%------------------------------------------------------------------------------
% File : ConnectPP---0.7.2
% Problem : SEU245+1 : TPTP v9.3.1. Released v3.3.0.
% 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 : n003.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Sep 24 08:58:41 AM UTC 2026
% Result : Theorem 9.36s 9.70s
% Output : Proof 9.52s
% Verified :
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)
% Comments :
%------------------------------------------------------------------------------
fof(rc3_funct_1,axiom,
? [A] :
( one_to_one(A)
& function(A)
& relation(A) ),
file('theBenchmark.p',rc3_funct_1) ).
fof(dt_k1_xboole_0,axiom,
$true,
file('theBenchmark.p',dt_k1_xboole_0) ).
fof(rc1_funct_1,axiom,
? [A] :
( function(A)
& relation(A) ),
file('theBenchmark.p',rc1_funct_1) ).
fof(rc2_funct_1,axiom,
? [A] :
( function(A)
& empty(A)
& relation(A) ),
file('theBenchmark.p',rc2_funct_1) ).
fof(cc2_funct_1,axiom,
! [A] :
( ( function(A)
& empty(A)
& relation(A) )
=> ( one_to_one(A)
& function(A)
& relation(A) ) ),
file('theBenchmark.p',cc2_funct_1) ).
fof(fc1_xboole_0,axiom,
empty(empty_set),
file('theBenchmark.p',fc1_xboole_0) ).
fof(t2_boole,axiom,
! [A] : set_intersection2(A,empty_set) = empty_set,
file('theBenchmark.p',t2_boole) ).
fof(existence_m1_subset_1,axiom,
! [A] :
? [B] : element(B,A),
file('theBenchmark.p',existence_m1_subset_1) ).
fof(dt_m1_subset_1,axiom,
$true,
file('theBenchmark.p',dt_m1_subset_1) ).
fof(cc1_funct_1,axiom,
! [A] :
( empty(A)
=> function(A) ),
file('theBenchmark.p',cc1_funct_1) ).
fof(rc1_xboole_0,axiom,
? [A] : empty(A),
file('theBenchmark.p',rc1_xboole_0) ).
fof(rc2_xboole_0,axiom,
? [A] : ~ empty(A),
file('theBenchmark.p',rc2_xboole_0) ).
fof(t2_subset,axiom,
! [A,B] :
( element(A,B)
=> ( in(A,B)
| empty(B) ) ),
file('theBenchmark.p',t2_subset) ).
fof(t6_boole,axiom,
! [A] :
( empty(A)
=> A = empty_set ),
file('theBenchmark.p',t6_boole) ).
fof(t8_boole,axiom,
! [A,B] :
~ ( empty(B)
& A != B
& empty(A) ),
file('theBenchmark.p',t8_boole) ).
fof(commutativity_k3_xboole_0,axiom,
! [A,B] : set_intersection2(A,B) = set_intersection2(B,A),
file('theBenchmark.p',commutativity_k3_xboole_0) ).
fof(idempotence_k3_xboole_0,axiom,
! [A,B] : set_intersection2(A,A) = A,
file('theBenchmark.p',idempotence_k3_xboole_0) ).
fof(antisymmetry_r2_hidden,axiom,
! [A,B] :
( in(A,B)
=> ~ in(B,A) ),
file('theBenchmark.p',antisymmetry_r2_hidden) ).
fof(dt_k2_wellord1,axiom,
! [A,B] :
( relation(A)
=> relation(relation_restriction(A,B)) ),
file('theBenchmark.p',dt_k2_wellord1) ).
fof(dt_k2_zfmisc_1,axiom,
$true,
file('theBenchmark.p',dt_k2_zfmisc_1) ).
fof(dt_k3_xboole_0,axiom,
$true,
file('theBenchmark.p',dt_k3_xboole_0) ).
fof(t1_subset,axiom,
! [A,B] :
( in(A,B)
=> element(A,B) ),
file('theBenchmark.p',t1_subset) ).
fof(t7_boole,axiom,
! [A,B] :
~ ( empty(B)
& in(A,B) ),
file('theBenchmark.p',t7_boole) ).
fof(d6_wellord1,axiom,
! [A] :
( relation(A)
=> ! [B] : relation_restriction(A,B) = set_intersection2(A,cartesian_product2(B,B)) ),
file('theBenchmark.p',d6_wellord1) ).
fof(t16_wellord1,conjecture,
! [A,B,C] :
( relation(C)
=> ( in(A,relation_restriction(C,B))
<=> ( in(A,cartesian_product2(B,B))
& in(A,C) ) ) ),
file('theBenchmark.p',t16_wellord1) ).
