%------------------------------------------------------------------------------
% File : ConnectPP---0.7.2
% Problem : SEU290+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 : n001.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 08:58:51 AM UTC 2026
% Result : Theorem 238.43s 238.79s
% Output : Proof 240.01s
% 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(d5_funct_1,axiom,
! [A] :
( ( function(A)
& relation(A) )
=> ! [B] :
( B = relation_rng(A)
<=> ! [C] :
( in(C,B)
<=> ? [D] :
( C = apply(A,D)
& in(D,relation_dom(A)) ) ) ) ),
file('theBenchmark.p',d5_funct_1) ).
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_relat_1,axiom,
$true,
file('theBenchmark.p',dt_k2_relat_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_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(fc12_relat_1,axiom,
( relation_empty_yielding(empty_set)
& relation(empty_set)
& empty(empty_set) ),
file('theBenchmark.p',fc12_relat_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(fc6_relat_1,axiom,
! [A] :
( ( relation(A)
& ~ empty(A) )
=> ~ empty(relation_rng(A)) ),
file('theBenchmark.p',fc6_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(fc8_relat_1,axiom,
! [A] :
( empty(A)
=> ( relation(relation_rng(A))
& empty(relation_rng(A)) ) ),
file('theBenchmark.p',fc8_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(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(t6_funct_2,conjecture,
! [A,B,C,D] :
( ( relation_of2_as_subset(D,A,B)
& quasi_total(D,A,B)
& function(D) )
=> ( in(C,A)
=> ( in(apply(D,C),relation_rng(D))
| B = empty_set ) ) ),
file('theBenchmark.p',t6_funct_2) ).
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_0,U_1] :
( ~ 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_6,U_4,U_5] :
( 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,
! [A] :
( ! [B] :
( ( B = relation_rng(A)
| ? [C] :
( ( ~ in(C,B)
& ? [D] :
( C = apply(A,D)
& in(D,relation_dom(A)) ) )
| ( ! [D] :
( C != apply(A,D)
| ~ in(D,relation_dom(A)) )
& in(C,B) ) ) )
& ( ! [C] :
( ( in(C,B)
| ! [D] :
( C != apply(A,D)
| ~ in(D,relation_dom(A)) ) )
& ( ? [D] :
( C = apply(A,D)
& in(D,relation_dom(A)) )
| ~ in(C,B) ) )
| B != relation_rng(A) ) )
| ~ function(A)
| ~ relation(A) ),
inference(fof_nnf,[status(thm)],[d5_funct_1]) ).
fof(f_7_2,plain,
! [U_18] :
( ! [U_17] :
( ( U_17 = relation_rng(U_18)
| ? [U_16] :
( ( ~ in(U_16,U_17)
& ? [U_15] :
( U_16 = apply(U_18,U_15)
& in(U_15,relation_dom(U_18)) ) )
| ( ! [U_14] :
( U_16 != apply(U_18,U_14)
| ~ in(U_14,relation_dom(U_18)) )
& in(U_16,U_17) ) ) )
& ( ! [U_13] :
( ( in(U_13,U_17)
| ! [U_12] :
( U_13 != apply(U_18,U_12)
| ~ in(U_12,relation_dom(U_18)) ) )
& ( ? [U_11] :
( U_13 = apply(U_18,U_11)
& in(U_11,relation_dom(U_18)) )
| ~ in(U_13,U_17) ) )
| U_17 != relation_rng(U_18) ) )
| ~ function(U_18)
| ~ relation(U_18) ),
inference(variable_rename,[status(thm)],[f_7_1]) ).
fof(f_7_3,plain,
! [U_18] :
( ( ! [U_24] :
( U_24 = relation_rng(U_18)
| ? [U_22] :
( ~ in(U_22,U_24)
& ? [U_15] :
( U_22 = apply(U_18,U_15)
& in(U_15,relation_dom(U_18)) ) )
| ? [U_21] :
( ! [U_14] :
( U_21 != apply(U_18,U_14)
| ~ in(U_14,relation_dom(U_18)) )
& in(U_21,U_24) ) )
& ! [U_23] :
( ( ! [U_20] :
( in(U_20,U_23)
| ! [U_12] :
( U_20 != apply(U_18,U_12)
| ~ in(U_12,relation_dom(U_18)) ) )
& ! [U_19] :
( ? [U_11] :
( U_19 = apply(U_18,U_11)
& in(U_11,relation_dom(U_18)) )
| ~ in(U_19,U_23) ) )
| U_23 != relation_rng(U_18) ) )
| ~ function(U_18)
| ~ relation(U_18) ),
inference(miniscope,[status(thm)],[f_7_2]) ).
fof(f_7_4,plain,
! [U_18] :
( ( ! [U_24] :
( U_24 = relation_rng(U_18)
| ? [U_22] :
( ~ in(U_22,U_24)
& ? [U_15] :
( U_22 = apply(U_18,U_15)
& in(U_15,relation_dom(U_18)) ) )
| ? [U_21] :
( ! [U_14] :
( U_21 != apply(U_18,U_14)
| ~ in(U_14,relation_dom(U_18)) )
& in(U_21,U_24) ) )
& ! [U_23] :
( ( ! [U_20] :
( in(U_20,U_23)
| ! [U_12] :
( U_20 != apply(U_18,U_12)
| ~ in(U_12,relation_dom(U_18)) ) )
& ! [U_19] :
( ( U_19 = apply(U_18,sK1(U_18,U_23,U_19))
& in(sK1(U_18,U_23,U_19),relation_dom(U_18)) )
| ~ in(U_19,U_23) ) )
| U_23 != relation_rng(U_18) ) )
| ~ function(U_18)
| ~ relation(U_18) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(U_11,sK1(U_18,U_23,U_19))],[f_7_3]) ).
fof(f_7_5,plain,
! [U_18] :
( ( ! [U_24] :
( U_24 = relation_rng(U_18)
| ? [U_22] :
( ~ in(U_22,U_24)
& ? [U_15] :
( U_22 = apply(U_18,U_15)
& in(U_15,relation_dom(U_18)) ) )
| ( ! [U_14] :
( sK2(U_18,U_24) != apply(U_18,U_14)
| ~ in(U_14,relation_dom(U_18)) )
& in(sK2(U_18,U_24),U_24) ) )
& ! [U_23] :
( ( ! [U_20] :
( in(U_20,U_23)
| ! [U_12] :
( U_20 != apply(U_18,U_12)
| ~ in(U_12,relation_dom(U_18)) ) )
& ! [U_19] :
( ( U_19 = apply(U_18,sK1(U_18,U_23,U_19))
& in(sK1(U_18,U_23,U_19),relation_dom(U_18)) )
| ~ in(U_19,U_23) ) )
| U_23 != relation_rng(U_18) ) )
| ~ function(U_18)
| ~ relation(U_18) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2]),skolemize(U_21,sK2(U_18,U_24))],[f_7_4]) ).
