%------------------------------------------------------------------------------
% File : ConnectPP---0.7.2
% Problem : SEU419+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 : n017.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 08:59:16 AM UTC 2026
% Result : Theorem 222.14s 227.48s
% Output : Proof 223.83s
% Verified :
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)
% Comments :
%------------------------------------------------------------------------------
fof(t12_relset_2,conjecture,
! [A,B] :
( v1_relat_1(B)
=> ! [C] :
( v1_relat_1(C)
=> k9_relat_1(k4_xboole_0(B,C),k1_tarski(A)) = k4_xboole_0(k9_relat_1(B,k1_tarski(A)),k9_relat_1(C,k1_tarski(A))) ) ),
file('theBenchmark.p',t12_relset_2) ).
fof(antisymmetry_r2_hidden,axiom,
! [A,B] :
( r2_hidden(A,B)
=> ~ r2_hidden(B,A) ),
file('theBenchmark.p',antisymmetry_r2_hidden) ).
fof(cc1_relat_1,axiom,
! [A] :
( v1_xboole_0(A)
=> v1_relat_1(A) ),
file('theBenchmark.p',cc1_relat_1) ).
fof(commutativity_k2_tarski,axiom,
! [A,B] : k2_tarski(A,B) = k2_tarski(B,A),
file('theBenchmark.p',commutativity_k2_tarski) ).
fof(d10_xboole_0,axiom,
! [A,B] :
( A = B
<=> ( r1_tarski(B,A)
& r1_tarski(A,B) ) ),
file('theBenchmark.p',d10_xboole_0) ).
fof(d3_tarski,axiom,
! [A,B] :
( r1_tarski(A,B)
<=> ! [C] :
( r2_hidden(C,A)
=> r2_hidden(C,B) ) ),
file('theBenchmark.p',d3_tarski) ).
fof(d4_xboole_0,axiom,
! [A,B,C] :
( C = k4_xboole_0(A,B)
<=> ! [D] :
( r2_hidden(D,C)
<=> ( ~ r2_hidden(D,B)
& r2_hidden(D,A) ) ) ),
file('theBenchmark.p',d4_xboole_0) ).
fof(d5_tarski,axiom,
! [A,B] : k4_tarski(A,B) = k2_tarski(k2_tarski(A,B),k1_tarski(A)),
file('theBenchmark.p',d5_tarski) ).
fof(dt_k1_tarski,axiom,
$true,
file('theBenchmark.p',dt_k1_tarski) ).
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_tarski,axiom,
$true,
file('theBenchmark.p',dt_k2_tarski) ).
fof(dt_k4_tarski,axiom,
$true,
file('theBenchmark.p',dt_k4_tarski) ).
fof(dt_k4_xboole_0,axiom,
$true,
file('theBenchmark.p',dt_k4_xboole_0) ).
fof(dt_k9_relat_1,axiom,
$true,
file('theBenchmark.p',dt_k9_relat_1) ).
fof(dt_m1_subset_1,axiom,
$true,
file('theBenchmark.p',dt_m1_subset_1) ).
fof(existence_m1_subset_1,axiom,
! [A] :
? [B] : m1_subset_1(B,A),
file('theBenchmark.p',existence_m1_subset_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(fc1_subset_1,axiom,
! [A] : ~ v1_xboole_0(k1_zfmisc_1(A)),
file('theBenchmark.p',fc1_subset_1) ).
fof(fc2_subset_1,axiom,
! [A] : ~ v1_xboole_0(k1_tarski(A)),
file('theBenchmark.p',fc2_subset_1) ).
fof(fc3_relat_1,axiom,
! [A,B] :
( ( v1_relat_1(B)
& v1_relat_1(A) )
=> v1_relat_1(k4_xboole_0(A,B)) ),
file('theBenchmark.p',fc3_relat_1) ).
fof(fc3_subset_1,axiom,
! [A,B] : ~ v1_xboole_0(k2_tarski(A,B)),
file('theBenchmark.p',fc3_subset_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(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(rc3_relat_1,axiom,
? [A] :
( v3_relat_1(A)
& v1_relat_1(A) ),
file('theBenchmark.p',rc3_relat_1) ).
fof(reflexivity_r1_tarski,axiom,
! [A,B] : r1_tarski(A,A),
file('theBenchmark.p',reflexivity_r1_tarski) ).
fof(t1_subset,axiom,
! [A,B] :
( r2_hidden(A,B)
=> m1_subset_1(A,B) ),
file('theBenchmark.p',t1_subset) ).
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(t3_boole,axiom,
! [A] : k4_xboole_0(A,k1_xboole_0) = A,
file('theBenchmark.p',t3_boole) ).
fof(t3_subset,axiom,
! [A,B] :
( m1_subset_1(A,k1_zfmisc_1(B))
<=> r1_tarski(A,B) ),
file('theBenchmark.p',t3_subset) ).
fof(t4_boole,axiom,
! [A] : k4_xboole_0(k1_xboole_0,A) = k1_xboole_0,
file('theBenchmark.p',t4_boole) ).
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(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(t9_relset_2,axiom,
! [A,B,C] :
( v1_relat_1(C)
=> ( r2_hidden(A,k9_relat_1(C,k1_tarski(B)))
<=> r2_hidden(k4_tarski(B,A),C) ) ),
file('theBenchmark.p',t9_relset_2) ).
fof(f_1_1,negated_conjecture,
~ ! [A,B] :
( v1_relat_1(B)
=> ! [C] :
( v1_relat_1(C)
=> k9_relat_1(k4_xboole_0(B,C),k1_tarski(A)) = k4_xboole_0(k9_relat_1(B,k1_tarski(A)),k9_relat_1(C,k1_tarski(A))) ) ),
inference(negate,[status(cth)],[t12_relset_2]) ).
fof(f_1_2,negated_conjecture,
? [A,B] :
( ? [C] :
( k9_relat_1(k4_xboole_0(B,C),k1_tarski(A)) != k4_xboole_0(k9_relat_1(B,k1_tarski(A)),k9_relat_1(C,k1_tarski(A)))
& v1_relat_1(C) )
& v1_relat_1(B) ),
inference(fof_nnf,[status(thm)],[f_1_1]) ).
fof(f_1_3,negated_conjecture,
? [U_2,U_1] :
( ? [U_0] :
( k9_relat_1(k4_xboole_0(U_1,U_0),k1_tarski(U_2)) != k4_xboole_0(k9_relat_1(U_1,k1_tarski(U_2)),k9_relat_1(U_0,k1_tarski(U_2)))
& v1_relat_1(U_0) )
& v1_relat_1(U_1) ),
inference(variable_rename,[status(thm)],[f_1_2]) ).
