%------------------------------------------------------------------------------
% File : ConnectPP---0.7.2
% Problem : SEU444+1 : TPTP v9.3.1. Released v3.4.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/connect++ --verbosity 1 --no-colour --tptp-proof --schedule default --timeout 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n010.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Sep 24 08:59:22 AM UTC 2026
% Result : Theorem 0.10s 0.42s
% Output : Proof 0.10s
% Verified :
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)
% Comments :
%------------------------------------------------------------------------------
fof(t56_relset_2,conjecture,
! [A,B,C] :
( m2_relset_1(C,B,A)
=> ( k10_relset_1(A,B,k6_relset_1(B,A,C),k10_relset_1(B,A,C,B)) = k10_relset_1(A,B,k6_relset_1(B,A,C),k2_funct_5(C))
& k1_funct_5(C) = k10_relset_1(A,B,k6_relset_1(B,A,C),A) ) ),
file('theBenchmark.p',t56_relset_2) ).
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(dt_k1_xboole_0,axiom,
$true,
file('theBenchmark.p',dt_k1_xboole_0) ).
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(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(reflexivity_r1_tarski,axiom,
! [A,B] : r1_tarski(A,A),
file('theBenchmark.p',reflexivity_r1_tarski) ).
fof(cc1_relat_1,axiom,
! [A] :
( v1_xboole_0(A)
=> v1_relat_1(A) ),
file('theBenchmark.p',cc1_relat_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(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_relat_1,axiom,
? [A] :
( v1_relat_1(A)
& v1_xboole_0(A) ),
file('theBenchmark.p',rc1_relat_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_relat_1,axiom,
? [A] :
( v1_relat_1(A)
& ~ v1_xboole_0(A) ),
file('theBenchmark.p',rc2_relat_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(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(existence_m1_subset_1,axiom,
! [A] :
? [B] : m1_subset_1(B,A),
file('theBenchmark.p',existence_m1_subset_1) ).
fof(dt_k1_zfmisc_1,axiom,
$true,
file('theBenchmark.p',dt_k1_zfmisc_1) ).
fof(dt_k2_zfmisc_1,axiom,
$true,
file('theBenchmark.p',dt_k2_zfmisc_1) ).
fof(dt_k4_relat_1,axiom,
! [A] :
( v1_relat_1(A)
=> v1_relat_1(k4_relat_1(A)) ),
file('theBenchmark.p',dt_k4_relat_1) ).
fof(dt_k9_relat_1,axiom,
$true,
file('theBenchmark.p',dt_k9_relat_1) ).
fof(dt_m1_relset_1,axiom,
$true,
file('theBenchmark.p',dt_m1_relset_1) ).
fof(dt_m1_subset_1,axiom,
$true,
file('theBenchmark.p',dt_m1_subset_1) ).
fof(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(fc1_subset_1,axiom,
! [A] : ~ v1_xboole_0(k1_zfmisc_1(A)),
file('theBenchmark.p',fc1_subset_1) ).
fof(fc1_sysrel,axiom,
! [A,B] : v1_relat_1(k2_zfmisc_1(A,B)),
file('theBenchmark.p',fc1_sysrel) ).
fof(t3_subset,axiom,
! [A,B] :
( m1_subset_1(A,k1_zfmisc_1(B))
<=> r1_tarski(A,B) ),
file('theBenchmark.p',t3_subset) ).
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(existence_m2_relset_1,axiom,
! [A,B] :
? [C] : m2_relset_1(C,A,B),
file('theBenchmark.p',existence_m2_relset_1) ).
fof(redefinition_k10_relset_1,axiom,
! [A,B,C,D] :
( m1_relset_1(C,A,B)
=> k10_relset_1(A,B,C,D) = k9_relat_1(C,D) ),
file('theBenchmark.p',redefinition_k10_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_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_k10_relset_1,axiom,
! [A,B,C,D] :
( m1_relset_1(C,A,B)
=> m1_subset_1(k10_relset_1(A,B,C,D),k1_zfmisc_1(B)) ),
file('theBenchmark.p',dt_k10_relset_1) ).
fof(dt_k1_funct_5,axiom,
$true,
file('theBenchmark.p',dt_k1_funct_5) ).
fof(dt_k2_funct_5,axiom,
$true,
file('theBenchmark.p',dt_k2_funct_5) ).
