%------------------------------------------------------------------------------
% File : ConnectPP---0.7.2
% Problem : SEU292+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 : n011.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 08:58:52 AM UTC 2026
% Result : Theorem 48.30s 63.48s
% Output : Proof 48.99s
% 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(cc1_relat_1,axiom,
! [A] :
( empty(A)
=> relation(A) ),
file('theBenchmark.p',cc1_relat_1) ).
fof(cc1_relset_1,axiom,
! [A,B,C] :
( element(C,powerset(cartesian_product2(A,B)))
=> relation(C) ),
file('theBenchmark.p',cc1_relset_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(d1_funct_2,axiom,
! [A,B,C] :
( relation_of2_as_subset(C,A,B)
=> ( ( B = empty_set
=> ( ( quasi_total(C,A,B)
<=> C = empty_set )
| A = empty_set ) )
& ( ( B = empty_set
=> A = empty_set )
=> ( quasi_total(C,A,B)
<=> A = relation_dom_as_subset(A,B,C) ) ) ) ),
file('theBenchmark.p',d1_funct_2) ).
fof(dt_k1_funct_1,axiom,
$true,
file('theBenchmark.p',dt_k1_funct_1) ).
fof(dt_k1_relat_1,axiom,
$true,
file('theBenchmark.p',dt_k1_relat_1) ).
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_zfmisc_1,axiom,
$true,
file('theBenchmark.p',dt_k2_zfmisc_1) ).
fof(dt_k4_relset_1,axiom,
! [A,B,C] :
( relation_of2(C,A,B)
=> element(relation_dom_as_subset(A,B,C),powerset(A)) ),
file('theBenchmark.p',dt_k4_relset_1) ).
fof(dt_k5_relat_1,axiom,
! [A,B] :
( ( relation(B)
& relation(A) )
=> relation(relation_composition(A,B)) ),
file('theBenchmark.p',dt_k5_relat_1) ).
fof(dt_m1_relset_1,axiom,
$true,
file('theBenchmark.p',dt_m1_relset_1) ).
fof(dt_m1_subset_1,axiom,
$true,
file('theBenchmark.p',dt_m1_subset_1) ).
fof(dt_m2_relset_1,axiom,
! [A,B,C] :
( relation_of2_as_subset(C,A,B)
=> element(C,powerset(cartesian_product2(A,B))) ),
file('theBenchmark.p',dt_m2_relset_1) ).
fof(existence_m1_relset_1,axiom,
! [A,B] :
? [C] : relation_of2(C,A,B),
file('theBenchmark.p',existence_m1_relset_1) ).
fof(existence_m1_subset_1,axiom,
! [A] :
? [B] : element(B,A),
file('theBenchmark.p',existence_m1_subset_1) ).
fof(existence_m2_relset_1,axiom,
! [A,B] :
? [C] : relation_of2_as_subset(C,A,B),
file('theBenchmark.p',existence_m2_relset_1) ).
fof(fc10_relat_1,axiom,
! [A,B] :
( ( relation(B)
& empty(A) )
=> ( relation(relation_composition(B,A))
& empty(relation_composition(B,A)) ) ),
file('theBenchmark.p',fc10_relat_1) ).
fof(fc12_relat_1,axiom,
( relation_empty_yielding(empty_set)
& relation(empty_set)
& empty(empty_set) ),
file('theBenchmark.p',fc12_relat_1) ).
fof(fc1_funct_1,axiom,
! [A,B] :
( ( function(B)
& relation(B)
& function(A)
& relation(A) )
=> ( function(relation_composition(A,B))
& relation(relation_composition(A,B)) ) ),
file('theBenchmark.p',fc1_funct_1) ).
fof(fc1_subset_1,axiom,
! [A] : ~ empty(powerset(A)),
file('theBenchmark.p',fc1_subset_1) ).
fof(fc1_xboole_0,axiom,
empty(empty_set),
file('theBenchmark.p',fc1_xboole_0) ).
fof(fc4_relat_1,axiom,
( relation(empty_set)
& empty(empty_set) ),
file('theBenchmark.p',fc4_relat_1) ).
fof(fc4_subset_1,axiom,
! [A,B] :
( ( ~ empty(B)
& ~ empty(A) )
=> ~ empty(cartesian_product2(A,B)) ),
file('theBenchmark.p',fc4_subset_1) ).
fof(fc5_relat_1,axiom,
! [A] :
( ( relation(A)
& ~ empty(A) )
=> ~ empty(relation_dom(A)) ),
file('theBenchmark.p',fc5_relat_1) ).
fof(fc7_relat_1,axiom,
! [A] :
( empty(A)
=> ( relation(relation_dom(A))
& empty(relation_dom(A)) ) ),
file('theBenchmark.p',fc7_relat_1) ).
fof(fc9_relat_1,axiom,
! [A,B] :
( ( relation(B)
& empty(A) )
=> ( relation(relation_composition(A,B))
& empty(relation_composition(A,B)) ) ),
file('theBenchmark.p',fc9_relat_1) ).
fof(rc1_funct_1,axiom,
? [A] :
( function(A)
& relation(A) ),
file('theBenchmark.p',rc1_funct_1) ).
fof(rc1_funct_2,axiom,
! [A,B] :
? [C] :
( quasi_total(C,A,B)
& function(C)
& relation(C)
& relation_of2(C,A,B) ),
file('theBenchmark.p',rc1_funct_2) ).
fof(rc1_partfun1,axiom,
? [A] :
( empty(A)
& one_to_one(A)
& function(A)
& relation(A) ),
file('theBenchmark.p',rc1_partfun1) ).
fof(rc1_relat_1,axiom,
? [A] :
( relation(A)
& empty(A) ),
file('theBenchmark.p',rc1_relat_1) ).
fof(rc1_subset_1,axiom,
! [A] :
( ~ empty(A)
=> ? [B] :
( ~ empty(B)
& element(B,powerset(A)) ) ),
file('theBenchmark.p',rc1_subset_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_partfun1,axiom,
! [A,B] :
? [C] :
( function(C)
& relation(C)
& relation_of2(C,A,B) ),
file('theBenchmark.p',rc2_partfun1) ).
fof(rc2_relat_1,axiom,
? [A] :
( relation(A)
& ~ empty(A) ),
file('theBenchmark.p',rc2_relat_1) ).
fof(rc2_subset_1,axiom,
! [A] :
? [B] :
( empty(B)
& element(B,powerset(A)) ),
file('theBenchmark.p',rc2_subset_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(rc3_relat_1,axiom,
? [A] :
( relation_empty_yielding(A)
& relation(A) ),
file('theBenchmark.p',rc3_relat_1) ).
fof(rc4_funct_1,axiom,
? [A] :
( function(A)
& relation_empty_yielding(A)
& relation(A) ),
file('theBenchmark.p',rc4_funct_1) ).
fof(redefinition_k4_relset_1,axiom,
! [A,B,C] :
( relation_of2(C,A,B)
=> relation_dom_as_subset(A,B,C) = relation_dom(C) ),
file('theBenchmark.p',redefinition_k4_relset_1) ).
fof(redefinition_m2_relset_1,axiom,
! [A,B,C] :
( relation_of2_as_subset(C,A,B)
<=> relation_of2(C,A,B) ),
file('theBenchmark.p',redefinition_m2_relset_1) ).
fof(reflexivity_r1_tarski,axiom,
! [A,B] : subset(A,A),
file('theBenchmark.p',reflexivity_r1_tarski) ).
fof(t1_subset,axiom,
! [A,B] :
( in(A,B)
=> element(A,B) ),
file('theBenchmark.p',t1_subset) ).
fof(t21_funct_2,conjecture,
! [A,B,C,D] :
( ( relation_of2_as_subset(D,A,B)
& quasi_total(D,A,B)
& function(D) )
=> ! [E] :
( ( function(E)
& relation(E) )
=> ( in(C,A)
=> ( apply(relation_composition(D,E),C) = apply(E,apply(D,C))
| B = empty_set ) ) ) ),
file('theBenchmark.p',t21_funct_2) ).
fof(t23_funct_1,axiom,
! [A,B] :
( ( function(B)
& relation(B) )
=> ! [C] :
( ( function(C)
& relation(C) )
=> ( in(A,relation_dom(B))
=> apply(relation_composition(B,C),A) = apply(C,apply(B,A)) ) ) ),
file('theBenchmark.p',t23_funct_1) ).
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(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]) ).
fof(f_1_3,plain,
! [U_1,U_0] :
( ~ in(U_0,U_1)
| ~ in(U_1,U_0) ),
inference(definitional_conversion,[status(esa)],[f_1_2]) ).
cnf(f_1_4,plain,
( ~ in(U_0,U_1)
| ~ in(U_1,U_0) ),
inference(clausify,[status(thm)],[f_1_3]) ).