fof(f_7_6,plain,
! [U_18] :
( ( ! [U_24] :
( U_24 = relation_rng(U_18)
| ( ~ in(sK3(U_18,U_24),U_24)
& ? [U_15] :
( sK3(U_18,U_24) = apply(U_18,U_15)
& in(U_15,relation_dom(U_18)) ) )
| ( ! [U_14] :
( sK2(U_18,U_24) != apply(U_18,U_14)
| ~ in(U_14,relation_dom(U_18)) )
& in(sK2(U_18,U_24),U_24) ) )
& ! [U_23] :
( ( ! [U_20] :
( in(U_20,U_23)
| ! [U_12] :
( U_20 != apply(U_18,U_12)
| ~ in(U_12,relation_dom(U_18)) ) )
& ! [U_19] :
( ( U_19 = apply(U_18,sK1(U_18,U_23,U_19))
& in(sK1(U_18,U_23,U_19),relation_dom(U_18)) )
| ~ in(U_19,U_23) ) )
| U_23 != relation_rng(U_18) ) )
| ~ function(U_18)
| ~ relation(U_18) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3]),skolemize(U_22,sK3(U_18,U_24))],[f_7_5]) ).
fof(f_7_7,plain,
! [U_18] :
( ( ! [U_24] :
( U_24 = relation_rng(U_18)
| ( ~ in(sK3(U_18,U_24),U_24)
& sK3(U_18,U_24) = apply(U_18,sK4(U_18,U_24))
& in(sK4(U_18,U_24),relation_dom(U_18)) )
| ( ! [U_14] :
( sK2(U_18,U_24) != apply(U_18,U_14)
| ~ in(U_14,relation_dom(U_18)) )
& in(sK2(U_18,U_24),U_24) ) )
& ! [U_23] :
( ( ! [U_20] :
( in(U_20,U_23)
| ! [U_12] :
( U_20 != apply(U_18,U_12)
| ~ in(U_12,relation_dom(U_18)) ) )
& ! [U_19] :
( ( U_19 = apply(U_18,sK1(U_18,U_23,U_19))
& in(sK1(U_18,U_23,U_19),relation_dom(U_18)) )
| ~ in(U_19,U_23) ) )
| U_23 != relation_rng(U_18) ) )
| ~ function(U_18)
| ~ relation(U_18) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4]),skolemize(U_15,sK4(U_18,U_24))],[f_7_6]) ).
fof(f_7_8,plain,
( ! [U_24,U_18] :
( ~ in(sK3(U_18,U_24),U_24)
| ~ sP8(U_24,U_18) )
& ! [U_24,U_18] :
( sK3(U_18,U_24) = apply(U_18,sK4(U_18,U_24))
| ~ sP8(U_24,U_18) )
& ! [U_24,U_18] :
( in(sK4(U_18,U_24),relation_dom(U_18))
| ~ sP8(U_24,U_18) )
& ! [U_14,U_24,U_18] :
( sK2(U_18,U_24) != apply(U_18,U_14)
| ~ in(U_14,relation_dom(U_18))
| ~ sP7(U_14,U_24,U_18) )
& ! [U_14,U_24,U_18] :
( in(sK2(U_18,U_24),U_24)
| ~ sP7(U_14,U_24,U_18) )
& ! [U_19,U_23,U_18] :
( U_19 = apply(U_18,sK1(U_18,U_23,U_19))
| ~ sP5(U_19,U_23,U_18) )
& ! [U_19,U_23,U_18] :
( in(sK1(U_18,U_23,U_19),relation_dom(U_18))
| ~ sP5(U_19,U_23,U_18) )
& ! [U_19,U_20,U_23,U_18,U_12] :
( in(U_20,U_23)
| U_20 != apply(U_18,U_12)
| ~ in(U_12,relation_dom(U_18))
| ~ sP6(U_19,U_20,U_23,U_18,U_12) )
& ! [U_19,U_20,U_23,U_18,U_12] :
( sP5(U_19,U_23,U_18)
| ~ in(U_19,U_23)
| ~ sP6(U_19,U_20,U_23,U_18,U_12) )
& ! [U_14,U_19,U_20,U_24,U_23,U_18,U_12] :
( U_24 = relation_rng(U_18)
| sP8(U_24,U_18)
| sP7(U_14,U_24,U_18)
| ~ sP9(U_14,U_19,U_20,U_24,U_23,U_18,U_12) )
& ! [U_14,U_19,U_20,U_24,U_23,U_18,U_12] :
( sP6(U_19,U_20,U_23,U_18,U_12)
| U_23 != relation_rng(U_18)
| ~ sP9(U_14,U_19,U_20,U_24,U_23,U_18,U_12) )
& ! [U_14,U_19,U_20,U_24,U_23,U_18,U_12] :
( sP9(U_14,U_19,U_20,U_24,U_23,U_18,U_12)
| ~ function(U_18)
| ~ relation(U_18) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP5,sP6,sP7,sP8,sP9])],[f_7_7]) ).
cnf(f_7_9,plain,
( sP9(U_14,U_19,U_20,U_24,U_23,U_18,U_12)
| ~ function(U_18)
| ~ relation(U_18) ),
inference(clausify,[status(thm)],[f_7_8]) ).
cnf(f_7_10,plain,
( sP6(U_19,U_20,U_23,U_18,U_12)
| U_23 != relation_rng(U_18)
| ~ sP9(U_14,U_19,U_20,U_24,U_23,U_18,U_12) ),
inference(clausify,[status(thm)],[f_7_8]) ).
cnf(f_7_11,plain,
( U_24 = relation_rng(U_18)
| sP8(U_24,U_18)
| sP7(U_14,U_24,U_18)
| ~ sP9(U_14,U_19,U_20,U_24,U_23,U_18,U_12) ),
inference(clausify,[status(thm)],[f_7_8]) ).
cnf(f_7_12,plain,
( sP5(U_19,U_23,U_18)
| ~ in(U_19,U_23)
| ~ sP6(U_19,U_20,U_23,U_18,U_12) ),
inference(clausify,[status(thm)],[f_7_8]) ).
cnf(f_7_13,plain,
( in(U_20,U_23)
| U_20 != apply(U_18,U_12)
| ~ in(U_12,relation_dom(U_18))
| ~ sP6(U_19,U_20,U_23,U_18,U_12) ),
inference(clausify,[status(thm)],[f_7_8]) ).
cnf(f_7_14,plain,
( in(sK1(U_18,U_23,U_19),relation_dom(U_18))
| ~ sP5(U_19,U_23,U_18) ),
inference(clausify,[status(thm)],[f_7_8]) ).
