%------------------------------------------------------------------------------
% File : ConnectPP---0.7.2
% Problem : ALG227+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 : n013.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 08:12:31 AM UTC 2026
% Result : Theorem 170.89s 176.25s
% Output : Proof 175.43s
% Verified :
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)
% Comments :
%------------------------------------------------------------------------------
fof(t8_closure3,conjecture,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( m1_pboole(B,A)
=> ! [C] :
( m1_subset_1(C,A)
=> ( ~ r2_hidden(C,k1_closure3(A,B))
=> k1_funct_1(B,C) = k1_xboole_0 ) ) ) ),
file('theBenchmark.p',t8_closure3) ).
fof(antisymmetry_r2_hidden,axiom,
! [A,B] :
( r2_hidden(A,B)
=> ~ r2_hidden(B,A) ),
file('theBenchmark.p',antisymmetry_r2_hidden) ).
fof(cc1_closure2,axiom,
! [A] :
( v1_xboole_0(A)
=> v1_fraenkel(A) ),
file('theBenchmark.p',cc1_closure2) ).
fof(cc1_finset_1,axiom,
! [A] :
( v1_xboole_0(A)
=> v1_finset_1(A) ),
file('theBenchmark.p',cc1_finset_1) ).
fof(cc1_funct_1,axiom,
! [A] :
( v1_xboole_0(A)
=> v1_funct_1(A) ),
file('theBenchmark.p',cc1_funct_1) ).
fof(cc2_funct_1,axiom,
! [A] :
( ( v1_funct_1(A)
& v1_xboole_0(A)
& v1_relat_1(A) )
=> ( v2_funct_1(A)
& v1_funct_1(A)
& v1_relat_1(A) ) ),
file('theBenchmark.p',cc2_funct_1) ).
fof(d3_closure3,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( m1_pboole(B,A)
=> ! [C] :
( C = k1_closure3(A,B)
<=> C = a_2_0_closure3(A,B) ) ) ),
file('theBenchmark.p',d3_closure3) ).
fof(dt_k1_closure3,axiom,
$true,
file('theBenchmark.p',dt_k1_closure3) ).
fof(dt_k1_funct_1,axiom,
$true,
file('theBenchmark.p',dt_k1_funct_1) ).
fof(dt_k1_xboole_0,axiom,
$true,
file('theBenchmark.p',dt_k1_xboole_0) ).
fof(dt_m1_pboole,axiom,
! [A,B] :
( m1_pboole(B,A)
=> ( v1_funct_1(B)
& v1_relat_1(B) ) ),
file('theBenchmark.p',dt_m1_pboole) ).
fof(dt_m1_subset_1,axiom,
$true,
file('theBenchmark.p',dt_m1_subset_1) ).
fof(existence_m1_pboole,axiom,
! [A] :
? [B] : m1_pboole(B,A),
file('theBenchmark.p',existence_m1_pboole) ).
fof(existence_m1_subset_1,axiom,
! [A] :
? [B] : m1_subset_1(B,A),
file('theBenchmark.p',existence_m1_subset_1) ).
fof(fc1_xboole_0,axiom,
v1_xboole_0(k1_xboole_0),
file('theBenchmark.p',fc1_xboole_0) ).
fof(fraenkel_a_2_0_closure3,axiom,
! [A,B,C] :
( ( m1_pboole(C,B)
& ~ v1_xboole_0(B) )
=> ( r2_hidden(A,a_2_0_closure3(B,C))
<=> ? [D] :
( k1_funct_1(C,D) != k1_xboole_0
& A = D
& m1_subset_1(D,B) ) ) ),
file('theBenchmark.p',fraenkel_a_2_0_closure3) ).
fof(rc1_closure2,axiom,
? [A] :
( v1_fraenkel(A)
& v1_finset_1(A)
& v2_funct_1(A)
& v1_funct_1(A)
& v1_relat_1(A)
& v1_xboole_0(A) ),
file('theBenchmark.p',rc1_closure2) ).
fof(rc1_finset_1,axiom,
? [A] :
( v1_finset_1(A)
& ~ v1_xboole_0(A) ),
file('theBenchmark.p',rc1_finset_1) ).
fof(rc1_funct_1,axiom,
? [A] :
( v1_funct_1(A)
& v1_relat_1(A) ),
file('theBenchmark.p',rc1_funct_1) ).
fof(rc1_xboole_0,axiom,
? [A] : v1_xboole_0(A),
file('theBenchmark.p',rc1_xboole_0) ).
fof(rc2_funct_1,axiom,
? [A] :
( v1_funct_1(A)
& v1_xboole_0(A)
& v1_relat_1(A) ),
file('theBenchmark.p',rc2_funct_1) ).
fof(rc2_xboole_0,axiom,
? [A] : ~ v1_xboole_0(A),
file('theBenchmark.p',rc2_xboole_0) ).
fof(rc3_funct_1,axiom,
? [A] :
( v2_funct_1(A)
& v1_funct_1(A)
& v1_relat_1(A) ),
file('theBenchmark.p',rc3_funct_1) ).