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]) ).
fof(f_2_3,plain,
! [U_2] :
( function(U_2)
| ~ empty(U_2) ),
inference(definitional_conversion,[status(esa)],[f_2_2]) ).
cnf(f_2_4,plain,
( function(U_2)
| ~ empty(U_2) ),
inference(clausify,[status(thm)],[f_2_3]) ).
fof(f_3_1,plain,
! [A] :
( relation(A)
| ~ empty(A) ),
inference(fof_nnf,[status(thm)],[cc1_relat_1]) ).
fof(f_3_2,plain,
! [U_3] :
( relation(U_3)
| ~ empty(U_3) ),
inference(variable_rename,[status(thm)],[f_3_1]) ).
fof(f_3_3,plain,
! [U_3] :
( relation(U_3)
| ~ empty(U_3) ),
inference(definitional_conversion,[status(esa)],[f_3_2]) ).
cnf(f_3_4,plain,
( relation(U_3)
| ~ empty(U_3) ),
inference(clausify,[status(thm)],[f_3_3]) ).
fof(f_4_1,plain,
! [A,B,C] :
( relation(C)
| ~ element(C,powerset(cartesian_product2(A,B))) ),
inference(fof_nnf,[status(thm)],[cc1_relset_1]) ).
fof(f_4_2,plain,
! [U_6,U_5,U_4] :
( relation(U_4)
| ~ element(U_4,powerset(cartesian_product2(U_6,U_5))) ),
inference(variable_rename,[status(thm)],[f_4_1]) ).
fof(f_4_3,plain,
! [U_5,U_6,U_4] :
( relation(U_4)
| ~ element(U_4,powerset(cartesian_product2(U_6,U_5))) ),
inference(definitional_conversion,[status(esa)],[f_4_2]) ).
cnf(f_4_4,plain,
( relation(U_4)
| ~ element(U_4,powerset(cartesian_product2(U_6,U_5))) ),
inference(clausify,[status(thm)],[f_4_3]) ).
fof(f_5_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_5_2,plain,
! [U_7] :
( ( one_to_one(U_7)
& function(U_7)
& relation(U_7) )
| ~ function(U_7)
| ~ empty(U_7)
| ~ relation(U_7) ),
inference(variable_rename,[status(thm)],[f_5_1]) ).
fof(f_5_3,plain,
( ! [U_7] :
( one_to_one(U_7)
| ~ sP0(U_7) )
& ! [U_7] :
( function(U_7)
| ~ sP0(U_7) )
& ! [U_7] :
( relation(U_7)
| ~ sP0(U_7) )
& ! [U_7] :
( sP0(U_7)
| ~ function(U_7)
| ~ empty(U_7)
| ~ relation(U_7) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP0])],[f_5_2]) ).
cnf(f_5_4,plain,
( sP0(U_7)
| ~ function(U_7)
| ~ empty(U_7)
| ~ relation(U_7) ),
inference(clausify,[status(thm)],[f_5_3]) ).
cnf(f_5_5,plain,
( relation(U_7)
| ~ sP0(U_7) ),
inference(clausify,[status(thm)],[f_5_3]) ).
cnf(f_5_6,plain,
( function(U_7)
| ~ sP0(U_7) ),
inference(clausify,[status(thm)],[f_5_3]) ).
cnf(f_5_7,plain,
( one_to_one(U_7)
| ~ sP0(U_7) ),
inference(clausify,[status(thm)],[f_5_3]) ).
fof(f_6_1,plain,
! [A,B,C] :
( ( ( ( ( quasi_total(C,A,B)
| C != empty_set )
& ( C = empty_set
| ~ quasi_total(C,A,B) ) )
| A = empty_set
| B != empty_set )
& ( ( ( quasi_total(C,A,B)
| A != relation_dom_as_subset(A,B,C) )
& ( A = relation_dom_as_subset(A,B,C)
| ~ quasi_total(C,A,B) ) )
| ( A != empty_set
& B = empty_set ) ) )
| ~ relation_of2_as_subset(C,A,B) ),
inference(fof_nnf,[status(thm)],[d1_funct_2]) ).
fof(f_6_2,plain,
! [U_10,U_9,U_8] :
( ( ( ( ( quasi_total(U_8,U_10,U_9)
| U_8 != empty_set )
& ( U_8 = empty_set
| ~ quasi_total(U_8,U_10,U_9) ) )
| U_10 = empty_set
| U_9 != empty_set )
& ( ( ( quasi_total(U_8,U_10,U_9)
| U_10 != relation_dom_as_subset(U_10,U_9,U_8) )
& ( U_10 = relation_dom_as_subset(U_10,U_9,U_8)
| ~ quasi_total(U_8,U_10,U_9) ) )
| ( U_10 != empty_set
& U_9 = empty_set ) ) )
| ~ relation_of2_as_subset(U_8,U_10,U_9) ),
inference(variable_rename,[status(thm)],[f_6_1]) ).
fof(f_6_3,plain,
( ! [U_9,U_8,U_10] :
( quasi_total(U_8,U_10,U_9)
| U_8 != empty_set
| ~ sP3(U_9,U_8,U_10) )
& ! [U_9,U_8,U_10] :
( U_8 = empty_set
| ~ quasi_total(U_8,U_10,U_9)
| ~ sP3(U_9,U_8,U_10) )
& ! [U_9,U_8,U_10] :
( quasi_total(U_8,U_10,U_9)
| U_10 != relation_dom_as_subset(U_10,U_9,U_8)
| ~ sP2(U_9,U_8,U_10) )
& ! [U_9,U_8,U_10] :
( U_10 = relation_dom_as_subset(U_10,U_9,U_8)
| ~ quasi_total(U_8,U_10,U_9)
| ~ sP2(U_9,U_8,U_10) )
& ! [U_9,U_10] :
( U_10 != empty_set
| ~ sP1(U_9,U_10) )
& ! [U_9,U_10] :
( U_9 = empty_set
| ~ sP1(U_9,U_10) )
& ! [U_9,U_8,U_10] :
( sP3(U_9,U_8,U_10)
| U_10 = empty_set
| U_9 != empty_set
| ~ sP4(U_9,U_8,U_10) )
& ! [U_9,U_8,U_10] :
( sP2(U_9,U_8,U_10)
| sP1(U_9,U_10)
| ~ sP4(U_9,U_8,U_10) )
& ! [U_9,U_8,U_10] :
( sP4(U_9,U_8,U_10)
| ~ relation_of2_as_subset(U_8,U_10,U_9) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP1,sP2,sP3,sP4])],[f_6_2]) ).
cnf(f_6_4,plain,
( sP4(U_9,U_8,U_10)
| ~ relation_of2_as_subset(U_8,U_10,U_9) ),
inference(clausify,[status(thm)],[f_6_3]) ).
cnf(f_6_5,plain,
( sP2(U_9,U_8,U_10)
| sP1(U_9,U_10)
| ~ sP4(U_9,U_8,U_10) ),
inference(clausify,[status(thm)],[f_6_3]) ).
cnf(f_6_6,plain,
( sP3(U_9,U_8,U_10)
| U_10 = empty_set
| U_9 != empty_set
| ~ sP4(U_9,U_8,U_10) ),
inference(clausify,[status(thm)],[f_6_3]) ).
cnf(f_6_7,plain,
( U_9 = empty_set
| ~ sP1(U_9,U_10) ),
inference(clausify,[status(thm)],[f_6_3]) ).
cnf(f_6_8,plain,
( U_10 != empty_set
| ~ sP1(U_9,U_10) ),
inference(clausify,[status(thm)],[f_6_3]) ).
cnf(f_6_9,plain,
( U_10 = relation_dom_as_subset(U_10,U_9,U_8)
| ~ quasi_total(U_8,U_10,U_9)
| ~ sP2(U_9,U_8,U_10) ),
inference(clausify,[status(thm)],[f_6_3]) ).
cnf(f_6_10,plain,
( quasi_total(U_8,U_10,U_9)
| U_10 != relation_dom_as_subset(U_10,U_9,U_8)
| ~ sP2(U_9,U_8,U_10) ),
inference(clausify,[status(thm)],[f_6_3]) ).
cnf(f_6_11,plain,
( U_8 = empty_set
| ~ quasi_total(U_8,U_10,U_9)
| ~ sP3(U_9,U_8,U_10) ),
inference(clausify,[status(thm)],[f_6_3]) ).
cnf(f_6_12,plain,
( quasi_total(U_8,U_10,U_9)
| U_8 != empty_set
| ~ sP3(U_9,U_8,U_10) ),
inference(clausify,[status(thm)],[f_6_3]) ).
fof(f_7_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_k1_funct_1]) ).
fof(f_7_2,plain,
$true,
inference(definitional_conversion,[status(esa)],[f_7_1]) ).
cnf(f_7_3,plain,
$true,
inference(clausify,[status(thm)],[f_7_2]) ).
fof(f_8_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_k1_relat_1]) ).
fof(f_8_2,plain,
$true,
inference(definitional_conversion,[status(esa)],[f_8_1]) ).
cnf(f_8_3,plain,
$true,
inference(clausify,[status(thm)],[f_8_2]) ).
fof(f_9_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_k1_xboole_0]) ).
fof(f_9_2,plain,
$true,
inference(definitional_conversion,[status(esa)],[f_9_1]) ).
cnf(f_9_3,plain,
$true,
inference(clausify,[status(thm)],[f_9_2]) ).
fof(f_10_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_k1_zfmisc_1]) ).