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_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(t51_relset_2,axiom,
! [A,B,C] :
( m2_relset_1(C,B,A)
=> ( k2_funct_5(C) = k10_relset_1(B,A,C,B)
& k1_funct_5(C) = k10_relset_1(A,B,k6_relset_1(B,A,C),A) ) ),
file('theBenchmark.p',t51_relset_2) ).
fof(f_1_1,negated_conjecture,
~ ! [A,B,C] :
( m2_relset_1(C,B,A)
=> ( k10_relset_1(A,B,k6_relset_1(B,A,C),k10_relset_1(B,A,C,B)) = k10_relset_1(A,B,k6_relset_1(B,A,C),k2_funct_5(C))
& k1_funct_5(C) = k10_relset_1(A,B,k6_relset_1(B,A,C),A) ) ),
inference(negate,[status(cth)],[t56_relset_2]) ).
fof(f_1_2,negated_conjecture,
? [A,B,C] :
( ( k10_relset_1(A,B,k6_relset_1(B,A,C),k10_relset_1(B,A,C,B)) != k10_relset_1(A,B,k6_relset_1(B,A,C),k2_funct_5(C))
| k1_funct_5(C) != k10_relset_1(A,B,k6_relset_1(B,A,C),A) )
& m2_relset_1(C,B,A) ),
inference(fof_nnf,[status(thm)],[f_1_1]) ).
fof(f_1_3,negated_conjecture,
? [U_2,U_1,U_0] :
( ( k10_relset_1(U_2,U_1,k6_relset_1(U_1,U_2,U_0),k10_relset_1(U_1,U_2,U_0,U_1)) != k10_relset_1(U_2,U_1,k6_relset_1(U_1,U_2,U_0),k2_funct_5(U_0))
| k1_funct_5(U_0) != k10_relset_1(U_2,U_1,k6_relset_1(U_1,U_2,U_0),U_2) )
& m2_relset_1(U_0,U_1,U_2) ),
inference(variable_rename,[status(thm)],[f_1_2]) ).
fof(f_1_4,negated_conjecture,
? [U_1,U_0] :
( ( k10_relset_1(sK1,U_1,k6_relset_1(U_1,sK1,U_0),k10_relset_1(U_1,sK1,U_0,U_1)) != k10_relset_1(sK1,U_1,k6_relset_1(U_1,sK1,U_0),k2_funct_5(U_0))
| k1_funct_5(U_0) != k10_relset_1(sK1,U_1,k6_relset_1(U_1,sK1,U_0),sK1) )
& m2_relset_1(U_0,U_1,sK1) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(U_2,sK1)],[f_1_3]) ).
fof(f_1_5,negated_conjecture,
? [U_0] :
( ( k10_relset_1(sK1,sK2,k6_relset_1(sK2,sK1,U_0),k10_relset_1(sK2,sK1,U_0,sK2)) != k10_relset_1(sK1,sK2,k6_relset_1(sK2,sK1,U_0),k2_funct_5(U_0))
| k1_funct_5(U_0) != k10_relset_1(sK1,sK2,k6_relset_1(sK2,sK1,U_0),sK1) )
& m2_relset_1(U_0,sK2,sK1) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2]),skolemize(U_1,sK2)],[f_1_4]) ).
fof(f_1_6,negated_conjecture,
( ( k10_relset_1(sK1,sK2,k6_relset_1(sK2,sK1,sK3),k10_relset_1(sK2,sK1,sK3,sK2)) != k10_relset_1(sK1,sK2,k6_relset_1(sK2,sK1,sK3),k2_funct_5(sK3))
| k1_funct_5(sK3) != k10_relset_1(sK1,sK2,k6_relset_1(sK2,sK1,sK3),sK1) )
& m2_relset_1(sK3,sK2,sK1) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3]),skolemize(U_0,sK3)],[f_1_5]) ).
fof(f_1_7,negated_conjecture,
( ( k10_relset_1(sK1,sK2,k6_relset_1(sK2,sK1,sK3),k10_relset_1(sK2,sK1,sK3,sK2)) != k10_relset_1(sK1,sK2,k6_relset_1(sK2,sK1,sK3),k2_funct_5(sK3))
| k1_funct_5(sK3) != k10_relset_1(sK1,sK2,k6_relset_1(sK2,sK1,sK3),sK1) )
& m2_relset_1(sK3,sK2,sK1) ),
inference(definitional_conversion,[status(esa)],[f_1_6]) ).
cnf(f_1_8,negated_conjecture,
m2_relset_1(sK3,sK2,sK1),
inference(clausify,[status(thm)],[f_1_7]) ).
cnf(f_1_9,negated_conjecture,
( k10_relset_1(sK1,sK2,k6_relset_1(sK2,sK1,sK3),k10_relset_1(sK2,sK1,sK3,sK2)) != k10_relset_1(sK1,sK2,k6_relset_1(sK2,sK1,sK3),k2_funct_5(sK3))
| k1_funct_5(sK3) != k10_relset_1(sK1,sK2,k6_relset_1(sK2,sK1,sK3),sK1) ),
inference(clausify,[status(thm)],[f_1_7]) ).
fof(f_2_1,plain,
? [A] :
( v3_relat_1(A)
& v1_relat_1(A) ),
inference(fof_nnf,[status(thm)],[rc3_relat_1]) ).
fof(f_2_2,plain,
? [U_3] :
( v3_relat_1(U_3)
& v1_relat_1(U_3) ),
inference(variable_rename,[status(thm)],[f_2_1]) ).
fof(f_2_3,plain,
( v3_relat_1(sK4)
& v1_relat_1(sK4) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4]),skolemize(U_3,sK4)],[f_2_2]) ).