fof(f_1_4,negated_conjecture,
? [U_1] :
( ? [U_0] :
( k9_relat_1(k4_xboole_0(U_1,U_0),k1_tarski(sK1)) != k4_xboole_0(k9_relat_1(U_1,k1_tarski(sK1)),k9_relat_1(U_0,k1_tarski(sK1)))
& v1_relat_1(U_0) )
& v1_relat_1(U_1) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(U_2,sK1)],[f_1_3]) ).
fof(f_1_5,negated_conjecture,
( ? [U_0] :
( k9_relat_1(k4_xboole_0(sK2,U_0),k1_tarski(sK1)) != k4_xboole_0(k9_relat_1(sK2,k1_tarski(sK1)),k9_relat_1(U_0,k1_tarski(sK1)))
& v1_relat_1(U_0) )
& v1_relat_1(sK2) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2]),skolemize(U_1,sK2)],[f_1_4]) ).
fof(f_1_6,negated_conjecture,
( k9_relat_1(k4_xboole_0(sK2,sK3),k1_tarski(sK1)) != k4_xboole_0(k9_relat_1(sK2,k1_tarski(sK1)),k9_relat_1(sK3,k1_tarski(sK1)))
& v1_relat_1(sK3)
& v1_relat_1(sK2) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3]),skolemize(U_0,sK3)],[f_1_5]) ).
fof(f_1_7,negated_conjecture,
( k9_relat_1(k4_xboole_0(sK2,sK3),k1_tarski(sK1)) != k4_xboole_0(k9_relat_1(sK2,k1_tarski(sK1)),k9_relat_1(sK3,k1_tarski(sK1)))
& v1_relat_1(sK3)
& v1_relat_1(sK2) ),
inference(definitional_conversion,[status(esa)],[f_1_6]) ).
cnf(f_1_8,negated_conjecture,
v1_relat_1(sK2),
inference(clausify,[status(thm)],[f_1_7]) ).
cnf(f_1_9,negated_conjecture,
v1_relat_1(sK3),
inference(clausify,[status(thm)],[f_1_7]) ).
cnf(f_1_10,negated_conjecture,
k9_relat_1(k4_xboole_0(sK2,sK3),k1_tarski(sK1)) != k4_xboole_0(k9_relat_1(sK2,k1_tarski(sK1)),k9_relat_1(sK3,k1_tarski(sK1))),
inference(clausify,[status(thm)],[f_1_7]) ).
fof(f_2_1,plain,
! [A,B] :
( ~ r2_hidden(B,A)
| ~ r2_hidden(A,B) ),
inference(fof_nnf,[status(thm)],[antisymmetry_r2_hidden]) ).
fof(f_2_2,plain,
! [U_4,U_3] :
( ~ r2_hidden(U_3,U_4)
| ~ r2_hidden(U_4,U_3) ),
inference(variable_rename,[status(thm)],[f_2_1]) ).
fof(f_2_3,plain,
! [U_3,U_4] :
( ~ r2_hidden(U_3,U_4)
| ~ r2_hidden(U_4,U_3) ),
inference(definitional_conversion,[status(esa)],[f_2_2]) ).
cnf(f_2_4,plain,
( ~ r2_hidden(U_3,U_4)
| ~ r2_hidden(U_4,U_3) ),
inference(clausify,[status(thm)],[f_2_3]) ).
fof(f_3_1,plain,
! [A] :
( v1_relat_1(A)
| ~ v1_xboole_0(A) ),
inference(fof_nnf,[status(thm)],[cc1_relat_1]) ).
fof(f_3_2,plain,
! [U_5] :
( v1_relat_1(U_5)
| ~ v1_xboole_0(U_5) ),
inference(variable_rename,[status(thm)],[f_3_1]) ).
fof(f_3_3,plain,
! [U_5] :
( v1_relat_1(U_5)
| ~ v1_xboole_0(U_5) ),
inference(definitional_conversion,[status(esa)],[f_3_2]) ).
cnf(f_3_4,plain,
( v1_relat_1(U_5)
| ~ v1_xboole_0(U_5) ),
inference(clausify,[status(thm)],[f_3_3]) ).
fof(f_4_1,plain,
! [A,B] : k2_tarski(A,B) = k2_tarski(B,A),
inference(fof_nnf,[status(thm)],[commutativity_k2_tarski]) ).
fof(f_4_2,plain,
! [U_7,U_6] : k2_tarski(U_7,U_6) = k2_tarski(U_6,U_7),
inference(variable_rename,[status(thm)],[f_4_1]) ).
fof(f_4_3,plain,
! [U_7,U_6] : k2_tarski(U_7,U_6) = k2_tarski(U_6,U_7),
inference(definitional_conversion,[status(esa)],[f_4_2]) ).
cnf(f_4_4,plain,
k2_tarski(U_7,U_6) = k2_tarski(U_6,U_7),
inference(clausify,[status(thm)],[f_4_3]) ).
fof(f_5_1,plain,
! [A,B] :
( ( A = B
| ~ r1_tarski(B,A)
| ~ r1_tarski(A,B) )
& ( ( r1_tarski(B,A)
& r1_tarski(A,B) )
| A != B ) ),
inference(fof_nnf,[status(thm)],[d10_xboole_0]) ).
fof(f_5_2,plain,
! [U_9,U_8] :
( ( U_9 = U_8
| ~ r1_tarski(U_8,U_9)
| ~ r1_tarski(U_9,U_8) )
& ( ( r1_tarski(U_8,U_9)
& r1_tarski(U_9,U_8) )
| U_9 != U_8 ) ),
inference(variable_rename,[status(thm)],[f_5_1]) ).
fof(f_5_3,plain,
( ! [U_13,U_11] :
( U_13 = U_11
| ~ r1_tarski(U_11,U_13)
| ~ r1_tarski(U_13,U_11) )
& ! [U_12,U_10] :
( ( r1_tarski(U_10,U_12)
& r1_tarski(U_12,U_10) )
| U_12 != U_10 ) ),
inference(miniscope,[status(thm)],[f_5_2]) ).
fof(f_5_4,plain,
( ! [U_12,U_10] :
( r1_tarski(U_10,U_12)
| ~ sP0(U_12,U_10) )
& ! [U_12,U_10] :
( r1_tarski(U_12,U_10)
| ~ sP0(U_12,U_10) )
& ! [U_13,U_11] :
( U_13 = U_11
| ~ r1_tarski(U_11,U_13)
| ~ r1_tarski(U_13,U_11) )
& ! [U_12,U_10] :
( sP0(U_12,U_10)
| U_12 != U_10 ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP0])],[f_5_3]) ).
cnf(f_5_5,plain,
( sP0(U_12,U_10)
| U_12 != U_10 ),
inference(clausify,[status(thm)],[f_5_4]) ).
cnf(f_5_6,plain,
( U_13 = U_11
| ~ r1_tarski(U_11,U_13)
| ~ r1_tarski(U_13,U_11) ),
inference(clausify,[status(thm)],[f_5_4]) ).