fof(f_10_2,plain,
$true,
inference(definitional_conversion,[status(esa)],[f_10_1]) ).
cnf(f_10_3,plain,
$true,
inference(clausify,[status(thm)],[f_10_2]) ).
fof(f_11_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_k2_zfmisc_1]) ).
fof(f_11_2,plain,
$true,
inference(definitional_conversion,[status(esa)],[f_11_1]) ).
cnf(f_11_3,plain,
$true,
inference(clausify,[status(thm)],[f_11_2]) ).
fof(f_12_1,plain,
! [A,B,C] :
( element(relation_dom_as_subset(A,B,C),powerset(A))
| ~ relation_of2(C,A,B) ),
inference(fof_nnf,[status(thm)],[dt_k4_relset_1]) ).
fof(f_12_2,plain,
! [U_13,U_12,U_11] :
( element(relation_dom_as_subset(U_13,U_12,U_11),powerset(U_13))
| ~ relation_of2(U_11,U_13,U_12) ),
inference(variable_rename,[status(thm)],[f_12_1]) ).
fof(f_12_3,plain,
! [U_13,U_11,U_12] :
( element(relation_dom_as_subset(U_13,U_12,U_11),powerset(U_13))
| ~ relation_of2(U_11,U_13,U_12) ),
inference(definitional_conversion,[status(esa)],[f_12_2]) ).
cnf(f_12_4,plain,
( element(relation_dom_as_subset(U_13,U_12,U_11),powerset(U_13))
| ~ relation_of2(U_11,U_13,U_12) ),
inference(clausify,[status(thm)],[f_12_3]) ).
fof(f_13_1,plain,
! [A,B] :
( relation(relation_composition(A,B))
| ~ relation(B)
| ~ relation(A) ),
inference(fof_nnf,[status(thm)],[dt_k5_relat_1]) ).
fof(f_13_2,plain,
! [U_15,U_14] :
( relation(relation_composition(U_15,U_14))
| ~ relation(U_14)
| ~ relation(U_15) ),
inference(variable_rename,[status(thm)],[f_13_1]) ).
fof(f_13_3,plain,
! [U_14,U_15] :
( relation(relation_composition(U_15,U_14))
| ~ relation(U_14)
| ~ relation(U_15) ),
inference(definitional_conversion,[status(esa)],[f_13_2]) ).
cnf(f_13_4,plain,
( relation(relation_composition(U_15,U_14))
| ~ relation(U_14)
| ~ relation(U_15) ),
inference(clausify,[status(thm)],[f_13_3]) ).
fof(f_14_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_m1_relset_1]) ).
fof(f_14_2,plain,
$true,
inference(definitional_conversion,[status(esa)],[f_14_1]) ).
cnf(f_14_3,plain,
$true,
inference(clausify,[status(thm)],[f_14_2]) ).
fof(f_15_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_m1_subset_1]) ).
fof(f_15_2,plain,
$true,
inference(definitional_conversion,[status(esa)],[f_15_1]) ).
cnf(f_15_3,plain,
$true,
inference(clausify,[status(thm)],[f_15_2]) ).
fof(f_16_1,plain,
! [A,B,C] :
( element(C,powerset(cartesian_product2(A,B)))
| ~ relation_of2_as_subset(C,A,B) ),
inference(fof_nnf,[status(thm)],[dt_m2_relset_1]) ).
fof(f_16_2,plain,
! [U_18,U_17,U_16] :
( element(U_16,powerset(cartesian_product2(U_18,U_17)))
| ~ relation_of2_as_subset(U_16,U_18,U_17) ),
inference(variable_rename,[status(thm)],[f_16_1]) ).
fof(f_16_3,plain,
! [U_18,U_17,U_16] :
( element(U_16,powerset(cartesian_product2(U_18,U_17)))
| ~ relation_of2_as_subset(U_16,U_18,U_17) ),
inference(definitional_conversion,[status(esa)],[f_16_2]) ).
cnf(f_16_4,plain,
( element(U_16,powerset(cartesian_product2(U_18,U_17)))
| ~ relation_of2_as_subset(U_16,U_18,U_17) ),
inference(clausify,[status(thm)],[f_16_3]) ).
fof(f_17_1,plain,
! [A,B] :
? [C] : relation_of2(C,A,B),
inference(fof_nnf,[status(thm)],[existence_m1_relset_1]) ).
fof(f_17_2,plain,
! [U_21,U_20] :
? [U_19] : relation_of2(U_19,U_21,U_20),
inference(variable_rename,[status(thm)],[f_17_1]) ).
fof(f_17_3,plain,
! [U_21,U_20] : relation_of2(sK1(U_21,U_20),U_21,U_20),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(U_19,sK1(U_21,U_20))],[f_17_2]) ).
fof(f_17_4,plain,
! [U_20,U_21] : relation_of2(sK1(U_21,U_20),U_21,U_20),
inference(definitional_conversion,[status(esa)],[f_17_3]) ).
cnf(f_17_5,plain,
relation_of2(sK1(U_21,U_20),U_21,U_20),
inference(clausify,[status(thm)],[f_17_4]) ).
fof(f_18_1,plain,
! [A] :
? [B] : element(B,A),
inference(fof_nnf,[status(thm)],[existence_m1_subset_1]) ).
fof(f_18_2,plain,
! [U_23] :
? [U_22] : element(U_22,U_23),
inference(variable_rename,[status(thm)],[f_18_1]) ).
fof(f_18_3,plain,
! [U_23] : element(sK2(U_23),U_23),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2]),skolemize(U_22,sK2(U_23))],[f_18_2]) ).
fof(f_18_4,plain,
! [U_23] : element(sK2(U_23),U_23),
inference(definitional_conversion,[status(esa)],[f_18_3]) ).
cnf(f_18_5,plain,
element(sK2(U_23),U_23),
inference(clausify,[status(thm)],[f_18_4]) ).
fof(f_19_1,plain,
! [A,B] :
? [C] : relation_of2_as_subset(C,A,B),
inference(fof_nnf,[status(thm)],[existence_m2_relset_1]) ).
fof(f_19_2,plain,
! [U_26,U_25] :
? [U_24] : relation_of2_as_subset(U_24,U_26,U_25),
inference(variable_rename,[status(thm)],[f_19_1]) ).
fof(f_19_3,plain,
! [U_26,U_25] : relation_of2_as_subset(sK3(U_26,U_25),U_26,U_25),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3]),skolemize(U_24,sK3(U_26,U_25))],[f_19_2]) ).
fof(f_19_4,plain,
! [U_25,U_26] : relation_of2_as_subset(sK3(U_26,U_25),U_26,U_25),
inference(definitional_conversion,[status(esa)],[f_19_3]) ).
cnf(f_19_5,plain,
relation_of2_as_subset(sK3(U_26,U_25),U_26,U_25),
inference(clausify,[status(thm)],[f_19_4]) ).
fof(f_20_1,plain,
! [A,B] :
( ( relation(relation_composition(B,A))
& empty(relation_composition(B,A)) )
| ~ relation(B)
| ~ empty(A) ),
inference(fof_nnf,[status(thm)],[fc10_relat_1]) ).
fof(f_20_2,plain,
! [U_28,U_27] :
( ( relation(relation_composition(U_27,U_28))
& empty(relation_composition(U_27,U_28)) )
| ~ relation(U_27)
| ~ empty(U_28) ),
inference(variable_rename,[status(thm)],[f_20_1]) ).
fof(f_20_3,plain,
( ! [U_27,U_28] :
( relation(relation_composition(U_27,U_28))
| ~ sP5(U_27,U_28) )
& ! [U_27,U_28] :
( empty(relation_composition(U_27,U_28))
| ~ sP5(U_27,U_28) )
& ! [U_27,U_28] :
( sP5(U_27,U_28)
| ~ relation(U_27)
| ~ empty(U_28) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP5])],[f_20_2]) ).
cnf(f_20_4,plain,
( sP5(U_27,U_28)
| ~ relation(U_27)
| ~ empty(U_28) ),
inference(clausify,[status(thm)],[f_20_3]) ).
cnf(f_20_5,plain,
( empty(relation_composition(U_27,U_28))
| ~ sP5(U_27,U_28) ),
inference(clausify,[status(thm)],[f_20_3]) ).
cnf(f_20_6,plain,
( relation(relation_composition(U_27,U_28))
| ~ sP5(U_27,U_28) ),
inference(clausify,[status(thm)],[f_20_3]) ).
fof(f_21_1,plain,
( relation_empty_yielding(empty_set)
& relation(empty_set)
& empty(empty_set) ),
inference(fof_nnf,[status(thm)],[fc12_relat_1]) ).
fof(f_21_2,plain,
( relation_empty_yielding(empty_set)
& relation(empty_set)
& empty(empty_set) ),
inference(definitional_conversion,[status(esa)],[f_21_1]) ).
cnf(f_21_3,plain,
empty(empty_set),
inference(clausify,[status(thm)],[f_21_2]) ).
cnf(f_21_4,plain,
relation(empty_set),
inference(clausify,[status(thm)],[f_21_2]) ).
