%------------------------------------------------------------------------------
% File : ConnectPP---0.7.2
% Problem : SEU449+1 : TPTP v9.3.1. Released v3.4.0.
% 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 : n005.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 08:59:23 AM UTC 2026
% Result : Theorem 1.06s 1.32s
% Output : Proof 1.06s
% Verified :
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)
% Comments :
%------------------------------------------------------------------------------
fof(t63_relset_2,conjecture,
! [A,B,C] :
( m1_subset_1(C,k1_zfmisc_1(A))
=> ! [D] :
( m1_subset_1(D,k1_zfmisc_1(B))
=> ! [E] :
( m2_relset_1(E,A,B)
=> ( r1_tarski(D,k8_relset_2(A,B,k8_relset_2(B,A,D,k6_relset_1(A,B,E)),E))
& r1_tarski(C,k8_relset_2(B,A,k8_relset_2(A,B,C,E),k6_relset_1(A,B,E))) ) ) ) ),
file('theBenchmark.p',t63_relset_2) ).
fof(existence_m1_eqrel_1,axiom,
! [A] :
? [B] : m1_eqrel_1(B,A),
file('theBenchmark.p',existence_m1_eqrel_1) ).
fof(dt_k5_relset_2,axiom,
! [A,B] :
( v1_relat_1(B)
=> ( v1_funct_1(k5_relset_2(A,B))
& v1_relat_1(k5_relset_2(A,B)) ) ),
file('theBenchmark.p',dt_k5_relset_2) ).
fof(dt_k9_relat_1,axiom,
$true,
file('theBenchmark.p',dt_k9_relat_1) ).
fof(dt_m1_eqrel_1,axiom,
! [A,B] :
( m1_eqrel_1(B,A)
=> m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A))) ),
file('theBenchmark.p',dt_m1_eqrel_1) ).
fof(rc2_partfun1,axiom,
! [A,B] :
? [C] :
( v1_funct_1(C)
& v1_relat_1(C)
& m1_relset_1(C,A,B) ),
file('theBenchmark.p',rc2_partfun1) ).
fof(rc3_relat_1,axiom,
? [A] :
( v3_relat_1(A)
& v1_relat_1(A) ),
file('theBenchmark.p',rc3_relat_1) ).
fof(antisymmetry_r2_hidden,axiom,
! [A,B] :
( r2_hidden(A,B)
=> ~ r2_hidden(B,A) ),
file('theBenchmark.p',antisymmetry_r2_hidden) ).
fof(redefinition_k4_relset_2,axiom,
! [A,B,C,D] :
( m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,k1_zfmisc_1(B))))
=> k4_relset_2(A,B,C,D) = k9_relat_1(C,D) ),
file('theBenchmark.p',redefinition_k4_relset_2) ).
fof(redefinition_k6_relset_2,axiom,
! [A,B,C] :
( m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(B,A)))
=> k6_relset_2(A,B,C) = k5_relset_2(B,C) ),
file('theBenchmark.p',redefinition_k6_relset_2) ).
fof(dt_k1_xboole_0,axiom,
$true,
file('theBenchmark.p',dt_k1_xboole_0) ).
fof(dt_k3_pua2mss1,axiom,
! [A] : m1_eqrel_1(k3_pua2mss1(A),A),
file('theBenchmark.p',dt_k3_pua2mss1) ).
fof(dt_k4_relset_2,axiom,
! [A,B,C,D] :
( m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,k1_zfmisc_1(B))))
=> m1_subset_1(k4_relset_2(A,B,C,D),k1_zfmisc_1(k1_zfmisc_1(B))) ),
file('theBenchmark.p',dt_k4_relset_2) ).
fof(dt_k6_relset_2,axiom,
! [A,B,C] :
( m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(B,A)))
=> ( m2_relset_1(k6_relset_2(A,B,C),k1_zfmisc_1(B),k1_zfmisc_1(A))
& v1_funct_2(k6_relset_2(A,B,C),k1_zfmisc_1(B),k1_zfmisc_1(A))
& v1_funct_1(k6_relset_2(A,B,C)) ) ),
file('theBenchmark.p',dt_k6_relset_2) ).
fof(dt_k8_setfam_1,axiom,
! [A,B] :
( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A)))
=> m1_subset_1(k8_setfam_1(A,B),k1_zfmisc_1(A)) ),
file('theBenchmark.p',dt_k8_setfam_1) ).
fof(fc12_relat_1,axiom,
( v3_relat_1(k1_xboole_0)
& v1_relat_1(k1_xboole_0)
& v1_xboole_0(k1_xboole_0) ),
file('theBenchmark.p',fc12_relat_1) ).
fof(fc4_relat_1,axiom,
( v1_relat_1(k1_xboole_0)
& v1_xboole_0(k1_xboole_0) ),
file('theBenchmark.p',fc4_relat_1) ).
fof(rc1_relat_1,axiom,
? [A] :
( v1_relat_1(A)
& v1_xboole_0(A) ),
file('theBenchmark.p',rc1_relat_1) ).
fof(rc2_relat_1,axiom,
? [A] :
( v1_relat_1(A)
& ~ v1_xboole_0(A) ),
file('theBenchmark.p',rc2_relat_1) ).
fof(t1_subset,axiom,
! [A,B] :
( r2_hidden(A,B)
=> m1_subset_1(A,B) ),
file('theBenchmark.p',t1_subset) ).
fof(t4_subset,axiom,
! [A,B,C] :
( ( m1_subset_1(B,k1_zfmisc_1(C))
& r2_hidden(A,B) )
=> m1_subset_1(A,C) ),
file('theBenchmark.p',t4_subset) ).
fof(t5_subset,axiom,
! [A,B,C] :
~ ( v1_xboole_0(C)
& m1_subset_1(B,k1_zfmisc_1(C))
& r2_hidden(A,B) ),
file('theBenchmark.p',t5_subset) ).
fof(involutiveness_k4_relat_1,axiom,
! [A] :
( v1_relat_1(A)
=> k4_relat_1(k4_relat_1(A)) = A ),
file('theBenchmark.p',involutiveness_k4_relat_1) ).
fof(existence_m1_relset_1,axiom,
! [A,B] :
? [C] : m1_relset_1(C,A,B),
file('theBenchmark.p',existence_m1_relset_1) ).
fof(dt_k2_zfmisc_1,axiom,
$true,
file('theBenchmark.p',dt_k2_zfmisc_1) ).
fof(dt_k4_relat_1,axiom,
! [A] :
( v1_relat_1(A)
=> v1_relat_1(k4_relat_1(A)) ),
file('theBenchmark.p',dt_k4_relat_1) ).
fof(dt_k7_relset_2,axiom,
$true,
file('theBenchmark.p',dt_k7_relset_2) ).
fof(dt_m1_relset_1,axiom,
$true,
file('theBenchmark.p',dt_m1_relset_1) ).
fof(cc1_relat_1,axiom,
! [A] :
( v1_xboole_0(A)
=> v1_relat_1(A) ),
file('theBenchmark.p',cc1_relat_1) ).
fof(cc1_relset_1,axiom,
! [A,B,C] :
( m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,B)))
=> v1_relat_1(C) ),
file('theBenchmark.p',cc1_relset_1) ).
fof(fc11_relat_1,axiom,
! [A] :
( v1_xboole_0(A)
=> ( v1_relat_1(k4_relat_1(A))
& v1_xboole_0(k4_relat_1(A)) ) ),
file('theBenchmark.p',fc11_relat_1) ).
fof(fc1_sysrel,axiom,
! [A,B] : v1_relat_1(k2_zfmisc_1(A,B)),
file('theBenchmark.p',fc1_sysrel) ).
fof(fc4_subset_1,axiom,
! [A,B] :
( ( ~ v1_xboole_0(B)
& ~ v1_xboole_0(A) )
=> ~ v1_xboole_0(k2_zfmisc_1(A,B)) ),
file('theBenchmark.p',fc4_subset_1) ).
fof(rc1_subset_1,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ? [B] :
( ~ v1_xboole_0(B)
& m1_subset_1(B,k1_zfmisc_1(A)) ) ),
file('theBenchmark.p',rc1_subset_1) ).
fof(rc2_subset_1,axiom,
! [A] :
? [B] :
( v1_xboole_0(B)
& m1_subset_1(B,k1_zfmisc_1(A)) ),
file('theBenchmark.p',rc2_subset_1) ).
fof(t2_subset,axiom,
! [A,B] :
( m1_subset_1(A,B)
=> ( r2_hidden(A,B)
| v1_xboole_0(B) ) ),
file('theBenchmark.p',t2_subset) ).
fof(t6_boole,axiom,
! [A] :
( v1_xboole_0(A)
=> A = k1_xboole_0 ),
file('theBenchmark.p',t6_boole) ).
fof(t7_boole,axiom,
! [A,B] :
~ ( v1_xboole_0(B)
& r2_hidden(A,B) ),
file('theBenchmark.p',t7_boole) ).
