%------------------------------------------------------------------------------
% File : ConnectPP---0.7.2
% Problem : SEU243+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 : 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 08:58:40 AM UTC 2026
% Result : Theorem 75.14s 75.47s
% Output : Proof 75.14s
% 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_xboole_0,axiom,
! [A,B] : set_union2(A,B) = set_union2(B,A),
file('theBenchmark.p',commutativity_k2_xboole_0) ).
fof(d2_wellord1,axiom,
! [A] :
( relation(A)
=> ( well_founded_relation(A)
<=> ! [B] :
~ ( ! [C] :
~ ( disjoint(fiber(A,C),B)
& in(C,B) )
& B != empty_set
& subset(B,relation_field(A)) ) ) ),
file('theBenchmark.p',d2_wellord1) ).
fof(d3_wellord1,axiom,
! [A] :
( relation(A)
=> ! [B] :
( is_well_founded_in(A,B)
<=> ! [C] :
~ ( ! [D] :
~ ( disjoint(fiber(A,D),C)
& in(D,C) )
& C != empty_set
& subset(C,B) ) ) ),
file('theBenchmark.p',d3_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(dt_k1_relat_1,axiom,
$true,
file('theBenchmark.p',dt_k1_relat_1) ).
fof(dt_k1_wellord1,axiom,
$true,
file('theBenchmark.p',dt_k1_wellord1) ).
fof(dt_k1_xboole_0,axiom,
$true,
file('theBenchmark.p',dt_k1_xboole_0) ).
fof(dt_k1_zfmisc_1,axiom,
$true,
file('theBenchmark.p',dt_k1_zfmisc_1) ).
fof(dt_k2_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(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(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(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(reflexivity_r1_tarski,axiom,
! [A,B] : subset(A,A),
file('theBenchmark.p',reflexivity_r1_tarski) ).
fof(symmetry_r1_xboole_0,axiom,
! [A,B] :
( disjoint(A,B)
=> disjoint(B,A) ),
file('theBenchmark.p',symmetry_r1_xboole_0) ).
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(t3_subset,axiom,
! [A,B] :
( element(A,powerset(B))
<=> subset(A,B) ),
file('theBenchmark.p',t3_subset) ).
fof(t4_subset,axiom,
! [A,B,C] :
( ( element(B,powerset(C))
& in(A,B) )
=> element(A,C) ),
file('theBenchmark.p',t4_subset) ).
fof(t5_subset,axiom,
! [A,B,C] :
~ ( empty(C)
& element(B,powerset(C))
& in(A,B) ),
file('theBenchmark.p',t5_subset) ).
fof(t5_wellord1,conjecture,
! [A] :
( relation(A)
=> ( well_founded_relation(A)
<=> is_well_founded_in(A,relation_field(A)) ) ),
file('theBenchmark.p',t5_wellord1) ).
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] : set_union2(A,B) = set_union2(B,A),
inference(fof_nnf,[status(thm)],[commutativity_k2_xboole_0]) ).
fof(f_4_2,plain,
! [U_5,U_4] : set_union2(U_5,U_4) = set_union2(U_4,U_5),
inference(variable_rename,[status(thm)],[f_4_1]) ).
cnf(f_4_3,plain,
set_union2(U_5,U_4) = set_union2(U_4,U_5),
inference(clausify,[status(thm)],[f_4_2]) ).
fof(f_5_1,plain,
! [A] :
( ( ( well_founded_relation(A)
| ? [B] :
( ! [C] :
( ~ disjoint(fiber(A,C),B)
| ~ in(C,B) )
& B != empty_set
& subset(B,relation_field(A)) ) )
& ( ! [B] :
( ? [C] :
( disjoint(fiber(A,C),B)
& in(C,B) )
| B = empty_set
| ~ subset(B,relation_field(A)) )
| ~ well_founded_relation(A) ) )
| ~ relation(A) ),
inference(fof_nnf,[status(thm)],[d2_wellord1]) ).