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(t2_tarski,axiom,
! [A,B] :
( ! [C] :
( r2_hidden(C,A)
<=> r2_hidden(C,B) )
=> A = B ),
file('theBenchmark.p',t2_tarski) ).
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(f_1_1,negated_conjecture,
~ ! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( m1_pboole(B,A)
=> ! [C] :
( m1_subset_1(C,A)
=> ( ~ r2_hidden(C,k1_closure3(A,B))
=> k1_funct_1(B,C) = k1_xboole_0 ) ) ) ),
inference(negate,[status(cth)],[t8_closure3]) ).
fof(f_1_2,negated_conjecture,
? [A] :
( ? [B] :
( ? [C] :
( k1_funct_1(B,C) != k1_xboole_0
& ~ r2_hidden(C,k1_closure3(A,B))
& m1_subset_1(C,A) )
& m1_pboole(B,A) )
& ~ v1_xboole_0(A) ),
inference(fof_nnf,[status(thm)],[f_1_1]) ).
fof(f_1_3,negated_conjecture,
? [U_2] :
( ? [U_1] :
( ? [U_0] :
( k1_funct_1(U_1,U_0) != k1_xboole_0
& ~ r2_hidden(U_0,k1_closure3(U_2,U_1))
& m1_subset_1(U_0,U_2) )
& m1_pboole(U_1,U_2) )
& ~ v1_xboole_0(U_2) ),
inference(variable_rename,[status(thm)],[f_1_2]) ).
fof(f_1_4,negated_conjecture,
( ? [U_1] :
( ? [U_0] :
( k1_funct_1(U_1,U_0) != k1_xboole_0
& ~ r2_hidden(U_0,k1_closure3(sK1,U_1))
& m1_subset_1(U_0,sK1) )
& m1_pboole(U_1,sK1) )
& ~ v1_xboole_0(sK1) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(U_2,sK1)],[f_1_3]) ).
fof(f_1_5,negated_conjecture,
( ? [U_0] :
( k1_funct_1(sK2,U_0) != k1_xboole_0
& ~ r2_hidden(U_0,k1_closure3(sK1,sK2))
& m1_subset_1(U_0,sK1) )
& m1_pboole(sK2,sK1)
& ~ v1_xboole_0(sK1) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2]),skolemize(U_1,sK2)],[f_1_4]) ).
fof(f_1_6,negated_conjecture,
( k1_funct_1(sK2,sK3) != k1_xboole_0
& ~ r2_hidden(sK3,k1_closure3(sK1,sK2))
& m1_subset_1(sK3,sK1)
& m1_pboole(sK2,sK1)
& ~ v1_xboole_0(sK1) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3]),skolemize(U_0,sK3)],[f_1_5]) ).
cnf(f_1_7,negated_conjecture,
~ v1_xboole_0(sK1),
inference(clausify,[status(thm)],[f_1_6]) ).
cnf(f_1_8,negated_conjecture,
m1_pboole(sK2,sK1),
inference(clausify,[status(thm)],[f_1_6]) ).
cnf(f_1_9,negated_conjecture,
m1_subset_1(sK3,sK1),
inference(clausify,[status(thm)],[f_1_6]) ).
cnf(f_1_10,negated_conjecture,
~ r2_hidden(sK3,k1_closure3(sK1,sK2)),
inference(clausify,[status(thm)],[f_1_6]) ).
cnf(f_1_11,negated_conjecture,
k1_funct_1(sK2,sK3) != k1_xboole_0,
inference(clausify,[status(thm)],[f_1_6]) ).