cnf(f_2_4,plain,
v1_relat_1(sK4),
inference(clausify,[status(thm)],[f_2_3]) ).
cnf(f_2_5,plain,
v3_relat_1(sK4),
inference(clausify,[status(thm)],[f_2_3]) ).
fof(f_3_1,plain,
! [A,B] :
( ~ r2_hidden(B,A)
| ~ r2_hidden(A,B) ),
inference(fof_nnf,[status(thm)],[antisymmetry_r2_hidden]) ).
fof(f_3_2,plain,
! [U_5,U_4] :
( ~ r2_hidden(U_4,U_5)
| ~ r2_hidden(U_5,U_4) ),
inference(variable_rename,[status(thm)],[f_3_1]) ).
cnf(f_3_3,plain,
( ~ r2_hidden(U_4,U_5)
| ~ r2_hidden(U_5,U_4) ),
inference(clausify,[status(thm)],[f_3_2]) ).
fof(f_4_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_k1_xboole_0]) ).
cnf(f_4_2,plain,
$true,
inference(clausify,[status(thm)],[f_4_1]) ).
fof(f_5_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_5_2,plain,
v1_xboole_0(k1_xboole_0),
inference(clausify,[status(thm)],[f_5_1]) ).
cnf(f_5_3,plain,
v1_relat_1(k1_xboole_0),
inference(clausify,[status(thm)],[f_5_1]) ).
cnf(f_5_4,plain,
v3_relat_1(k1_xboole_0),
inference(clausify,[status(thm)],[f_5_1]) ).
fof(f_6_1,plain,
( v1_relat_1(k1_xboole_0)
& v1_xboole_0(k1_xboole_0) ),
inference(fof_nnf,[status(thm)],[fc4_relat_1]) ).
cnf(f_6_2,plain,
v1_xboole_0(k1_xboole_0),
inference(clausify,[status(thm)],[f_6_1]) ).
cnf(f_6_3,plain,
v1_relat_1(k1_xboole_0),
inference(clausify,[status(thm)],[f_6_1]) ).
fof(f_7_1,plain,
! [A,B] :
( m1_subset_1(A,B)
| ~ r2_hidden(A,B) ),
inference(fof_nnf,[status(thm)],[t1_subset]) ).
fof(f_7_2,plain,
! [U_7,U_6] :
( m1_subset_1(U_7,U_6)
| ~ r2_hidden(U_7,U_6) ),
inference(variable_rename,[status(thm)],[f_7_1]) ).
cnf(f_7_3,plain,
( m1_subset_1(U_7,U_6)
| ~ r2_hidden(U_7,U_6) ),
inference(clausify,[status(thm)],[f_7_2]) ).
fof(f_8_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_8_2,plain,
! [U_10,U_9,U_8] :
( m1_subset_1(U_10,U_8)
| ~ m1_subset_1(U_9,k1_zfmisc_1(U_8))
| ~ r2_hidden(U_10,U_9) ),
inference(variable_rename,[status(thm)],[f_8_1]) ).
cnf(f_8_3,plain,
( m1_subset_1(U_10,U_8)
| ~ m1_subset_1(U_9,k1_zfmisc_1(U_8))
| ~ r2_hidden(U_10,U_9) ),
inference(clausify,[status(thm)],[f_8_2]) ).
fof(f_9_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_9_2,plain,
! [U_13,U_12,U_11] :
( ~ v1_xboole_0(U_11)
| ~ m1_subset_1(U_12,k1_zfmisc_1(U_11))
| ~ r2_hidden(U_13,U_12) ),
inference(variable_rename,[status(thm)],[f_9_1]) ).
fof(f_9_3,plain,
! [U_13,U_12] :
( ! [U_11] :
( ~ v1_xboole_0(U_11)
| ~ m1_subset_1(U_12,k1_zfmisc_1(U_11)) )
| ~ r2_hidden(U_13,U_12) ),
inference(miniscope,[status(thm)],[f_9_2]) ).
cnf(f_9_4,plain,
( ~ v1_xboole_0(U_11)
| ~ m1_subset_1(U_12,k1_zfmisc_1(U_11))
| ~ r2_hidden(U_13,U_12) ),
inference(clausify,[status(thm)],[f_9_3]) ).
fof(f_10_1,plain,
! [A,B] : r1_tarski(A,A),
inference(fof_nnf,[status(thm)],[reflexivity_r1_tarski]) ).
fof(f_10_2,plain,
! [U_15,U_14] : r1_tarski(U_15,U_15),
inference(variable_rename,[status(thm)],[f_10_1]) ).
fof(f_10_3,plain,
! [U_15] : r1_tarski(U_15,U_15),
inference(miniscope,[status(thm)],[f_10_2]) ).
cnf(f_10_4,plain,
r1_tarski(U_15,U_15),
inference(clausify,[status(thm)],[f_10_3]) ).