cnf(f_21_5,plain,
relation_empty_yielding(empty_set),
inference(clausify,[status(thm)],[f_21_2]) ).
fof(f_22_1,plain,
! [A,B] :
( ( function(relation_composition(A,B))
& relation(relation_composition(A,B)) )
| ~ function(B)
| ~ relation(B)
| ~ function(A)
| ~ relation(A) ),
inference(fof_nnf,[status(thm)],[fc1_funct_1]) ).
fof(f_22_2,plain,
! [U_30,U_29] :
( ( function(relation_composition(U_30,U_29))
& relation(relation_composition(U_30,U_29)) )
| ~ function(U_29)
| ~ relation(U_29)
| ~ function(U_30)
| ~ relation(U_30) ),
inference(variable_rename,[status(thm)],[f_22_1]) ).
fof(f_22_3,plain,
( ! [U_30,U_29] :
( function(relation_composition(U_30,U_29))
| ~ sP6(U_30,U_29) )
& ! [U_30,U_29] :
( relation(relation_composition(U_30,U_29))
| ~ sP6(U_30,U_29) )
& ! [U_30,U_29] :
( sP6(U_30,U_29)
| ~ function(U_29)
| ~ relation(U_29)
| ~ function(U_30)
| ~ relation(U_30) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP6])],[f_22_2]) ).
cnf(f_22_4,plain,
( sP6(U_30,U_29)
| ~ function(U_29)
| ~ relation(U_29)
| ~ function(U_30)
| ~ relation(U_30) ),
inference(clausify,[status(thm)],[f_22_3]) ).
cnf(f_22_5,plain,
( relation(relation_composition(U_30,U_29))
| ~ sP6(U_30,U_29) ),
inference(clausify,[status(thm)],[f_22_3]) ).
cnf(f_22_6,plain,
( function(relation_composition(U_30,U_29))
| ~ sP6(U_30,U_29) ),
inference(clausify,[status(thm)],[f_22_3]) ).
fof(f_23_1,plain,
! [A] : ~ empty(powerset(A)),
inference(fof_nnf,[status(thm)],[fc1_subset_1]) ).
fof(f_23_2,plain,
! [U_31] : ~ empty(powerset(U_31)),
inference(variable_rename,[status(thm)],[f_23_1]) ).
fof(f_23_3,plain,
! [U_31] : ~ empty(powerset(U_31)),
inference(definitional_conversion,[status(esa)],[f_23_2]) ).
cnf(f_23_4,plain,
~ empty(powerset(U_31)),
inference(clausify,[status(thm)],[f_23_3]) ).
fof(f_24_1,plain,
empty(empty_set),
inference(fof_nnf,[status(thm)],[fc1_xboole_0]) ).
fof(f_24_2,plain,
empty(empty_set),
inference(definitional_conversion,[status(esa)],[f_24_1]) ).
cnf(f_24_3,plain,
empty(empty_set),
inference(clausify,[status(thm)],[f_24_2]) ).
fof(f_25_1,plain,
( relation(empty_set)
& empty(empty_set) ),
inference(fof_nnf,[status(thm)],[fc4_relat_1]) ).
fof(f_25_2,plain,
( relation(empty_set)
& empty(empty_set) ),
inference(definitional_conversion,[status(esa)],[f_25_1]) ).
cnf(f_25_3,plain,
empty(empty_set),
inference(clausify,[status(thm)],[f_25_2]) ).
cnf(f_25_4,plain,
relation(empty_set),
inference(clausify,[status(thm)],[f_25_2]) ).
fof(f_26_1,plain,
! [A,B] :
( ~ empty(cartesian_product2(A,B))
| empty(B)
| empty(A) ),
inference(fof_nnf,[status(thm)],[fc4_subset_1]) ).
fof(f_26_2,plain,
! [U_33,U_32] :
( ~ empty(cartesian_product2(U_33,U_32))
| empty(U_32)
| empty(U_33) ),
inference(variable_rename,[status(thm)],[f_26_1]) ).
fof(f_26_3,plain,
! [U_32,U_33] :
( ~ empty(cartesian_product2(U_33,U_32))
| empty(U_32)
| empty(U_33) ),
inference(definitional_conversion,[status(esa)],[f_26_2]) ).
cnf(f_26_4,plain,
( ~ empty(cartesian_product2(U_33,U_32))
| empty(U_32)
| empty(U_33) ),
inference(clausify,[status(thm)],[f_26_3]) ).
fof(f_27_1,plain,
! [A] :
( ~ empty(relation_dom(A))
| ~ relation(A)
| empty(A) ),
inference(fof_nnf,[status(thm)],[fc5_relat_1]) ).
fof(f_27_2,plain,
! [U_34] :
( ~ empty(relation_dom(U_34))
| ~ relation(U_34)
| empty(U_34) ),
inference(variable_rename,[status(thm)],[f_27_1]) ).
fof(f_27_3,plain,
! [U_34] :
( ~ empty(relation_dom(U_34))
| ~ relation(U_34)
| empty(U_34) ),
inference(definitional_conversion,[status(esa)],[f_27_2]) ).
cnf(f_27_4,plain,
( ~ empty(relation_dom(U_34))
| ~ relation(U_34)
| empty(U_34) ),
inference(clausify,[status(thm)],[f_27_3]) ).
fof(f_28_1,plain,
! [A] :
( ( relation(relation_dom(A))
& empty(relation_dom(A)) )
| ~ empty(A) ),
inference(fof_nnf,[status(thm)],[fc7_relat_1]) ).
fof(f_28_2,plain,
! [U_35] :
( ( relation(relation_dom(U_35))
& empty(relation_dom(U_35)) )
| ~ empty(U_35) ),
inference(variable_rename,[status(thm)],[f_28_1]) ).
fof(f_28_3,plain,
( ! [U_35] :
( relation(relation_dom(U_35))
| ~ sP7(U_35) )
& ! [U_35] :
( empty(relation_dom(U_35))
| ~ sP7(U_35) )
& ! [U_35] :
( sP7(U_35)
| ~ empty(U_35) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP7])],[f_28_2]) ).
cnf(f_28_4,plain,
( sP7(U_35)
| ~ empty(U_35) ),
inference(clausify,[status(thm)],[f_28_3]) ).
cnf(f_28_5,plain,
( empty(relation_dom(U_35))
| ~ sP7(U_35) ),
inference(clausify,[status(thm)],[f_28_3]) ).
cnf(f_28_6,plain,
( relation(relation_dom(U_35))
| ~ sP7(U_35) ),
inference(clausify,[status(thm)],[f_28_3]) ).
fof(f_29_1,plain,
! [A,B] :
( ( relation(relation_composition(A,B))
& empty(relation_composition(A,B)) )
| ~ relation(B)
| ~ empty(A) ),
inference(fof_nnf,[status(thm)],[fc9_relat_1]) ).
fof(f_29_2,plain,
! [U_37,U_36] :
( ( relation(relation_composition(U_37,U_36))
& empty(relation_composition(U_37,U_36)) )
| ~ relation(U_36)
| ~ empty(U_37) ),
inference(variable_rename,[status(thm)],[f_29_1]) ).
fof(f_29_3,plain,
( ! [U_37,U_36] :
( relation(relation_composition(U_37,U_36))
| ~ sP8(U_37,U_36) )
& ! [U_37,U_36] :
( empty(relation_composition(U_37,U_36))
| ~ sP8(U_37,U_36) )
& ! [U_37,U_36] :
( sP8(U_37,U_36)
| ~ relation(U_36)
| ~ empty(U_37) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP8])],[f_29_2]) ).
cnf(f_29_4,plain,
( sP8(U_37,U_36)
| ~ relation(U_36)
| ~ empty(U_37) ),
inference(clausify,[status(thm)],[f_29_3]) ).
cnf(f_29_5,plain,
( empty(relation_composition(U_37,U_36))
| ~ sP8(U_37,U_36) ),
inference(clausify,[status(thm)],[f_29_3]) ).
cnf(f_29_6,plain,
( relation(relation_composition(U_37,U_36))
| ~ sP8(U_37,U_36) ),
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_38] :
( function(U_38)
& relation(U_38) ),
inference(variable_rename,[status(thm)],[f_30_1]) ).
fof(f_30_3,plain,
( function(sK4)
& relation(sK4) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4]),skolemize(U_38,sK4)],[f_30_2]) ).
fof(f_30_4,plain,
( function(sK4)
& relation(sK4) ),
inference(definitional_conversion,[status(esa)],[f_30_3]) ).
cnf(f_30_5,plain,
relation(sK4),
inference(clausify,[status(thm)],[f_30_4]) ).
cnf(f_30_6,plain,
function(sK4),
inference(clausify,[status(thm)],[f_30_4]) ).
fof(f_31_1,plain,
! [A,B] :
? [C] :
( quasi_total(C,A,B)
& function(C)
& relation(C)
& relation_of2(C,A,B) ),
inference(fof_nnf,[status(thm)],[rc1_funct_2]) ).
fof(f_31_2,plain,
! [U_41,U_40] :
? [U_39] :
( quasi_total(U_39,U_41,U_40)
& function(U_39)
& relation(U_39)
& relation_of2(U_39,U_41,U_40) ),
inference(variable_rename,[status(thm)],[f_31_1]) ).