cnf(f_7_15,plain,
( U_19 = apply(U_18,sK1(U_18,U_23,U_19))
| ~ sP5(U_19,U_23,U_18) ),
inference(clausify,[status(thm)],[f_7_8]) ).
cnf(f_7_16,plain,
( in(sK2(U_18,U_24),U_24)
| ~ sP7(U_14,U_24,U_18) ),
inference(clausify,[status(thm)],[f_7_8]) ).
cnf(f_7_17,plain,
( sK2(U_18,U_24) != apply(U_18,U_14)
| ~ in(U_14,relation_dom(U_18))
| ~ sP7(U_14,U_24,U_18) ),
inference(clausify,[status(thm)],[f_7_8]) ).
cnf(f_7_18,plain,
( in(sK4(U_18,U_24),relation_dom(U_18))
| ~ sP8(U_24,U_18) ),
inference(clausify,[status(thm)],[f_7_8]) ).
cnf(f_7_19,plain,
( sK3(U_18,U_24) = apply(U_18,sK4(U_18,U_24))
| ~ sP8(U_24,U_18) ),
inference(clausify,[status(thm)],[f_7_8]) ).
cnf(f_7_20,plain,
( ~ in(sK3(U_18,U_24),U_24)
| ~ sP8(U_24,U_18) ),
inference(clausify,[status(thm)],[f_7_8]) ).
fof(f_8_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_k1_funct_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_relat_1]) ).
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_xboole_0]) ).
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_k1_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,
$true,
inference(fof_nnf,[status(thm)],[dt_k2_relat_1]) ).
fof(f_12_2,plain,
$true,
inference(definitional_conversion,[status(esa)],[f_12_1]) ).
cnf(f_12_3,plain,
$true,
inference(clausify,[status(thm)],[f_12_2]) ).
fof(f_13_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_k2_zfmisc_1]) ).
fof(f_13_2,plain,
$true,
inference(definitional_conversion,[status(esa)],[f_13_1]) ).
cnf(f_13_3,plain,
$true,
inference(clausify,[status(thm)],[f_13_2]) ).
fof(f_14_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_14_2,plain,
! [U_27,U_26,U_25] :
( element(relation_dom_as_subset(U_27,U_26,U_25),powerset(U_27))
| ~ relation_of2(U_25,U_27,U_26) ),
inference(variable_rename,[status(thm)],[f_14_1]) ).
fof(f_14_3,plain,
! [U_27,U_26,U_25] :
( element(relation_dom_as_subset(U_27,U_26,U_25),powerset(U_27))
| ~ relation_of2(U_25,U_27,U_26) ),
inference(definitional_conversion,[status(esa)],[f_14_2]) ).
cnf(f_14_4,plain,
( element(relation_dom_as_subset(U_27,U_26,U_25),powerset(U_27))
| ~ relation_of2(U_25,U_27,U_26) ),
inference(clausify,[status(thm)],[f_14_3]) ).
fof(f_15_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_m1_relset_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,
$true,
inference(fof_nnf,[status(thm)],[dt_m1_subset_1]) ).
fof(f_16_2,plain,
$true,
inference(definitional_conversion,[status(esa)],[f_16_1]) ).
cnf(f_16_3,plain,
$true,
inference(clausify,[status(thm)],[f_16_2]) ).
fof(f_17_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_17_2,plain,
! [U_30,U_29,U_28] :
( element(U_28,powerset(cartesian_product2(U_30,U_29)))
| ~ relation_of2_as_subset(U_28,U_30,U_29) ),
inference(variable_rename,[status(thm)],[f_17_1]) ).
fof(f_17_3,plain,
! [U_29,U_28,U_30] :
( element(U_28,powerset(cartesian_product2(U_30,U_29)))
| ~ relation_of2_as_subset(U_28,U_30,U_29) ),
inference(definitional_conversion,[status(esa)],[f_17_2]) ).
cnf(f_17_4,plain,
( element(U_28,powerset(cartesian_product2(U_30,U_29)))
| ~ relation_of2_as_subset(U_28,U_30,U_29) ),
inference(clausify,[status(thm)],[f_17_3]) ).
fof(f_18_1,plain,
! [A,B] :
? [C] : relation_of2(C,A,B),
inference(fof_nnf,[status(thm)],[existence_m1_relset_1]) ).
fof(f_18_2,plain,
! [U_33,U_32] :
? [U_31] : relation_of2(U_31,U_33,U_32),
inference(variable_rename,[status(thm)],[f_18_1]) ).
fof(f_18_3,plain,
! [U_33,U_32] : relation_of2(sK5(U_33,U_32),U_33,U_32),
inference(skolemize,[status(esa),new_symbols(skolem,[sK5]),skolemize(U_31,sK5(U_33,U_32))],[f_18_2]) ).
fof(f_18_4,plain,
! [U_32,U_33] : relation_of2(sK5(U_33,U_32),U_33,U_32),
inference(definitional_conversion,[status(esa)],[f_18_3]) ).
cnf(f_18_5,plain,
relation_of2(sK5(U_33,U_32),U_33,U_32),
inference(clausify,[status(thm)],[f_18_4]) ).
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_35] :
? [U_34] : element(U_34,U_35),
inference(variable_rename,[status(thm)],[f_19_1]) ).
fof(f_19_3,plain,
! [U_35] : element(sK6(U_35),U_35),
inference(skolemize,[status(esa),new_symbols(skolem,[sK6]),skolemize(U_34,sK6(U_35))],[f_19_2]) ).
fof(f_19_4,plain,
! [U_35] : element(sK6(U_35),U_35),
inference(definitional_conversion,[status(esa)],[f_19_3]) ).
cnf(f_19_5,plain,
element(sK6(U_35),U_35),
inference(clausify,[status(thm)],[f_19_4]) ).
fof(f_20_1,plain,
! [A,B] :
? [C] : relation_of2_as_subset(C,A,B),
inference(fof_nnf,[status(thm)],[existence_m2_relset_1]) ).
fof(f_20_2,plain,
! [U_38,U_37] :
? [U_36] : relation_of2_as_subset(U_36,U_38,U_37),
inference(variable_rename,[status(thm)],[f_20_1]) ).
fof(f_20_3,plain,
! [U_38,U_37] : relation_of2_as_subset(sK7(U_38,U_37),U_38,U_37),
inference(skolemize,[status(esa),new_symbols(skolem,[sK7]),skolemize(U_36,sK7(U_38,U_37))],[f_20_2]) ).
fof(f_20_4,plain,
! [U_38,U_37] : relation_of2_as_subset(sK7(U_38,U_37),U_38,U_37),
inference(definitional_conversion,[status(esa)],[f_20_3]) ).
cnf(f_20_5,plain,
relation_of2_as_subset(sK7(U_38,U_37),U_38,U_37),
inference(clausify,[status(thm)],[f_20_4]) ).