fof(f_5_2,plain,
! [U_10] :
( ( ( well_founded_relation(U_10)
| ? [U_9] :
( ! [U_8] :
( ~ disjoint(fiber(U_10,U_8),U_9)
| ~ in(U_8,U_9) )
& U_9 != empty_set
& subset(U_9,relation_field(U_10)) ) )
& ( ! [U_7] :
( ? [U_6] :
( disjoint(fiber(U_10,U_6),U_7)
& in(U_6,U_7) )
| U_7 = empty_set
| ~ subset(U_7,relation_field(U_10)) )
| ~ well_founded_relation(U_10) ) )
| ~ relation(U_10) ),
inference(variable_rename,[status(thm)],[f_5_1]) ).
fof(f_5_3,plain,
! [U_10] :
( ( ( well_founded_relation(U_10)
| ? [U_9] :
( ! [U_8] :
( ~ disjoint(fiber(U_10,U_8),U_9)
| ~ in(U_8,U_9) )
& U_9 != empty_set
& subset(U_9,relation_field(U_10)) ) )
& ( ! [U_7] :
( ( disjoint(fiber(U_10,sK1(U_10,U_7)),U_7)
& in(sK1(U_10,U_7),U_7) )
| U_7 = empty_set
| ~ subset(U_7,relation_field(U_10)) )
| ~ well_founded_relation(U_10) ) )
| ~ relation(U_10) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(U_6,sK1(U_10,U_7))],[f_5_2]) ).
fof(f_5_4,plain,
! [U_10] :
( ( ( well_founded_relation(U_10)
| ( ! [U_8] :
( ~ disjoint(fiber(U_10,U_8),sK2(U_10))
| ~ in(U_8,sK2(U_10)) )
& sK2(U_10) != empty_set
& subset(sK2(U_10),relation_field(U_10)) ) )
& ( ! [U_7] :
( ( disjoint(fiber(U_10,sK1(U_10,U_7)),U_7)
& in(sK1(U_10,U_7),U_7) )
| U_7 = empty_set
| ~ subset(U_7,relation_field(U_10)) )
| ~ well_founded_relation(U_10) ) )
| ~ relation(U_10) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2]),skolemize(U_9,sK2(U_10))],[f_5_3]) ).
cnf(f_5_5,plain,
( in(sK1(U_10,U_7),U_7)
| U_7 = empty_set
| ~ subset(U_7,relation_field(U_10))
| ~ well_founded_relation(U_10)
| ~ relation(U_10) ),
inference(clausify,[status(thm)],[f_5_4]) ).
cnf(f_5_6,plain,
( disjoint(fiber(U_10,sK1(U_10,U_7)),U_7)
| U_7 = empty_set
| ~ subset(U_7,relation_field(U_10))
| ~ well_founded_relation(U_10)
| ~ relation(U_10) ),
inference(clausify,[status(thm)],[f_5_4]) ).
cnf(f_5_7,plain,
( subset(sK2(U_10),relation_field(U_10))
| well_founded_relation(U_10)
| ~ relation(U_10) ),
inference(clausify,[status(thm)],[f_5_4]) ).
cnf(f_5_8,plain,
( sK2(U_10) != empty_set
| well_founded_relation(U_10)
| ~ relation(U_10) ),
inference(clausify,[status(thm)],[f_5_4]) ).
cnf(f_5_9,plain,
( ~ disjoint(fiber(U_10,U_8),sK2(U_10))
| ~ in(U_8,sK2(U_10))
| well_founded_relation(U_10)
| ~ relation(U_10) ),
inference(clausify,[status(thm)],[f_5_4]) ).
fof(f_6_1,plain,
! [A] :
( ! [B] :
( ( is_well_founded_in(A,B)
| ? [C] :
( ! [D] :
( ~ disjoint(fiber(A,D),C)
| ~ in(D,C) )
& C != empty_set
& subset(C,B) ) )
& ( ! [C] :
( ? [D] :
( disjoint(fiber(A,D),C)
& in(D,C) )
| C = empty_set
| ~ subset(C,B) )
| ~ is_well_founded_in(A,B) ) )
| ~ relation(A) ),
inference(fof_nnf,[status(thm)],[d3_wellord1]) ).