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]) ).
cnf(f_2_3,plain,
( ~ r2_hidden(U_3,U_4)
| ~ r2_hidden(U_4,U_3) ),
inference(clausify,[status(thm)],[f_2_2]) ).
fof(f_3_1,plain,
! [A] :
( v1_fraenkel(A)
| ~ v1_xboole_0(A) ),
inference(fof_nnf,[status(thm)],[cc1_closure2]) ).
fof(f_3_2,plain,
! [U_5] :
( v1_fraenkel(U_5)
| ~ v1_xboole_0(U_5) ),
inference(variable_rename,[status(thm)],[f_3_1]) ).
cnf(f_3_3,plain,
( v1_fraenkel(U_5)
| ~ v1_xboole_0(U_5) ),
inference(clausify,[status(thm)],[f_3_2]) ).
fof(f_4_1,plain,
! [A] :
( v1_finset_1(A)
| ~ v1_xboole_0(A) ),
inference(fof_nnf,[status(thm)],[cc1_finset_1]) ).
fof(f_4_2,plain,
! [U_6] :
( v1_finset_1(U_6)
| ~ v1_xboole_0(U_6) ),
inference(variable_rename,[status(thm)],[f_4_1]) ).
cnf(f_4_3,plain,
( v1_finset_1(U_6)
| ~ v1_xboole_0(U_6) ),
inference(clausify,[status(thm)],[f_4_2]) ).
fof(f_5_1,plain,
! [A] :
( v1_funct_1(A)
| ~ v1_xboole_0(A) ),
inference(fof_nnf,[status(thm)],[cc1_funct_1]) ).
fof(f_5_2,plain,
! [U_7] :
( v1_funct_1(U_7)
| ~ v1_xboole_0(U_7) ),
inference(variable_rename,[status(thm)],[f_5_1]) ).
cnf(f_5_3,plain,
( v1_funct_1(U_7)
| ~ v1_xboole_0(U_7) ),
inference(clausify,[status(thm)],[f_5_2]) ).
fof(f_6_1,plain,
! [A] :
( ( v2_funct_1(A)
& v1_funct_1(A)
& v1_relat_1(A) )
| ~ v1_funct_1(A)
| ~ v1_xboole_0(A)
| ~ v1_relat_1(A) ),
inference(fof_nnf,[status(thm)],[cc2_funct_1]) ).
fof(f_6_2,plain,
! [U_8] :
( ( v2_funct_1(U_8)
& v1_funct_1(U_8)
& v1_relat_1(U_8) )
| ~ v1_funct_1(U_8)
| ~ v1_xboole_0(U_8)
| ~ v1_relat_1(U_8) ),
inference(variable_rename,[status(thm)],[f_6_1]) ).
cnf(f_6_3,plain,
( v1_relat_1(U_8)
| ~ v1_funct_1(U_8)
| ~ v1_xboole_0(U_8)
| ~ v1_relat_1(U_8) ),
inference(clausify,[status(thm)],[f_6_2]) ).
cnf(f_6_4,plain,
( v1_funct_1(U_8)
| ~ v1_funct_1(U_8)
| ~ v1_xboole_0(U_8)
| ~ v1_relat_1(U_8) ),
inference(clausify,[status(thm)],[f_6_2]) ).
cnf(f_6_5,plain,
( v2_funct_1(U_8)
| ~ v1_funct_1(U_8)
| ~ v1_xboole_0(U_8)
| ~ v1_relat_1(U_8) ),
inference(clausify,[status(thm)],[f_6_2]) ).
fof(f_7_1,plain,
! [A] :
( ! [B] :
( ! [C] :
( ( C = k1_closure3(A,B)
| C != a_2_0_closure3(A,B) )
& ( C = a_2_0_closure3(A,B)
| C != k1_closure3(A,B) ) )
| ~ m1_pboole(B,A) )
| v1_xboole_0(A) ),
inference(fof_nnf,[status(thm)],[d3_closure3]) ).
fof(f_7_2,plain,
! [U_11] :
( ! [U_10] :
( ! [U_9] :
( ( U_9 = k1_closure3(U_11,U_10)
| U_9 != a_2_0_closure3(U_11,U_10) )
& ( U_9 = a_2_0_closure3(U_11,U_10)
| U_9 != k1_closure3(U_11,U_10) ) )
| ~ m1_pboole(U_10,U_11) )
| v1_xboole_0(U_11) ),
inference(variable_rename,[status(thm)],[f_7_1]) ).
fof(f_7_3,plain,
! [U_11] :
( ! [U_10] :
( ( ! [U_13] :
( U_13 = k1_closure3(U_11,U_10)
| U_13 != a_2_0_closure3(U_11,U_10) )
& ! [U_12] :
( U_12 = a_2_0_closure3(U_11,U_10)
| U_12 != k1_closure3(U_11,U_10) ) )
| ~ m1_pboole(U_10,U_11) )
| v1_xboole_0(U_11) ),
inference(miniscope,[status(thm)],[f_7_2]) ).
cnf(f_7_4,plain,
( U_12 = a_2_0_closure3(U_11,U_10)
| U_12 != k1_closure3(U_11,U_10)
| ~ m1_pboole(U_10,U_11)
| v1_xboole_0(U_11) ),
inference(clausify,[status(thm)],[f_7_3]) ).