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] : ~ empty(powerset(A)),
inference(fof_nnf,[status(thm)],[fc1_subset_1]) ).
fof(f_22_2,plain,
! [U_39] : ~ empty(powerset(U_39)),
inference(variable_rename,[status(thm)],[f_22_1]) ).
fof(f_22_3,plain,
! [U_39] : ~ empty(powerset(U_39)),
inference(definitional_conversion,[status(esa)],[f_22_2]) ).
cnf(f_22_4,plain,
~ empty(powerset(U_39)),
inference(clausify,[status(thm)],[f_22_3]) ).
fof(f_23_1,plain,
empty(empty_set),
inference(fof_nnf,[status(thm)],[fc1_xboole_0]) ).
fof(f_23_2,plain,
empty(empty_set),
inference(definitional_conversion,[status(esa)],[f_23_1]) ).
cnf(f_23_3,plain,
empty(empty_set),
inference(clausify,[status(thm)],[f_23_2]) ).
fof(f_24_1,plain,
( relation(empty_set)
& empty(empty_set) ),
inference(fof_nnf,[status(thm)],[fc4_relat_1]) ).
fof(f_24_2,plain,
( relation(empty_set)
& 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]) ).
cnf(f_24_4,plain,
relation(empty_set),
inference(clausify,[status(thm)],[f_24_2]) ).
fof(f_25_1,plain,
! [A,B] :
( ~ empty(cartesian_product2(A,B))
| empty(B)
| empty(A) ),
inference(fof_nnf,[status(thm)],[fc4_subset_1]) ).
fof(f_25_2,plain,
! [U_41,U_40] :
( ~ empty(cartesian_product2(U_41,U_40))
| empty(U_40)
| empty(U_41) ),
inference(variable_rename,[status(thm)],[f_25_1]) ).
fof(f_25_3,plain,
! [U_40,U_41] :
( ~ empty(cartesian_product2(U_41,U_40))
| empty(U_40)
| empty(U_41) ),
inference(definitional_conversion,[status(esa)],[f_25_2]) ).
cnf(f_25_4,plain,
( ~ empty(cartesian_product2(U_41,U_40))
| empty(U_40)
| empty(U_41) ),
inference(clausify,[status(thm)],[f_25_3]) ).
fof(f_26_1,plain,
! [A] :
( ~ empty(relation_dom(A))
| ~ relation(A)
| empty(A) ),
inference(fof_nnf,[status(thm)],[fc5_relat_1]) ).
fof(f_26_2,plain,
! [U_42] :
( ~ empty(relation_dom(U_42))
| ~ relation(U_42)
| empty(U_42) ),
inference(variable_rename,[status(thm)],[f_26_1]) ).
fof(f_26_3,plain,
! [U_42] :
( ~ empty(relation_dom(U_42))
| ~ relation(U_42)
| empty(U_42) ),
inference(definitional_conversion,[status(esa)],[f_26_2]) ).
cnf(f_26_4,plain,
( ~ empty(relation_dom(U_42))
| ~ relation(U_42)
| empty(U_42) ),
inference(clausify,[status(thm)],[f_26_3]) ).
fof(f_27_1,plain,
! [A] :
( ~ empty(relation_rng(A))
| ~ relation(A)
| empty(A) ),
inference(fof_nnf,[status(thm)],[fc6_relat_1]) ).
fof(f_27_2,plain,
! [U_43] :
( ~ empty(relation_rng(U_43))
| ~ relation(U_43)
| empty(U_43) ),
inference(variable_rename,[status(thm)],[f_27_1]) ).
fof(f_27_3,plain,
! [U_43] :
( ~ empty(relation_rng(U_43))
| ~ relation(U_43)
| empty(U_43) ),
inference(definitional_conversion,[status(esa)],[f_27_2]) ).
cnf(f_27_4,plain,
( ~ empty(relation_rng(U_43))
| ~ relation(U_43)
| empty(U_43) ),
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_44] :
( ( relation(relation_dom(U_44))
& empty(relation_dom(U_44)) )
| ~ empty(U_44) ),
inference(variable_rename,[status(thm)],[f_28_1]) ).
fof(f_28_3,plain,
( ! [U_44] :
( relation(relation_dom(U_44))
| ~ sP10(U_44) )
& ! [U_44] :
( empty(relation_dom(U_44))
| ~ sP10(U_44) )
& ! [U_44] :
( sP10(U_44)
| ~ empty(U_44) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP10])],[f_28_2]) ).
cnf(f_28_4,plain,
( sP10(U_44)
| ~ empty(U_44) ),
inference(clausify,[status(thm)],[f_28_3]) ).
cnf(f_28_5,plain,
( empty(relation_dom(U_44))
| ~ sP10(U_44) ),
inference(clausify,[status(thm)],[f_28_3]) ).
cnf(f_28_6,plain,
( relation(relation_dom(U_44))
| ~ sP10(U_44) ),
inference(clausify,[status(thm)],[f_28_3]) ).
fof(f_29_1,plain,
! [A] :
( ( relation(relation_rng(A))
& empty(relation_rng(A)) )
| ~ empty(A) ),
inference(fof_nnf,[status(thm)],[fc8_relat_1]) ).
fof(f_29_2,plain,
! [U_45] :
( ( relation(relation_rng(U_45))
& empty(relation_rng(U_45)) )
| ~ empty(U_45) ),
inference(variable_rename,[status(thm)],[f_29_1]) ).
fof(f_29_3,plain,
( ! [U_45] :
( relation(relation_rng(U_45))
| ~ sP11(U_45) )
& ! [U_45] :
( empty(relation_rng(U_45))
| ~ sP11(U_45) )
& ! [U_45] :
( sP11(U_45)
| ~ empty(U_45) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP11])],[f_29_2]) ).
cnf(f_29_4,plain,
( sP11(U_45)
| ~ empty(U_45) ),
inference(clausify,[status(thm)],[f_29_3]) ).
cnf(f_29_5,plain,
( empty(relation_rng(U_45))
| ~ sP11(U_45) ),
inference(clausify,[status(thm)],[f_29_3]) ).
cnf(f_29_6,plain,
( relation(relation_rng(U_45))
| ~ sP11(U_45) ),
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_46] :
( function(U_46)
& relation(U_46) ),
inference(variable_rename,[status(thm)],[f_30_1]) ).
fof(f_30_3,plain,
( function(sK8)
& relation(sK8) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK8]),skolemize(U_46,sK8)],[f_30_2]) ).