fof(f_6_2,plain,
! [U_16] :
( ! [U_15] :
( ( is_well_founded_in(U_16,U_15)
| ? [U_14] :
( ! [U_13] :
( ~ disjoint(fiber(U_16,U_13),U_14)
| ~ in(U_13,U_14) )
& U_14 != empty_set
& subset(U_14,U_15) ) )
& ( ! [U_12] :
( ? [U_11] :
( disjoint(fiber(U_16,U_11),U_12)
& in(U_11,U_12) )
| U_12 = empty_set
| ~ subset(U_12,U_15) )
| ~ is_well_founded_in(U_16,U_15) ) )
| ~ relation(U_16) ),
inference(variable_rename,[status(thm)],[f_6_1]) ).
fof(f_6_3,plain,
! [U_16] :
( ( ! [U_18] :
( is_well_founded_in(U_16,U_18)
| ? [U_14] :
( ! [U_13] :
( ~ disjoint(fiber(U_16,U_13),U_14)
| ~ in(U_13,U_14) )
& U_14 != empty_set
& subset(U_14,U_18) ) )
& ! [U_17] :
( ! [U_12] :
( ? [U_11] :
( disjoint(fiber(U_16,U_11),U_12)
& in(U_11,U_12) )
| U_12 = empty_set
| ~ subset(U_12,U_17) )
| ~ is_well_founded_in(U_16,U_17) ) )
| ~ relation(U_16) ),
inference(miniscope,[status(thm)],[f_6_2]) ).
fof(f_6_4,plain,
! [U_16] :
( ( ! [U_18] :
( is_well_founded_in(U_16,U_18)
| ? [U_14] :
( ! [U_13] :
( ~ disjoint(fiber(U_16,U_13),U_14)
| ~ in(U_13,U_14) )
& U_14 != empty_set
& subset(U_14,U_18) ) )
& ! [U_17] :
( ! [U_12] :
( ( disjoint(fiber(U_16,sK3(U_16,U_17,U_12)),U_12)
& in(sK3(U_16,U_17,U_12),U_12) )
| U_12 = empty_set
| ~ subset(U_12,U_17) )
| ~ is_well_founded_in(U_16,U_17) ) )
| ~ relation(U_16) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3]),skolemize(U_11,sK3(U_16,U_17,U_12))],[f_6_3]) ).
fof(f_6_5,plain,
! [U_16] :
( ( ! [U_18] :
( is_well_founded_in(U_16,U_18)
| ( ! [U_13] :
( ~ disjoint(fiber(U_16,U_13),sK4(U_16,U_18))
| ~ in(U_13,sK4(U_16,U_18)) )
& sK4(U_16,U_18) != empty_set
& subset(sK4(U_16,U_18),U_18) ) )
& ! [U_17] :
( ! [U_12] :
( ( disjoint(fiber(U_16,sK3(U_16,U_17,U_12)),U_12)
& in(sK3(U_16,U_17,U_12),U_12) )
| U_12 = empty_set
| ~ subset(U_12,U_17) )
| ~ is_well_founded_in(U_16,U_17) ) )
| ~ relation(U_16) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4]),skolemize(U_14,sK4(U_16,U_18))],[f_6_4]) ).
cnf(f_6_6,plain,
( in(sK3(U_16,U_17,U_12),U_12)
| U_12 = empty_set
| ~ subset(U_12,U_17)
| ~ is_well_founded_in(U_16,U_17)
| ~ relation(U_16) ),
inference(clausify,[status(thm)],[f_6_5]) ).
cnf(f_6_7,plain,
( disjoint(fiber(U_16,sK3(U_16,U_17,U_12)),U_12)
| U_12 = empty_set
| ~ subset(U_12,U_17)
| ~ is_well_founded_in(U_16,U_17)
| ~ relation(U_16) ),
inference(clausify,[status(thm)],[f_6_5]) ).
cnf(f_6_8,plain,
( subset(sK4(U_16,U_18),U_18)
| is_well_founded_in(U_16,U_18)
| ~ relation(U_16) ),
inference(clausify,[status(thm)],[f_6_5]) ).
cnf(f_6_9,plain,
( sK4(U_16,U_18) != empty_set
| is_well_founded_in(U_16,U_18)
| ~ relation(U_16) ),
inference(clausify,[status(thm)],[f_6_5]) ).
cnf(f_6_10,plain,
( ~ disjoint(fiber(U_16,U_13),sK4(U_16,U_18))
| ~ in(U_13,sK4(U_16,U_18))
| is_well_founded_in(U_16,U_18)
| ~ relation(U_16) ),
inference(clausify,[status(thm)],[f_6_5]) ).