fof(f_31_3,plain,
! [U_41,U_40] :
( quasi_total(sK5(U_41,U_40),U_41,U_40)
& function(sK5(U_41,U_40))
& relation(sK5(U_41,U_40))
& relation_of2(sK5(U_41,U_40),U_41,U_40) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK5]),skolemize(U_39,sK5(U_41,U_40))],[f_31_2]) ).
fof(f_31_4,plain,
( ! [U_41,U_40] : quasi_total(sK5(U_41,U_40),U_41,U_40)
& ! [U_41,U_40] : function(sK5(U_41,U_40))
& ! [U_41,U_40] : relation(sK5(U_41,U_40))
& ! [U_41,U_40] : relation_of2(sK5(U_41,U_40),U_41,U_40) ),
inference(definitional_conversion,[status(esa)],[f_31_3]) ).
cnf(f_31_5,plain,
relation_of2(sK5(U_41,U_40),U_41,U_40),
inference(clausify,[status(thm)],[f_31_4]) ).
cnf(f_31_6,plain,
relation(sK5(U_41,U_40)),
inference(clausify,[status(thm)],[f_31_4]) ).
cnf(f_31_7,plain,
function(sK5(U_41,U_40)),
inference(clausify,[status(thm)],[f_31_4]) ).
cnf(f_31_8,plain,
quasi_total(sK5(U_41,U_40),U_41,U_40),
inference(clausify,[status(thm)],[f_31_4]) ).
fof(f_32_1,plain,
? [A] :
( empty(A)
& one_to_one(A)
& function(A)
& relation(A) ),
inference(fof_nnf,[status(thm)],[rc1_partfun1]) ).
fof(f_32_2,plain,
? [U_42] :
( empty(U_42)
& one_to_one(U_42)
& function(U_42)
& relation(U_42) ),
inference(variable_rename,[status(thm)],[f_32_1]) ).
fof(f_32_3,plain,
( empty(sK6)
& one_to_one(sK6)
& function(sK6)
& relation(sK6) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK6]),skolemize(U_42,sK6)],[f_32_2]) ).
fof(f_32_4,plain,
( empty(sK6)
& one_to_one(sK6)
& function(sK6)
& relation(sK6) ),
inference(definitional_conversion,[status(esa)],[f_32_3]) ).
cnf(f_32_5,plain,
relation(sK6),
inference(clausify,[status(thm)],[f_32_4]) ).
cnf(f_32_6,plain,
function(sK6),
inference(clausify,[status(thm)],[f_32_4]) ).
cnf(f_32_7,plain,
one_to_one(sK6),
inference(clausify,[status(thm)],[f_32_4]) ).
cnf(f_32_8,plain,
empty(sK6),
inference(clausify,[status(thm)],[f_32_4]) ).
fof(f_33_1,plain,
? [A] :
( relation(A)
& empty(A) ),
inference(fof_nnf,[status(thm)],[rc1_relat_1]) ).
fof(f_33_2,plain,
? [U_43] :
( relation(U_43)
& empty(U_43) ),
inference(variable_rename,[status(thm)],[f_33_1]) ).
fof(f_33_3,plain,
( relation(sK7)
& empty(sK7) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK7]),skolemize(U_43,sK7)],[f_33_2]) ).
fof(f_33_4,plain,
( relation(sK7)
& empty(sK7) ),
inference(definitional_conversion,[status(esa)],[f_33_3]) ).
cnf(f_33_5,plain,
empty(sK7),
inference(clausify,[status(thm)],[f_33_4]) ).
cnf(f_33_6,plain,
relation(sK7),
inference(clausify,[status(thm)],[f_33_4]) ).
fof(f_34_1,plain,
! [A] :
( ? [B] :
( ~ empty(B)
& element(B,powerset(A)) )
| empty(A) ),
inference(fof_nnf,[status(thm)],[rc1_subset_1]) ).
fof(f_34_2,plain,
! [U_45] :
( ? [U_44] :
( ~ empty(U_44)
& element(U_44,powerset(U_45)) )
| empty(U_45) ),
inference(variable_rename,[status(thm)],[f_34_1]) ).
fof(f_34_3,plain,
! [U_45] :
( ( ~ empty(sK8(U_45))
& element(sK8(U_45),powerset(U_45)) )
| empty(U_45) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK8]),skolemize(U_44,sK8(U_45))],[f_34_2]) ).
fof(f_34_4,plain,
( ! [U_45] :
( ~ empty(sK8(U_45))
| ~ sP9(U_45) )
& ! [U_45] :
( element(sK8(U_45),powerset(U_45))
| ~ sP9(U_45) )
& ! [U_45] :
( sP9(U_45)
| empty(U_45) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP9])],[f_34_3]) ).
cnf(f_34_5,plain,
( sP9(U_45)
| empty(U_45) ),
inference(clausify,[status(thm)],[f_34_4]) ).
cnf(f_34_6,plain,
( element(sK8(U_45),powerset(U_45))
| ~ sP9(U_45) ),
inference(clausify,[status(thm)],[f_34_4]) ).
cnf(f_34_7,plain,
( ~ empty(sK8(U_45))
| ~ sP9(U_45) ),
inference(clausify,[status(thm)],[f_34_4]) ).
fof(f_35_1,plain,
? [A] : empty(A),
inference(fof_nnf,[status(thm)],[rc1_xboole_0]) ).
fof(f_35_2,plain,
? [U_46] : empty(U_46),
inference(variable_rename,[status(thm)],[f_35_1]) ).
fof(f_35_3,plain,
empty(sK9),
inference(skolemize,[status(esa),new_symbols(skolem,[sK9]),skolemize(U_46,sK9)],[f_35_2]) ).
fof(f_35_4,plain,
empty(sK9),
inference(definitional_conversion,[status(esa)],[f_35_3]) ).
cnf(f_35_5,plain,
empty(sK9),
inference(clausify,[status(thm)],[f_35_4]) ).
fof(f_36_1,plain,
? [A] :
( function(A)
& empty(A)
& relation(A) ),
inference(fof_nnf,[status(thm)],[rc2_funct_1]) ).
fof(f_36_2,plain,
? [U_47] :
( function(U_47)
& empty(U_47)
& relation(U_47) ),
inference(variable_rename,[status(thm)],[f_36_1]) ).
fof(f_36_3,plain,
( function(sK10)
& empty(sK10)
& relation(sK10) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK10]),skolemize(U_47,sK10)],[f_36_2]) ).
fof(f_36_4,plain,
( function(sK10)
& empty(sK10)
& relation(sK10) ),
inference(definitional_conversion,[status(esa)],[f_36_3]) ).
cnf(f_36_5,plain,
relation(sK10),
inference(clausify,[status(thm)],[f_36_4]) ).
cnf(f_36_6,plain,
empty(sK10),
inference(clausify,[status(thm)],[f_36_4]) ).
cnf(f_36_7,plain,
function(sK10),
inference(clausify,[status(thm)],[f_36_4]) ).
fof(f_37_1,plain,
! [A,B] :
? [C] :
( function(C)
& relation(C)
& relation_of2(C,A,B) ),
inference(fof_nnf,[status(thm)],[rc2_partfun1]) ).
fof(f_37_2,plain,
! [U_50,U_49] :
? [U_48] :
( function(U_48)
& relation(U_48)
& relation_of2(U_48,U_50,U_49) ),
inference(variable_rename,[status(thm)],[f_37_1]) ).
fof(f_37_3,plain,
! [U_50,U_49] :
( function(sK11(U_50,U_49))
& relation(sK11(U_50,U_49))
& relation_of2(sK11(U_50,U_49),U_50,U_49) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK11]),skolemize(U_48,sK11(U_50,U_49))],[f_37_2]) ).
fof(f_37_4,plain,
( ! [U_49,U_50] : function(sK11(U_50,U_49))
& ! [U_49,U_50] : relation(sK11(U_50,U_49))
& ! [U_49,U_50] : relation_of2(sK11(U_50,U_49),U_50,U_49) ),
inference(definitional_conversion,[status(esa)],[f_37_3]) ).
cnf(f_37_5,plain,
relation_of2(sK11(U_50,U_49),U_50,U_49),
inference(clausify,[status(thm)],[f_37_4]) ).
cnf(f_37_6,plain,
relation(sK11(U_50,U_49)),
inference(clausify,[status(thm)],[f_37_4]) ).
cnf(f_37_7,plain,
function(sK11(U_50,U_49)),
inference(clausify,[status(thm)],[f_37_4]) ).
fof(f_38_1,plain,
? [A] :
( relation(A)
& ~ empty(A) ),
inference(fof_nnf,[status(thm)],[rc2_relat_1]) ).
fof(f_38_2,plain,
? [U_51] :
( relation(U_51)
& ~ empty(U_51) ),
inference(variable_rename,[status(thm)],[f_38_1]) ).
fof(f_38_3,plain,
( relation(sK12)
& ~ empty(sK12) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK12]),skolemize(U_51,sK12)],[f_38_2]) ).