fof(t8_boole,axiom,
! [A,B] :
~ ( v1_xboole_0(B)
& A != B
& v1_xboole_0(A) ),
file('theBenchmark.p',t8_boole) ).
fof(d4_relset_2,axiom,
! [A,B,C] :
( m1_subset_1(C,k1_zfmisc_1(A))
=> ! [D] :
( m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(A,B)))
=> k7_relset_2(A,B,C,D) = k8_setfam_1(B,k4_relset_2(k1_zfmisc_1(A),B,k6_relset_2(B,A,D),k3_pua2mss1(C))) ) ),
file('theBenchmark.p',d4_relset_2) ).
fof(involutiveness_k6_relset_1,axiom,
! [A,B,C] :
( m1_relset_1(C,A,B)
=> k6_relset_1(A,B,k6_relset_1(A,B,C)) = C ),
file('theBenchmark.p',involutiveness_k6_relset_1) ).
fof(reflexivity_r1_tarski,axiom,
! [A,B] : r1_tarski(A,A),
file('theBenchmark.p',reflexivity_r1_tarski) ).
fof(existence_m1_subset_1,axiom,
! [A] :
? [B] : m1_subset_1(B,A),
file('theBenchmark.p',existence_m1_subset_1) ).
fof(existence_m2_relset_1,axiom,
! [A,B] :
? [C] : m2_relset_1(C,A,B),
file('theBenchmark.p',existence_m2_relset_1) ).
fof(redefinition_k6_relset_1,axiom,
! [A,B,C] :
( m1_relset_1(C,A,B)
=> k6_relset_1(A,B,C) = k4_relat_1(C) ),
file('theBenchmark.p',redefinition_k6_relset_1) ).
fof(redefinition_k8_relset_2,axiom,
! [A,B,C,D] :
( ( m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(A,B)))
& m1_subset_1(C,k1_zfmisc_1(A)) )
=> k8_relset_2(A,B,C,D) = k7_relset_2(A,B,C,D) ),
file('theBenchmark.p',redefinition_k8_relset_2) ).
fof(redefinition_m2_relset_1,axiom,
! [A,B,C] :
( m2_relset_1(C,A,B)
<=> m1_relset_1(C,A,B) ),
file('theBenchmark.p',redefinition_m2_relset_1) ).
fof(dt_k1_zfmisc_1,axiom,
$true,
file('theBenchmark.p',dt_k1_zfmisc_1) ).
fof(dt_k6_relset_1,axiom,
! [A,B,C] :
( m1_relset_1(C,A,B)
=> m2_relset_1(k6_relset_1(A,B,C),B,A) ),
file('theBenchmark.p',dt_k6_relset_1) ).
fof(dt_k8_relset_2,axiom,
! [A,B,C,D] :
( ( m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(A,B)))
& m1_subset_1(C,k1_zfmisc_1(A)) )
=> m1_subset_1(k8_relset_2(A,B,C,D),k1_zfmisc_1(B)) ),
file('theBenchmark.p',dt_k8_relset_2) ).
fof(dt_m1_subset_1,axiom,
$true,
file('theBenchmark.p',dt_m1_subset_1) ).
fof(dt_m2_relset_1,axiom,
! [A,B,C] :
( m2_relset_1(C,A,B)
=> m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,B))) ),
file('theBenchmark.p',dt_m2_relset_1) ).
fof(fc1_subset_1,axiom,
! [A] : ~ v1_xboole_0(k1_zfmisc_1(A)),
file('theBenchmark.p',fc1_subset_1) ).
fof(t3_subset,axiom,
! [A,B] :
( m1_subset_1(A,k1_zfmisc_1(B))
<=> r1_tarski(A,B) ),
file('theBenchmark.p',t3_subset) ).
fof(t61_relset_2,axiom,
! [A,B,C] :
( m1_subset_1(C,k1_zfmisc_1(A))
=> ! [D] :
( m1_subset_1(D,k1_zfmisc_1(B))
=> ! [E] :
( m2_relset_1(E,A,B)
=> ( r1_tarski(C,k8_relset_2(B,A,D,k6_relset_1(A,B,E)))
<=> r1_tarski(D,k8_relset_2(A,B,C,E)) ) ) ) ),
file('theBenchmark.p',t61_relset_2) ).
fof(f_1_1,negated_conjecture,
~ ! [A,B,C] :
( m1_subset_1(C,k1_zfmisc_1(A))
=> ! [D] :
( m1_subset_1(D,k1_zfmisc_1(B))
=> ! [E] :
( m2_relset_1(E,A,B)
=> ( r1_tarski(D,k8_relset_2(A,B,k8_relset_2(B,A,D,k6_relset_1(A,B,E)),E))
& r1_tarski(C,k8_relset_2(B,A,k8_relset_2(A,B,C,E),k6_relset_1(A,B,E))) ) ) ) ),
inference(negate,[status(cth)],[t63_relset_2]) ).
fof(f_1_2,negated_conjecture,
? [A,B,C] :
( ? [D] :
( ? [E] :
( ( ~ r1_tarski(D,k8_relset_2(A,B,k8_relset_2(B,A,D,k6_relset_1(A,B,E)),E))
| ~ r1_tarski(C,k8_relset_2(B,A,k8_relset_2(A,B,C,E),k6_relset_1(A,B,E))) )
& m2_relset_1(E,A,B) )
& m1_subset_1(D,k1_zfmisc_1(B)) )
& m1_subset_1(C,k1_zfmisc_1(A)) ),
inference(fof_nnf,[status(thm)],[f_1_1]) ).
fof(f_1_3,negated_conjecture,
? [U_4,U_3,U_2] :
( ? [U_1] :
( ? [U_0] :
( ( ~ r1_tarski(U_1,k8_relset_2(U_4,U_3,k8_relset_2(U_3,U_4,U_1,k6_relset_1(U_4,U_3,U_0)),U_0))
| ~ r1_tarski(U_2,k8_relset_2(U_3,U_4,k8_relset_2(U_4,U_3,U_2,U_0),k6_relset_1(U_4,U_3,U_0))) )
& m2_relset_1(U_0,U_4,U_3) )
& m1_subset_1(U_1,k1_zfmisc_1(U_3)) )
& m1_subset_1(U_2,k1_zfmisc_1(U_4)) ),
inference(variable_rename,[status(thm)],[f_1_2]) ).
fof(f_1_4,negated_conjecture,
? [U_3,U_2] :
( ? [U_1] :
( ? [U_0] :
( ( ~ r1_tarski(U_1,k8_relset_2(sK1,U_3,k8_relset_2(U_3,sK1,U_1,k6_relset_1(sK1,U_3,U_0)),U_0))
| ~ r1_tarski(U_2,k8_relset_2(U_3,sK1,k8_relset_2(sK1,U_3,U_2,U_0),k6_relset_1(sK1,U_3,U_0))) )
& m2_relset_1(U_0,sK1,U_3) )
& m1_subset_1(U_1,k1_zfmisc_1(U_3)) )
& m1_subset_1(U_2,k1_zfmisc_1(sK1)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(U_4,sK1)],[f_1_3]) ).
fof(f_1_5,negated_conjecture,
? [U_2] :
( ? [U_1] :
( ? [U_0] :
( ( ~ r1_tarski(U_1,k8_relset_2(sK1,sK2,k8_relset_2(sK2,sK1,U_1,k6_relset_1(sK1,sK2,U_0)),U_0))
| ~ r1_tarski(U_2,k8_relset_2(sK2,sK1,k8_relset_2(sK1,sK2,U_2,U_0),k6_relset_1(sK1,sK2,U_0))) )
& m2_relset_1(U_0,sK1,sK2) )
& m1_subset_1(U_1,k1_zfmisc_1(sK2)) )
& m1_subset_1(U_2,k1_zfmisc_1(sK1)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2]),skolemize(U_3,sK2)],[f_1_4]) ).
fof(f_1_6,negated_conjecture,
( ? [U_1] :
( ? [U_0] :
( ( ~ r1_tarski(U_1,k8_relset_2(sK1,sK2,k8_relset_2(sK2,sK1,U_1,k6_relset_1(sK1,sK2,U_0)),U_0))
| ~ r1_tarski(sK3,k8_relset_2(sK2,sK1,k8_relset_2(sK1,sK2,sK3,U_0),k6_relset_1(sK1,sK2,U_0))) )
& m2_relset_1(U_0,sK1,sK2) )
& m1_subset_1(U_1,k1_zfmisc_1(sK2)) )
& m1_subset_1(sK3,k1_zfmisc_1(sK1)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3]),skolemize(U_2,sK3)],[f_1_5]) ).
fof(f_1_7,negated_conjecture,
( ? [U_0] :
( ( ~ r1_tarski(sK4,k8_relset_2(sK1,sK2,k8_relset_2(sK2,sK1,sK4,k6_relset_1(sK1,sK2,U_0)),U_0))
| ~ r1_tarski(sK3,k8_relset_2(sK2,sK1,k8_relset_2(sK1,sK2,sK3,U_0),k6_relset_1(sK1,sK2,U_0))) )
& m2_relset_1(U_0,sK1,sK2) )
& m1_subset_1(sK4,k1_zfmisc_1(sK2))
& m1_subset_1(sK3,k1_zfmisc_1(sK1)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4]),skolemize(U_1,sK4)],[f_1_6]) ).