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_19] :
( relation_field(U_19) = set_union2(relation_dom(U_19),relation_rng(U_19))
| ~ relation(U_19) ),
inference(variable_rename,[status(thm)],[f_7_1]) ).
cnf(f_7_3,plain,
( relation_field(U_19) = set_union2(relation_dom(U_19),relation_rng(U_19))
| ~ relation(U_19) ),
inference(clausify,[status(thm)],[f_7_2]) ).
fof(f_8_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_k1_relat_1]) ).
cnf(f_8_2,plain,
$true,
inference(clausify,[status(thm)],[f_8_1]) ).
fof(f_9_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_k1_wellord1]) ).
cnf(f_9_2,plain,
$true,
inference(clausify,[status(thm)],[f_9_1]) ).
fof(f_10_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_k1_xboole_0]) ).
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_zfmisc_1]) ).
cnf(f_11_2,plain,
$true,
inference(clausify,[status(thm)],[f_11_1]) ).
fof(f_12_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_k2_relat_1]) ).
cnf(f_12_2,plain,
$true,
inference(clausify,[status(thm)],[f_12_1]) ).
fof(f_13_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_k2_xboole_0]) ).
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_k3_relat_1]) ).
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_m1_subset_1]) ).
cnf(f_15_2,plain,
$true,
inference(clausify,[status(thm)],[f_15_1]) ).
fof(f_16_1,plain,
! [A] :
? [B] : element(B,A),
inference(fof_nnf,[status(thm)],[existence_m1_subset_1]) ).
fof(f_16_2,plain,
! [U_21] :
? [U_20] : element(U_20,U_21),
inference(variable_rename,[status(thm)],[f_16_1]) ).
fof(f_16_3,plain,
! [U_21] : element(sK5(U_21),U_21),
inference(skolemize,[status(esa),new_symbols(skolem,[sK5]),skolemize(U_20,sK5(U_21))],[f_16_2]) ).
cnf(f_16_4,plain,
element(sK5(U_21),U_21),
inference(clausify,[status(thm)],[f_16_3]) ).
fof(f_17_1,plain,
empty(empty_set),
inference(fof_nnf,[status(thm)],[fc1_xboole_0]) ).
cnf(f_17_2,plain,
empty(empty_set),
inference(clausify,[status(thm)],[f_17_1]) ).
fof(f_18_1,plain,
! [A,B] :
( ~ empty(set_union2(A,B))
| empty(A) ),
inference(fof_nnf,[status(thm)],[fc2_xboole_0]) ).
fof(f_18_2,plain,
! [U_23,U_22] :
( ~ empty(set_union2(U_23,U_22))
| empty(U_23) ),
inference(variable_rename,[status(thm)],[f_18_1]) ).
fof(f_18_3,plain,
! [U_23] :
( ! [U_22] : ~ empty(set_union2(U_23,U_22))
| empty(U_23) ),
inference(miniscope,[status(thm)],[f_18_2]) ).
cnf(f_18_4,plain,
( ~ empty(set_union2(U_23,U_22))
| empty(U_23) ),
inference(clausify,[status(thm)],[f_18_3]) ).
fof(f_19_1,plain,
! [A,B] :
( ~ empty(set_union2(B,A))
| empty(A) ),
inference(fof_nnf,[status(thm)],[fc3_xboole_0]) ).
fof(f_19_2,plain,
! [U_25,U_24] :
( ~ empty(set_union2(U_24,U_25))
| empty(U_25) ),
inference(variable_rename,[status(thm)],[f_19_1]) ).
fof(f_19_3,plain,
! [U_25] :
( ! [U_24] : ~ empty(set_union2(U_24,U_25))
| empty(U_25) ),
inference(miniscope,[status(thm)],[f_19_2]) ).