cnf(f_7_5,plain,
( U_13 = k1_closure3(U_11,U_10)
| U_13 != a_2_0_closure3(U_11,U_10)
| ~ m1_pboole(U_10,U_11)
| v1_xboole_0(U_11) ),
inference(clausify,[status(thm)],[f_7_3]) ).
fof(f_8_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_k1_closure3]) ).
cnf(f_8_2,plain,
$true,
inference(clausify,[status(thm)],[f_8_1]) ).
fof(f_9_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_k1_funct_1]) ).
cnf(f_9_2,plain,
$true,
inference(clausify,[status(thm)],[f_9_1]) ).
fof(f_10_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_k1_xboole_0]) ).
cnf(f_10_2,plain,
$true,
inference(clausify,[status(thm)],[f_10_1]) ).
fof(f_11_1,plain,
! [A,B] :
( ( v1_funct_1(B)
& v1_relat_1(B) )
| ~ m1_pboole(B,A) ),
inference(fof_nnf,[status(thm)],[dt_m1_pboole]) ).
fof(f_11_2,plain,
! [U_15,U_14] :
( ( v1_funct_1(U_14)
& v1_relat_1(U_14) )
| ~ m1_pboole(U_14,U_15) ),
inference(variable_rename,[status(thm)],[f_11_1]) ).
cnf(f_11_3,plain,
( v1_relat_1(U_14)
| ~ m1_pboole(U_14,U_15) ),
inference(clausify,[status(thm)],[f_11_2]) ).
cnf(f_11_4,plain,
( v1_funct_1(U_14)
| ~ m1_pboole(U_14,U_15) ),
inference(clausify,[status(thm)],[f_11_2]) ).
fof(f_12_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_m1_subset_1]) ).
cnf(f_12_2,plain,
$true,
inference(clausify,[status(thm)],[f_12_1]) ).
fof(f_13_1,plain,
! [A] :
? [B] : m1_pboole(B,A),
inference(fof_nnf,[status(thm)],[existence_m1_pboole]) ).
fof(f_13_2,plain,
! [U_17] :
? [U_16] : m1_pboole(U_16,U_17),
inference(variable_rename,[status(thm)],[f_13_1]) ).
fof(f_13_3,plain,
! [U_17] : m1_pboole(sK4(U_17),U_17),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4]),skolemize(U_16,sK4(U_17))],[f_13_2]) ).
cnf(f_13_4,plain,
m1_pboole(sK4(U_17),U_17),
inference(clausify,[status(thm)],[f_13_3]) ).
fof(f_14_1,plain,
! [A] :
? [B] : m1_subset_1(B,A),
inference(fof_nnf,[status(thm)],[existence_m1_subset_1]) ).
fof(f_14_2,plain,
! [U_19] :
? [U_18] : m1_subset_1(U_18,U_19),
inference(variable_rename,[status(thm)],[f_14_1]) ).
fof(f_14_3,plain,
! [U_19] : m1_subset_1(sK5(U_19),U_19),
inference(skolemize,[status(esa),new_symbols(skolem,[sK5]),skolemize(U_18,sK5(U_19))],[f_14_2]) ).
cnf(f_14_4,plain,
m1_subset_1(sK5(U_19),U_19),
inference(clausify,[status(thm)],[f_14_3]) ).
fof(f_15_1,plain,
v1_xboole_0(k1_xboole_0),
inference(fof_nnf,[status(thm)],[fc1_xboole_0]) ).
cnf(f_15_2,plain,
v1_xboole_0(k1_xboole_0),
inference(clausify,[status(thm)],[f_15_1]) ).
fof(f_16_1,plain,
! [A,B,C] :
( ( ( r2_hidden(A,a_2_0_closure3(B,C))
| ! [D] :
( k1_funct_1(C,D) = k1_xboole_0
| A != D
| ~ m1_subset_1(D,B) ) )
& ( ? [D] :
( k1_funct_1(C,D) != k1_xboole_0
& A = D
& m1_subset_1(D,B) )
| ~ r2_hidden(A,a_2_0_closure3(B,C)) ) )
| ~ m1_pboole(C,B)
| v1_xboole_0(B) ),
inference(fof_nnf,[status(thm)],[fraenkel_a_2_0_closure3]) ).