fof(f_1_8,negated_conjecture,
( ( ~ r1_tarski(sK4,k8_relset_2(sK1,sK2,k8_relset_2(sK2,sK1,sK4,k6_relset_1(sK1,sK2,sK5)),sK5))
| ~ r1_tarski(sK3,k8_relset_2(sK2,sK1,k8_relset_2(sK1,sK2,sK3,sK5),k6_relset_1(sK1,sK2,sK5))) )
& m2_relset_1(sK5,sK1,sK2)
& m1_subset_1(sK4,k1_zfmisc_1(sK2))
& m1_subset_1(sK3,k1_zfmisc_1(sK1)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK5]),skolemize(U_0,sK5)],[f_1_7]) ).
fof(f_1_9,negated_conjecture,
( ( ~ r1_tarski(sK4,k8_relset_2(sK1,sK2,k8_relset_2(sK2,sK1,sK4,k6_relset_1(sK1,sK2,sK5)),sK5))
| ~ r1_tarski(sK3,k8_relset_2(sK2,sK1,k8_relset_2(sK1,sK2,sK3,sK5),k6_relset_1(sK1,sK2,sK5))) )
& m2_relset_1(sK5,sK1,sK2)
& m1_subset_1(sK4,k1_zfmisc_1(sK2))
& m1_subset_1(sK3,k1_zfmisc_1(sK1)) ),
inference(definitional_conversion,[status(esa)],[f_1_8]) ).
cnf(f_1_10,negated_conjecture,
m1_subset_1(sK3,k1_zfmisc_1(sK1)),
inference(clausify,[status(thm)],[f_1_9]) ).
cnf(f_1_11,negated_conjecture,
m1_subset_1(sK4,k1_zfmisc_1(sK2)),
inference(clausify,[status(thm)],[f_1_9]) ).
cnf(f_1_12,negated_conjecture,
m2_relset_1(sK5,sK1,sK2),
inference(clausify,[status(thm)],[f_1_9]) ).
cnf(f_1_13,negated_conjecture,
( ~ r1_tarski(sK4,k8_relset_2(sK1,sK2,k8_relset_2(sK2,sK1,sK4,k6_relset_1(sK1,sK2,sK5)),sK5))
| ~ r1_tarski(sK3,k8_relset_2(sK2,sK1,k8_relset_2(sK1,sK2,sK3,sK5),k6_relset_1(sK1,sK2,sK5))) ),
inference(clausify,[status(thm)],[f_1_9]) ).
fof(f_2_1,plain,
! [A] :
? [B] : m1_eqrel_1(B,A),
inference(fof_nnf,[status(thm)],[existence_m1_eqrel_1]) ).
fof(f_2_2,plain,
! [U_6] :
? [U_5] : m1_eqrel_1(U_5,U_6),
inference(variable_rename,[status(thm)],[f_2_1]) ).
fof(f_2_3,plain,
! [U_6] : m1_eqrel_1(sK6(U_6),U_6),
inference(skolemize,[status(esa),new_symbols(skolem,[sK6]),skolemize(U_5,sK6(U_6))],[f_2_2]) ).
cnf(f_2_4,plain,
m1_eqrel_1(sK6(U_6),U_6),
inference(clausify,[status(thm)],[f_2_3]) ).
fof(f_3_1,plain,
! [A,B] :
( ( v1_funct_1(k5_relset_2(A,B))
& v1_relat_1(k5_relset_2(A,B)) )
| ~ v1_relat_1(B) ),
inference(fof_nnf,[status(thm)],[dt_k5_relset_2]) ).
fof(f_3_2,plain,
! [U_8,U_7] :
( ( v1_funct_1(k5_relset_2(U_8,U_7))
& v1_relat_1(k5_relset_2(U_8,U_7)) )
| ~ v1_relat_1(U_7) ),
inference(variable_rename,[status(thm)],[f_3_1]) ).
cnf(f_3_3,plain,
( v1_relat_1(k5_relset_2(U_8,U_7))
| ~ v1_relat_1(U_7) ),
inference(clausify,[status(thm)],[f_3_2]) ).
cnf(f_3_4,plain,
( v1_funct_1(k5_relset_2(U_8,U_7))
| ~ v1_relat_1(U_7) ),
inference(clausify,[status(thm)],[f_3_2]) ).
fof(f_4_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_k9_relat_1]) ).
cnf(f_4_2,plain,
$true,
inference(clausify,[status(thm)],[f_4_1]) ).
fof(f_5_1,plain,
! [A,B] :
( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A)))
| ~ m1_eqrel_1(B,A) ),
inference(fof_nnf,[status(thm)],[dt_m1_eqrel_1]) ).
fof(f_5_2,plain,
! [U_10,U_9] :
( m1_subset_1(U_9,k1_zfmisc_1(k1_zfmisc_1(U_10)))
| ~ m1_eqrel_1(U_9,U_10) ),
inference(variable_rename,[status(thm)],[f_5_1]) ).
cnf(f_5_3,plain,
( m1_subset_1(U_9,k1_zfmisc_1(k1_zfmisc_1(U_10)))
| ~ m1_eqrel_1(U_9,U_10) ),
inference(clausify,[status(thm)],[f_5_2]) ).
fof(f_6_1,plain,
! [A,B] :
? [C] :
( v1_funct_1(C)
& v1_relat_1(C)
& m1_relset_1(C,A,B) ),
inference(fof_nnf,[status(thm)],[rc2_partfun1]) ).
fof(f_6_2,plain,
! [U_13,U_12] :
? [U_11] :
( v1_funct_1(U_11)
& v1_relat_1(U_11)
& m1_relset_1(U_11,U_13,U_12) ),
inference(variable_rename,[status(thm)],[f_6_1]) ).
fof(f_6_3,plain,
! [U_13,U_12] :
( v1_funct_1(sK7(U_13,U_12))
& v1_relat_1(sK7(U_13,U_12))
& m1_relset_1(sK7(U_13,U_12),U_13,U_12) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK7]),skolemize(U_11,sK7(U_13,U_12))],[f_6_2]) ).
cnf(f_6_4,plain,
m1_relset_1(sK7(U_13,U_12),U_13,U_12),
inference(clausify,[status(thm)],[f_6_3]) ).
cnf(f_6_5,plain,
v1_relat_1(sK7(U_13,U_12)),
inference(clausify,[status(thm)],[f_6_3]) ).
cnf(f_6_6,plain,
v1_funct_1(sK7(U_13,U_12)),
inference(clausify,[status(thm)],[f_6_3]) ).
fof(f_7_1,plain,
? [A] :
( v3_relat_1(A)
& v1_relat_1(A) ),
inference(fof_nnf,[status(thm)],[rc3_relat_1]) ).
fof(f_7_2,plain,
? [U_14] :
( v3_relat_1(U_14)
& v1_relat_1(U_14) ),
inference(variable_rename,[status(thm)],[f_7_1]) ).
fof(f_7_3,plain,
( v3_relat_1(sK8)
& v1_relat_1(sK8) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK8]),skolemize(U_14,sK8)],[f_7_2]) ).
cnf(f_7_4,plain,
v1_relat_1(sK8),
inference(clausify,[status(thm)],[f_7_3]) ).
cnf(f_7_5,plain,
v3_relat_1(sK8),
inference(clausify,[status(thm)],[f_7_3]) ).
fof(f_8_1,plain,
! [A,B] :
( ~ r2_hidden(B,A)
| ~ r2_hidden(A,B) ),
inference(fof_nnf,[status(thm)],[antisymmetry_r2_hidden]) ).
fof(f_8_2,plain,
! [U_16,U_15] :
( ~ r2_hidden(U_15,U_16)
| ~ r2_hidden(U_16,U_15) ),
inference(variable_rename,[status(thm)],[f_8_1]) ).
cnf(f_8_3,plain,
( ~ r2_hidden(U_15,U_16)
| ~ r2_hidden(U_16,U_15) ),
inference(clausify,[status(thm)],[f_8_2]) ).
fof(f_9_1,plain,
! [A,B,C,D] :
( k4_relset_2(A,B,C,D) = k9_relat_1(C,D)
| ~ m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,k1_zfmisc_1(B)))) ),
inference(fof_nnf,[status(thm)],[redefinition_k4_relset_2]) ).
fof(f_9_2,plain,
! [U_20,U_19,U_18,U_17] :
( k4_relset_2(U_20,U_19,U_18,U_17) = k9_relat_1(U_18,U_17)
| ~ m1_subset_1(U_18,k1_zfmisc_1(k2_zfmisc_1(U_20,k1_zfmisc_1(U_19)))) ),
inference(variable_rename,[status(thm)],[f_9_1]) ).