cnf(f_19_4,plain,
( ~ empty(set_union2(U_24,U_25))
| empty(U_25) ),
inference(clausify,[status(thm)],[f_19_3]) ).
fof(f_20_1,plain,
! [A,B] : set_union2(A,A) = A,
inference(fof_nnf,[status(thm)],[idempotence_k2_xboole_0]) ).
fof(f_20_2,plain,
! [U_27,U_26] : set_union2(U_27,U_27) = U_27,
inference(variable_rename,[status(thm)],[f_20_1]) ).
fof(f_20_3,plain,
! [U_27] : set_union2(U_27,U_27) = U_27,
inference(miniscope,[status(thm)],[f_20_2]) ).
cnf(f_20_4,plain,
set_union2(U_27,U_27) = U_27,
inference(clausify,[status(thm)],[f_20_3]) ).
fof(f_21_1,plain,
? [A] :
( function(A)
& relation(A) ),
inference(fof_nnf,[status(thm)],[rc1_funct_1]) ).
fof(f_21_2,plain,
? [U_28] :
( function(U_28)
& relation(U_28) ),
inference(variable_rename,[status(thm)],[f_21_1]) ).
fof(f_21_3,plain,
( function(sK6)
& relation(sK6) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK6]),skolemize(U_28,sK6)],[f_21_2]) ).
cnf(f_21_4,plain,
relation(sK6),
inference(clausify,[status(thm)],[f_21_3]) ).
cnf(f_21_5,plain,
function(sK6),
inference(clausify,[status(thm)],[f_21_3]) ).
fof(f_22_1,plain,
? [A] : empty(A),
inference(fof_nnf,[status(thm)],[rc1_xboole_0]) ).
fof(f_22_2,plain,
? [U_29] : empty(U_29),
inference(variable_rename,[status(thm)],[f_22_1]) ).
fof(f_22_3,plain,
empty(sK7),
inference(skolemize,[status(esa),new_symbols(skolem,[sK7]),skolemize(U_29,sK7)],[f_22_2]) ).
cnf(f_22_4,plain,
empty(sK7),
inference(clausify,[status(thm)],[f_22_3]) ).
fof(f_23_1,plain,
? [A] :
( function(A)
& empty(A)
& relation(A) ),
inference(fof_nnf,[status(thm)],[rc2_funct_1]) ).
fof(f_23_2,plain,
? [U_30] :
( function(U_30)
& empty(U_30)
& relation(U_30) ),
inference(variable_rename,[status(thm)],[f_23_1]) ).
fof(f_23_3,plain,
( function(sK8)
& empty(sK8)
& relation(sK8) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK8]),skolemize(U_30,sK8)],[f_23_2]) ).
cnf(f_23_4,plain,
relation(sK8),
inference(clausify,[status(thm)],[f_23_3]) ).
cnf(f_23_5,plain,
empty(sK8),
inference(clausify,[status(thm)],[f_23_3]) ).
cnf(f_23_6,plain,
function(sK8),
inference(clausify,[status(thm)],[f_23_3]) ).
fof(f_24_1,plain,
? [A] : ~ empty(A),
inference(fof_nnf,[status(thm)],[rc2_xboole_0]) ).
fof(f_24_2,plain,
? [U_31] : ~ empty(U_31),
inference(variable_rename,[status(thm)],[f_24_1]) ).
fof(f_24_3,plain,
~ empty(sK9),
inference(skolemize,[status(esa),new_symbols(skolem,[sK9]),skolemize(U_31,sK9)],[f_24_2]) ).
cnf(f_24_4,plain,
~ empty(sK9),
inference(clausify,[status(thm)],[f_24_3]) ).
fof(f_25_1,plain,
? [A] :
( one_to_one(A)
& function(A)
& relation(A) ),
inference(fof_nnf,[status(thm)],[rc3_funct_1]) ).
fof(f_25_2,plain,
? [U_32] :
( one_to_one(U_32)
& function(U_32)
& relation(U_32) ),
inference(variable_rename,[status(thm)],[f_25_1]) ).