fof(f_16_2,plain,
! [U_24,U_23,U_22] :
( ( ( r2_hidden(U_24,a_2_0_closure3(U_23,U_22))
| ! [U_21] :
( k1_funct_1(U_22,U_21) = k1_xboole_0
| U_24 != U_21
| ~ m1_subset_1(U_21,U_23) ) )
& ( ? [U_20] :
( k1_funct_1(U_22,U_20) != k1_xboole_0
& U_24 = U_20
& m1_subset_1(U_20,U_23) )
| ~ r2_hidden(U_24,a_2_0_closure3(U_23,U_22)) ) )
| ~ m1_pboole(U_22,U_23)
| v1_xboole_0(U_23) ),
inference(variable_rename,[status(thm)],[f_16_1]) ).
fof(f_16_3,plain,
! [U_24,U_23,U_22] :
( ( ( r2_hidden(U_24,a_2_0_closure3(U_23,U_22))
| ! [U_21] :
( k1_funct_1(U_22,U_21) = k1_xboole_0
| U_24 != U_21
| ~ m1_subset_1(U_21,U_23) ) )
& ( ( k1_funct_1(U_22,sK6(U_24,U_23,U_22)) != k1_xboole_0
& U_24 = sK6(U_24,U_23,U_22)
& m1_subset_1(sK6(U_24,U_23,U_22),U_23) )
| ~ r2_hidden(U_24,a_2_0_closure3(U_23,U_22)) ) )
| ~ m1_pboole(U_22,U_23)
| v1_xboole_0(U_23) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK6]),skolemize(U_20,sK6(U_24,U_23,U_22))],[f_16_2]) ).
cnf(f_16_4,plain,
( m1_subset_1(sK6(U_24,U_23,U_22),U_23)
| ~ r2_hidden(U_24,a_2_0_closure3(U_23,U_22))
| ~ m1_pboole(U_22,U_23)
| v1_xboole_0(U_23) ),
inference(clausify,[status(thm)],[f_16_3]) ).
cnf(f_16_5,plain,
( U_24 = sK6(U_24,U_23,U_22)
| ~ r2_hidden(U_24,a_2_0_closure3(U_23,U_22))
| ~ m1_pboole(U_22,U_23)
| v1_xboole_0(U_23) ),
inference(clausify,[status(thm)],[f_16_3]) ).
cnf(f_16_6,plain,
( k1_funct_1(U_22,sK6(U_24,U_23,U_22)) != k1_xboole_0
| ~ r2_hidden(U_24,a_2_0_closure3(U_23,U_22))
| ~ m1_pboole(U_22,U_23)
| v1_xboole_0(U_23) ),
inference(clausify,[status(thm)],[f_16_3]) ).
cnf(f_16_7,plain,
( r2_hidden(U_24,a_2_0_closure3(U_23,U_22))
| k1_funct_1(U_22,U_21) = k1_xboole_0
| U_24 != U_21
| ~ m1_subset_1(U_21,U_23)
| ~ m1_pboole(U_22,U_23)
| v1_xboole_0(U_23) ),
inference(clausify,[status(thm)],[f_16_3]) ).
fof(f_17_1,plain,
? [A] :
( v1_fraenkel(A)
& v1_finset_1(A)
& v2_funct_1(A)
& v1_funct_1(A)
& v1_relat_1(A)
& v1_xboole_0(A) ),
inference(fof_nnf,[status(thm)],[rc1_closure2]) ).
fof(f_17_2,plain,
? [U_25] :
( v1_fraenkel(U_25)
& v1_finset_1(U_25)
& v2_funct_1(U_25)
& v1_funct_1(U_25)
& v1_relat_1(U_25)
& v1_xboole_0(U_25) ),
inference(variable_rename,[status(thm)],[f_17_1]) ).
fof(f_17_3,plain,
( v1_fraenkel(sK7)
& v1_finset_1(sK7)
& v2_funct_1(sK7)
& v1_funct_1(sK7)
& v1_relat_1(sK7)
& v1_xboole_0(sK7) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK7]),skolemize(U_25,sK7)],[f_17_2]) ).
cnf(f_17_4,plain,
v1_xboole_0(sK7),
inference(clausify,[status(thm)],[f_17_3]) ).
cnf(f_17_5,plain,
v1_relat_1(sK7),
inference(clausify,[status(thm)],[f_17_3]) ).
cnf(f_17_6,plain,
v1_funct_1(sK7),
inference(clausify,[status(thm)],[f_17_3]) ).
cnf(f_17_7,plain,
v2_funct_1(sK7),
inference(clausify,[status(thm)],[f_17_3]) ).
cnf(f_17_8,plain,
v1_finset_1(sK7),
inference(clausify,[status(thm)],[f_17_3]) ).
cnf(f_17_9,plain,
v1_fraenkel(sK7),
inference(clausify,[status(thm)],[f_17_3]) ).