fof(f_9_3,plain,
! [U_20,U_19,U_18] :
( ! [U_17] : k4_relset_2(U_20,U_19,U_18,U_17) = k9_relat_1(U_18,U_17)
| ~ m1_subset_1(U_18,k1_zfmisc_1(k2_zfmisc_1(U_20,k1_zfmisc_1(U_19)))) ),
inference(miniscope,[status(thm)],[f_9_2]) ).
cnf(f_9_4,plain,
( k4_relset_2(U_20,U_19,U_18,U_17) = k9_relat_1(U_18,U_17)
| ~ m1_subset_1(U_18,k1_zfmisc_1(k2_zfmisc_1(U_20,k1_zfmisc_1(U_19)))) ),
inference(clausify,[status(thm)],[f_9_3]) ).
fof(f_10_1,plain,
! [A,B,C] :
( k6_relset_2(A,B,C) = k5_relset_2(B,C)
| ~ m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(B,A))) ),
inference(fof_nnf,[status(thm)],[redefinition_k6_relset_2]) ).
fof(f_10_2,plain,
! [U_23,U_22,U_21] :
( k6_relset_2(U_23,U_22,U_21) = k5_relset_2(U_22,U_21)
| ~ m1_subset_1(U_21,k1_zfmisc_1(k2_zfmisc_1(U_22,U_23))) ),
inference(variable_rename,[status(thm)],[f_10_1]) ).
cnf(f_10_3,plain,
( k6_relset_2(U_23,U_22,U_21) = k5_relset_2(U_22,U_21)
| ~ m1_subset_1(U_21,k1_zfmisc_1(k2_zfmisc_1(U_22,U_23))) ),
inference(clausify,[status(thm)],[f_10_2]) ).
fof(f_11_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_k1_xboole_0]) ).
cnf(f_11_2,plain,
$true,
inference(clausify,[status(thm)],[f_11_1]) ).
fof(f_12_1,plain,
! [A] : m1_eqrel_1(k3_pua2mss1(A),A),
inference(fof_nnf,[status(thm)],[dt_k3_pua2mss1]) ).
fof(f_12_2,plain,
! [U_24] : m1_eqrel_1(k3_pua2mss1(U_24),U_24),
inference(variable_rename,[status(thm)],[f_12_1]) ).
cnf(f_12_3,plain,
m1_eqrel_1(k3_pua2mss1(U_24),U_24),
inference(clausify,[status(thm)],[f_12_2]) ).
fof(f_13_1,plain,
! [A,B,C,D] :
( m1_subset_1(k4_relset_2(A,B,C,D),k1_zfmisc_1(k1_zfmisc_1(B)))
| ~ m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,k1_zfmisc_1(B)))) ),
inference(fof_nnf,[status(thm)],[dt_k4_relset_2]) ).
fof(f_13_2,plain,
! [U_28,U_27,U_26,U_25] :
( m1_subset_1(k4_relset_2(U_28,U_27,U_26,U_25),k1_zfmisc_1(k1_zfmisc_1(U_27)))
| ~ m1_subset_1(U_26,k1_zfmisc_1(k2_zfmisc_1(U_28,k1_zfmisc_1(U_27)))) ),
inference(variable_rename,[status(thm)],[f_13_1]) ).
fof(f_13_3,plain,
! [U_28,U_27,U_26] :
( ! [U_25] : m1_subset_1(k4_relset_2(U_28,U_27,U_26,U_25),k1_zfmisc_1(k1_zfmisc_1(U_27)))
| ~ m1_subset_1(U_26,k1_zfmisc_1(k2_zfmisc_1(U_28,k1_zfmisc_1(U_27)))) ),
inference(miniscope,[status(thm)],[f_13_2]) ).
cnf(f_13_4,plain,
( m1_subset_1(k4_relset_2(U_28,U_27,U_26,U_25),k1_zfmisc_1(k1_zfmisc_1(U_27)))
| ~ m1_subset_1(U_26,k1_zfmisc_1(k2_zfmisc_1(U_28,k1_zfmisc_1(U_27)))) ),
inference(clausify,[status(thm)],[f_13_3]) ).
fof(f_14_1,plain,
! [A,B,C] :
( ( m2_relset_1(k6_relset_2(A,B,C),k1_zfmisc_1(B),k1_zfmisc_1(A))
& v1_funct_2(k6_relset_2(A,B,C),k1_zfmisc_1(B),k1_zfmisc_1(A))
& v1_funct_1(k6_relset_2(A,B,C)) )
| ~ m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(B,A))) ),
inference(fof_nnf,[status(thm)],[dt_k6_relset_2]) ).
fof(f_14_2,plain,
! [U_31,U_30,U_29] :
( ( m2_relset_1(k6_relset_2(U_31,U_30,U_29),k1_zfmisc_1(U_30),k1_zfmisc_1(U_31))
& v1_funct_2(k6_relset_2(U_31,U_30,U_29),k1_zfmisc_1(U_30),k1_zfmisc_1(U_31))
& v1_funct_1(k6_relset_2(U_31,U_30,U_29)) )
| ~ m1_subset_1(U_29,k1_zfmisc_1(k2_zfmisc_1(U_30,U_31))) ),
inference(variable_rename,[status(thm)],[f_14_1]) ).
cnf(f_14_3,plain,
( v1_funct_1(k6_relset_2(U_31,U_30,U_29))
| ~ m1_subset_1(U_29,k1_zfmisc_1(k2_zfmisc_1(U_30,U_31))) ),
inference(clausify,[status(thm)],[f_14_2]) ).
cnf(f_14_4,plain,
( v1_funct_2(k6_relset_2(U_31,U_30,U_29),k1_zfmisc_1(U_30),k1_zfmisc_1(U_31))
| ~ m1_subset_1(U_29,k1_zfmisc_1(k2_zfmisc_1(U_30,U_31))) ),
inference(clausify,[status(thm)],[f_14_2]) ).
cnf(f_14_5,plain,
( m2_relset_1(k6_relset_2(U_31,U_30,U_29),k1_zfmisc_1(U_30),k1_zfmisc_1(U_31))
| ~ m1_subset_1(U_29,k1_zfmisc_1(k2_zfmisc_1(U_30,U_31))) ),
inference(clausify,[status(thm)],[f_14_2]) ).
fof(f_15_1,plain,
! [A,B] :
( m1_subset_1(k8_setfam_1(A,B),k1_zfmisc_1(A))
| ~ m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A))) ),
inference(fof_nnf,[status(thm)],[dt_k8_setfam_1]) ).
fof(f_15_2,plain,
! [U_33,U_32] :
( m1_subset_1(k8_setfam_1(U_33,U_32),k1_zfmisc_1(U_33))
| ~ m1_subset_1(U_32,k1_zfmisc_1(k1_zfmisc_1(U_33))) ),
inference(variable_rename,[status(thm)],[f_15_1]) ).
cnf(f_15_3,plain,
( m1_subset_1(k8_setfam_1(U_33,U_32),k1_zfmisc_1(U_33))
| ~ m1_subset_1(U_32,k1_zfmisc_1(k1_zfmisc_1(U_33))) ),
inference(clausify,[status(thm)],[f_15_2]) ).
fof(f_16_1,plain,
( v3_relat_1(k1_xboole_0)
& v1_relat_1(k1_xboole_0)
& v1_xboole_0(k1_xboole_0) ),
inference(fof_nnf,[status(thm)],[fc12_relat_1]) ).
cnf(f_16_2,plain,
v1_xboole_0(k1_xboole_0),
inference(clausify,[status(thm)],[f_16_1]) ).
cnf(f_16_3,plain,
v1_relat_1(k1_xboole_0),
inference(clausify,[status(thm)],[f_16_1]) ).
cnf(f_16_4,plain,
v3_relat_1(k1_xboole_0),
inference(clausify,[status(thm)],[f_16_1]) ).
fof(f_17_1,plain,
( v1_relat_1(k1_xboole_0)
& v1_xboole_0(k1_xboole_0) ),
inference(fof_nnf,[status(thm)],[fc4_relat_1]) ).
cnf(f_17_2,plain,
v1_xboole_0(k1_xboole_0),
inference(clausify,[status(thm)],[f_17_1]) ).
cnf(f_17_3,plain,
v1_relat_1(k1_xboole_0),
inference(clausify,[status(thm)],[f_17_1]) ).
fof(f_18_1,plain,
? [A] :
( v1_relat_1(A)
& v1_xboole_0(A) ),
inference(fof_nnf,[status(thm)],[rc1_relat_1]) ).
fof(f_18_2,plain,
? [U_34] :
( v1_relat_1(U_34)
& v1_xboole_0(U_34) ),
inference(variable_rename,[status(thm)],[f_18_1]) ).
fof(f_18_3,plain,
( v1_relat_1(sK9)
& v1_xboole_0(sK9) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK9]),skolemize(U_34,sK9)],[f_18_2]) ).