fof(f_38_4,plain,
( relation(sK12)
& ~ empty(sK12) ),
inference(definitional_conversion,[status(esa)],[f_38_3]) ).
cnf(f_38_5,plain,
~ empty(sK12),
inference(clausify,[status(thm)],[f_38_4]) ).
cnf(f_38_6,plain,
relation(sK12),
inference(clausify,[status(thm)],[f_38_4]) ).
fof(f_39_1,plain,
! [A] :
? [B] :
( empty(B)
& element(B,powerset(A)) ),
inference(fof_nnf,[status(thm)],[rc2_subset_1]) ).
fof(f_39_2,plain,
! [U_53] :
? [U_52] :
( empty(U_52)
& element(U_52,powerset(U_53)) ),
inference(variable_rename,[status(thm)],[f_39_1]) ).
fof(f_39_3,plain,
! [U_53] :
( empty(sK13(U_53))
& element(sK13(U_53),powerset(U_53)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK13]),skolemize(U_52,sK13(U_53))],[f_39_2]) ).
fof(f_39_4,plain,
( ! [U_53] : empty(sK13(U_53))
& ! [U_53] : element(sK13(U_53),powerset(U_53)) ),
inference(definitional_conversion,[status(esa)],[f_39_3]) ).
cnf(f_39_5,plain,
element(sK13(U_53),powerset(U_53)),
inference(clausify,[status(thm)],[f_39_4]) ).
cnf(f_39_6,plain,
empty(sK13(U_53)),
inference(clausify,[status(thm)],[f_39_4]) ).
fof(f_40_1,plain,
? [A] : ~ empty(A),
inference(fof_nnf,[status(thm)],[rc2_xboole_0]) ).
fof(f_40_2,plain,
? [U_54] : ~ empty(U_54),
inference(variable_rename,[status(thm)],[f_40_1]) ).
fof(f_40_3,plain,
~ empty(sK14),
inference(skolemize,[status(esa),new_symbols(skolem,[sK14]),skolemize(U_54,sK14)],[f_40_2]) ).
fof(f_40_4,plain,
~ empty(sK14),
inference(definitional_conversion,[status(esa)],[f_40_3]) ).
cnf(f_40_5,plain,
~ empty(sK14),
inference(clausify,[status(thm)],[f_40_4]) ).
fof(f_41_1,plain,
? [A] :
( one_to_one(A)
& function(A)
& relation(A) ),
inference(fof_nnf,[status(thm)],[rc3_funct_1]) ).
fof(f_41_2,plain,
? [U_55] :
( one_to_one(U_55)
& function(U_55)
& relation(U_55) ),
inference(variable_rename,[status(thm)],[f_41_1]) ).
fof(f_41_3,plain,
( one_to_one(sK15)
& function(sK15)
& relation(sK15) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK15]),skolemize(U_55,sK15)],[f_41_2]) ).
fof(f_41_4,plain,
( one_to_one(sK15)
& function(sK15)
& relation(sK15) ),
inference(definitional_conversion,[status(esa)],[f_41_3]) ).
cnf(f_41_5,plain,
relation(sK15),
inference(clausify,[status(thm)],[f_41_4]) ).
cnf(f_41_6,plain,
function(sK15),
inference(clausify,[status(thm)],[f_41_4]) ).
cnf(f_41_7,plain,
one_to_one(sK15),
inference(clausify,[status(thm)],[f_41_4]) ).
fof(f_42_1,plain,
? [A] :
( relation_empty_yielding(A)
& relation(A) ),
inference(fof_nnf,[status(thm)],[rc3_relat_1]) ).
fof(f_42_2,plain,
? [U_56] :
( relation_empty_yielding(U_56)
& relation(U_56) ),
inference(variable_rename,[status(thm)],[f_42_1]) ).
fof(f_42_3,plain,
( relation_empty_yielding(sK16)
& relation(sK16) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK16]),skolemize(U_56,sK16)],[f_42_2]) ).
fof(f_42_4,plain,
( relation_empty_yielding(sK16)
& relation(sK16) ),
inference(definitional_conversion,[status(esa)],[f_42_3]) ).
cnf(f_42_5,plain,
relation(sK16),
inference(clausify,[status(thm)],[f_42_4]) ).
cnf(f_42_6,plain,
relation_empty_yielding(sK16),
inference(clausify,[status(thm)],[f_42_4]) ).
fof(f_43_1,plain,
? [A] :
( function(A)
& relation_empty_yielding(A)
& relation(A) ),
inference(fof_nnf,[status(thm)],[rc4_funct_1]) ).
fof(f_43_2,plain,
? [U_57] :
( function(U_57)
& relation_empty_yielding(U_57)
& relation(U_57) ),
inference(variable_rename,[status(thm)],[f_43_1]) ).
fof(f_43_3,plain,
( function(sK17)
& relation_empty_yielding(sK17)
& relation(sK17) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK17]),skolemize(U_57,sK17)],[f_43_2]) ).
fof(f_43_4,plain,
( function(sK17)
& relation_empty_yielding(sK17)
& relation(sK17) ),
inference(definitional_conversion,[status(esa)],[f_43_3]) ).
cnf(f_43_5,plain,
relation(sK17),
inference(clausify,[status(thm)],[f_43_4]) ).
cnf(f_43_6,plain,
relation_empty_yielding(sK17),
inference(clausify,[status(thm)],[f_43_4]) ).
cnf(f_43_7,plain,
function(sK17),
inference(clausify,[status(thm)],[f_43_4]) ).
fof(f_44_1,plain,
! [A,B,C] :
( relation_dom_as_subset(A,B,C) = relation_dom(C)
| ~ relation_of2(C,A,B) ),
inference(fof_nnf,[status(thm)],[redefinition_k4_relset_1]) ).
fof(f_44_2,plain,
! [U_60,U_59,U_58] :
( relation_dom_as_subset(U_60,U_59,U_58) = relation_dom(U_58)
| ~ relation_of2(U_58,U_60,U_59) ),
inference(variable_rename,[status(thm)],[f_44_1]) ).
fof(f_44_3,plain,
! [U_58,U_59,U_60] :
( relation_dom_as_subset(U_60,U_59,U_58) = relation_dom(U_58)
| ~ relation_of2(U_58,U_60,U_59) ),
inference(definitional_conversion,[status(esa)],[f_44_2]) ).
cnf(f_44_4,plain,
( relation_dom_as_subset(U_60,U_59,U_58) = relation_dom(U_58)
| ~ relation_of2(U_58,U_60,U_59) ),
inference(clausify,[status(thm)],[f_44_3]) ).
fof(f_45_1,plain,
! [A,B,C] :
( ( relation_of2_as_subset(C,A,B)
| ~ relation_of2(C,A,B) )
& ( relation_of2(C,A,B)
| ~ relation_of2_as_subset(C,A,B) ) ),
inference(fof_nnf,[status(thm)],[redefinition_m2_relset_1]) ).
fof(f_45_2,plain,
! [U_63,U_62,U_61] :
( ( relation_of2_as_subset(U_61,U_63,U_62)
| ~ relation_of2(U_61,U_63,U_62) )
& ( relation_of2(U_61,U_63,U_62)
| ~ relation_of2_as_subset(U_61,U_63,U_62) ) ),
inference(variable_rename,[status(thm)],[f_45_1]) ).
fof(f_45_3,plain,
( ! [U_69,U_67,U_65] :
( relation_of2_as_subset(U_65,U_69,U_67)
| ~ relation_of2(U_65,U_69,U_67) )
& ! [U_68,U_66,U_64] :
( relation_of2(U_64,U_68,U_66)
| ~ relation_of2_as_subset(U_64,U_68,U_66) ) ),
inference(miniscope,[status(thm)],[f_45_2]) ).
fof(f_45_4,plain,
( ! [U_67,U_65,U_69] :
( relation_of2_as_subset(U_65,U_69,U_67)
| ~ relation_of2(U_65,U_69,U_67) )
& ! [U_66,U_64,U_68] :
( relation_of2(U_64,U_68,U_66)
| ~ relation_of2_as_subset(U_64,U_68,U_66) ) ),
inference(definitional_conversion,[status(esa)],[f_45_3]) ).
cnf(f_45_5,plain,
( relation_of2(U_64,U_68,U_66)
| ~ relation_of2_as_subset(U_64,U_68,U_66) ),
inference(clausify,[status(thm)],[f_45_4]) ).
cnf(f_45_6,plain,
( relation_of2_as_subset(U_65,U_69,U_67)
| ~ relation_of2(U_65,U_69,U_67) ),
inference(clausify,[status(thm)],[f_45_4]) ).
fof(f_46_1,plain,
! [A,B] : subset(A,A),
inference(fof_nnf,[status(thm)],[reflexivity_r1_tarski]) ).
fof(f_46_2,plain,
! [U_71,U_70] : subset(U_71,U_71),
inference(variable_rename,[status(thm)],[f_46_1]) ).
fof(f_46_3,plain,
! [U_71] : subset(U_71,U_71),
inference(miniscope,[status(thm)],[f_46_2]) ).
fof(f_46_4,plain,
! [U_71] : subset(U_71,U_71),
inference(definitional_conversion,[status(esa)],[f_46_3]) ).