fof(f_25_3,plain,
( one_to_one(sK10)
& function(sK10)
& relation(sK10) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK10]),skolemize(U_32,sK10)],[f_25_2]) ).
cnf(f_25_4,plain,
relation(sK10),
inference(clausify,[status(thm)],[f_25_3]) ).
cnf(f_25_5,plain,
function(sK10),
inference(clausify,[status(thm)],[f_25_3]) ).
cnf(f_25_6,plain,
one_to_one(sK10),
inference(clausify,[status(thm)],[f_25_3]) ).
fof(f_26_1,plain,
! [A,B] : subset(A,A),
inference(fof_nnf,[status(thm)],[reflexivity_r1_tarski]) ).
fof(f_26_2,plain,
! [U_34,U_33] : subset(U_34,U_34),
inference(variable_rename,[status(thm)],[f_26_1]) ).
fof(f_26_3,plain,
! [U_34] : subset(U_34,U_34),
inference(miniscope,[status(thm)],[f_26_2]) ).
cnf(f_26_4,plain,
subset(U_34,U_34),
inference(clausify,[status(thm)],[f_26_3]) ).
fof(f_27_1,plain,
! [A,B] :
( disjoint(B,A)
| ~ disjoint(A,B) ),
inference(fof_nnf,[status(thm)],[symmetry_r1_xboole_0]) ).
fof(f_27_2,plain,
! [U_36,U_35] :
( disjoint(U_35,U_36)
| ~ disjoint(U_36,U_35) ),
inference(variable_rename,[status(thm)],[f_27_1]) ).
cnf(f_27_3,plain,
( disjoint(U_35,U_36)
| ~ disjoint(U_36,U_35) ),
inference(clausify,[status(thm)],[f_27_2]) ).
fof(f_28_1,plain,
! [A] : set_union2(A,empty_set) = A,
inference(fof_nnf,[status(thm)],[t1_boole]) ).
fof(f_28_2,plain,
! [U_37] : set_union2(U_37,empty_set) = U_37,
inference(variable_rename,[status(thm)],[f_28_1]) ).
cnf(f_28_3,plain,
set_union2(U_37,empty_set) = U_37,
inference(clausify,[status(thm)],[f_28_2]) ).
fof(f_29_1,plain,
! [A,B] :
( element(A,B)
| ~ in(A,B) ),
inference(fof_nnf,[status(thm)],[t1_subset]) ).
fof(f_29_2,plain,
! [U_39,U_38] :
( element(U_39,U_38)
| ~ in(U_39,U_38) ),
inference(variable_rename,[status(thm)],[f_29_1]) ).
cnf(f_29_3,plain,
( element(U_39,U_38)
| ~ in(U_39,U_38) ),
inference(clausify,[status(thm)],[f_29_2]) ).
fof(f_30_1,plain,
! [A,B] :
( in(A,B)
| empty(B)
| ~ element(A,B) ),
inference(fof_nnf,[status(thm)],[t2_subset]) ).
fof(f_30_2,plain,
! [U_41,U_40] :
( in(U_41,U_40)
| empty(U_40)
| ~ element(U_41,U_40) ),
inference(variable_rename,[status(thm)],[f_30_1]) ).
cnf(f_30_3,plain,
( in(U_41,U_40)
| empty(U_40)
| ~ element(U_41,U_40) ),
inference(clausify,[status(thm)],[f_30_2]) ).
fof(f_31_1,plain,
! [A,B] :
( ( element(A,powerset(B))
| ~ subset(A,B) )
& ( subset(A,B)
| ~ element(A,powerset(B)) ) ),
inference(fof_nnf,[status(thm)],[t3_subset]) ).
fof(f_31_2,plain,
! [U_43,U_42] :
( ( element(U_43,powerset(U_42))
| ~ subset(U_43,U_42) )
& ( subset(U_43,U_42)
| ~ element(U_43,powerset(U_42)) ) ),
inference(variable_rename,[status(thm)],[f_31_1]) ).
fof(f_31_3,plain,
( ! [U_47,U_45] :
( element(U_47,powerset(U_45))
| ~ subset(U_47,U_45) )
& ! [U_46,U_44] :
( subset(U_46,U_44)
| ~ element(U_46,powerset(U_44)) ) ),
inference(miniscope,[status(thm)],[f_31_2]) ).