cnf(f_18_4,plain,
v1_xboole_0(sK9),
inference(clausify,[status(thm)],[f_18_3]) ).
cnf(f_18_5,plain,
v1_relat_1(sK9),
inference(clausify,[status(thm)],[f_18_3]) ).
fof(f_19_1,plain,
? [A] :
( v1_relat_1(A)
& ~ v1_xboole_0(A) ),
inference(fof_nnf,[status(thm)],[rc2_relat_1]) ).
fof(f_19_2,plain,
? [U_35] :
( v1_relat_1(U_35)
& ~ v1_xboole_0(U_35) ),
inference(variable_rename,[status(thm)],[f_19_1]) ).
fof(f_19_3,plain,
( v1_relat_1(sK10)
& ~ v1_xboole_0(sK10) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK10]),skolemize(U_35,sK10)],[f_19_2]) ).
cnf(f_19_4,plain,
~ v1_xboole_0(sK10),
inference(clausify,[status(thm)],[f_19_3]) ).
cnf(f_19_5,plain,
v1_relat_1(sK10),
inference(clausify,[status(thm)],[f_19_3]) ).
fof(f_20_1,plain,
! [A,B] :
( m1_subset_1(A,B)
| ~ r2_hidden(A,B) ),
inference(fof_nnf,[status(thm)],[t1_subset]) ).
fof(f_20_2,plain,
! [U_37,U_36] :
( m1_subset_1(U_37,U_36)
| ~ r2_hidden(U_37,U_36) ),
inference(variable_rename,[status(thm)],[f_20_1]) ).
cnf(f_20_3,plain,
( m1_subset_1(U_37,U_36)
| ~ r2_hidden(U_37,U_36) ),
inference(clausify,[status(thm)],[f_20_2]) ).
fof(f_21_1,plain,
! [A,B,C] :
( m1_subset_1(A,C)
| ~ m1_subset_1(B,k1_zfmisc_1(C))
| ~ r2_hidden(A,B) ),
inference(fof_nnf,[status(thm)],[t4_subset]) ).
fof(f_21_2,plain,
! [U_40,U_39,U_38] :
( m1_subset_1(U_40,U_38)
| ~ m1_subset_1(U_39,k1_zfmisc_1(U_38))
| ~ r2_hidden(U_40,U_39) ),
inference(variable_rename,[status(thm)],[f_21_1]) ).
cnf(f_21_3,plain,
( m1_subset_1(U_40,U_38)
| ~ m1_subset_1(U_39,k1_zfmisc_1(U_38))
| ~ r2_hidden(U_40,U_39) ),
inference(clausify,[status(thm)],[f_21_2]) ).
fof(f_22_1,plain,
! [A,B,C] :
( ~ v1_xboole_0(C)
| ~ m1_subset_1(B,k1_zfmisc_1(C))
| ~ r2_hidden(A,B) ),
inference(fof_nnf,[status(thm)],[t5_subset]) ).
fof(f_22_2,plain,
! [U_43,U_42,U_41] :
( ~ v1_xboole_0(U_41)
| ~ m1_subset_1(U_42,k1_zfmisc_1(U_41))
| ~ r2_hidden(U_43,U_42) ),
inference(variable_rename,[status(thm)],[f_22_1]) ).
fof(f_22_3,plain,
! [U_43,U_42] :
( ! [U_41] :
( ~ v1_xboole_0(U_41)
| ~ m1_subset_1(U_42,k1_zfmisc_1(U_41)) )
| ~ r2_hidden(U_43,U_42) ),
inference(miniscope,[status(thm)],[f_22_2]) ).
cnf(f_22_4,plain,
( ~ v1_xboole_0(U_41)
| ~ m1_subset_1(U_42,k1_zfmisc_1(U_41))
| ~ r2_hidden(U_43,U_42) ),
inference(clausify,[status(thm)],[f_22_3]) ).
fof(f_23_1,plain,
! [A] :
( k4_relat_1(k4_relat_1(A)) = A
| ~ v1_relat_1(A) ),
inference(fof_nnf,[status(thm)],[involutiveness_k4_relat_1]) ).
fof(f_23_2,plain,
! [U_44] :
( k4_relat_1(k4_relat_1(U_44)) = U_44
| ~ v1_relat_1(U_44) ),
inference(variable_rename,[status(thm)],[f_23_1]) ).
cnf(f_23_3,plain,
( k4_relat_1(k4_relat_1(U_44)) = U_44
| ~ v1_relat_1(U_44) ),
inference(clausify,[status(thm)],[f_23_2]) ).
fof(f_24_1,plain,
! [A,B] :
? [C] : m1_relset_1(C,A,B),
inference(fof_nnf,[status(thm)],[existence_m1_relset_1]) ).
fof(f_24_2,plain,
! [U_47,U_46] :
? [U_45] : m1_relset_1(U_45,U_47,U_46),
inference(variable_rename,[status(thm)],[f_24_1]) ).
fof(f_24_3,plain,
! [U_47,U_46] : m1_relset_1(sK11(U_47,U_46),U_47,U_46),
inference(skolemize,[status(esa),new_symbols(skolem,[sK11]),skolemize(U_45,sK11(U_47,U_46))],[f_24_2]) ).
cnf(f_24_4,plain,
m1_relset_1(sK11(U_47,U_46),U_47,U_46),
inference(clausify,[status(thm)],[f_24_3]) ).
fof(f_25_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_k2_zfmisc_1]) ).
cnf(f_25_2,plain,
$true,
inference(clausify,[status(thm)],[f_25_1]) ).
fof(f_26_1,plain,
! [A] :
( v1_relat_1(k4_relat_1(A))
| ~ v1_relat_1(A) ),
inference(fof_nnf,[status(thm)],[dt_k4_relat_1]) ).
fof(f_26_2,plain,
! [U_48] :
( v1_relat_1(k4_relat_1(U_48))
| ~ v1_relat_1(U_48) ),
inference(variable_rename,[status(thm)],[f_26_1]) ).
cnf(f_26_3,plain,
( v1_relat_1(k4_relat_1(U_48))
| ~ v1_relat_1(U_48) ),
inference(clausify,[status(thm)],[f_26_2]) ).
fof(f_27_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_k7_relset_2]) ).
cnf(f_27_2,plain,
$true,
inference(clausify,[status(thm)],[f_27_1]) ).
fof(f_28_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_m1_relset_1]) ).
cnf(f_28_2,plain,
$true,
inference(clausify,[status(thm)],[f_28_1]) ).
fof(f_29_1,plain,
! [A] :
( v1_relat_1(A)
| ~ v1_xboole_0(A) ),
inference(fof_nnf,[status(thm)],[cc1_relat_1]) ).
fof(f_29_2,plain,
! [U_49] :
( v1_relat_1(U_49)
| ~ v1_xboole_0(U_49) ),
inference(variable_rename,[status(thm)],[f_29_1]) ).
cnf(f_29_3,plain,
( v1_relat_1(U_49)
| ~ v1_xboole_0(U_49) ),
inference(clausify,[status(thm)],[f_29_2]) ).
fof(f_30_1,plain,
! [A,B,C] :
( v1_relat_1(C)
| ~ m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,B))) ),
inference(fof_nnf,[status(thm)],[cc1_relset_1]) ).
fof(f_30_2,plain,
! [U_52,U_51,U_50] :
( v1_relat_1(U_50)
| ~ m1_subset_1(U_50,k1_zfmisc_1(k2_zfmisc_1(U_52,U_51))) ),
inference(variable_rename,[status(thm)],[f_30_1]) ).
cnf(f_30_3,plain,
( v1_relat_1(U_50)
| ~ m1_subset_1(U_50,k1_zfmisc_1(k2_zfmisc_1(U_52,U_51))) ),
inference(clausify,[status(thm)],[f_30_2]) ).
fof(f_31_1,plain,
! [A] :
( ( v1_relat_1(k4_relat_1(A))
& v1_xboole_0(k4_relat_1(A)) )
| ~ v1_xboole_0(A) ),
inference(fof_nnf,[status(thm)],[fc11_relat_1]) ).
fof(f_31_2,plain,
! [U_53] :
( ( v1_relat_1(k4_relat_1(U_53))
& v1_xboole_0(k4_relat_1(U_53)) )
| ~ v1_xboole_0(U_53) ),
inference(variable_rename,[status(thm)],[f_31_1]) ).
cnf(f_31_3,plain,
( v1_xboole_0(k4_relat_1(U_53))
| ~ v1_xboole_0(U_53) ),
inference(clausify,[status(thm)],[f_31_2]) ).
cnf(f_31_4,plain,
( v1_relat_1(k4_relat_1(U_53))
| ~ v1_xboole_0(U_53) ),
inference(clausify,[status(thm)],[f_31_2]) ).
fof(f_32_1,plain,
! [A,B] : v1_relat_1(k2_zfmisc_1(A,B)),
inference(fof_nnf,[status(thm)],[fc1_sysrel]) ).