cnf(f_5_7,plain,
( r1_tarski(U_12,U_10)
| ~ sP0(U_12,U_10) ),
inference(clausify,[status(thm)],[f_5_4]) ).
cnf(f_5_8,plain,
( r1_tarski(U_10,U_12)
| ~ sP0(U_12,U_10) ),
inference(clausify,[status(thm)],[f_5_4]) ).
fof(f_6_1,plain,
! [A,B] :
( ( r1_tarski(A,B)
| ? [C] :
( ~ r2_hidden(C,B)
& r2_hidden(C,A) ) )
& ( ! [C] :
( r2_hidden(C,B)
| ~ r2_hidden(C,A) )
| ~ r1_tarski(A,B) ) ),
inference(fof_nnf,[status(thm)],[d3_tarski]) ).
fof(f_6_2,plain,
! [U_17,U_16] :
( ( r1_tarski(U_17,U_16)
| ? [U_15] :
( ~ r2_hidden(U_15,U_16)
& r2_hidden(U_15,U_17) ) )
& ( ! [U_14] :
( r2_hidden(U_14,U_16)
| ~ r2_hidden(U_14,U_17) )
| ~ r1_tarski(U_17,U_16) ) ),
inference(variable_rename,[status(thm)],[f_6_1]) ).
fof(f_6_3,plain,
( ! [U_21,U_19] :
( r1_tarski(U_21,U_19)
| ? [U_15] :
( ~ r2_hidden(U_15,U_19)
& r2_hidden(U_15,U_21) ) )
& ! [U_20,U_18] :
( ! [U_14] :
( r2_hidden(U_14,U_18)
| ~ r2_hidden(U_14,U_20) )
| ~ r1_tarski(U_20,U_18) ) ),
inference(miniscope,[status(thm)],[f_6_2]) ).
fof(f_6_4,plain,
( ! [U_21,U_19] :
( r1_tarski(U_21,U_19)
| ( ~ r2_hidden(sK4(U_21,U_19),U_19)
& r2_hidden(sK4(U_21,U_19),U_21) ) )
& ! [U_20,U_18] :
( ! [U_14] :
( r2_hidden(U_14,U_18)
| ~ r2_hidden(U_14,U_20) )
| ~ r1_tarski(U_20,U_18) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4]),skolemize(U_15,sK4(U_21,U_19))],[f_6_3]) ).
fof(f_6_5,plain,
( ! [U_21,U_19] :
( ~ r2_hidden(sK4(U_21,U_19),U_19)
| ~ sP1(U_21,U_19) )
& ! [U_21,U_19] :
( r2_hidden(sK4(U_21,U_19),U_21)
| ~ sP1(U_21,U_19) )
& ! [U_21,U_19] :
( r1_tarski(U_21,U_19)
| sP1(U_21,U_19) )
& ! [U_20,U_14,U_18] :
( r2_hidden(U_14,U_18)
| ~ r2_hidden(U_14,U_20)
| ~ r1_tarski(U_20,U_18) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP1])],[f_6_4]) ).
cnf(f_6_6,plain,
( r2_hidden(U_14,U_18)
| ~ r2_hidden(U_14,U_20)
| ~ r1_tarski(U_20,U_18) ),
inference(clausify,[status(thm)],[f_6_5]) ).
cnf(f_6_7,plain,
( r1_tarski(U_21,U_19)
| sP1(U_21,U_19) ),
inference(clausify,[status(thm)],[f_6_5]) ).
cnf(f_6_8,plain,
( r2_hidden(sK4(U_21,U_19),U_21)
| ~ sP1(U_21,U_19) ),
inference(clausify,[status(thm)],[f_6_5]) ).
cnf(f_6_9,plain,
( ~ r2_hidden(sK4(U_21,U_19),U_19)
| ~ sP1(U_21,U_19) ),
inference(clausify,[status(thm)],[f_6_5]) ).
fof(f_7_1,plain,
! [A,B,C] :
( ( C = k4_xboole_0(A,B)
| ? [D] :
( ( ~ r2_hidden(D,C)
& ~ r2_hidden(D,B)
& r2_hidden(D,A) )
| ( ( r2_hidden(D,B)
| ~ r2_hidden(D,A) )
& r2_hidden(D,C) ) ) )
& ( ! [D] :
( ( r2_hidden(D,C)
| r2_hidden(D,B)
| ~ r2_hidden(D,A) )
& ( ( ~ r2_hidden(D,B)
& r2_hidden(D,A) )
| ~ r2_hidden(D,C) ) )
| C != k4_xboole_0(A,B) ) ),
inference(fof_nnf,[status(thm)],[d4_xboole_0]) ).
fof(f_7_2,plain,
! [U_26,U_25,U_24] :
( ( U_24 = k4_xboole_0(U_26,U_25)
| ? [U_23] :
( ( ~ r2_hidden(U_23,U_24)
& ~ r2_hidden(U_23,U_25)
& r2_hidden(U_23,U_26) )
| ( ( r2_hidden(U_23,U_25)
| ~ r2_hidden(U_23,U_26) )
& r2_hidden(U_23,U_24) ) ) )
& ( ! [U_22] :
( ( r2_hidden(U_22,U_24)
| r2_hidden(U_22,U_25)
| ~ r2_hidden(U_22,U_26) )
& ( ( ~ r2_hidden(U_22,U_25)
& r2_hidden(U_22,U_26) )
| ~ r2_hidden(U_22,U_24) ) )
| U_24 != k4_xboole_0(U_26,U_25) ) ),
inference(variable_rename,[status(thm)],[f_7_1]) ).
fof(f_7_3,plain,
( ! [U_36,U_34,U_32] :
( U_32 = k4_xboole_0(U_36,U_34)
| ? [U_30] :
( ~ r2_hidden(U_30,U_32)
& ~ r2_hidden(U_30,U_34)
& r2_hidden(U_30,U_36) )
| ? [U_29] :
( ( r2_hidden(U_29,U_34)
| ~ r2_hidden(U_29,U_36) )
& r2_hidden(U_29,U_32) ) )
& ! [U_35,U_33,U_31] :
( ( ! [U_28] :
( r2_hidden(U_28,U_31)
| r2_hidden(U_28,U_33)
| ~ r2_hidden(U_28,U_35) )
& ! [U_27] :
( ( ~ r2_hidden(U_27,U_33)
& r2_hidden(U_27,U_35) )
| ~ r2_hidden(U_27,U_31) ) )
| U_31 != k4_xboole_0(U_35,U_33) ) ),
inference(miniscope,[status(thm)],[f_7_2]) ).