cnf(f_31_4,plain,
( subset(U_46,U_44)
| ~ element(U_46,powerset(U_44)) ),
inference(clausify,[status(thm)],[f_31_3]) ).
cnf(f_31_5,plain,
( element(U_47,powerset(U_45))
| ~ subset(U_47,U_45) ),
inference(clausify,[status(thm)],[f_31_3]) ).
fof(f_32_1,plain,
! [A,B,C] :
( element(A,C)
| ~ element(B,powerset(C))
| ~ in(A,B) ),
inference(fof_nnf,[status(thm)],[t4_subset]) ).
fof(f_32_2,plain,
! [U_50,U_49,U_48] :
( element(U_50,U_48)
| ~ element(U_49,powerset(U_48))
| ~ in(U_50,U_49) ),
inference(variable_rename,[status(thm)],[f_32_1]) ).
cnf(f_32_3,plain,
( element(U_50,U_48)
| ~ element(U_49,powerset(U_48))
| ~ in(U_50,U_49) ),
inference(clausify,[status(thm)],[f_32_2]) ).
fof(f_33_1,plain,
! [A,B,C] :
( ~ empty(C)
| ~ element(B,powerset(C))
| ~ in(A,B) ),
inference(fof_nnf,[status(thm)],[t5_subset]) ).
fof(f_33_2,plain,
! [U_53,U_52,U_51] :
( ~ empty(U_51)
| ~ element(U_52,powerset(U_51))
| ~ in(U_53,U_52) ),
inference(variable_rename,[status(thm)],[f_33_1]) ).
fof(f_33_3,plain,
! [U_53,U_52] :
( ! [U_51] :
( ~ empty(U_51)
| ~ element(U_52,powerset(U_51)) )
| ~ in(U_53,U_52) ),
inference(miniscope,[status(thm)],[f_33_2]) ).
cnf(f_33_4,plain,
( ~ empty(U_51)
| ~ element(U_52,powerset(U_51))
| ~ in(U_53,U_52) ),
inference(clausify,[status(thm)],[f_33_3]) ).
fof(f_34_1,negated_conjecture,
~ ! [A] :
( relation(A)
=> ( well_founded_relation(A)
<=> is_well_founded_in(A,relation_field(A)) ) ),
inference(negate,[status(cth)],[t5_wellord1]) ).
fof(f_34_2,negated_conjecture,
? [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)],[f_34_1]) ).
fof(f_34_3,negated_conjecture,
? [U_54] :
( ( ( ~ well_founded_relation(U_54)
& is_well_founded_in(U_54,relation_field(U_54)) )
| ( ~ is_well_founded_in(U_54,relation_field(U_54))
& well_founded_relation(U_54) ) )
& relation(U_54) ),
inference(variable_rename,[status(thm)],[f_34_2]) ).
fof(f_34_4,negated_conjecture,
( ( ( ~ well_founded_relation(sK11)
& is_well_founded_in(sK11,relation_field(sK11)) )
| ( ~ is_well_founded_in(sK11,relation_field(sK11))
& well_founded_relation(sK11) ) )
& relation(sK11) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK11]),skolemize(U_54,sK11)],[f_34_3]) ).
cnf(f_34_5,negated_conjecture,
relation(sK11),
inference(clausify,[status(thm)],[f_34_4]) ).
cnf(f_34_6,negated_conjecture,
( is_well_founded_in(sK11,relation_field(sK11))
| well_founded_relation(sK11) ),
inference(clausify,[status(thm)],[f_34_4]) ).
cnf(f_34_7,negated_conjecture,
( ~ well_founded_relation(sK11)
| well_founded_relation(sK11) ),
inference(clausify,[status(thm)],[f_34_4]) ).
cnf(f_34_8,negated_conjecture,
( is_well_founded_in(sK11,relation_field(sK11))
| ~ is_well_founded_in(sK11,relation_field(sK11)) ),
inference(clausify,[status(thm)],[f_34_4]) ).