fof(f_32_2,plain,
! [U_55,U_54] : v1_relat_1(k2_zfmisc_1(U_55,U_54)),
inference(variable_rename,[status(thm)],[f_32_1]) ).
cnf(f_32_3,plain,
v1_relat_1(k2_zfmisc_1(U_55,U_54)),
inference(clausify,[status(thm)],[f_32_2]) ).
fof(f_33_1,plain,
! [A,B] :
( ~ v1_xboole_0(k2_zfmisc_1(A,B))
| v1_xboole_0(B)
| v1_xboole_0(A) ),
inference(fof_nnf,[status(thm)],[fc4_subset_1]) ).
fof(f_33_2,plain,
! [U_57,U_56] :
( ~ v1_xboole_0(k2_zfmisc_1(U_57,U_56))
| v1_xboole_0(U_56)
| v1_xboole_0(U_57) ),
inference(variable_rename,[status(thm)],[f_33_1]) ).
cnf(f_33_3,plain,
( ~ v1_xboole_0(k2_zfmisc_1(U_57,U_56))
| v1_xboole_0(U_56)
| v1_xboole_0(U_57) ),
inference(clausify,[status(thm)],[f_33_2]) ).
fof(f_34_1,plain,
! [A] :
( ? [B] :
( ~ v1_xboole_0(B)
& m1_subset_1(B,k1_zfmisc_1(A)) )
| v1_xboole_0(A) ),
inference(fof_nnf,[status(thm)],[rc1_subset_1]) ).
fof(f_34_2,plain,
! [U_59] :
( ? [U_58] :
( ~ v1_xboole_0(U_58)
& m1_subset_1(U_58,k1_zfmisc_1(U_59)) )
| v1_xboole_0(U_59) ),
inference(variable_rename,[status(thm)],[f_34_1]) ).
fof(f_34_3,plain,
! [U_59] :
( ( ~ v1_xboole_0(sK12(U_59))
& m1_subset_1(sK12(U_59),k1_zfmisc_1(U_59)) )
| v1_xboole_0(U_59) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK12]),skolemize(U_58,sK12(U_59))],[f_34_2]) ).
cnf(f_34_4,plain,
( m1_subset_1(sK12(U_59),k1_zfmisc_1(U_59))
| v1_xboole_0(U_59) ),
inference(clausify,[status(thm)],[f_34_3]) ).
cnf(f_34_5,plain,
( ~ v1_xboole_0(sK12(U_59))
| v1_xboole_0(U_59) ),
inference(clausify,[status(thm)],[f_34_3]) ).
fof(f_35_1,plain,
! [A] :
? [B] :
( v1_xboole_0(B)
& m1_subset_1(B,k1_zfmisc_1(A)) ),
inference(fof_nnf,[status(thm)],[rc2_subset_1]) ).
fof(f_35_2,plain,
! [U_61] :
? [U_60] :
( v1_xboole_0(U_60)
& m1_subset_1(U_60,k1_zfmisc_1(U_61)) ),
inference(variable_rename,[status(thm)],[f_35_1]) ).
fof(f_35_3,plain,
! [U_61] :
( v1_xboole_0(sK13(U_61))
& m1_subset_1(sK13(U_61),k1_zfmisc_1(U_61)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK13]),skolemize(U_60,sK13(U_61))],[f_35_2]) ).
cnf(f_35_4,plain,
m1_subset_1(sK13(U_61),k1_zfmisc_1(U_61)),
inference(clausify,[status(thm)],[f_35_3]) ).
cnf(f_35_5,plain,
v1_xboole_0(sK13(U_61)),
inference(clausify,[status(thm)],[f_35_3]) ).
fof(f_36_1,plain,
! [A,B] :
( r2_hidden(A,B)
| v1_xboole_0(B)
| ~ m1_subset_1(A,B) ),
inference(fof_nnf,[status(thm)],[t2_subset]) ).
fof(f_36_2,plain,
! [U_63,U_62] :
( r2_hidden(U_63,U_62)
| v1_xboole_0(U_62)
| ~ m1_subset_1(U_63,U_62) ),
inference(variable_rename,[status(thm)],[f_36_1]) ).
cnf(f_36_3,plain,
( r2_hidden(U_63,U_62)
| v1_xboole_0(U_62)
| ~ m1_subset_1(U_63,U_62) ),
inference(clausify,[status(thm)],[f_36_2]) ).
fof(f_37_1,plain,
! [A] :
( A = k1_xboole_0
| ~ v1_xboole_0(A) ),
inference(fof_nnf,[status(thm)],[t6_boole]) ).
fof(f_37_2,plain,
! [U_64] :
( U_64 = k1_xboole_0
| ~ v1_xboole_0(U_64) ),
inference(variable_rename,[status(thm)],[f_37_1]) ).
cnf(f_37_3,plain,
( U_64 = k1_xboole_0
| ~ v1_xboole_0(U_64) ),
inference(clausify,[status(thm)],[f_37_2]) ).
fof(f_38_1,plain,
! [A,B] :
( ~ v1_xboole_0(B)
| ~ r2_hidden(A,B) ),
inference(fof_nnf,[status(thm)],[t7_boole]) ).
fof(f_38_2,plain,
! [U_66,U_65] :
( ~ v1_xboole_0(U_65)
| ~ r2_hidden(U_66,U_65) ),
inference(variable_rename,[status(thm)],[f_38_1]) ).
cnf(f_38_3,plain,
( ~ v1_xboole_0(U_65)
| ~ r2_hidden(U_66,U_65) ),
inference(clausify,[status(thm)],[f_38_2]) ).
fof(f_39_1,plain,
! [A,B] :
( ~ v1_xboole_0(B)
| A = B
| ~ v1_xboole_0(A) ),
inference(fof_nnf,[status(thm)],[t8_boole]) ).
fof(f_39_2,plain,
! [U_68,U_67] :
( ~ v1_xboole_0(U_67)
| U_68 = U_67
| ~ v1_xboole_0(U_68) ),
inference(variable_rename,[status(thm)],[f_39_1]) ).
fof(f_39_3,plain,
! [U_68] :
( ! [U_67] :
( ~ v1_xboole_0(U_67)
| U_68 = U_67 )
| ~ v1_xboole_0(U_68) ),
inference(miniscope,[status(thm)],[f_39_2]) ).
cnf(f_39_4,plain,
( ~ v1_xboole_0(U_67)
| U_68 = U_67
| ~ v1_xboole_0(U_68) ),
inference(clausify,[status(thm)],[f_39_3]) ).
fof(f_40_1,plain,
! [A,B,C] :
( ! [D] :
( k7_relset_2(A,B,C,D) = k8_setfam_1(B,k4_relset_2(k1_zfmisc_1(A),B,k6_relset_2(B,A,D),k3_pua2mss1(C)))
| ~ m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(A,B))) )
| ~ m1_subset_1(C,k1_zfmisc_1(A)) ),
inference(fof_nnf,[status(thm)],[d4_relset_2]) ).
fof(f_40_2,plain,
! [U_72,U_71,U_70] :
( ! [U_69] :
( k7_relset_2(U_72,U_71,U_70,U_69) = k8_setfam_1(U_71,k4_relset_2(k1_zfmisc_1(U_72),U_71,k6_relset_2(U_71,U_72,U_69),k3_pua2mss1(U_70)))
| ~ m1_subset_1(U_69,k1_zfmisc_1(k2_zfmisc_1(U_72,U_71))) )
| ~ m1_subset_1(U_70,k1_zfmisc_1(U_72)) ),
inference(variable_rename,[status(thm)],[f_40_1]) ).
cnf(f_40_3,plain,
( k7_relset_2(U_72,U_71,U_70,U_69) = k8_setfam_1(U_71,k4_relset_2(k1_zfmisc_1(U_72),U_71,k6_relset_2(U_71,U_72,U_69),k3_pua2mss1(U_70)))
| ~ m1_subset_1(U_69,k1_zfmisc_1(k2_zfmisc_1(U_72,U_71)))
| ~ m1_subset_1(U_70,k1_zfmisc_1(U_72)) ),
inference(clausify,[status(thm)],[f_40_2]) ).
fof(f_41_1,plain,
! [A,B,C] :
( k6_relset_1(A,B,k6_relset_1(A,B,C)) = C
| ~ m1_relset_1(C,A,B) ),
inference(fof_nnf,[status(thm)],[involutiveness_k6_relset_1]) ).
fof(f_41_2,plain,
! [U_75,U_74,U_73] :
( k6_relset_1(U_75,U_74,k6_relset_1(U_75,U_74,U_73)) = U_73
| ~ m1_relset_1(U_73,U_75,U_74) ),
inference(variable_rename,[status(thm)],[f_41_1]) ).
cnf(f_41_3,plain,
( k6_relset_1(U_75,U_74,k6_relset_1(U_75,U_74,U_73)) = U_73
| ~ m1_relset_1(U_73,U_75,U_74) ),
inference(clausify,[status(thm)],[f_41_2]) ).
fof(f_42_1,plain,
! [A,B] : r1_tarski(A,A),
inference(fof_nnf,[status(thm)],[reflexivity_r1_tarski]) ).