cnf(f_46_5,plain,
subset(U_71,U_71),
inference(clausify,[status(thm)],[f_46_4]) ).
fof(f_47_1,plain,
! [A,B] :
( element(A,B)
| ~ in(A,B) ),
inference(fof_nnf,[status(thm)],[t1_subset]) ).
fof(f_47_2,plain,
! [U_73,U_72] :
( element(U_73,U_72)
| ~ in(U_73,U_72) ),
inference(variable_rename,[status(thm)],[f_47_1]) ).
fof(f_47_3,plain,
! [U_73,U_72] :
( element(U_73,U_72)
| ~ in(U_73,U_72) ),
inference(definitional_conversion,[status(esa)],[f_47_2]) ).
cnf(f_47_4,plain,
( element(U_73,U_72)
| ~ in(U_73,U_72) ),
inference(clausify,[status(thm)],[f_47_3]) ).
fof(f_48_1,negated_conjecture,
~ ! [A,B,C,D] :
( ( relation_of2_as_subset(D,A,B)
& quasi_total(D,A,B)
& function(D) )
=> ! [E] :
( ( function(E)
& relation(E) )
=> ( in(C,A)
=> ( apply(relation_composition(D,E),C) = apply(E,apply(D,C))
| B = empty_set ) ) ) ),
inference(negate,[status(cth)],[t21_funct_2]) ).
fof(f_48_2,negated_conjecture,
? [A,B,C,D] :
( ? [E] :
( apply(relation_composition(D,E),C) != apply(E,apply(D,C))
& B != empty_set
& in(C,A)
& function(E)
& relation(E) )
& relation_of2_as_subset(D,A,B)
& quasi_total(D,A,B)
& function(D) ),
inference(fof_nnf,[status(thm)],[f_48_1]) ).
fof(f_48_3,negated_conjecture,
? [U_78,U_77,U_76,U_75] :
( ? [U_74] :
( apply(relation_composition(U_75,U_74),U_76) != apply(U_74,apply(U_75,U_76))
& U_77 != empty_set
& in(U_76,U_78)
& function(U_74)
& relation(U_74) )
& relation_of2_as_subset(U_75,U_78,U_77)
& quasi_total(U_75,U_78,U_77)
& function(U_75) ),
inference(variable_rename,[status(thm)],[f_48_2]) ).
fof(f_48_4,negated_conjecture,
? [U_77,U_76,U_75] :
( ? [U_74] :
( apply(relation_composition(U_75,U_74),U_76) != apply(U_74,apply(U_75,U_76))
& U_77 != empty_set
& in(U_76,sK18)
& function(U_74)
& relation(U_74) )
& relation_of2_as_subset(U_75,sK18,U_77)
& quasi_total(U_75,sK18,U_77)
& function(U_75) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK18]),skolemize(U_78,sK18)],[f_48_3]) ).
fof(f_48_5,negated_conjecture,
? [U_76,U_75] :
( ? [U_74] :
( apply(relation_composition(U_75,U_74),U_76) != apply(U_74,apply(U_75,U_76))
& sK19 != empty_set
& in(U_76,sK18)
& function(U_74)
& relation(U_74) )
& relation_of2_as_subset(U_75,sK18,sK19)
& quasi_total(U_75,sK18,sK19)
& function(U_75) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK19]),skolemize(U_77,sK19)],[f_48_4]) ).
fof(f_48_6,negated_conjecture,
? [U_75] :
( ? [U_74] :
( apply(relation_composition(U_75,U_74),sK20) != apply(U_74,apply(U_75,sK20))
& sK19 != empty_set
& in(sK20,sK18)
& function(U_74)
& relation(U_74) )
& relation_of2_as_subset(U_75,sK18,sK19)
& quasi_total(U_75,sK18,sK19)
& function(U_75) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK20]),skolemize(U_76,sK20)],[f_48_5]) ).
fof(f_48_7,negated_conjecture,
( ? [U_74] :
( apply(relation_composition(sK21,U_74),sK20) != apply(U_74,apply(sK21,sK20))
& sK19 != empty_set
& in(sK20,sK18)
& function(U_74)
& relation(U_74) )
& relation_of2_as_subset(sK21,sK18,sK19)
& quasi_total(sK21,sK18,sK19)
& function(sK21) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK21]),skolemize(U_75,sK21)],[f_48_6]) ).
fof(f_48_8,negated_conjecture,
( apply(relation_composition(sK21,sK22),sK20) != apply(sK22,apply(sK21,sK20))
& sK19 != empty_set
& in(sK20,sK18)
& function(sK22)
& relation(sK22)
& relation_of2_as_subset(sK21,sK18,sK19)
& quasi_total(sK21,sK18,sK19)
& function(sK21) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK22]),skolemize(U_74,sK22)],[f_48_7]) ).
fof(f_48_9,negated_conjecture,
( apply(relation_composition(sK21,sK22),sK20) != apply(sK22,apply(sK21,sK20))
& sK19 != empty_set
& in(sK20,sK18)
& function(sK22)
& relation(sK22)
& relation_of2_as_subset(sK21,sK18,sK19)
& quasi_total(sK21,sK18,sK19)
& function(sK21) ),
inference(definitional_conversion,[status(esa)],[f_48_8]) ).
cnf(f_48_10,negated_conjecture,
function(sK21),
inference(clausify,[status(thm)],[f_48_9]) ).
cnf(f_48_11,negated_conjecture,
quasi_total(sK21,sK18,sK19),
inference(clausify,[status(thm)],[f_48_9]) ).
cnf(f_48_12,negated_conjecture,
relation_of2_as_subset(sK21,sK18,sK19),
inference(clausify,[status(thm)],[f_48_9]) ).
cnf(f_48_13,negated_conjecture,
relation(sK22),
inference(clausify,[status(thm)],[f_48_9]) ).
cnf(f_48_14,negated_conjecture,
function(sK22),
inference(clausify,[status(thm)],[f_48_9]) ).
cnf(f_48_15,negated_conjecture,
in(sK20,sK18),
inference(clausify,[status(thm)],[f_48_9]) ).
cnf(f_48_16,negated_conjecture,
sK19 != empty_set,
inference(clausify,[status(thm)],[f_48_9]) ).
cnf(f_48_17,negated_conjecture,
apply(relation_composition(sK21,sK22),sK20) != apply(sK22,apply(sK21,sK20)),
inference(clausify,[status(thm)],[f_48_9]) ).
fof(f_49_1,plain,
! [A,B] :
( ! [C] :
( apply(relation_composition(B,C),A) = apply(C,apply(B,A))
| ~ in(A,relation_dom(B))
| ~ function(C)
| ~ relation(C) )
| ~ function(B)
| ~ relation(B) ),
inference(fof_nnf,[status(thm)],[t23_funct_1]) ).
fof(f_49_2,plain,
! [U_81,U_80] :
( ! [U_79] :
( apply(relation_composition(U_80,U_79),U_81) = apply(U_79,apply(U_80,U_81))
| ~ in(U_81,relation_dom(U_80))
| ~ function(U_79)
| ~ relation(U_79) )
| ~ function(U_80)
| ~ relation(U_80) ),
inference(variable_rename,[status(thm)],[f_49_1]) ).
fof(f_49_3,plain,
! [U_79,U_80,U_81] :
( apply(relation_composition(U_80,U_79),U_81) = apply(U_79,apply(U_80,U_81))
| ~ in(U_81,relation_dom(U_80))
| ~ function(U_79)
| ~ relation(U_79)
| ~ function(U_80)
| ~ relation(U_80) ),
inference(definitional_conversion,[status(esa)],[f_49_2]) ).
cnf(f_49_4,plain,
( apply(relation_composition(U_80,U_79),U_81) = apply(U_79,apply(U_80,U_81))
| ~ in(U_81,relation_dom(U_80))
| ~ function(U_79)
| ~ relation(U_79)
| ~ function(U_80)
| ~ relation(U_80) ),
inference(clausify,[status(thm)],[f_49_3]) ).
fof(f_50_1,plain,
! [A,B] :
( in(A,B)
| empty(B)
| ~ element(A,B) ),
inference(fof_nnf,[status(thm)],[t2_subset]) ).
fof(f_50_2,plain,
! [U_83,U_82] :
( in(U_83,U_82)
| empty(U_82)
| ~ element(U_83,U_82) ),
inference(variable_rename,[status(thm)],[f_50_1]) ).
fof(f_50_3,plain,
! [U_82,U_83] :
( in(U_83,U_82)
| empty(U_82)
| ~ element(U_83,U_82) ),
inference(definitional_conversion,[status(esa)],[f_50_2]) ).
cnf(f_50_4,plain,
( in(U_83,U_82)
| empty(U_82)
| ~ element(U_83,U_82) ),
inference(clausify,[status(thm)],[f_50_3]) ).
fof(f_51_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_51_2,plain,
! [U_85,U_84] :
( ( element(U_85,powerset(U_84))
| ~ subset(U_85,U_84) )
& ( subset(U_85,U_84)
| ~ element(U_85,powerset(U_84)) ) ),
inference(variable_rename,[status(thm)],[f_51_1]) ).