fof(f_30_4,plain,
( function(sK8)
& relation(sK8) ),
inference(definitional_conversion,[status(esa)],[f_30_3]) ).
cnf(f_30_5,plain,
relation(sK8),
inference(clausify,[status(thm)],[f_30_4]) ).
cnf(f_30_6,plain,
function(sK8),
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_49,U_48] :
? [U_47] :
( quasi_total(U_47,U_49,U_48)
& function(U_47)
& relation(U_47)
& relation_of2(U_47,U_49,U_48) ),
inference(variable_rename,[status(thm)],[f_31_1]) ).
fof(f_31_3,plain,
! [U_49,U_48] :
( quasi_total(sK9(U_49,U_48),U_49,U_48)
& function(sK9(U_49,U_48))
& relation(sK9(U_49,U_48))
& relation_of2(sK9(U_49,U_48),U_49,U_48) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK9]),skolemize(U_47,sK9(U_49,U_48))],[f_31_2]) ).
fof(f_31_4,plain,
( ! [U_48,U_49] : quasi_total(sK9(U_49,U_48),U_49,U_48)
& ! [U_48,U_49] : function(sK9(U_49,U_48))
& ! [U_48,U_49] : relation(sK9(U_49,U_48))
& ! [U_48,U_49] : relation_of2(sK9(U_49,U_48),U_49,U_48) ),
inference(definitional_conversion,[status(esa)],[f_31_3]) ).
cnf(f_31_5,plain,
relation_of2(sK9(U_49,U_48),U_49,U_48),
inference(clausify,[status(thm)],[f_31_4]) ).
cnf(f_31_6,plain,
relation(sK9(U_49,U_48)),
inference(clausify,[status(thm)],[f_31_4]) ).
cnf(f_31_7,plain,
function(sK9(U_49,U_48)),
inference(clausify,[status(thm)],[f_31_4]) ).
cnf(f_31_8,plain,
quasi_total(sK9(U_49,U_48),U_49,U_48),
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_50] :
( empty(U_50)
& one_to_one(U_50)
& function(U_50)
& relation(U_50) ),
inference(variable_rename,[status(thm)],[f_32_1]) ).
fof(f_32_3,plain,
( empty(sK10)
& one_to_one(sK10)
& function(sK10)
& relation(sK10) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK10]),skolemize(U_50,sK10)],[f_32_2]) ).
fof(f_32_4,plain,
( empty(sK10)
& one_to_one(sK10)
& function(sK10)
& relation(sK10) ),
inference(definitional_conversion,[status(esa)],[f_32_3]) ).
cnf(f_32_5,plain,
relation(sK10),
inference(clausify,[status(thm)],[f_32_4]) ).
cnf(f_32_6,plain,
function(sK10),
inference(clausify,[status(thm)],[f_32_4]) ).
cnf(f_32_7,plain,
one_to_one(sK10),
inference(clausify,[status(thm)],[f_32_4]) ).
cnf(f_32_8,plain,
empty(sK10),
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_51] :
( relation(U_51)
& empty(U_51) ),
inference(variable_rename,[status(thm)],[f_33_1]) ).
fof(f_33_3,plain,
( relation(sK11)
& empty(sK11) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK11]),skolemize(U_51,sK11)],[f_33_2]) ).
fof(f_33_4,plain,
( relation(sK11)
& empty(sK11) ),
inference(definitional_conversion,[status(esa)],[f_33_3]) ).
cnf(f_33_5,plain,
empty(sK11),
inference(clausify,[status(thm)],[f_33_4]) ).
cnf(f_33_6,plain,
relation(sK11),
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_53] :
( ? [U_52] :
( ~ empty(U_52)
& element(U_52,powerset(U_53)) )
| empty(U_53) ),
inference(variable_rename,[status(thm)],[f_34_1]) ).
fof(f_34_3,plain,
! [U_53] :
( ( ~ empty(sK12(U_53))
& element(sK12(U_53),powerset(U_53)) )
| empty(U_53) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK12]),skolemize(U_52,sK12(U_53))],[f_34_2]) ).
fof(f_34_4,plain,
( ! [U_53] :
( ~ empty(sK12(U_53))
| ~ sP12(U_53) )
& ! [U_53] :
( element(sK12(U_53),powerset(U_53))
| ~ sP12(U_53) )
& ! [U_53] :
( sP12(U_53)
| empty(U_53) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP12])],[f_34_3]) ).
cnf(f_34_5,plain,
( sP12(U_53)
| empty(U_53) ),
inference(clausify,[status(thm)],[f_34_4]) ).
cnf(f_34_6,plain,
( element(sK12(U_53),powerset(U_53))
| ~ sP12(U_53) ),
inference(clausify,[status(thm)],[f_34_4]) ).
cnf(f_34_7,plain,
( ~ empty(sK12(U_53))
| ~ sP12(U_53) ),
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_54] : empty(U_54),
inference(variable_rename,[status(thm)],[f_35_1]) ).
fof(f_35_3,plain,
empty(sK13),
inference(skolemize,[status(esa),new_symbols(skolem,[sK13]),skolemize(U_54,sK13)],[f_35_2]) ).
fof(f_35_4,plain,
empty(sK13),
inference(definitional_conversion,[status(esa)],[f_35_3]) ).
cnf(f_35_5,plain,
empty(sK13),
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_55] :
( function(U_55)
& empty(U_55)
& relation(U_55) ),
inference(variable_rename,[status(thm)],[f_36_1]) ).
fof(f_36_3,plain,
( function(sK14)
& empty(sK14)
& relation(sK14) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK14]),skolemize(U_55,sK14)],[f_36_2]) ).
fof(f_36_4,plain,
( function(sK14)
& empty(sK14)
& relation(sK14) ),
inference(definitional_conversion,[status(esa)],[f_36_3]) ).
cnf(f_36_5,plain,
relation(sK14),
inference(clausify,[status(thm)],[f_36_4]) ).
cnf(f_36_6,plain,
empty(sK14),
inference(clausify,[status(thm)],[f_36_4]) ).
cnf(f_36_7,plain,
function(sK14),
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_58,U_57] :
? [U_56] :
( function(U_56)
& relation(U_56)
& relation_of2(U_56,U_58,U_57) ),
inference(variable_rename,[status(thm)],[f_37_1]) ).
fof(f_37_3,plain,
! [U_58,U_57] :
( function(sK15(U_58,U_57))
& relation(sK15(U_58,U_57))
& relation_of2(sK15(U_58,U_57),U_58,U_57) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK15]),skolemize(U_56,sK15(U_58,U_57))],[f_37_2]) ).