fof(f_42_2,plain,
! [U_77,U_76] : r1_tarski(U_77,U_77),
inference(variable_rename,[status(thm)],[f_42_1]) ).
fof(f_42_3,plain,
! [U_77] : r1_tarski(U_77,U_77),
inference(miniscope,[status(thm)],[f_42_2]) ).
cnf(f_42_4,plain,
r1_tarski(U_77,U_77),
inference(clausify,[status(thm)],[f_42_3]) ).
fof(f_43_1,plain,
! [A] :
? [B] : m1_subset_1(B,A),
inference(fof_nnf,[status(thm)],[existence_m1_subset_1]) ).
fof(f_43_2,plain,
! [U_79] :
? [U_78] : m1_subset_1(U_78,U_79),
inference(variable_rename,[status(thm)],[f_43_1]) ).
fof(f_43_3,plain,
! [U_79] : m1_subset_1(sK14(U_79),U_79),
inference(skolemize,[status(esa),new_symbols(skolem,[sK14]),skolemize(U_78,sK14(U_79))],[f_43_2]) ).
cnf(f_43_4,plain,
m1_subset_1(sK14(U_79),U_79),
inference(clausify,[status(thm)],[f_43_3]) ).
fof(f_44_1,plain,
! [A,B] :
? [C] : m2_relset_1(C,A,B),
inference(fof_nnf,[status(thm)],[existence_m2_relset_1]) ).
fof(f_44_2,plain,
! [U_82,U_81] :
? [U_80] : m2_relset_1(U_80,U_82,U_81),
inference(variable_rename,[status(thm)],[f_44_1]) ).
fof(f_44_3,plain,
! [U_82,U_81] : m2_relset_1(sK15(U_82,U_81),U_82,U_81),
inference(skolemize,[status(esa),new_symbols(skolem,[sK15]),skolemize(U_80,sK15(U_82,U_81))],[f_44_2]) ).
cnf(f_44_4,plain,
m2_relset_1(sK15(U_82,U_81),U_82,U_81),
inference(clausify,[status(thm)],[f_44_3]) ).
fof(f_45_1,plain,
! [A,B,C] :
( k6_relset_1(A,B,C) = k4_relat_1(C)
| ~ m1_relset_1(C,A,B) ),
inference(fof_nnf,[status(thm)],[redefinition_k6_relset_1]) ).
fof(f_45_2,plain,
! [U_85,U_84,U_83] :
( k6_relset_1(U_85,U_84,U_83) = k4_relat_1(U_83)
| ~ m1_relset_1(U_83,U_85,U_84) ),
inference(variable_rename,[status(thm)],[f_45_1]) ).
cnf(f_45_3,plain,
( k6_relset_1(U_85,U_84,U_83) = k4_relat_1(U_83)
| ~ m1_relset_1(U_83,U_85,U_84) ),
inference(clausify,[status(thm)],[f_45_2]) ).
fof(f_46_1,plain,
! [A,B,C,D] :
( k8_relset_2(A,B,C,D) = k7_relset_2(A,B,C,D)
| ~ m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(A,B)))
| ~ m1_subset_1(C,k1_zfmisc_1(A)) ),
inference(fof_nnf,[status(thm)],[redefinition_k8_relset_2]) ).
fof(f_46_2,plain,
! [U_89,U_88,U_87,U_86] :
( k8_relset_2(U_89,U_88,U_87,U_86) = k7_relset_2(U_89,U_88,U_87,U_86)
| ~ m1_subset_1(U_86,k1_zfmisc_1(k2_zfmisc_1(U_89,U_88)))
| ~ m1_subset_1(U_87,k1_zfmisc_1(U_89)) ),
inference(variable_rename,[status(thm)],[f_46_1]) ).
cnf(f_46_3,plain,
( k8_relset_2(U_89,U_88,U_87,U_86) = k7_relset_2(U_89,U_88,U_87,U_86)
| ~ m1_subset_1(U_86,k1_zfmisc_1(k2_zfmisc_1(U_89,U_88)))
| ~ m1_subset_1(U_87,k1_zfmisc_1(U_89)) ),
inference(clausify,[status(thm)],[f_46_2]) ).
fof(f_47_1,plain,
! [A,B,C] :
( ( m2_relset_1(C,A,B)
| ~ m1_relset_1(C,A,B) )
& ( m1_relset_1(C,A,B)
| ~ m2_relset_1(C,A,B) ) ),
inference(fof_nnf,[status(thm)],[redefinition_m2_relset_1]) ).
fof(f_47_2,plain,
! [U_92,U_91,U_90] :
( ( m2_relset_1(U_90,U_92,U_91)
| ~ m1_relset_1(U_90,U_92,U_91) )
& ( m1_relset_1(U_90,U_92,U_91)
| ~ m2_relset_1(U_90,U_92,U_91) ) ),
inference(variable_rename,[status(thm)],[f_47_1]) ).
fof(f_47_3,plain,
( ! [U_98,U_96,U_94] :
( m2_relset_1(U_94,U_98,U_96)
| ~ m1_relset_1(U_94,U_98,U_96) )
& ! [U_97,U_95,U_93] :
( m1_relset_1(U_93,U_97,U_95)
| ~ m2_relset_1(U_93,U_97,U_95) ) ),
inference(miniscope,[status(thm)],[f_47_2]) ).
cnf(f_47_4,plain,
( m1_relset_1(U_93,U_97,U_95)
| ~ m2_relset_1(U_93,U_97,U_95) ),
inference(clausify,[status(thm)],[f_47_3]) ).
cnf(f_47_5,plain,
( m2_relset_1(U_94,U_98,U_96)
| ~ m1_relset_1(U_94,U_98,U_96) ),
inference(clausify,[status(thm)],[f_47_3]) ).
fof(f_48_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_k1_zfmisc_1]) ).
cnf(f_48_2,plain,
$true,
inference(clausify,[status(thm)],[f_48_1]) ).
fof(f_49_1,plain,
! [A,B,C] :
( m2_relset_1(k6_relset_1(A,B,C),B,A)
| ~ m1_relset_1(C,A,B) ),
inference(fof_nnf,[status(thm)],[dt_k6_relset_1]) ).
fof(f_49_2,plain,
! [U_101,U_100,U_99] :
( m2_relset_1(k6_relset_1(U_101,U_100,U_99),U_100,U_101)
| ~ m1_relset_1(U_99,U_101,U_100) ),
inference(variable_rename,[status(thm)],[f_49_1]) ).
cnf(f_49_3,plain,
( m2_relset_1(k6_relset_1(U_101,U_100,U_99),U_100,U_101)
| ~ m1_relset_1(U_99,U_101,U_100) ),
inference(clausify,[status(thm)],[f_49_2]) ).
fof(f_50_1,plain,
! [A,B,C,D] :
( m1_subset_1(k8_relset_2(A,B,C,D),k1_zfmisc_1(B))
| ~ m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(A,B)))
| ~ m1_subset_1(C,k1_zfmisc_1(A)) ),
inference(fof_nnf,[status(thm)],[dt_k8_relset_2]) ).
fof(f_50_2,plain,
! [U_105,U_104,U_103,U_102] :
( m1_subset_1(k8_relset_2(U_105,U_104,U_103,U_102),k1_zfmisc_1(U_104))
| ~ m1_subset_1(U_102,k1_zfmisc_1(k2_zfmisc_1(U_105,U_104)))
| ~ m1_subset_1(U_103,k1_zfmisc_1(U_105)) ),
inference(variable_rename,[status(thm)],[f_50_1]) ).
cnf(f_50_3,plain,
( m1_subset_1(k8_relset_2(U_105,U_104,U_103,U_102),k1_zfmisc_1(U_104))
| ~ m1_subset_1(U_102,k1_zfmisc_1(k2_zfmisc_1(U_105,U_104)))
| ~ m1_subset_1(U_103,k1_zfmisc_1(U_105)) ),
inference(clausify,[status(thm)],[f_50_2]) ).
fof(f_51_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_m1_subset_1]) ).
cnf(f_51_2,plain,
$true,
inference(clausify,[status(thm)],[f_51_1]) ).
fof(f_52_1,plain,
! [A,B,C] :
( m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,B)))
| ~ m2_relset_1(C,A,B) ),
inference(fof_nnf,[status(thm)],[dt_m2_relset_1]) ).
fof(f_52_2,plain,
! [U_108,U_107,U_106] :
( m1_subset_1(U_106,k1_zfmisc_1(k2_zfmisc_1(U_108,U_107)))
| ~ m2_relset_1(U_106,U_108,U_107) ),
inference(variable_rename,[status(thm)],[f_52_1]) ).
cnf(f_52_3,plain,
( m1_subset_1(U_106,k1_zfmisc_1(k2_zfmisc_1(U_108,U_107)))
| ~ m2_relset_1(U_106,U_108,U_107) ),
inference(clausify,[status(thm)],[f_52_2]) ).