fof(f_7_4,plain,
( ! [U_36,U_34,U_32] :
( U_32 = k4_xboole_0(U_36,U_34)
| ? [U_30] :
( ~ r2_hidden(U_30,U_32)
& ~ r2_hidden(U_30,U_34)
& r2_hidden(U_30,U_36) )
| ( ( r2_hidden(sK5(U_36,U_34,U_32),U_34)
| ~ r2_hidden(sK5(U_36,U_34,U_32),U_36) )
& r2_hidden(sK5(U_36,U_34,U_32),U_32) ) )
& ! [U_35,U_33,U_31] :
( ( ! [U_28] :
( r2_hidden(U_28,U_31)
| r2_hidden(U_28,U_33)
| ~ r2_hidden(U_28,U_35) )
& ! [U_27] :
( ( ~ r2_hidden(U_27,U_33)
& r2_hidden(U_27,U_35) )
| ~ r2_hidden(U_27,U_31) ) )
| U_31 != k4_xboole_0(U_35,U_33) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK5]),skolemize(U_29,sK5(U_36,U_34,U_32))],[f_7_3]) ).
fof(f_7_5,plain,
( ! [U_36,U_34,U_32] :
( U_32 = k4_xboole_0(U_36,U_34)
| ( ~ r2_hidden(sK6(U_36,U_34,U_32),U_32)
& ~ r2_hidden(sK6(U_36,U_34,U_32),U_34)
& r2_hidden(sK6(U_36,U_34,U_32),U_36) )
| ( ( r2_hidden(sK5(U_36,U_34,U_32),U_34)
| ~ r2_hidden(sK5(U_36,U_34,U_32),U_36) )
& r2_hidden(sK5(U_36,U_34,U_32),U_32) ) )
& ! [U_35,U_33,U_31] :
( ( ! [U_28] :
( r2_hidden(U_28,U_31)
| r2_hidden(U_28,U_33)
| ~ r2_hidden(U_28,U_35) )
& ! [U_27] :
( ( ~ r2_hidden(U_27,U_33)
& r2_hidden(U_27,U_35) )
| ~ r2_hidden(U_27,U_31) ) )
| U_31 != k4_xboole_0(U_35,U_33) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK6]),skolemize(U_30,sK6(U_36,U_34,U_32))],[f_7_4]) ).
fof(f_7_6,plain,
( ! [U_32,U_36,U_34] :
( ~ r2_hidden(sK6(U_36,U_34,U_32),U_32)
| ~ sP5(U_32,U_36,U_34) )
& ! [U_32,U_36,U_34] :
( ~ r2_hidden(sK6(U_36,U_34,U_32),U_34)
| ~ sP5(U_32,U_36,U_34) )
& ! [U_32,U_36,U_34] :
( r2_hidden(sK6(U_36,U_34,U_32),U_36)
| ~ sP5(U_32,U_36,U_34) )
& ! [U_32,U_36,U_34] :
( r2_hidden(sK5(U_36,U_34,U_32),U_34)
| ~ r2_hidden(sK5(U_36,U_34,U_32),U_36)
| ~ sP4(U_32,U_36,U_34) )
& ! [U_32,U_36,U_34] :
( r2_hidden(sK5(U_36,U_34,U_32),U_32)
| ~ sP4(U_32,U_36,U_34) )
& ! [U_35,U_27,U_33] :
( ~ r2_hidden(U_27,U_33)
| ~ sP2(U_35,U_27,U_33) )
& ! [U_35,U_27,U_33] :
( r2_hidden(U_27,U_35)
| ~ sP2(U_35,U_27,U_33) )
& ! [U_35,U_31,U_27,U_28,U_33] :
( r2_hidden(U_28,U_31)
| r2_hidden(U_28,U_33)
| ~ r2_hidden(U_28,U_35)
| ~ sP3(U_35,U_31,U_27,U_28,U_33) )
& ! [U_35,U_31,U_27,U_28,U_33] :
( sP2(U_35,U_27,U_33)
| ~ r2_hidden(U_27,U_31)
| ~ sP3(U_35,U_31,U_27,U_28,U_33) )
& ! [U_32,U_36,U_34] :
( U_32 = k4_xboole_0(U_36,U_34)
| sP5(U_32,U_36,U_34)
| sP4(U_32,U_36,U_34) )
& ! [U_35,U_31,U_27,U_28,U_33] :
( sP3(U_35,U_31,U_27,U_28,U_33)
| U_31 != k4_xboole_0(U_35,U_33) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP2,sP3,sP4,sP5])],[f_7_5]) ).
cnf(f_7_7,plain,
( sP3(U_35,U_31,U_27,U_28,U_33)
| U_31 != k4_xboole_0(U_35,U_33) ),
inference(clausify,[status(thm)],[f_7_6]) ).
cnf(f_7_8,plain,
( U_32 = k4_xboole_0(U_36,U_34)
| sP5(U_32,U_36,U_34)
| sP4(U_32,U_36,U_34) ),
inference(clausify,[status(thm)],[f_7_6]) ).
cnf(f_7_9,plain,
( sP2(U_35,U_27,U_33)
| ~ r2_hidden(U_27,U_31)
| ~ sP3(U_35,U_31,U_27,U_28,U_33) ),
inference(clausify,[status(thm)],[f_7_6]) ).
cnf(f_7_10,plain,
( r2_hidden(U_28,U_31)
| r2_hidden(U_28,U_33)
| ~ r2_hidden(U_28,U_35)
| ~ sP3(U_35,U_31,U_27,U_28,U_33) ),
inference(clausify,[status(thm)],[f_7_6]) ).
cnf(f_7_11,plain,
( r2_hidden(U_27,U_35)
| ~ sP2(U_35,U_27,U_33) ),
inference(clausify,[status(thm)],[f_7_6]) ).
cnf(f_7_12,plain,
( ~ r2_hidden(U_27,U_33)
| ~ sP2(U_35,U_27,U_33) ),
inference(clausify,[status(thm)],[f_7_6]) ).
cnf(f_7_13,plain,
( r2_hidden(sK5(U_36,U_34,U_32),U_32)
| ~ sP4(U_32,U_36,U_34) ),
inference(clausify,[status(thm)],[f_7_6]) ).
cnf(f_7_14,plain,
( r2_hidden(sK5(U_36,U_34,U_32),U_34)
| ~ r2_hidden(sK5(U_36,U_34,U_32),U_36)
| ~ sP4(U_32,U_36,U_34) ),
inference(clausify,[status(thm)],[f_7_6]) ).
cnf(f_7_15,plain,
( r2_hidden(sK6(U_36,U_34,U_32),U_36)
| ~ sP5(U_32,U_36,U_34) ),
inference(clausify,[status(thm)],[f_7_6]) ).
cnf(f_7_16,plain,
( ~ r2_hidden(sK6(U_36,U_34,U_32),U_34)
| ~ sP5(U_32,U_36,U_34) ),
inference(clausify,[status(thm)],[f_7_6]) ).
cnf(f_7_17,plain,
( ~ r2_hidden(sK6(U_36,U_34,U_32),U_32)
| ~ sP5(U_32,U_36,U_34) ),
inference(clausify,[status(thm)],[f_7_6]) ).
fof(f_8_1,plain,
! [A,B] : k4_tarski(A,B) = k2_tarski(k2_tarski(A,B),k1_tarski(A)),
inference(fof_nnf,[status(thm)],[d5_tarski]) ).
fof(f_8_2,plain,
! [U_38,U_37] : k4_tarski(U_38,U_37) = k2_tarski(k2_tarski(U_38,U_37),k1_tarski(U_38)),
inference(variable_rename,[status(thm)],[f_8_1]) ).
fof(f_8_3,plain,
! [U_37,U_38] : k4_tarski(U_38,U_37) = k2_tarski(k2_tarski(U_38,U_37),k1_tarski(U_38)),
inference(definitional_conversion,[status(esa)],[f_8_2]) ).
cnf(f_8_4,plain,
k4_tarski(U_38,U_37) = k2_tarski(k2_tarski(U_38,U_37),k1_tarski(U_38)),
inference(clausify,[status(thm)],[f_8_3]) ).
fof(f_9_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_k1_tarski]) ).