fof(f_11_1,plain,
! [A] :
( v1_relat_1(A)
| ~ v1_xboole_0(A) ),
inference(fof_nnf,[status(thm)],[cc1_relat_1]) ).
fof(f_11_2,plain,
! [U_16] :
( v1_relat_1(U_16)
| ~ v1_xboole_0(U_16) ),
inference(variable_rename,[status(thm)],[f_11_1]) ).
cnf(f_11_3,plain,
( v1_relat_1(U_16)
| ~ v1_xboole_0(U_16) ),
inference(clausify,[status(thm)],[f_11_2]) ).
fof(f_12_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_12_2,plain,
! [U_17] :
( ( v1_relat_1(k4_relat_1(U_17))
& v1_xboole_0(k4_relat_1(U_17)) )
| ~ v1_xboole_0(U_17) ),
inference(variable_rename,[status(thm)],[f_12_1]) ).
cnf(f_12_3,plain,
( v1_xboole_0(k4_relat_1(U_17))
| ~ v1_xboole_0(U_17) ),
inference(clausify,[status(thm)],[f_12_2]) ).
cnf(f_12_4,plain,
( v1_relat_1(k4_relat_1(U_17))
| ~ v1_xboole_0(U_17) ),
inference(clausify,[status(thm)],[f_12_2]) ).
fof(f_13_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_13_2,plain,
! [U_19,U_18] :
( ~ v1_xboole_0(k2_zfmisc_1(U_19,U_18))
| v1_xboole_0(U_18)
| v1_xboole_0(U_19) ),
inference(variable_rename,[status(thm)],[f_13_1]) ).
cnf(f_13_3,plain,
( ~ v1_xboole_0(k2_zfmisc_1(U_19,U_18))
| v1_xboole_0(U_18)
| v1_xboole_0(U_19) ),
inference(clausify,[status(thm)],[f_13_2]) ).
fof(f_14_1,plain,
? [A] :
( v1_relat_1(A)
& v1_xboole_0(A) ),
inference(fof_nnf,[status(thm)],[rc1_relat_1]) ).
fof(f_14_2,plain,
? [U_20] :
( v1_relat_1(U_20)
& v1_xboole_0(U_20) ),
inference(variable_rename,[status(thm)],[f_14_1]) ).
fof(f_14_3,plain,
( v1_relat_1(sK5)
& v1_xboole_0(sK5) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK5]),skolemize(U_20,sK5)],[f_14_2]) ).
cnf(f_14_4,plain,
v1_xboole_0(sK5),
inference(clausify,[status(thm)],[f_14_3]) ).
cnf(f_14_5,plain,
v1_relat_1(sK5),
inference(clausify,[status(thm)],[f_14_3]) ).
fof(f_15_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_15_2,plain,
! [U_22] :
( ? [U_21] :
( ~ v1_xboole_0(U_21)
& m1_subset_1(U_21,k1_zfmisc_1(U_22)) )
| v1_xboole_0(U_22) ),
inference(variable_rename,[status(thm)],[f_15_1]) ).
fof(f_15_3,plain,
! [U_22] :
( ( ~ v1_xboole_0(sK6(U_22))
& m1_subset_1(sK6(U_22),k1_zfmisc_1(U_22)) )
| v1_xboole_0(U_22) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK6]),skolemize(U_21,sK6(U_22))],[f_15_2]) ).
cnf(f_15_4,plain,
( m1_subset_1(sK6(U_22),k1_zfmisc_1(U_22))
| v1_xboole_0(U_22) ),
inference(clausify,[status(thm)],[f_15_3]) ).
cnf(f_15_5,plain,
( ~ v1_xboole_0(sK6(U_22))
| v1_xboole_0(U_22) ),
inference(clausify,[status(thm)],[f_15_3]) ).
fof(f_16_1,plain,
? [A] :
( v1_relat_1(A)
& ~ v1_xboole_0(A) ),
inference(fof_nnf,[status(thm)],[rc2_relat_1]) ).
fof(f_16_2,plain,
? [U_23] :
( v1_relat_1(U_23)
& ~ v1_xboole_0(U_23) ),
inference(variable_rename,[status(thm)],[f_16_1]) ).
fof(f_16_3,plain,
( v1_relat_1(sK7)
& ~ v1_xboole_0(sK7) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK7]),skolemize(U_23,sK7)],[f_16_2]) ).
cnf(f_16_4,plain,
~ v1_xboole_0(sK7),
inference(clausify,[status(thm)],[f_16_3]) ).
cnf(f_16_5,plain,
v1_relat_1(sK7),
inference(clausify,[status(thm)],[f_16_3]) ).
fof(f_17_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_17_2,plain,
! [U_25] :
? [U_24] :
( v1_xboole_0(U_24)
& m1_subset_1(U_24,k1_zfmisc_1(U_25)) ),
inference(variable_rename,[status(thm)],[f_17_1]) ).
fof(f_17_3,plain,
! [U_25] :
( v1_xboole_0(sK8(U_25))
& m1_subset_1(sK8(U_25),k1_zfmisc_1(U_25)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK8]),skolemize(U_24,sK8(U_25))],[f_17_2]) ).