fof(f_51_3,plain,
( ! [U_89,U_87] :
( element(U_89,powerset(U_87))
| ~ subset(U_89,U_87) )
& ! [U_88,U_86] :
( subset(U_88,U_86)
| ~ element(U_88,powerset(U_86)) ) ),
inference(miniscope,[status(thm)],[f_51_2]) ).
fof(f_51_4,plain,
( ! [U_89,U_87] :
( element(U_89,powerset(U_87))
| ~ subset(U_89,U_87) )
& ! [U_88,U_86] :
( subset(U_88,U_86)
| ~ element(U_88,powerset(U_86)) ) ),
inference(definitional_conversion,[status(esa)],[f_51_3]) ).
cnf(f_51_5,plain,
( subset(U_88,U_86)
| ~ element(U_88,powerset(U_86)) ),
inference(clausify,[status(thm)],[f_51_4]) ).
cnf(f_51_6,plain,
( element(U_89,powerset(U_87))
| ~ subset(U_89,U_87) ),
inference(clausify,[status(thm)],[f_51_4]) ).
fof(f_52_1,plain,
! [A,B,C] :
( element(A,C)
| ~ element(B,powerset(C))
| ~ in(A,B) ),
inference(fof_nnf,[status(thm)],[t4_subset]) ).
fof(f_52_2,plain,
! [U_92,U_91,U_90] :
( element(U_92,U_90)
| ~ element(U_91,powerset(U_90))
| ~ in(U_92,U_91) ),
inference(variable_rename,[status(thm)],[f_52_1]) ).
fof(f_52_3,plain,
! [U_90,U_91,U_92] :
( element(U_92,U_90)
| ~ element(U_91,powerset(U_90))
| ~ in(U_92,U_91) ),
inference(definitional_conversion,[status(esa)],[f_52_2]) ).
cnf(f_52_4,plain,
( element(U_92,U_90)
| ~ element(U_91,powerset(U_90))
| ~ in(U_92,U_91) ),
inference(clausify,[status(thm)],[f_52_3]) ).
fof(f_53_1,plain,
! [A,B,C] :
( ~ empty(C)
| ~ element(B,powerset(C))
| ~ in(A,B) ),
inference(fof_nnf,[status(thm)],[t5_subset]) ).
fof(f_53_2,plain,
! [U_95,U_94,U_93] :
( ~ empty(U_93)
| ~ element(U_94,powerset(U_93))
| ~ in(U_95,U_94) ),
inference(variable_rename,[status(thm)],[f_53_1]) ).
fof(f_53_3,plain,
! [U_95,U_94] :
( ! [U_93] :
( ~ empty(U_93)
| ~ element(U_94,powerset(U_93)) )
| ~ in(U_95,U_94) ),
inference(miniscope,[status(thm)],[f_53_2]) ).
fof(f_53_4,plain,
! [U_94,U_93,U_95] :
( ~ empty(U_93)
| ~ element(U_94,powerset(U_93))
| ~ in(U_95,U_94) ),
inference(definitional_conversion,[status(esa)],[f_53_3]) ).
cnf(f_53_5,plain,
( ~ empty(U_93)
| ~ element(U_94,powerset(U_93))
| ~ in(U_95,U_94) ),
inference(clausify,[status(thm)],[f_53_4]) ).
fof(f_54_1,plain,
! [A] :
( A = empty_set
| ~ empty(A) ),
inference(fof_nnf,[status(thm)],[t6_boole]) ).
fof(f_54_2,plain,
! [U_96] :
( U_96 = empty_set
| ~ empty(U_96) ),
inference(variable_rename,[status(thm)],[f_54_1]) ).
fof(f_54_3,plain,
! [U_96] :
( U_96 = empty_set
| ~ empty(U_96) ),
inference(definitional_conversion,[status(esa)],[f_54_2]) ).
cnf(f_54_4,plain,
( U_96 = empty_set
| ~ empty(U_96) ),
inference(clausify,[status(thm)],[f_54_3]) ).
fof(f_55_1,plain,
! [A,B] :
( ~ empty(B)
| ~ in(A,B) ),
inference(fof_nnf,[status(thm)],[t7_boole]) ).
fof(f_55_2,plain,
! [U_98,U_97] :
( ~ empty(U_97)
| ~ in(U_98,U_97) ),
inference(variable_rename,[status(thm)],[f_55_1]) ).
fof(f_55_3,plain,
! [U_97,U_98] :
( ~ empty(U_97)
| ~ in(U_98,U_97) ),
inference(definitional_conversion,[status(esa)],[f_55_2]) ).
cnf(f_55_4,plain,
( ~ empty(U_97)
| ~ in(U_98,U_97) ),
inference(clausify,[status(thm)],[f_55_3]) ).
fof(f_56_1,plain,
! [A,B] :
( ~ empty(B)
| A = B
| ~ empty(A) ),
inference(fof_nnf,[status(thm)],[t8_boole]) ).
fof(f_56_2,plain,
! [U_100,U_99] :
( ~ empty(U_99)
| U_100 = U_99
| ~ empty(U_100) ),
inference(variable_rename,[status(thm)],[f_56_1]) ).
fof(f_56_3,plain,
! [U_100] :
( ! [U_99] :
( ~ empty(U_99)
| U_100 = U_99 )
| ~ empty(U_100) ),
inference(miniscope,[status(thm)],[f_56_2]) ).
fof(f_56_4,plain,
! [U_99,U_100] :
( ~ empty(U_99)
| U_100 = U_99
| ~ empty(U_100) ),
inference(definitional_conversion,[status(esa)],[f_56_3]) ).
cnf(f_56_5,plain,
( ~ empty(U_99)
| U_100 = U_99
| ~ empty(U_100) ),
inference(clausify,[status(thm)],[f_56_4]) ).
cnf(f_7_3_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_7_3]) ).
cnf(f_8_3_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_8_3]) ).
cnf(f_9_3_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_9_3]) ).
cnf(f_10_3_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_10_3]) ).
cnf(f_11_3_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_11_3]) ).
cnf(f_14_3_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_14_3]) ).
cnf(f_15_3_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_15_3]) ).
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,
( 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_5,axiom,
( powerset(Eq_x_0) = powerset(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_6,axiom,
( relation_dom_as_subset(Eq_x_0,Eq_x_1,Eq_x_2) = relation_dom_as_subset(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_7,axiom,
( relation_composition(Eq_x_0,Eq_x_1) = relation_composition(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,
( relation_dom(Eq_x_0) = relation_dom(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_9,axiom,
( apply(Eq_x_0,Eq_x_1) = apply(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| 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) = sK3(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,
( sK5(Eq_x_0,Eq_x_1) = sK5(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,
( sK8(Eq_x_0) = sK8(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_15,axiom,
( sK11(Eq_x_0,Eq_x_1) = sK11(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_16,axiom,
( sK13(Eq_x_0) = sK13(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_17,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_18,axiom,
( empty(Eq_y_0)
| ~ empty(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_19,axiom,
( function(Eq_y_0)
| ~ function(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_20,axiom,
( relation(Eq_y_0)
| ~ relation(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,
( one_to_one(Eq_y_0)
| ~ one_to_one(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_23,axiom,
( relation_of2_as_subset(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ relation_of2_as_subset(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_24,axiom,
( quasi_total(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ quasi_total(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_25,axiom,
( relation_of2(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ relation_of2(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_26,axiom,
( relation_empty_yielding(Eq_y_0)
| ~ relation_empty_yielding(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_27,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_28,axiom,
( sP0(Eq_y_0)
| ~ sP0(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_29,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(equality_30,axiom,
( sP2(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP2(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_31,axiom,
( sP3(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP3(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_32,axiom,
( sP4(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP4(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_33,axiom,
( sP5(Eq_y_0,Eq_y_1)
| ~ sP5(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_34,axiom,
( sP6(Eq_y_0,Eq_y_1)
| ~ sP6(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_35,axiom,
( sP7(Eq_y_0)
| ~ sP7(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_36,axiom,
( sP8(Eq_y_0,Eq_y_1)
| ~ sP8(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_37,axiom,
( sP9(Eq_y_0)
| ~ sP9(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
% 0.00/0.01 % Problem : SEU292+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.01 This is a FOF_THM_RFO_SEQ problem
% 0.00/0.02 % Command : /export/starexec/sandbox2/solver/bin/connect++ --verbosity 1 --no-colour --tptp-proof --schedule default --timeout 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/0.34 % Computer : n011.cluster.edu
% 0.08/0.34 % Model : x86_64 x86_64
% 0.08/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.34 % Memory : 8046.5625MB
% 0.08/0.34 % OS : Linux 6.8.0-71-generic
% 0.02/15.22 % CPULimit : 300
% 0.02/15.22 % WCLimit : 300
% 0.02/15.22 % DateTime : Sat Sep 19 23:49:07 UTC 2026
% 0.02/15.22 % CPUTime :
% 48.30/63.48 % SZS status Theorem for theBenchmark
% 48.30/63.48 % SZS output start Proof for theBenchmark
% See solution above
%------------------------------------------------------------------------------