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_tarski]) ).
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_k4_tarski]) ).
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,
$true,
inference(fof_nnf,[status(thm)],[dt_k4_xboole_0]) ).
fof(f_14_2,plain,
$true,
inference(definitional_conversion,[status(esa)],[f_14_1]) ).
cnf(f_14_3,plain,
$true,
inference(clausify,[status(thm)],[f_14_2]) ).
fof(f_15_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_k9_relat_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] : m1_subset_1(B,A),
inference(fof_nnf,[status(thm)],[existence_m1_subset_1]) ).
fof(f_17_2,plain,
! [U_40] :
? [U_39] : m1_subset_1(U_39,U_40),
inference(variable_rename,[status(thm)],[f_17_1]) ).
fof(f_17_3,plain,
! [U_40] : m1_subset_1(sK7(U_40),U_40),
inference(skolemize,[status(esa),new_symbols(skolem,[sK7]),skolemize(U_39,sK7(U_40))],[f_17_2]) ).
fof(f_17_4,plain,
! [U_40] : m1_subset_1(sK7(U_40),U_40),
inference(definitional_conversion,[status(esa)],[f_17_3]) ).
cnf(f_17_5,plain,
m1_subset_1(sK7(U_40),U_40),
inference(clausify,[status(thm)],[f_17_4]) ).
fof(f_18_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]) ).
fof(f_18_2,plain,
( v3_relat_1(k1_xboole_0)
& v1_relat_1(k1_xboole_0)
& v1_xboole_0(k1_xboole_0) ),
inference(definitional_conversion,[status(esa)],[f_18_1]) ).
cnf(f_18_3,plain,
v1_xboole_0(k1_xboole_0),
inference(clausify,[status(thm)],[f_18_2]) ).
cnf(f_18_4,plain,
v1_relat_1(k1_xboole_0),
inference(clausify,[status(thm)],[f_18_2]) ).
cnf(f_18_5,plain,
v3_relat_1(k1_xboole_0),
inference(clausify,[status(thm)],[f_18_2]) ).
fof(f_19_1,plain,
! [A] : ~ v1_xboole_0(k1_zfmisc_1(A)),
inference(fof_nnf,[status(thm)],[fc1_subset_1]) ).
fof(f_19_2,plain,
! [U_41] : ~ v1_xboole_0(k1_zfmisc_1(U_41)),
inference(variable_rename,[status(thm)],[f_19_1]) ).
fof(f_19_3,plain,
! [U_41] : ~ v1_xboole_0(k1_zfmisc_1(U_41)),
inference(definitional_conversion,[status(esa)],[f_19_2]) ).
cnf(f_19_4,plain,
~ v1_xboole_0(k1_zfmisc_1(U_41)),
inference(clausify,[status(thm)],[f_19_3]) ).
fof(f_20_1,plain,
! [A] : ~ v1_xboole_0(k1_tarski(A)),
inference(fof_nnf,[status(thm)],[fc2_subset_1]) ).
fof(f_20_2,plain,
! [U_42] : ~ v1_xboole_0(k1_tarski(U_42)),
inference(variable_rename,[status(thm)],[f_20_1]) ).
fof(f_20_3,plain,
! [U_42] : ~ v1_xboole_0(k1_tarski(U_42)),
inference(definitional_conversion,[status(esa)],[f_20_2]) ).
cnf(f_20_4,plain,
~ v1_xboole_0(k1_tarski(U_42)),
inference(clausify,[status(thm)],[f_20_3]) ).
fof(f_21_1,plain,
! [A,B] :
( v1_relat_1(k4_xboole_0(A,B))
| ~ v1_relat_1(B)
| ~ v1_relat_1(A) ),
inference(fof_nnf,[status(thm)],[fc3_relat_1]) ).
fof(f_21_2,plain,
! [U_44,U_43] :
( v1_relat_1(k4_xboole_0(U_44,U_43))
| ~ v1_relat_1(U_43)
| ~ v1_relat_1(U_44) ),
inference(variable_rename,[status(thm)],[f_21_1]) ).
fof(f_21_3,plain,
! [U_44,U_43] :
( v1_relat_1(k4_xboole_0(U_44,U_43))
| ~ v1_relat_1(U_43)
| ~ v1_relat_1(U_44) ),
inference(definitional_conversion,[status(esa)],[f_21_2]) ).
cnf(f_21_4,plain,
( v1_relat_1(k4_xboole_0(U_44,U_43))
| ~ v1_relat_1(U_43)
| ~ v1_relat_1(U_44) ),
inference(clausify,[status(thm)],[f_21_3]) ).
fof(f_22_1,plain,
! [A,B] : ~ v1_xboole_0(k2_tarski(A,B)),
inference(fof_nnf,[status(thm)],[fc3_subset_1]) ).
fof(f_22_2,plain,
! [U_46,U_45] : ~ v1_xboole_0(k2_tarski(U_46,U_45)),
inference(variable_rename,[status(thm)],[f_22_1]) ).
fof(f_22_3,plain,
! [U_45,U_46] : ~ v1_xboole_0(k2_tarski(U_46,U_45)),
inference(definitional_conversion,[status(esa)],[f_22_2]) ).
cnf(f_22_4,plain,
~ v1_xboole_0(k2_tarski(U_46,U_45)),
inference(clausify,[status(thm)],[f_22_3]) ).
fof(f_23_1,plain,
( v1_relat_1(k1_xboole_0)
& v1_xboole_0(k1_xboole_0) ),
inference(fof_nnf,[status(thm)],[fc4_relat_1]) ).
fof(f_23_2,plain,
( v1_relat_1(k1_xboole_0)
& v1_xboole_0(k1_xboole_0) ),
inference(definitional_conversion,[status(esa)],[f_23_1]) ).
cnf(f_23_3,plain,
v1_xboole_0(k1_xboole_0),
inference(clausify,[status(thm)],[f_23_2]) ).