cnf(f_34_9,negated_conjecture,
( ~ well_founded_relation(sK11)
| ~ is_well_founded_in(sK11,relation_field(sK11)) ),
inference(clausify,[status(thm)],[f_34_4]) ).
fof(f_35_1,plain,
! [A] :
( A = empty_set
| ~ empty(A) ),
inference(fof_nnf,[status(thm)],[t6_boole]) ).
fof(f_35_2,plain,
! [U_55] :
( U_55 = empty_set
| ~ empty(U_55) ),
inference(variable_rename,[status(thm)],[f_35_1]) ).
cnf(f_35_3,plain,
( U_55 = empty_set
| ~ empty(U_55) ),
inference(clausify,[status(thm)],[f_35_2]) ).
fof(f_36_1,plain,
! [A,B] :
( ~ empty(B)
| ~ in(A,B) ),
inference(fof_nnf,[status(thm)],[t7_boole]) ).
fof(f_36_2,plain,
! [U_57,U_56] :
( ~ empty(U_56)
| ~ in(U_57,U_56) ),
inference(variable_rename,[status(thm)],[f_36_1]) ).
cnf(f_36_3,plain,
( ~ empty(U_56)
| ~ in(U_57,U_56) ),
inference(clausify,[status(thm)],[f_36_2]) ).
fof(f_37_1,plain,
! [A,B] :
( ~ empty(B)
| A = B
| ~ empty(A) ),
inference(fof_nnf,[status(thm)],[t8_boole]) ).
fof(f_37_2,plain,
! [U_59,U_58] :
( ~ empty(U_58)
| U_59 = U_58
| ~ empty(U_59) ),
inference(variable_rename,[status(thm)],[f_37_1]) ).
fof(f_37_3,plain,
! [U_59] :
( ! [U_58] :
( ~ empty(U_58)
| U_59 = U_58 )
| ~ empty(U_59) ),
inference(miniscope,[status(thm)],[f_37_2]) ).
cnf(f_37_4,plain,
( ~ empty(U_58)
| U_59 = U_58
| ~ empty(U_59) ),
inference(clausify,[status(thm)],[f_37_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_8_2_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_8_2]) ).
cnf(f_9_2_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_9_2]) ).
cnf(f_10_2_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_10_2]) ).
cnf(f_11_2_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_11_2]) ).
cnf(f_12_2_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_12_2]) ).
cnf(f_13_2_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_13_2]) ).
cnf(f_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_34_7_true,negated_conjecture,
$true,
inference(clause_is_true,[status(thm)],[f_34_7]) ).
cnf(f_34_8_true,negated_conjecture,
$true,
inference(clause_is_true,[status(thm)],[f_34_8]) ).
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,
( fiber(Eq_x_0,Eq_x_1) = fiber(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,
( relation_dom(Eq_x_0) = relation_dom(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_8,axiom,
( relation_rng(Eq_x_0) = relation_rng(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_9,axiom,
( powerset(Eq_x_0) = powerset(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_10,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_11,axiom,
( sK2(Eq_x_0) = sK2(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_12,axiom,
( sK3(Eq_x_0,Eq_x_1,Eq_x_2) = sK3(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_13,axiom,
( sK4(Eq_x_0,Eq_x_1) = sK4(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,
( sK5(Eq_x_0) = sK5(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_15,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_16,axiom,
( empty(Eq_y_0)
| ~ empty(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_17,axiom,
( function(Eq_y_0)
| ~ function(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_18,axiom,
( relation(Eq_y_0)
| ~ relation(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_19,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_20,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_21,axiom,
( subset(Eq_y_0,Eq_y_1)
| ~ subset(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_22,axiom,
( disjoint(Eq_y_0,Eq_y_1)
| ~ disjoint(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_23,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(equality_24,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(sat_proved,plain,
$false,
inference(cadical,[status(thm)],[]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU243+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.03 This is a FOF_THM_RFO_SEQ problem
% 0.00/0.03 % 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 : n010.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 23:37:38 UTC 2026
% 0.09/0.35 % CPUTime :
% 75.14/75.47 % SZS status Theorem for theBenchmark
% 75.14/75.47 % SZS output start Proof for theBenchmark
% See solution above
%------------------------------------------------------------------------------