cnf(f_17_4,plain,
m1_subset_1(sK8(U_25),k1_zfmisc_1(U_25)),
inference(clausify,[status(thm)],[f_17_3]) ).
cnf(f_17_5,plain,
v1_xboole_0(sK8(U_25)),
inference(clausify,[status(thm)],[f_17_3]) ).
fof(f_18_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_18_2,plain,
! [U_27,U_26] :
( r2_hidden(U_27,U_26)
| v1_xboole_0(U_26)
| ~ m1_subset_1(U_27,U_26) ),
inference(variable_rename,[status(thm)],[f_18_1]) ).
cnf(f_18_3,plain,
( r2_hidden(U_27,U_26)
| v1_xboole_0(U_26)
| ~ m1_subset_1(U_27,U_26) ),
inference(clausify,[status(thm)],[f_18_2]) ).
fof(f_19_1,plain,
! [A] :
( A = k1_xboole_0
| ~ v1_xboole_0(A) ),
inference(fof_nnf,[status(thm)],[t6_boole]) ).
fof(f_19_2,plain,
! [U_28] :
( U_28 = k1_xboole_0
| ~ v1_xboole_0(U_28) ),
inference(variable_rename,[status(thm)],[f_19_1]) ).
cnf(f_19_3,plain,
( U_28 = k1_xboole_0
| ~ v1_xboole_0(U_28) ),
inference(clausify,[status(thm)],[f_19_2]) ).
fof(f_20_1,plain,
! [A,B] :
( ~ v1_xboole_0(B)
| ~ r2_hidden(A,B) ),
inference(fof_nnf,[status(thm)],[t7_boole]) ).
fof(f_20_2,plain,
! [U_30,U_29] :
( ~ v1_xboole_0(U_29)
| ~ r2_hidden(U_30,U_29) ),
inference(variable_rename,[status(thm)],[f_20_1]) ).
cnf(f_20_3,plain,
( ~ v1_xboole_0(U_29)
| ~ r2_hidden(U_30,U_29) ),
inference(clausify,[status(thm)],[f_20_2]) ).
fof(f_21_1,plain,
! [A,B] :
( ~ v1_xboole_0(B)
| A = B
| ~ v1_xboole_0(A) ),
inference(fof_nnf,[status(thm)],[t8_boole]) ).
fof(f_21_2,plain,
! [U_32,U_31] :
( ~ v1_xboole_0(U_31)
| U_32 = U_31
| ~ v1_xboole_0(U_32) ),
inference(variable_rename,[status(thm)],[f_21_1]) ).
fof(f_21_3,plain,
! [U_32] :
( ! [U_31] :
( ~ v1_xboole_0(U_31)
| U_32 = U_31 )
| ~ v1_xboole_0(U_32) ),
inference(miniscope,[status(thm)],[f_21_2]) ).
cnf(f_21_4,plain,
( ~ v1_xboole_0(U_31)
| U_32 = U_31
| ~ v1_xboole_0(U_32) ),
inference(clausify,[status(thm)],[f_21_3]) ).
fof(f_22_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_22_2,plain,
! [U_33] :
( k4_relat_1(k4_relat_1(U_33)) = U_33
| ~ v1_relat_1(U_33) ),
inference(variable_rename,[status(thm)],[f_22_1]) ).
cnf(f_22_3,plain,
( k4_relat_1(k4_relat_1(U_33)) = U_33
| ~ v1_relat_1(U_33) ),
inference(clausify,[status(thm)],[f_22_2]) ).
fof(f_23_1,plain,
! [A,B] :
? [C] : m1_relset_1(C,A,B),
inference(fof_nnf,[status(thm)],[existence_m1_relset_1]) ).
fof(f_23_2,plain,
! [U_36,U_35] :
? [U_34] : m1_relset_1(U_34,U_36,U_35),
inference(variable_rename,[status(thm)],[f_23_1]) ).
fof(f_23_3,plain,
! [U_36,U_35] : m1_relset_1(sK9(U_36,U_35),U_36,U_35),
inference(skolemize,[status(esa),new_symbols(skolem,[sK9]),skolemize(U_34,sK9(U_36,U_35))],[f_23_2]) ).
cnf(f_23_4,plain,
m1_relset_1(sK9(U_36,U_35),U_36,U_35),
inference(clausify,[status(thm)],[f_23_3]) ).
fof(f_24_1,plain,
! [A] :
? [B] : m1_subset_1(B,A),
inference(fof_nnf,[status(thm)],[existence_m1_subset_1]) ).
fof(f_24_2,plain,
! [U_38] :
? [U_37] : m1_subset_1(U_37,U_38),
inference(variable_rename,[status(thm)],[f_24_1]) ).
fof(f_24_3,plain,
! [U_38] : m1_subset_1(sK10(U_38),U_38),
inference(skolemize,[status(esa),new_symbols(skolem,[sK10]),skolemize(U_37,sK10(U_38))],[f_24_2]) ).