fof(f_37_4,plain,
( ! [U_57,U_58] : function(sK15(U_58,U_57))
& ! [U_57,U_58] : relation(sK15(U_58,U_57))
& ! [U_57,U_58] : relation_of2(sK15(U_58,U_57),U_58,U_57) ),
inference(definitional_conversion,[status(esa)],[f_37_3]) ).
cnf(f_37_5,plain,
relation_of2(sK15(U_58,U_57),U_58,U_57),
inference(clausify,[status(thm)],[f_37_4]) ).
cnf(f_37_6,plain,
relation(sK15(U_58,U_57)),
inference(clausify,[status(thm)],[f_37_4]) ).
cnf(f_37_7,plain,
function(sK15(U_58,U_57)),
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_59] :
( relation(U_59)
& ~ empty(U_59) ),
inference(variable_rename,[status(thm)],[f_38_1]) ).
fof(f_38_3,plain,
( relation(sK16)
& ~ empty(sK16) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK16]),skolemize(U_59,sK16)],[f_38_2]) ).
fof(f_38_4,plain,
( relation(sK16)
& ~ empty(sK16) ),
inference(definitional_conversion,[status(esa)],[f_38_3]) ).
cnf(f_38_5,plain,
~ empty(sK16),
inference(clausify,[status(thm)],[f_38_4]) ).
cnf(f_38_6,plain,
relation(sK16),
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_61] :
? [U_60] :
( empty(U_60)
& element(U_60,powerset(U_61)) ),
inference(variable_rename,[status(thm)],[f_39_1]) ).
fof(f_39_3,plain,
! [U_61] :
( empty(sK17(U_61))
& element(sK17(U_61),powerset(U_61)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK17]),skolemize(U_60,sK17(U_61))],[f_39_2]) ).
fof(f_39_4,plain,
( ! [U_61] : empty(sK17(U_61))
& ! [U_61] : element(sK17(U_61),powerset(U_61)) ),
inference(definitional_conversion,[status(esa)],[f_39_3]) ).
cnf(f_39_5,plain,
element(sK17(U_61),powerset(U_61)),
inference(clausify,[status(thm)],[f_39_4]) ).
cnf(f_39_6,plain,
empty(sK17(U_61)),
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_62] : ~ empty(U_62),
inference(variable_rename,[status(thm)],[f_40_1]) ).
fof(f_40_3,plain,
~ empty(sK18),
inference(skolemize,[status(esa),new_symbols(skolem,[sK18]),skolemize(U_62,sK18)],[f_40_2]) ).
fof(f_40_4,plain,
~ empty(sK18),
inference(definitional_conversion,[status(esa)],[f_40_3]) ).
cnf(f_40_5,plain,
~ empty(sK18),
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_63] :
( one_to_one(U_63)
& function(U_63)
& relation(U_63) ),
inference(variable_rename,[status(thm)],[f_41_1]) ).
fof(f_41_3,plain,
( one_to_one(sK19)
& function(sK19)
& relation(sK19) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK19]),skolemize(U_63,sK19)],[f_41_2]) ).
fof(f_41_4,plain,
( one_to_one(sK19)
& function(sK19)
& relation(sK19) ),
inference(definitional_conversion,[status(esa)],[f_41_3]) ).
cnf(f_41_5,plain,
relation(sK19),
inference(clausify,[status(thm)],[f_41_4]) ).
cnf(f_41_6,plain,
function(sK19),
inference(clausify,[status(thm)],[f_41_4]) ).
cnf(f_41_7,plain,
one_to_one(sK19),
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_64] :
( relation_empty_yielding(U_64)
& relation(U_64) ),
inference(variable_rename,[status(thm)],[f_42_1]) ).
fof(f_42_3,plain,
( relation_empty_yielding(sK20)
& relation(sK20) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK20]),skolemize(U_64,sK20)],[f_42_2]) ).
fof(f_42_4,plain,
( relation_empty_yielding(sK20)
& relation(sK20) ),
inference(definitional_conversion,[status(esa)],[f_42_3]) ).
cnf(f_42_5,plain,
relation(sK20),
inference(clausify,[status(thm)],[f_42_4]) ).
cnf(f_42_6,plain,
relation_empty_yielding(sK20),
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_65] :
( function(U_65)
& relation_empty_yielding(U_65)
& relation(U_65) ),
inference(variable_rename,[status(thm)],[f_43_1]) ).
fof(f_43_3,plain,
( function(sK21)
& relation_empty_yielding(sK21)
& relation(sK21) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK21]),skolemize(U_65,sK21)],[f_43_2]) ).
fof(f_43_4,plain,
( function(sK21)
& relation_empty_yielding(sK21)
& relation(sK21) ),
inference(definitional_conversion,[status(esa)],[f_43_3]) ).
cnf(f_43_5,plain,
relation(sK21),
inference(clausify,[status(thm)],[f_43_4]) ).
cnf(f_43_6,plain,
relation_empty_yielding(sK21),
inference(clausify,[status(thm)],[f_43_4]) ).
cnf(f_43_7,plain,
function(sK21),
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_68,U_67,U_66] :
( relation_dom_as_subset(U_68,U_67,U_66) = relation_dom(U_66)
| ~ relation_of2(U_66,U_68,U_67) ),
inference(variable_rename,[status(thm)],[f_44_1]) ).
fof(f_44_3,plain,
! [U_66,U_67,U_68] :
( relation_dom_as_subset(U_68,U_67,U_66) = relation_dom(U_66)
| ~ relation_of2(U_66,U_68,U_67) ),
inference(definitional_conversion,[status(esa)],[f_44_2]) ).
cnf(f_44_4,plain,
( relation_dom_as_subset(U_68,U_67,U_66) = relation_dom(U_66)
| ~ relation_of2(U_66,U_68,U_67) ),
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_71,U_70,U_69] :
( ( relation_of2_as_subset(U_69,U_71,U_70)
| ~ relation_of2(U_69,U_71,U_70) )
& ( relation_of2(U_69,U_71,U_70)
| ~ relation_of2_as_subset(U_69,U_71,U_70) ) ),
inference(variable_rename,[status(thm)],[f_45_1]) ).
fof(f_45_3,plain,
( ! [U_77,U_75,U_73] :
( relation_of2_as_subset(U_73,U_77,U_75)
| ~ relation_of2(U_73,U_77,U_75) )
& ! [U_76,U_74,U_72] :
( relation_of2(U_72,U_76,U_74)
| ~ relation_of2_as_subset(U_72,U_76,U_74) ) ),
inference(miniscope,[status(thm)],[f_45_2]) ).
fof(f_45_4,plain,
( ! [U_75,U_73,U_77] :
( relation_of2_as_subset(U_73,U_77,U_75)
| ~ relation_of2(U_73,U_77,U_75) )
& ! [U_76,U_74,U_72] :
( relation_of2(U_72,U_76,U_74)
| ~ relation_of2_as_subset(U_72,U_76,U_74) ) ),
inference(definitional_conversion,[status(esa)],[f_45_3]) ).