cnf(f_23_4,plain,
v1_relat_1(k1_xboole_0),
inference(clausify,[status(thm)],[f_23_2]) ).
fof(f_24_1,plain,
? [A] :
( v1_relat_1(A)
& v1_xboole_0(A) ),
inference(fof_nnf,[status(thm)],[rc1_relat_1]) ).
fof(f_24_2,plain,
? [U_47] :
( v1_relat_1(U_47)
& v1_xboole_0(U_47) ),
inference(variable_rename,[status(thm)],[f_24_1]) ).
fof(f_24_3,plain,
( v1_relat_1(sK8)
& v1_xboole_0(sK8) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK8]),skolemize(U_47,sK8)],[f_24_2]) ).
fof(f_24_4,plain,
( v1_relat_1(sK8)
& v1_xboole_0(sK8) ),
inference(definitional_conversion,[status(esa)],[f_24_3]) ).
cnf(f_24_5,plain,
v1_xboole_0(sK8),
inference(clausify,[status(thm)],[f_24_4]) ).
cnf(f_24_6,plain,
v1_relat_1(sK8),
inference(clausify,[status(thm)],[f_24_4]) ).
fof(f_25_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_25_2,plain,
! [U_49] :
( ? [U_48] :
( ~ v1_xboole_0(U_48)
& m1_subset_1(U_48,k1_zfmisc_1(U_49)) )
| v1_xboole_0(U_49) ),
inference(variable_rename,[status(thm)],[f_25_1]) ).
fof(f_25_3,plain,
! [U_49] :
( ( ~ v1_xboole_0(sK9(U_49))
& m1_subset_1(sK9(U_49),k1_zfmisc_1(U_49)) )
| v1_xboole_0(U_49) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK9]),skolemize(U_48,sK9(U_49))],[f_25_2]) ).
fof(f_25_4,plain,
( ! [U_49] :
( ~ v1_xboole_0(sK9(U_49))
| ~ sP6(U_49) )
& ! [U_49] :
( m1_subset_1(sK9(U_49),k1_zfmisc_1(U_49))
| ~ sP6(U_49) )
& ! [U_49] :
( sP6(U_49)
| v1_xboole_0(U_49) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP6])],[f_25_3]) ).
cnf(f_25_5,plain,
( sP6(U_49)
| v1_xboole_0(U_49) ),
inference(clausify,[status(thm)],[f_25_4]) ).
cnf(f_25_6,plain,
( m1_subset_1(sK9(U_49),k1_zfmisc_1(U_49))
| ~ sP6(U_49) ),
inference(clausify,[status(thm)],[f_25_4]) ).
cnf(f_25_7,plain,
( ~ v1_xboole_0(sK9(U_49))
| ~ sP6(U_49) ),
inference(clausify,[status(thm)],[f_25_4]) ).
fof(f_26_1,plain,
? [A] :
( v1_relat_1(A)
& ~ v1_xboole_0(A) ),
inference(fof_nnf,[status(thm)],[rc2_relat_1]) ).
fof(f_26_2,plain,
? [U_50] :
( v1_relat_1(U_50)
& ~ v1_xboole_0(U_50) ),
inference(variable_rename,[status(thm)],[f_26_1]) ).
fof(f_26_3,plain,
( v1_relat_1(sK10)
& ~ v1_xboole_0(sK10) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK10]),skolemize(U_50,sK10)],[f_26_2]) ).
fof(f_26_4,plain,
( v1_relat_1(sK10)
& ~ v1_xboole_0(sK10) ),
inference(definitional_conversion,[status(esa)],[f_26_3]) ).
cnf(f_26_5,plain,
~ v1_xboole_0(sK10),
inference(clausify,[status(thm)],[f_26_4]) ).
cnf(f_26_6,plain,
v1_relat_1(sK10),
inference(clausify,[status(thm)],[f_26_4]) ).
fof(f_27_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_27_2,plain,
! [U_52] :
? [U_51] :
( v1_xboole_0(U_51)
& m1_subset_1(U_51,k1_zfmisc_1(U_52)) ),
inference(variable_rename,[status(thm)],[f_27_1]) ).
fof(f_27_3,plain,
! [U_52] :
( v1_xboole_0(sK11(U_52))
& m1_subset_1(sK11(U_52),k1_zfmisc_1(U_52)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK11]),skolemize(U_51,sK11(U_52))],[f_27_2]) ).
fof(f_27_4,plain,
( ! [U_52] : v1_xboole_0(sK11(U_52))
& ! [U_52] : m1_subset_1(sK11(U_52),k1_zfmisc_1(U_52)) ),
inference(definitional_conversion,[status(esa)],[f_27_3]) ).
cnf(f_27_5,plain,
m1_subset_1(sK11(U_52),k1_zfmisc_1(U_52)),
inference(clausify,[status(thm)],[f_27_4]) ).
cnf(f_27_6,plain,
v1_xboole_0(sK11(U_52)),
inference(clausify,[status(thm)],[f_27_4]) ).
fof(f_28_1,plain,
? [A] :
( v3_relat_1(A)
& v1_relat_1(A) ),
inference(fof_nnf,[status(thm)],[rc3_relat_1]) ).
fof(f_28_2,plain,
? [U_53] :
( v3_relat_1(U_53)
& v1_relat_1(U_53) ),
inference(variable_rename,[status(thm)],[f_28_1]) ).
fof(f_28_3,plain,
( v3_relat_1(sK12)
& v1_relat_1(sK12) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK12]),skolemize(U_53,sK12)],[f_28_2]) ).
fof(f_28_4,plain,
( v3_relat_1(sK12)
& v1_relat_1(sK12) ),
inference(definitional_conversion,[status(esa)],[f_28_3]) ).
cnf(f_28_5,plain,
v1_relat_1(sK12),
inference(clausify,[status(thm)],[f_28_4]) ).
cnf(f_28_6,plain,
v3_relat_1(sK12),
inference(clausify,[status(thm)],[f_28_4]) ).
fof(f_29_1,plain,
! [A,B] : r1_tarski(A,A),
inference(fof_nnf,[status(thm)],[reflexivity_r1_tarski]) ).
fof(f_29_2,plain,
! [U_55,U_54] : r1_tarski(U_55,U_55),
inference(variable_rename,[status(thm)],[f_29_1]) ).
fof(f_29_3,plain,
! [U_55] : r1_tarski(U_55,U_55),
inference(miniscope,[status(thm)],[f_29_2]) ).
fof(f_29_4,plain,
! [U_55] : r1_tarski(U_55,U_55),
inference(definitional_conversion,[status(esa)],[f_29_3]) ).
cnf(f_29_5,plain,
r1_tarski(U_55,U_55),
inference(clausify,[status(thm)],[f_29_4]) ).
fof(f_30_1,plain,
! [A,B] :
( m1_subset_1(A,B)
| ~ r2_hidden(A,B) ),
inference(fof_nnf,[status(thm)],[t1_subset]) ).