fof(f_18_1,plain,
? [A] :
( v1_finset_1(A)
& ~ v1_xboole_0(A) ),
inference(fof_nnf,[status(thm)],[rc1_finset_1]) ).
fof(f_18_2,plain,
? [U_26] :
( v1_finset_1(U_26)
& ~ v1_xboole_0(U_26) ),
inference(variable_rename,[status(thm)],[f_18_1]) ).
fof(f_18_3,plain,
( v1_finset_1(sK8)
& ~ v1_xboole_0(sK8) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK8]),skolemize(U_26,sK8)],[f_18_2]) ).
cnf(f_18_4,plain,
~ v1_xboole_0(sK8),
inference(clausify,[status(thm)],[f_18_3]) ).
cnf(f_18_5,plain,
v1_finset_1(sK8),
inference(clausify,[status(thm)],[f_18_3]) ).
fof(f_19_1,plain,
? [A] :
( v1_funct_1(A)
& v1_relat_1(A) ),
inference(fof_nnf,[status(thm)],[rc1_funct_1]) ).
fof(f_19_2,plain,
? [U_27] :
( v1_funct_1(U_27)
& v1_relat_1(U_27) ),
inference(variable_rename,[status(thm)],[f_19_1]) ).
fof(f_19_3,plain,
( v1_funct_1(sK9)
& v1_relat_1(sK9) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK9]),skolemize(U_27,sK9)],[f_19_2]) ).
cnf(f_19_4,plain,
v1_relat_1(sK9),
inference(clausify,[status(thm)],[f_19_3]) ).
cnf(f_19_5,plain,
v1_funct_1(sK9),
inference(clausify,[status(thm)],[f_19_3]) ).
fof(f_20_1,plain,
? [A] : v1_xboole_0(A),
inference(fof_nnf,[status(thm)],[rc1_xboole_0]) ).
fof(f_20_2,plain,
? [U_28] : v1_xboole_0(U_28),
inference(variable_rename,[status(thm)],[f_20_1]) ).
fof(f_20_3,plain,
v1_xboole_0(sK10),
inference(skolemize,[status(esa),new_symbols(skolem,[sK10]),skolemize(U_28,sK10)],[f_20_2]) ).
cnf(f_20_4,plain,
v1_xboole_0(sK10),
inference(clausify,[status(thm)],[f_20_3]) ).
fof(f_21_1,plain,
? [A] :
( v1_funct_1(A)
& v1_xboole_0(A)
& v1_relat_1(A) ),
inference(fof_nnf,[status(thm)],[rc2_funct_1]) ).
fof(f_21_2,plain,
? [U_29] :
( v1_funct_1(U_29)
& v1_xboole_0(U_29)
& v1_relat_1(U_29) ),
inference(variable_rename,[status(thm)],[f_21_1]) ).
fof(f_21_3,plain,
( v1_funct_1(sK11)
& v1_xboole_0(sK11)
& v1_relat_1(sK11) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK11]),skolemize(U_29,sK11)],[f_21_2]) ).
cnf(f_21_4,plain,
v1_relat_1(sK11),
inference(clausify,[status(thm)],[f_21_3]) ).
cnf(f_21_5,plain,
v1_xboole_0(sK11),
inference(clausify,[status(thm)],[f_21_3]) ).
cnf(f_21_6,plain,
v1_funct_1(sK11),
inference(clausify,[status(thm)],[f_21_3]) ).
fof(f_22_1,plain,
? [A] : ~ v1_xboole_0(A),
inference(fof_nnf,[status(thm)],[rc2_xboole_0]) ).
fof(f_22_2,plain,
? [U_30] : ~ v1_xboole_0(U_30),
inference(variable_rename,[status(thm)],[f_22_1]) ).
fof(f_22_3,plain,
~ v1_xboole_0(sK12),
inference(skolemize,[status(esa),new_symbols(skolem,[sK12]),skolemize(U_30,sK12)],[f_22_2]) ).
cnf(f_22_4,plain,
~ v1_xboole_0(sK12),
inference(clausify,[status(thm)],[f_22_3]) ).
fof(f_23_1,plain,
? [A] :
( v2_funct_1(A)
& v1_funct_1(A)
& v1_relat_1(A) ),
inference(fof_nnf,[status(thm)],[rc3_funct_1]) ).
fof(f_23_2,plain,
? [U_31] :
( v2_funct_1(U_31)
& v1_funct_1(U_31)
& v1_relat_1(U_31) ),
inference(variable_rename,[status(thm)],[f_23_1]) ).