cnf(f_45_5,plain,
( relation_of2(U_72,U_76,U_74)
| ~ relation_of2_as_subset(U_72,U_76,U_74) ),
inference(clausify,[status(thm)],[f_45_4]) ).
cnf(f_45_6,plain,
( relation_of2_as_subset(U_73,U_77,U_75)
| ~ relation_of2(U_73,U_77,U_75) ),
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_79,U_78] : subset(U_79,U_79),
inference(variable_rename,[status(thm)],[f_46_1]) ).
fof(f_46_3,plain,
! [U_79] : subset(U_79,U_79),
inference(miniscope,[status(thm)],[f_46_2]) ).
fof(f_46_4,plain,
! [U_79] : subset(U_79,U_79),
inference(definitional_conversion,[status(esa)],[f_46_3]) ).
cnf(f_46_5,plain,
subset(U_79,U_79),
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_81,U_80] :
( element(U_81,U_80)
| ~ in(U_81,U_80) ),
inference(variable_rename,[status(thm)],[f_47_1]) ).
fof(f_47_3,plain,
! [U_81,U_80] :
( element(U_81,U_80)
| ~ in(U_81,U_80) ),
inference(definitional_conversion,[status(esa)],[f_47_2]) ).
cnf(f_47_4,plain,
( element(U_81,U_80)
| ~ in(U_81,U_80) ),
inference(clausify,[status(thm)],[f_47_3]) ).
fof(f_48_1,plain,
! [A,B] :
( in(A,B)
| empty(B)
| ~ element(A,B) ),
inference(fof_nnf,[status(thm)],[t2_subset]) ).
fof(f_48_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_48_1]) ).
fof(f_48_3,plain,
! [U_83,U_82] :
( in(U_83,U_82)
| empty(U_82)
| ~ element(U_83,U_82) ),
inference(definitional_conversion,[status(esa)],[f_48_2]) ).
cnf(f_48_4,plain,
( in(U_83,U_82)
| empty(U_82)
| ~ element(U_83,U_82) ),
inference(clausify,[status(thm)],[f_48_3]) ).
fof(f_49_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_49_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_49_1]) ).
fof(f_49_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_49_2]) ).
fof(f_49_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_49_3]) ).
cnf(f_49_5,plain,
( subset(U_88,U_86)
| ~ element(U_88,powerset(U_86)) ),
inference(clausify,[status(thm)],[f_49_4]) ).
cnf(f_49_6,plain,
( element(U_89,powerset(U_87))
| ~ subset(U_89,U_87) ),
inference(clausify,[status(thm)],[f_49_4]) ).
fof(f_50_1,plain,
! [A,B,C] :
( element(A,C)
| ~ element(B,powerset(C))
| ~ in(A,B) ),
inference(fof_nnf,[status(thm)],[t4_subset]) ).
fof(f_50_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_50_1]) ).
fof(f_50_3,plain,
! [U_90,U_92,U_91] :
( element(U_92,U_90)
| ~ element(U_91,powerset(U_90))
| ~ in(U_92,U_91) ),
inference(definitional_conversion,[status(esa)],[f_50_2]) ).
cnf(f_50_4,plain,
( element(U_92,U_90)
| ~ element(U_91,powerset(U_90))
| ~ in(U_92,U_91) ),
inference(clausify,[status(thm)],[f_50_3]) ).
fof(f_51_1,plain,
! [A,B,C] :
( ~ empty(C)
| ~ element(B,powerset(C))
| ~ in(A,B) ),
inference(fof_nnf,[status(thm)],[t5_subset]) ).
fof(f_51_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_51_1]) ).
fof(f_51_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_51_2]) ).
fof(f_51_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_51_3]) ).
cnf(f_51_5,plain,
( ~ empty(U_93)
| ~ element(U_94,powerset(U_93))
| ~ in(U_95,U_94) ),
inference(clausify,[status(thm)],[f_51_4]) ).
fof(f_52_1,plain,
! [A] :
( A = empty_set
| ~ empty(A) ),
inference(fof_nnf,[status(thm)],[t6_boole]) ).
fof(f_52_2,plain,
! [U_96] :
( U_96 = empty_set
| ~ empty(U_96) ),
inference(variable_rename,[status(thm)],[f_52_1]) ).
fof(f_52_3,plain,
! [U_96] :
( U_96 = empty_set
| ~ empty(U_96) ),
inference(definitional_conversion,[status(esa)],[f_52_2]) ).
cnf(f_52_4,plain,
( U_96 = empty_set
| ~ empty(U_96) ),
inference(clausify,[status(thm)],[f_52_3]) ).
fof(f_53_1,negated_conjecture,
~ ! [A,B,C,D] :
( ( relation_of2_as_subset(D,A,B)
& quasi_total(D,A,B)
& function(D) )
=> ( in(C,A)
=> ( in(apply(D,C),relation_rng(D))
| B = empty_set ) ) ),
inference(negate,[status(cth)],[t6_funct_2]) ).
fof(f_53_2,negated_conjecture,
? [A,B,C,D] :
( ~ in(apply(D,C),relation_rng(D))
& B != empty_set
& in(C,A)
& relation_of2_as_subset(D,A,B)
& quasi_total(D,A,B)
& function(D) ),
inference(fof_nnf,[status(thm)],[f_53_1]) ).
fof(f_53_3,negated_conjecture,
? [U_100,U_99,U_98,U_97] :
( ~ in(apply(U_97,U_98),relation_rng(U_97))
& U_99 != empty_set
& in(U_98,U_100)
& relation_of2_as_subset(U_97,U_100,U_99)
& quasi_total(U_97,U_100,U_99)
& function(U_97) ),
inference(variable_rename,[status(thm)],[f_53_2]) ).
fof(f_53_4,negated_conjecture,
? [U_99,U_98,U_97] :
( ~ in(apply(U_97,U_98),relation_rng(U_97))
& U_99 != empty_set
& in(U_98,sK22)
& relation_of2_as_subset(U_97,sK22,U_99)
& quasi_total(U_97,sK22,U_99)
& function(U_97) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK22]),skolemize(U_100,sK22)],[f_53_3]) ).
fof(f_53_5,negated_conjecture,
? [U_98,U_97] :
( ~ in(apply(U_97,U_98),relation_rng(U_97))
& sK23 != empty_set
& in(U_98,sK22)
& relation_of2_as_subset(U_97,sK22,sK23)
& quasi_total(U_97,sK22,sK23)
& function(U_97) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK23]),skolemize(U_99,sK23)],[f_53_4]) ).