fof(f_30_2,plain,
! [U_57,U_56] :
( m1_subset_1(U_57,U_56)
| ~ r2_hidden(U_57,U_56) ),
inference(variable_rename,[status(thm)],[f_30_1]) ).
fof(f_30_3,plain,
! [U_57,U_56] :
( m1_subset_1(U_57,U_56)
| ~ r2_hidden(U_57,U_56) ),
inference(definitional_conversion,[status(esa)],[f_30_2]) ).
cnf(f_30_4,plain,
( m1_subset_1(U_57,U_56)
| ~ r2_hidden(U_57,U_56) ),
inference(clausify,[status(thm)],[f_30_3]) ).
fof(f_31_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_31_2,plain,
! [U_59,U_58] :
( r2_hidden(U_59,U_58)
| v1_xboole_0(U_58)
| ~ m1_subset_1(U_59,U_58) ),
inference(variable_rename,[status(thm)],[f_31_1]) ).
fof(f_31_3,plain,
! [U_59,U_58] :
( r2_hidden(U_59,U_58)
| v1_xboole_0(U_58)
| ~ m1_subset_1(U_59,U_58) ),
inference(definitional_conversion,[status(esa)],[f_31_2]) ).
cnf(f_31_4,plain,
( r2_hidden(U_59,U_58)
| v1_xboole_0(U_58)
| ~ m1_subset_1(U_59,U_58) ),
inference(clausify,[status(thm)],[f_31_3]) ).
fof(f_32_1,plain,
! [A] : k4_xboole_0(A,k1_xboole_0) = A,
inference(fof_nnf,[status(thm)],[t3_boole]) ).
fof(f_32_2,plain,
! [U_60] : k4_xboole_0(U_60,k1_xboole_0) = U_60,
inference(variable_rename,[status(thm)],[f_32_1]) ).
fof(f_32_3,plain,
! [U_60] : k4_xboole_0(U_60,k1_xboole_0) = U_60,
inference(definitional_conversion,[status(esa)],[f_32_2]) ).
cnf(f_32_4,plain,
k4_xboole_0(U_60,k1_xboole_0) = U_60,
inference(clausify,[status(thm)],[f_32_3]) ).
fof(f_33_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_33_2,plain,
! [U_62,U_61] :
( ( m1_subset_1(U_62,k1_zfmisc_1(U_61))
| ~ r1_tarski(U_62,U_61) )
& ( r1_tarski(U_62,U_61)
| ~ m1_subset_1(U_62,k1_zfmisc_1(U_61)) ) ),
inference(variable_rename,[status(thm)],[f_33_1]) ).
fof(f_33_3,plain,
( ! [U_66,U_64] :
( m1_subset_1(U_66,k1_zfmisc_1(U_64))
| ~ r1_tarski(U_66,U_64) )
& ! [U_65,U_63] :
( r1_tarski(U_65,U_63)
| ~ m1_subset_1(U_65,k1_zfmisc_1(U_63)) ) ),
inference(miniscope,[status(thm)],[f_33_2]) ).
fof(f_33_4,plain,
( ! [U_66,U_64] :
( m1_subset_1(U_66,k1_zfmisc_1(U_64))
| ~ r1_tarski(U_66,U_64) )
& ! [U_63,U_65] :
( r1_tarski(U_65,U_63)
| ~ m1_subset_1(U_65,k1_zfmisc_1(U_63)) ) ),
inference(definitional_conversion,[status(esa)],[f_33_3]) ).
cnf(f_33_5,plain,
( r1_tarski(U_65,U_63)
| ~ m1_subset_1(U_65,k1_zfmisc_1(U_63)) ),
inference(clausify,[status(thm)],[f_33_4]) ).
cnf(f_33_6,plain,
( m1_subset_1(U_66,k1_zfmisc_1(U_64))
| ~ r1_tarski(U_66,U_64) ),
inference(clausify,[status(thm)],[f_33_4]) ).
fof(f_34_1,plain,
! [A] : k4_xboole_0(k1_xboole_0,A) = k1_xboole_0,
inference(fof_nnf,[status(thm)],[t4_boole]) ).
fof(f_34_2,plain,
! [U_67] : k4_xboole_0(k1_xboole_0,U_67) = k1_xboole_0,
inference(variable_rename,[status(thm)],[f_34_1]) ).
fof(f_34_3,plain,
! [U_67] : k4_xboole_0(k1_xboole_0,U_67) = k1_xboole_0,
inference(definitional_conversion,[status(esa)],[f_34_2]) ).
cnf(f_34_4,plain,
k4_xboole_0(k1_xboole_0,U_67) = k1_xboole_0,
inference(clausify,[status(thm)],[f_34_3]) ).
fof(f_35_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_35_2,plain,
! [U_70,U_69,U_68] :
( m1_subset_1(U_70,U_68)
| ~ m1_subset_1(U_69,k1_zfmisc_1(U_68))
| ~ r2_hidden(U_70,U_69) ),
inference(variable_rename,[status(thm)],[f_35_1]) ).
fof(f_35_3,plain,
! [U_69,U_70,U_68] :
( m1_subset_1(U_70,U_68)
| ~ m1_subset_1(U_69,k1_zfmisc_1(U_68))
| ~ r2_hidden(U_70,U_69) ),
inference(definitional_conversion,[status(esa)],[f_35_2]) ).
cnf(f_35_4,plain,
( m1_subset_1(U_70,U_68)
| ~ m1_subset_1(U_69,k1_zfmisc_1(U_68))
| ~ r2_hidden(U_70,U_69) ),
inference(clausify,[status(thm)],[f_35_3]) ).
fof(f_36_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_36_2,plain,
! [U_73,U_72,U_71] :
( ~ v1_xboole_0(U_71)
| ~ m1_subset_1(U_72,k1_zfmisc_1(U_71))
| ~ r2_hidden(U_73,U_72) ),
inference(variable_rename,[status(thm)],[f_36_1]) ).
fof(f_36_3,plain,
! [U_73,U_72] :
( ! [U_71] :
( ~ v1_xboole_0(U_71)
| ~ m1_subset_1(U_72,k1_zfmisc_1(U_71)) )
| ~ r2_hidden(U_73,U_72) ),
inference(miniscope,[status(thm)],[f_36_2]) ).
fof(f_36_4,plain,
! [U_71,U_72,U_73] :
( ~ v1_xboole_0(U_71)
| ~ m1_subset_1(U_72,k1_zfmisc_1(U_71))
| ~ r2_hidden(U_73,U_72) ),
inference(definitional_conversion,[status(esa)],[f_36_3]) ).
cnf(f_36_5,plain,
( ~ v1_xboole_0(U_71)
| ~ m1_subset_1(U_72,k1_zfmisc_1(U_71))
| ~ r2_hidden(U_73,U_72) ),
inference(clausify,[status(thm)],[f_36_4]) ).