cnf(f_24_4,plain,
m1_subset_1(sK10(U_38),U_38),
inference(clausify,[status(thm)],[f_24_3]) ).
fof(f_25_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_k1_zfmisc_1]) ).
cnf(f_25_2,plain,
$true,
inference(clausify,[status(thm)],[f_25_1]) ).
fof(f_26_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_k2_zfmisc_1]) ).
cnf(f_26_2,plain,
$true,
inference(clausify,[status(thm)],[f_26_1]) ).
fof(f_27_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_27_2,plain,
! [U_39] :
( v1_relat_1(k4_relat_1(U_39))
| ~ v1_relat_1(U_39) ),
inference(variable_rename,[status(thm)],[f_27_1]) ).
cnf(f_27_3,plain,
( v1_relat_1(k4_relat_1(U_39))
| ~ v1_relat_1(U_39) ),
inference(clausify,[status(thm)],[f_27_2]) ).
fof(f_28_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_k9_relat_1]) ).
cnf(f_28_2,plain,
$true,
inference(clausify,[status(thm)],[f_28_1]) ).
fof(f_29_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_m1_relset_1]) ).
cnf(f_29_2,plain,
$true,
inference(clausify,[status(thm)],[f_29_1]) ).
fof(f_30_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_m1_subset_1]) ).
cnf(f_30_2,plain,
$true,
inference(clausify,[status(thm)],[f_30_1]) ).
fof(f_31_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_31_2,plain,
! [U_42,U_41,U_40] :
( v1_relat_1(U_40)
| ~ m1_subset_1(U_40,k1_zfmisc_1(k2_zfmisc_1(U_42,U_41))) ),
inference(variable_rename,[status(thm)],[f_31_1]) ).
cnf(f_31_3,plain,
( v1_relat_1(U_40)
| ~ m1_subset_1(U_40,k1_zfmisc_1(k2_zfmisc_1(U_42,U_41))) ),
inference(clausify,[status(thm)],[f_31_2]) ).
fof(f_32_1,plain,
! [A] : ~ v1_xboole_0(k1_zfmisc_1(A)),
inference(fof_nnf,[status(thm)],[fc1_subset_1]) ).
fof(f_32_2,plain,
! [U_43] : ~ v1_xboole_0(k1_zfmisc_1(U_43)),
inference(variable_rename,[status(thm)],[f_32_1]) ).
cnf(f_32_3,plain,
~ v1_xboole_0(k1_zfmisc_1(U_43)),
inference(clausify,[status(thm)],[f_32_2]) ).
fof(f_33_1,plain,
! [A,B] : v1_relat_1(k2_zfmisc_1(A,B)),
inference(fof_nnf,[status(thm)],[fc1_sysrel]) ).
fof(f_33_2,plain,
! [U_45,U_44] : v1_relat_1(k2_zfmisc_1(U_45,U_44)),
inference(variable_rename,[status(thm)],[f_33_1]) ).
cnf(f_33_3,plain,
v1_relat_1(k2_zfmisc_1(U_45,U_44)),
inference(clausify,[status(thm)],[f_33_2]) ).
fof(f_34_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_34_2,plain,
! [U_47,U_46] :
( ( m1_subset_1(U_47,k1_zfmisc_1(U_46))
| ~ r1_tarski(U_47,U_46) )
& ( r1_tarski(U_47,U_46)
| ~ m1_subset_1(U_47,k1_zfmisc_1(U_46)) ) ),
inference(variable_rename,[status(thm)],[f_34_1]) ).
fof(f_34_3,plain,
( ! [U_51,U_49] :
( m1_subset_1(U_51,k1_zfmisc_1(U_49))
| ~ r1_tarski(U_51,U_49) )
& ! [U_50,U_48] :
( r1_tarski(U_50,U_48)
| ~ m1_subset_1(U_50,k1_zfmisc_1(U_48)) ) ),
inference(miniscope,[status(thm)],[f_34_2]) ).
cnf(f_34_4,plain,
( r1_tarski(U_50,U_48)
| ~ m1_subset_1(U_50,k1_zfmisc_1(U_48)) ),
inference(clausify,[status(thm)],[f_34_3]) ).
cnf(f_34_5,plain,
( m1_subset_1(U_51,k1_zfmisc_1(U_49))
| ~ r1_tarski(U_51,U_49) ),
inference(clausify,[status(thm)],[f_34_3]) ).
fof(f_35_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_35_2,plain,
! [U_54,U_53,U_52] :
( k6_relset_1(U_54,U_53,k6_relset_1(U_54,U_53,U_52)) = U_52
| ~ m1_relset_1(U_52,U_54,U_53) ),
inference(variable_rename,[status(thm)],[f_35_1]) ).
cnf(f_35_3,plain,
( k6_relset_1(U_54,U_53,k6_relset_1(U_54,U_53,U_52)) = U_52
| ~ m1_relset_1(U_52,U_54,U_53) ),
inference(clausify,[status(thm)],[f_35_2]) ).