fof(f_53_6,negated_conjecture,
? [U_97] :
( ~ in(apply(U_97,sK24),relation_rng(U_97))
& sK23 != empty_set
& in(sK24,sK22)
& relation_of2_as_subset(U_97,sK22,sK23)
& quasi_total(U_97,sK22,sK23)
& function(U_97) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK24]),skolemize(U_98,sK24)],[f_53_5]) ).
fof(f_53_7,negated_conjecture,
( ~ in(apply(sK25,sK24),relation_rng(sK25))
& sK23 != empty_set
& in(sK24,sK22)
& relation_of2_as_subset(sK25,sK22,sK23)
& quasi_total(sK25,sK22,sK23)
& function(sK25) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK25]),skolemize(U_97,sK25)],[f_53_6]) ).
fof(f_53_8,negated_conjecture,
( ~ in(apply(sK25,sK24),relation_rng(sK25))
& sK23 != empty_set
& in(sK24,sK22)
& relation_of2_as_subset(sK25,sK22,sK23)
& quasi_total(sK25,sK22,sK23)
& function(sK25) ),
inference(definitional_conversion,[status(esa)],[f_53_7]) ).
cnf(f_53_9,negated_conjecture,
function(sK25),
inference(clausify,[status(thm)],[f_53_8]) ).
cnf(f_53_10,negated_conjecture,
quasi_total(sK25,sK22,sK23),
inference(clausify,[status(thm)],[f_53_8]) ).
cnf(f_53_11,negated_conjecture,
relation_of2_as_subset(sK25,sK22,sK23),
inference(clausify,[status(thm)],[f_53_8]) ).
cnf(f_53_12,negated_conjecture,
in(sK24,sK22),
inference(clausify,[status(thm)],[f_53_8]) ).
cnf(f_53_13,negated_conjecture,
sK23 != empty_set,
inference(clausify,[status(thm)],[f_53_8]) ).
cnf(f_53_14,negated_conjecture,
~ in(apply(sK25,sK24),relation_rng(sK25)),
inference(clausify,[status(thm)],[f_53_8]) ).
fof(f_54_1,plain,
! [A,B] :
( ~ empty(B)
| ~ in(A,B) ),
inference(fof_nnf,[status(thm)],[t7_boole]) ).
fof(f_54_2,plain,
! [U_102,U_101] :
( ~ empty(U_101)
| ~ in(U_102,U_101) ),
inference(variable_rename,[status(thm)],[f_54_1]) ).
fof(f_54_3,plain,
! [U_102,U_101] :
( ~ empty(U_101)
| ~ in(U_102,U_101) ),
inference(definitional_conversion,[status(esa)],[f_54_2]) ).
cnf(f_54_4,plain,
( ~ empty(U_101)
| ~ in(U_102,U_101) ),
inference(clausify,[status(thm)],[f_54_3]) ).
fof(f_55_1,plain,
! [A,B] :
( ~ empty(B)
| A = B
| ~ empty(A) ),
inference(fof_nnf,[status(thm)],[t8_boole]) ).
fof(f_55_2,plain,
! [U_104,U_103] :
( ~ empty(U_103)
| U_104 = U_103
| ~ empty(U_104) ),
inference(variable_rename,[status(thm)],[f_55_1]) ).
fof(f_55_3,plain,
! [U_104] :
( ! [U_103] :
( ~ empty(U_103)
| U_104 = U_103 )
| ~ empty(U_104) ),
inference(miniscope,[status(thm)],[f_55_2]) ).
fof(f_55_4,plain,
! [U_103,U_104] :
( ~ empty(U_103)
| U_104 = U_103
| ~ empty(U_104) ),
inference(definitional_conversion,[status(esa)],[f_55_3]) ).
cnf(f_55_5,plain,
( ~ empty(U_103)
| U_104 = U_103
| ~ empty(U_104) ),
inference(clausify,[status(thm)],[f_55_4]) ).
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_12_3_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_12_3]) ).
cnf(f_13_3_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_13_3]) ).
cnf(f_15_3_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_15_3]) ).
cnf(f_16_3_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_16_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_rng(Eq_x_0) = relation_rng(Eq_y_0)
| 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,Eq_x_2) = sK1(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_11,axiom,
( sK2(Eq_x_0,Eq_x_1) = sK2(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_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,
( 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,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_15,axiom,
( sK6(Eq_x_0) = sK6(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_16,axiom,
( sK7(Eq_x_0,Eq_x_1) = sK7(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_17,axiom,
( sK9(Eq_x_0,Eq_x_1) = sK9(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_18,axiom,
( sK12(Eq_x_0) = sK12(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_19,axiom,
( sK15(Eq_x_0,Eq_x_1) = sK15(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_20,axiom,
( sK17(Eq_x_0) = sK17(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_21,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_22,axiom,
( empty(Eq_y_0)
| ~ empty(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_23,axiom,
( function(Eq_y_0)
| ~ function(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_24,axiom,
( relation(Eq_y_0)
| ~ relation(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_25,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_26,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_27,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_28,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_29,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_30,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_31,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_32,axiom,
( sP0(Eq_y_0)
| ~ sP0(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_33,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_34,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_35,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_36,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_37,axiom,
( sP5(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP5(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_38,axiom,
( sP6(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
| ~ sP6(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4)
| Eq_x_4 != Eq_y_4
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_39,axiom,
( sP7(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP7(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_40,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_41,axiom,
( sP9(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5,Eq_y_6)
| ~ sP9(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5,Eq_x_6)
| Eq_x_6 != Eq_y_6
| Eq_x_5 != Eq_y_5
| Eq_x_4 != Eq_y_4
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_42,axiom,
( sP10(Eq_y_0)
| ~ sP10(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_43,axiom,
( sP11(Eq_y_0)
| ~ sP11(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_44,axiom,
( sP12(Eq_y_0)
| ~ sP12(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 : SEU290+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.04 This is a FOF_THM_RFO_SEQ problem
% 0.00/0.04 % Command : /export/starexec/sandbox/solver/bin/connect++ --verbosity 1 --no-colour --tptp-proof --schedule default --timeout 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.12/0.39 % Computer : n001.cluster.edu
% 0.12/0.39 % Model : x86_64 x86_64
% 0.12/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.39 % Memory : 8046.5625MB
% 0.12/0.39 % OS : Linux 6.8.0-71-generic
% 0.12/0.39 % CPULimit : 300
% 0.12/0.39 % WCLimit : 300
% 0.12/0.39 % DateTime : Sat Sep 19 23:53:40 UTC 2026
% 0.12/0.39 % CPUTime :
% 238.43/238.79 % SZS status Theorem for theBenchmark
% 238.43/238.79 % SZS output start Proof for theBenchmark
% See solution above
%------------------------------------------------------------------------------