fof(f_23_3,plain,
( v2_funct_1(sK13)
& v1_funct_1(sK13)
& v1_relat_1(sK13) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK13]),skolemize(U_31,sK13)],[f_23_2]) ).
cnf(f_23_4,plain,
v1_relat_1(sK13),
inference(clausify,[status(thm)],[f_23_3]) ).
cnf(f_23_5,plain,
v1_funct_1(sK13),
inference(clausify,[status(thm)],[f_23_3]) ).
cnf(f_23_6,plain,
v2_funct_1(sK13),
inference(clausify,[status(thm)],[f_23_3]) ).
fof(f_24_1,plain,
! [A,B] :
( m1_subset_1(A,B)
| ~ r2_hidden(A,B) ),
inference(fof_nnf,[status(thm)],[t1_subset]) ).
fof(f_24_2,plain,
! [U_33,U_32] :
( m1_subset_1(U_33,U_32)
| ~ r2_hidden(U_33,U_32) ),
inference(variable_rename,[status(thm)],[f_24_1]) ).
cnf(f_24_3,plain,
( m1_subset_1(U_33,U_32)
| ~ r2_hidden(U_33,U_32) ),
inference(clausify,[status(thm)],[f_24_2]) ).
fof(f_25_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_25_2,plain,
! [U_35,U_34] :
( r2_hidden(U_35,U_34)
| v1_xboole_0(U_34)
| ~ m1_subset_1(U_35,U_34) ),
inference(variable_rename,[status(thm)],[f_25_1]) ).
cnf(f_25_3,plain,
( r2_hidden(U_35,U_34)
| v1_xboole_0(U_34)
| ~ m1_subset_1(U_35,U_34) ),
inference(clausify,[status(thm)],[f_25_2]) ).
fof(f_26_1,plain,
! [A,B] :
( A = B
| ? [C] :
( ( ~ r2_hidden(C,A)
& r2_hidden(C,B) )
| ( ~ r2_hidden(C,B)
& r2_hidden(C,A) ) ) ),
inference(fof_nnf,[status(thm)],[t2_tarski]) ).
fof(f_26_2,plain,
! [U_38,U_37] :
( U_38 = U_37
| ? [U_36] :
( ( ~ r2_hidden(U_36,U_38)
& r2_hidden(U_36,U_37) )
| ( ~ r2_hidden(U_36,U_37)
& r2_hidden(U_36,U_38) ) ) ),
inference(variable_rename,[status(thm)],[f_26_1]) ).
fof(f_26_3,plain,
! [U_38,U_37] :
( U_38 = U_37
| ? [U_40] :
( ~ r2_hidden(U_40,U_38)
& r2_hidden(U_40,U_37) )
| ? [U_39] :
( ~ r2_hidden(U_39,U_37)
& r2_hidden(U_39,U_38) ) ),
inference(miniscope,[status(thm)],[f_26_2]) ).
fof(f_26_4,plain,
! [U_38,U_37] :
( U_38 = U_37
| ? [U_40] :
( ~ r2_hidden(U_40,U_38)
& r2_hidden(U_40,U_37) )
| ( ~ r2_hidden(sK14(U_38,U_37),U_37)
& r2_hidden(sK14(U_38,U_37),U_38) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK14]),skolemize(U_39,sK14(U_38,U_37))],[f_26_3]) ).
fof(f_26_5,plain,
! [U_38,U_37] :
( U_38 = U_37
| ( ~ r2_hidden(sK15(U_38,U_37),U_38)
& r2_hidden(sK15(U_38,U_37),U_37) )
| ( ~ r2_hidden(sK14(U_38,U_37),U_37)
& r2_hidden(sK14(U_38,U_37),U_38) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK15]),skolemize(U_40,sK15(U_38,U_37))],[f_26_4]) ).
cnf(f_26_6,plain,
( r2_hidden(sK15(U_38,U_37),U_37)
| r2_hidden(sK14(U_38,U_37),U_38)
| U_38 = U_37 ),
inference(clausify,[status(thm)],[f_26_5]) ).
cnf(f_26_7,plain,
( ~ r2_hidden(sK15(U_38,U_37),U_38)
| r2_hidden(sK14(U_38,U_37),U_38)
| U_38 = U_37 ),
inference(clausify,[status(thm)],[f_26_5]) ).
cnf(f_26_8,plain,
( r2_hidden(sK15(U_38,U_37),U_37)
| ~ r2_hidden(sK14(U_38,U_37),U_37)
| U_38 = U_37 ),
inference(clausify,[status(thm)],[f_26_5]) ).
cnf(f_26_9,plain,
( ~ r2_hidden(sK15(U_38,U_37),U_38)
| ~ r2_hidden(sK14(U_38,U_37),U_37)
| U_38 = U_37 ),
inference(clausify,[status(thm)],[f_26_5]) ).