fof(f_36_1,plain,
! [A,B] :
? [C] : m2_relset_1(C,A,B),
inference(fof_nnf,[status(thm)],[existence_m2_relset_1]) ).
fof(f_36_2,plain,
! [U_57,U_56] :
? [U_55] : m2_relset_1(U_55,U_57,U_56),
inference(variable_rename,[status(thm)],[f_36_1]) ).
fof(f_36_3,plain,
! [U_57,U_56] : m2_relset_1(sK11(U_57,U_56),U_57,U_56),
inference(skolemize,[status(esa),new_symbols(skolem,[sK11]),skolemize(U_55,sK11(U_57,U_56))],[f_36_2]) ).
cnf(f_36_4,plain,
m2_relset_1(sK11(U_57,U_56),U_57,U_56),
inference(clausify,[status(thm)],[f_36_3]) ).
fof(f_37_1,plain,
! [A,B,C,D] :
( k10_relset_1(A,B,C,D) = k9_relat_1(C,D)
| ~ m1_relset_1(C,A,B) ),
inference(fof_nnf,[status(thm)],[redefinition_k10_relset_1]) ).
fof(f_37_2,plain,
! [U_61,U_60,U_59,U_58] :
( k10_relset_1(U_61,U_60,U_59,U_58) = k9_relat_1(U_59,U_58)
| ~ m1_relset_1(U_59,U_61,U_60) ),
inference(variable_rename,[status(thm)],[f_37_1]) ).
fof(f_37_3,plain,
! [U_61,U_60,U_59] :
( ! [U_58] : k10_relset_1(U_61,U_60,U_59,U_58) = k9_relat_1(U_59,U_58)
| ~ m1_relset_1(U_59,U_61,U_60) ),
inference(miniscope,[status(thm)],[f_37_2]) ).
cnf(f_37_4,plain,
( k10_relset_1(U_61,U_60,U_59,U_58) = k9_relat_1(U_59,U_58)
| ~ m1_relset_1(U_59,U_61,U_60) ),
inference(clausify,[status(thm)],[f_37_3]) ).
fof(f_38_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_38_2,plain,
! [U_64,U_63,U_62] :
( k6_relset_1(U_64,U_63,U_62) = k4_relat_1(U_62)
| ~ m1_relset_1(U_62,U_64,U_63) ),
inference(variable_rename,[status(thm)],[f_38_1]) ).
cnf(f_38_3,plain,
( k6_relset_1(U_64,U_63,U_62) = k4_relat_1(U_62)
| ~ m1_relset_1(U_62,U_64,U_63) ),
inference(clausify,[status(thm)],[f_38_2]) ).
fof(f_39_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_39_2,plain,
! [U_67,U_66,U_65] :
( ( m2_relset_1(U_65,U_67,U_66)
| ~ m1_relset_1(U_65,U_67,U_66) )
& ( m1_relset_1(U_65,U_67,U_66)
| ~ m2_relset_1(U_65,U_67,U_66) ) ),
inference(variable_rename,[status(thm)],[f_39_1]) ).
fof(f_39_3,plain,
( ! [U_73,U_71,U_69] :
( m2_relset_1(U_69,U_73,U_71)
| ~ m1_relset_1(U_69,U_73,U_71) )
& ! [U_72,U_70,U_68] :
( m1_relset_1(U_68,U_72,U_70)
| ~ m2_relset_1(U_68,U_72,U_70) ) ),
inference(miniscope,[status(thm)],[f_39_2]) ).
cnf(f_39_4,plain,
( m1_relset_1(U_68,U_72,U_70)
| ~ m2_relset_1(U_68,U_72,U_70) ),
inference(clausify,[status(thm)],[f_39_3]) ).
cnf(f_39_5,plain,
( m2_relset_1(U_69,U_73,U_71)
| ~ m1_relset_1(U_69,U_73,U_71) ),
inference(clausify,[status(thm)],[f_39_3]) ).
fof(f_40_1,plain,
! [A,B,C,D] :
( m1_subset_1(k10_relset_1(A,B,C,D),k1_zfmisc_1(B))
| ~ m1_relset_1(C,A,B) ),
inference(fof_nnf,[status(thm)],[dt_k10_relset_1]) ).
fof(f_40_2,plain,
! [U_77,U_76,U_75,U_74] :
( m1_subset_1(k10_relset_1(U_77,U_76,U_75,U_74),k1_zfmisc_1(U_76))
| ~ m1_relset_1(U_75,U_77,U_76) ),
inference(variable_rename,[status(thm)],[f_40_1]) ).
fof(f_40_3,plain,
! [U_77,U_76,U_75] :
( ! [U_74] : m1_subset_1(k10_relset_1(U_77,U_76,U_75,U_74),k1_zfmisc_1(U_76))
| ~ m1_relset_1(U_75,U_77,U_76) ),
inference(miniscope,[status(thm)],[f_40_2]) ).