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_74] :
( U_74 = k1_xboole_0
| ~ v1_xboole_0(U_74) ),
inference(variable_rename,[status(thm)],[f_37_1]) ).
fof(f_37_3,plain,
! [U_74] :
( U_74 = k1_xboole_0
| ~ v1_xboole_0(U_74) ),
inference(definitional_conversion,[status(esa)],[f_37_2]) ).
cnf(f_37_4,plain,
( U_74 = k1_xboole_0
| ~ v1_xboole_0(U_74) ),
inference(clausify,[status(thm)],[f_37_3]) ).
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_76,U_75] :
( ~ v1_xboole_0(U_75)
| ~ r2_hidden(U_76,U_75) ),
inference(variable_rename,[status(thm)],[f_38_1]) ).
fof(f_38_3,plain,
! [U_76,U_75] :
( ~ v1_xboole_0(U_75)
| ~ r2_hidden(U_76,U_75) ),
inference(definitional_conversion,[status(esa)],[f_38_2]) ).
cnf(f_38_4,plain,
( ~ v1_xboole_0(U_75)
| ~ r2_hidden(U_76,U_75) ),
inference(clausify,[status(thm)],[f_38_3]) ).
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_78,U_77] :
( ~ v1_xboole_0(U_77)
| U_78 = U_77
| ~ v1_xboole_0(U_78) ),
inference(variable_rename,[status(thm)],[f_39_1]) ).
fof(f_39_3,plain,
! [U_78] :
( ! [U_77] :
( ~ v1_xboole_0(U_77)
| U_78 = U_77 )
| ~ v1_xboole_0(U_78) ),
inference(miniscope,[status(thm)],[f_39_2]) ).
fof(f_39_4,plain,
! [U_77,U_78] :
( ~ v1_xboole_0(U_77)
| U_78 = U_77
| ~ v1_xboole_0(U_78) ),
inference(definitional_conversion,[status(esa)],[f_39_3]) ).
cnf(f_39_5,plain,
( ~ v1_xboole_0(U_77)
| U_78 = U_77
| ~ v1_xboole_0(U_78) ),
inference(clausify,[status(thm)],[f_39_4]) ).
fof(f_40_1,plain,
! [A,B,C] :
( ( ( r2_hidden(A,k9_relat_1(C,k1_tarski(B)))
| ~ r2_hidden(k4_tarski(B,A),C) )
& ( r2_hidden(k4_tarski(B,A),C)
| ~ r2_hidden(A,k9_relat_1(C,k1_tarski(B))) ) )
| ~ v1_relat_1(C) ),
inference(fof_nnf,[status(thm)],[t9_relset_2]) ).
fof(f_40_2,plain,
! [U_81,U_80,U_79] :
( ( ( r2_hidden(U_81,k9_relat_1(U_79,k1_tarski(U_80)))
| ~ r2_hidden(k4_tarski(U_80,U_81),U_79) )
& ( r2_hidden(k4_tarski(U_80,U_81),U_79)
| ~ r2_hidden(U_81,k9_relat_1(U_79,k1_tarski(U_80))) ) )
| ~ v1_relat_1(U_79) ),
inference(variable_rename,[status(thm)],[f_40_1]) ).
fof(f_40_3,plain,
( ! [U_80,U_79,U_81] :
( r2_hidden(U_81,k9_relat_1(U_79,k1_tarski(U_80)))
| ~ r2_hidden(k4_tarski(U_80,U_81),U_79)
| ~ sP7(U_80,U_79,U_81) )
& ! [U_80,U_79,U_81] :
( r2_hidden(k4_tarski(U_80,U_81),U_79)
| ~ r2_hidden(U_81,k9_relat_1(U_79,k1_tarski(U_80)))
| ~ sP7(U_80,U_79,U_81) )
& ! [U_80,U_79,U_81] :
( sP7(U_80,U_79,U_81)
| ~ v1_relat_1(U_79) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP7])],[f_40_2]) ).
cnf(f_40_4,plain,
( sP7(U_80,U_79,U_81)
| ~ v1_relat_1(U_79) ),
inference(clausify,[status(thm)],[f_40_3]) ).
cnf(f_40_5,plain,
( r2_hidden(k4_tarski(U_80,U_81),U_79)
| ~ r2_hidden(U_81,k9_relat_1(U_79,k1_tarski(U_80)))
| ~ sP7(U_80,U_79,U_81) ),
inference(clausify,[status(thm)],[f_40_3]) ).
cnf(f_40_6,plain,
( r2_hidden(U_81,k9_relat_1(U_79,k1_tarski(U_80)))
| ~ r2_hidden(k4_tarski(U_80,U_81),U_79)
| ~ sP7(U_80,U_79,U_81) ),
inference(clausify,[status(thm)],[f_40_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_14_3_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_14_3]) ).
cnf(f_15_3_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_15_3]) ).
cnf(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,
( k4_xboole_0(Eq_x_0,Eq_x_1) = k4_xboole_0(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,
( k1_tarski(Eq_x_0) = k1_tarski(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_6,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_7,axiom,
( k2_tarski(Eq_x_0,Eq_x_1) = k2_tarski(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,
( k4_tarski(Eq_x_0,Eq_x_1) = k4_tarski(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,
( k1_zfmisc_1(Eq_x_0) = k1_zfmisc_1(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_10,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_11,axiom,
( sK5(Eq_x_0,Eq_x_1,Eq_x_2) = sK5(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,
( sK6(Eq_x_0,Eq_x_1,Eq_x_2) = sK6(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_13,axiom,
( sK7(Eq_x_0) = sK7(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_14,axiom,
( sK9(Eq_x_0) = sK9(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_15,axiom,
( sK11(Eq_x_0) = sK11(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_16,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_17,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_18,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_19,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_20,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_21,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_22,axiom,
( sP0(Eq_y_0,Eq_y_1)
| ~ sP0(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,
( 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_24,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_25,axiom,
( sP3(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
| ~ sP3(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_26,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_27,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_28,axiom,
( sP6(Eq_y_0)
| ~ sP6(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_29,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(sat_proved,plain,
$false,
inference(cadical,[status(thm)],[]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU419+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
% 0.09/5.38 % Computer : n017.cluster.edu
% 0.09/5.38 % Model : x86_64 x86_64
% 0.09/5.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/5.38 % Memory : 8046.5625MB
% 0.09/5.38 % OS : Linux 6.8.0-71-generic
% 0.09/5.38 % CPULimit : 300
% 0.09/5.38 % WCLimit : 300
% 0.09/5.38 % DateTime : Sun Sep 20 00:16:01 UTC 2026
% 0.09/5.38 % CPUTime :
% 222.14/227.48 % SZS status Theorem for theBenchmark
% 222.14/227.48 % SZS output start Proof for theBenchmark
% See solution above
%------------------------------------------------------------------------------