem for theBenchmark
% 0.46/0.75 % SZS output start Proof for theBenchmark
% See solution above
%------------------------------------------------------------------------------