cnf(f_40_4,plain,
( m1_subset_1(k10_relset_1(U_77,U_76,U_75,U_74),k1_zfmisc_1(U_76))
| ~ m1_relset_1(U_75,U_77,U_76) ),
inference(clausify,[status(thm)],[f_40_3]) ).
fof(f_41_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_k1_funct_5]) ).
cnf(f_41_2,plain,
$true,
inference(clausify,[status(thm)],[f_41_1]) ).
fof(f_42_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_k2_funct_5]) ).
cnf(f_42_2,plain,
$true,
inference(clausify,[status(thm)],[f_42_1]) ).
fof(f_43_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_43_2,plain,
! [U_80,U_79,U_78] :
( m2_relset_1(k6_relset_1(U_80,U_79,U_78),U_79,U_80)
| ~ m1_relset_1(U_78,U_80,U_79) ),
inference(variable_rename,[status(thm)],[f_43_1]) ).
cnf(f_43_3,plain,
( m2_relset_1(k6_relset_1(U_80,U_79,U_78),U_79,U_80)
| ~ m1_relset_1(U_78,U_80,U_79) ),
inference(clausify,[status(thm)],[f_43_2]) ).
fof(f_44_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_44_2,plain,
! [U_83,U_82,U_81] :
( m1_subset_1(U_81,k1_zfmisc_1(k2_zfmisc_1(U_83,U_82)))
| ~ m2_relset_1(U_81,U_83,U_82) ),
inference(variable_rename,[status(thm)],[f_44_1]) ).
cnf(f_44_3,plain,
( m1_subset_1(U_81,k1_zfmisc_1(k2_zfmisc_1(U_83,U_82)))
| ~ m2_relset_1(U_81,U_83,U_82) ),
inference(clausify,[status(thm)],[f_44_2]) ).
fof(f_45_1,plain,
! [A,B,C] :
( ( k2_funct_5(C) = k10_relset_1(B,A,C,B)
& k1_funct_5(C) = k10_relset_1(A,B,k6_relset_1(B,A,C),A) )
| ~ m2_relset_1(C,B,A) ),
inference(fof_nnf,[status(thm)],[t51_relset_2]) ).
fof(f_45_2,plain,
! [U_86,U_85,U_84] :
( ( k2_funct_5(U_84) = k10_relset_1(U_85,U_86,U_84,U_85)
& k1_funct_5(U_84) = k10_relset_1(U_86,U_85,k6_relset_1(U_85,U_86,U_84),U_86) )
| ~ m2_relset_1(U_84,U_85,U_86) ),
inference(variable_rename,[status(thm)],[f_45_1]) ).
cnf(f_45_3,plain,
( k1_funct_5(U_84) = k10_relset_1(U_86,U_85,k6_relset_1(U_85,U_86,U_84),U_86)
| ~ m2_relset_1(U_84,U_85,U_86) ),
inference(clausify,[status(thm)],[f_45_2]) ).
cnf(f_45_4,plain,
( k2_funct_5(U_84) = k10_relset_1(U_85,U_86,U_84,U_85)
| ~ m2_relset_1(U_84,U_85,U_86) ),
inference(clausify,[status(thm)],[f_45_2]) ).
cnf(f_4_2_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_4_2]) ).
cnf(f_25_2_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_25_2]) ).
cnf(f_26_2_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_26_2]) ).
cnf(f_28_2_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_28_2]) ).
cnf(f_29_2_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_29_2]) ).
cnf(f_30_2_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_30_2]) ).
cnf(f_41_2_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_41_2]) ).
cnf(f_42_2_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_42_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_funct_5(Eq_x_0) = k1_funct_5(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_5,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_6,axiom,
( k10_relset_1(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = k10_relset_1(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_7,axiom,
( k2_funct_5(Eq_x_0) = k2_funct_5(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_8,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_9,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_10,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_11,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_12,axiom,
( sK6(Eq_x_0) = sK6(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_13,axiom,
( sK8(Eq_x_0) = sK8(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_14,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_15,axiom,
( sK10(Eq_x_0) = sK10(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_16,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_17,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_18,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_19,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_20,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_21,axiom,
( v1_xboole_0(Eq_y_0)
| ~ v1_xboole_0(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_22,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_23,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_24,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(sat_proved,plain,
$false,
inference(cadical,[status(thm)],[]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU444+1 : TPTP v9.3.1. Released v3.4.0.
% 0.00/0.03 This is a FOF_THM_RFO_SEQ problem
% 0.00/0.03 % Command : /export/starexec/sandbox/solver/bin/connect++ --verbosity 1 --no-colour --tptp-proof --schedule default --timeout 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.36 % Computer : n010.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Sun Sep 20 00:32:38 UTC 2026
% 0.10/0.36 % CPUTime :
% 0.10/0.42 % SZS status Theorem for theBenchmark
% 0.10/0.42 % SZS output start Proof for theBenchmark
% See solution above
%------------------------------------------------------------------------------