fof(f_27_1,plain,
! [A] :
( A = k1_xboole_0
| ~ v1_xboole_0(A) ),
inference(fof_nnf,[status(thm)],[t6_boole]) ).
fof(f_27_2,plain,
! [U_41] :
( U_41 = k1_xboole_0
| ~ v1_xboole_0(U_41) ),
inference(variable_rename,[status(thm)],[f_27_1]) ).
cnf(f_27_3,plain,
( U_41 = k1_xboole_0
| ~ v1_xboole_0(U_41) ),
inference(clausify,[status(thm)],[f_27_2]) ).
fof(f_28_1,plain,
! [A,B] :
( ~ v1_xboole_0(B)
| ~ r2_hidden(A,B) ),
inference(fof_nnf,[status(thm)],[t7_boole]) ).
fof(f_28_2,plain,
! [U_43,U_42] :
( ~ v1_xboole_0(U_42)
| ~ r2_hidden(U_43,U_42) ),
inference(variable_rename,[status(thm)],[f_28_1]) ).
cnf(f_28_3,plain,
( ~ v1_xboole_0(U_42)
| ~ r2_hidden(U_43,U_42) ),
inference(clausify,[status(thm)],[f_28_2]) ).
fof(f_29_1,plain,
! [A,B] :
( ~ v1_xboole_0(B)
| A = B
| ~ v1_xboole_0(A) ),
inference(fof_nnf,[status(thm)],[t8_boole]) ).
fof(f_29_2,plain,
! [U_45,U_44] :
( ~ v1_xboole_0(U_44)
| U_45 = U_44
| ~ v1_xboole_0(U_45) ),
inference(variable_rename,[status(thm)],[f_29_1]) ).
fof(f_29_3,plain,
! [U_45] :
( ! [U_44] :
( ~ v1_xboole_0(U_44)
| U_45 = U_44 )
| ~ v1_xboole_0(U_45) ),
inference(miniscope,[status(thm)],[f_29_2]) ).
cnf(f_29_4,plain,
( ~ v1_xboole_0(U_44)
| U_45 = U_44
| ~ v1_xboole_0(U_45) ),
inference(clausify,[status(thm)],[f_29_3]) ).
cnf(f_6_3_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_6_3]) ).
cnf(f_6_4_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_6_4]) ).
cnf(f_8_2_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_8_2]) ).
cnf(f_9_2_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_9_2]) ).
cnf(f_10_2_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_10_2]) ).
cnf(f_12_2_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_12_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_closure3(Eq_x_0,Eq_x_1) = k1_closure3(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_funct_1(Eq_x_0,Eq_x_1) = k1_funct_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_6,axiom,
( a_2_0_closure3(Eq_x_0,Eq_x_1) = a_2_0_closure3(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,
( sK4(Eq_x_0) = sK4(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_8,axiom,
( sK5(Eq_x_0) = sK5(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_9,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_10,axiom,
( sK14(Eq_x_0,Eq_x_1) = sK14(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,
( 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_12,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_13,axiom,
( m1_pboole(Eq_y_0,Eq_y_1)
| ~ m1_pboole(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_14,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_15,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_16,axiom,
( v1_fraenkel(Eq_y_0)
| ~ v1_fraenkel(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_17,axiom,
( v1_finset_1(Eq_y_0)
| ~ v1_finset_1(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_18,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_19,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_20,axiom,
( v2_funct_1(Eq_y_0)
| ~ v2_funct_1(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
% 0.00/0.04 % Problem : ALG227+1 : TPTP v9.3.1. Released v3.4.0.
% 0.00/0.05 This is a FOF_THM_RFO_SEQ problem
% 0.00/0.06 % Command : /export/starexec/sandbox/solver/bin/connect++ --verbosity 1 --no-colour --tptp-proof --schedule default --timeout 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.16/5.43 % Computer : n013.cluster.edu
% 0.16/5.43 % Model : x86_64 x86_64
% 0.16/5.43 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/5.43 % Memory : 8046.5625MB
% 0.16/5.43 % OS : Linux 6.8.0-71-generic
% 0.16/5.43 % CPULimit : 300
% 0.16/5.43 % WCLimit : 300
% 0.16/5.43 % DateTime : Sun Sep 20 10:11:00 UTC 2026
% 0.16/5.43 % CPUTime :
% 170.89/176.25 % SZS status Theorem for theBenchmark
% 170.89/176.25 % SZS output start Proof for theBenchmark
% See solution above
%------------------------------------------------------------------------------