fof(f_53_1,plain,
! [A] : ~ v1_xboole_0(k1_zfmisc_1(A)),
inference(fof_nnf,[status(thm)],[fc1_subset_1]) ).
fof(f_53_2,plain,
! [U_109] : ~ v1_xboole_0(k1_zfmisc_1(U_109)),
inference(variable_rename,[status(thm)],[f_53_1]) ).
cnf(f_53_3,plain,
~ v1_xboole_0(k1_zfmisc_1(U_109)),
inference(clausify,[status(thm)],[f_53_2]) ).
fof(f_54_1,plain,
! [A,B] :
( ( m1_subset_1(A,k1_zfmisc_1(B))
| ~ r1_tarski(A,B) )
& ( r1_tarski(A,B)
| ~ m1_subset_1(A,k1_zfmisc_1(B)) ) ),
inference(fof_nnf,[status(thm)],[t3_subset]) ).
fof(f_54_2,plain,
! [U_111,U_110] :
( ( m1_subset_1(U_111,k1_zfmisc_1(U_110))
| ~ r1_tarski(U_111,U_110) )
& ( r1_tarski(U_111,U_110)
| ~ m1_subset_1(U_111,k1_zfmisc_1(U_110)) ) ),
inference(variable_rename,[status(thm)],[f_54_1]) ).
fof(f_54_3,plain,
( ! [U_115,U_113] :
( m1_subset_1(U_115,k1_zfmisc_1(U_113))
| ~ r1_tarski(U_115,U_113) )
& ! [U_114,U_112] :
( r1_tarski(U_114,U_112)
| ~ m1_subset_1(U_114,k1_zfmisc_1(U_112)) ) ),
inference(miniscope,[status(thm)],[f_54_2]) ).
cnf(f_54_4,plain,
( r1_tarski(U_114,U_112)
| ~ m1_subset_1(U_114,k1_zfmisc_1(U_112)) ),
inference(clausify,[status(thm)],[f_54_3]) ).
cnf(f_54_5,plain,
( m1_subset_1(U_115,k1_zfmisc_1(U_113))
| ~ r1_tarski(U_115,U_113) ),
inference(clausify,[status(thm)],[f_54_3]) ).
fof(f_55_1,plain,
! [A,B,C] :
( ! [D] :
( ! [E] :
( ( ( r1_tarski(C,k8_relset_2(B,A,D,k6_relset_1(A,B,E)))
| ~ r1_tarski(D,k8_relset_2(A,B,C,E)) )
& ( r1_tarski(D,k8_relset_2(A,B,C,E))
| ~ r1_tarski(C,k8_relset_2(B,A,D,k6_relset_1(A,B,E))) ) )
| ~ m2_relset_1(E,A,B) )
| ~ m1_subset_1(D,k1_zfmisc_1(B)) )
| ~ m1_subset_1(C,k1_zfmisc_1(A)) ),
inference(fof_nnf,[status(thm)],[t61_relset_2]) ).
fof(f_55_2,plain,
! [U_120,U_119,U_118] :
( ! [U_117] :
( ! [U_116] :
( ( ( r1_tarski(U_118,k8_relset_2(U_119,U_120,U_117,k6_relset_1(U_120,U_119,U_116)))
| ~ r1_tarski(U_117,k8_relset_2(U_120,U_119,U_118,U_116)) )
& ( r1_tarski(U_117,k8_relset_2(U_120,U_119,U_118,U_116))
| ~ r1_tarski(U_118,k8_relset_2(U_119,U_120,U_117,k6_relset_1(U_120,U_119,U_116))) ) )
| ~ m2_relset_1(U_116,U_120,U_119) )
| ~ m1_subset_1(U_117,k1_zfmisc_1(U_119)) )
| ~ m1_subset_1(U_118,k1_zfmisc_1(U_120)) ),
inference(variable_rename,[status(thm)],[f_55_1]) ).
cnf(f_55_3,plain,
( r1_tarski(U_117,k8_relset_2(U_120,U_119,U_118,U_116))
| ~ r1_tarski(U_118,k8_relset_2(U_119,U_120,U_117,k6_relset_1(U_120,U_119,U_116)))
| ~ m2_relset_1(U_116,U_120,U_119)
| ~ m1_subset_1(U_117,k1_zfmisc_1(U_119))
| ~ m1_subset_1(U_118,k1_zfmisc_1(U_120)) ),
inference(clausify,[status(thm)],[f_55_2]) ).
cnf(f_55_4,plain,
( r1_tarski(U_118,k8_relset_2(U_119,U_120,U_117,k6_relset_1(U_120,U_119,U_116)))
| ~ r1_tarski(U_117,k8_relset_2(U_120,U_119,U_118,U_116))
| ~ m2_relset_1(U_116,U_120,U_119)
| ~ m1_subset_1(U_117,k1_zfmisc_1(U_119))
| ~ m1_subset_1(U_118,k1_zfmisc_1(U_120)) ),
inference(clausify,[status(thm)],[f_55_2]) ).
cnf(f_4_2_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_4_2]) ).
cnf(f_11_2_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_11_2]) ).
cnf(f_25_2_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_25_2]) ).
cnf(f_27_2_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_27_2]) ).
cnf(f_28_2_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_28_2]) ).
cnf(f_48_2_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_48_2]) ).
cnf(f_51_2_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_51_2]) ).
cnf(equality_1,axiom,
Eq_x_0 = Eq_x_0,
theory(equality,[reflexivity]) ).
cnf(equality_2,axiom,
( Eq_x_1 = Eq_x_0
| Eq_x_0 != Eq_x_1 ),
theory(equality,[symmetry]) ).
cnf(equality_3,axiom,
( Eq_x_0 = Eq_x_2
| Eq_x_1 != Eq_x_2
| Eq_x_0 != Eq_x_1 ),
theory(equality,[transitivity]) ).
cnf(equality_4,axiom,
( k1_zfmisc_1(Eq_x_0) = k1_zfmisc_1(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_5,axiom,
( k8_relset_2(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = k8_relset_2(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| 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_functions]) ).
cnf(equality_6,axiom,
( k6_relset_1(Eq_x_0,Eq_x_1,Eq_x_2) = k6_relset_1(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,
( k5_relset_2(Eq_x_0,Eq_x_1) = k5_relset_2(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,
( k2_zfmisc_1(Eq_x_0,Eq_x_1) = k2_zfmisc_1(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_9,axiom,
( k4_relset_2(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = k4_relset_2(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| 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_functions]) ).
cnf(equality_10,axiom,
( k9_relat_1(Eq_x_0,Eq_x_1) = k9_relat_1(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,
( k6_relset_2(Eq_x_0,Eq_x_1,Eq_x_2) = k6_relset_2(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_12,axiom,
( k3_pua2mss1(Eq_x_0) = k3_pua2mss1(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_13,axiom,
( k8_setfam_1(Eq_x_0,Eq_x_1) = k8_setfam_1(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,
( k4_relat_1(Eq_x_0) = k4_relat_1(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_15,axiom,
( k7_relset_2(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = k7_relset_2(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| 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_functions]) ).
cnf(equality_16,axiom,
( sK6(Eq_x_0) = sK6(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_17,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_18,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_19,axiom,
( sK12(Eq_x_0) = sK12(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_20,axiom,
( sK13(Eq_x_0) = sK13(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_21,axiom,
( sK14(Eq_x_0) = sK14(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_22,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_23,axiom,
( m1_subset_1(Eq_y_0,Eq_y_1)
| ~ m1_subset_1(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_24,axiom,
( m2_relset_1(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ m2_relset_1(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,
( r1_tarski(Eq_y_0,Eq_y_1)
| ~ r1_tarski(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,
( m1_eqrel_1(Eq_y_0,Eq_y_1)
| ~ m1_eqrel_1(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_27,axiom,
( v1_relat_1(Eq_y_0)
| ~ v1_relat_1(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_28,axiom,
( v1_funct_1(Eq_y_0)
| ~ v1_funct_1(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_29,axiom,
( m1_relset_1(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ m1_relset_1(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,
( v3_relat_1(Eq_y_0)
| ~ v3_relat_1(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_31,axiom,
( r2_hidden(Eq_y_0,Eq_y_1)
| ~ r2_hidden(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,
( v1_funct_2(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ v1_funct_2(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,
( v1_xboole_0(Eq_y_0)
| ~ v1_xboole_0(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 : SEU449+1 : TPTP v9.3.1. Released v3.4.0.
% 0.00/0.03 This is a FOF_THM_RFO_SEQ problem
% 0.00/0.04 % Command : /export/starexec/sandbox2/solver/bin/connect++ --verbosity 1 --no-colour --tptp-proof --schedule default --timeout 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n005.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Sun Sep 20 00:35:03 UTC 2026
% 0.09/0.36 % CPUTime :
% 1.06/1.32 % SZS status Theorem for theBenchmark
% 1.06/1.32 % SZS output start Proof for theBenchmark
% See solution above
%------------------------------------------------------------------------------