fof(d3_xboole_0,axiom,
! [A,B,C] :
( C = set_intersection2(A,B)
<=> ! [D] :
( in(D,C)
<=> ( in(D,B)
& in(D,A) ) ) ),
file('theBenchmark.p',d3_xboole_0) ).
fof(f_1_1,plain,
? [A] :
( one_to_one(A)
& function(A)
& relation(A) ),
inference(fof_nnf,[status(thm)],[rc3_funct_1]) ).
fof(f_1_2,plain,
? [U_0] :
( one_to_one(U_0)
& function(U_0)
& relation(U_0) ),
inference(variable_rename,[status(thm)],[f_1_1]) ).
fof(f_1_3,plain,
( one_to_one(sK1)
& function(sK1)
& relation(sK1) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(U_0,sK1)],[f_1_2]) ).
cnf(f_1_4,plain,
relation(sK1),
inference(clausify,[status(thm)],[f_1_3]) ).
cnf(f_1_5,plain,
function(sK1),
inference(clausify,[status(thm)],[f_1_3]) ).
cnf(f_1_6,plain,
one_to_one(sK1),
inference(clausify,[status(thm)],[f_1_3]) ).
fof(f_2_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_k1_xboole_0]) ).
cnf(f_2_2,plain,
$true,
inference(clausify,[status(thm)],[f_2_1]) ).
fof(f_3_1,plain,
? [A] :
( function(A)
& relation(A) ),
inference(fof_nnf,[status(thm)],[rc1_funct_1]) ).
fof(f_3_2,plain,
? [U_1] :
( function(U_1)
& relation(U_1) ),
inference(variable_rename,[status(thm)],[f_3_1]) ).
fof(f_3_3,plain,
( function(sK2)
& relation(sK2) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2]),skolemize(U_1,sK2)],[f_3_2]) ).
cnf(f_3_4,plain,
relation(sK2),
inference(clausify,[status(thm)],[f_3_3]) ).
cnf(f_3_5,plain,
function(sK2),
inference(clausify,[status(thm)],[f_3_3]) ).
fof(f_4_1,plain,
? [A] :
( function(A)
& empty(A)
& relation(A) ),
inference(fof_nnf,[status(thm)],[rc2_funct_1]) ).
fof(f_4_2,plain,
? [U_2] :
( function(U_2)
& empty(U_2)
& relation(U_2) ),
inference(variable_rename,[status(thm)],[f_4_1]) ).
fof(f_4_3,plain,
( function(sK3)
& empty(sK3)
& relation(sK3) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3]),skolemize(U_2,sK3)],[f_4_2]) ).
cnf(f_4_4,plain,
relation(sK3),
inference(clausify,[status(thm)],[f_4_3]) ).
cnf(f_4_5,plain,
empty(sK3),
inference(clausify,[status(thm)],[f_4_3]) ).
cnf(f_4_6,plain,
function(sK3),
inference(clausify,[status(thm)],[f_4_3]) ).
fof(f_5_1,plain,
! [A] :
( ( one_to_one(A)
& function(A)
& relation(A) )
| ~ function(A)
| ~ empty(A)
| ~ relation(A) ),
inference(fof_nnf,[status(thm)],[cc2_funct_1]) ).
fof(f_5_2,plain,
! [U_3] :
( ( one_to_one(U_3)
& function(U_3)
& relation(U_3) )
| ~ function(U_3)
| ~ empty(U_3)
| ~ relation(U_3) ),
inference(variable_rename,[status(thm)],[f_5_1]) ).
cnf(f_5_3,plain,
( relation(U_3)
| ~ function(U_3)
| ~ empty(U_3)
| ~ relation(U_3) ),
inference(clausify,[status(thm)],[f_5_2]) ).
cnf(f_5_4,plain,
( function(U_3)
| ~ function(U_3)
| ~ empty(U_3)
| ~ relation(U_3) ),
inference(clausify,[status(thm)],[f_5_2]) ).
cnf(f_5_5,plain,
( one_to_one(U_3)
| ~ function(U_3)
| ~ empty(U_3)
| ~ relation(U_3) ),
inference(clausify,[status(thm)],[f_5_2]) ).
fof(f_6_1,plain,
empty(empty_set),
inference(fof_nnf,[status(thm)],[fc1_xboole_0]) ).
cnf(f_6_2,plain,
empty(empty_set),
inference(clausify,[status(thm)],[f_6_1]) ).
fof(f_7_1,plain,
! [A] : set_intersection2(A,empty_set) = empty_set,
inference(fof_nnf,[status(thm)],[t2_boole]) ).
fof(f_7_2,plain,
! [U_4] : set_intersection2(U_4,empty_set) = empty_set,
inference(variable_rename,[status(thm)],[f_7_1]) ).
cnf(f_7_3,plain,
set_intersection2(U_4,empty_set) = empty_set,
inference(clausify,[status(thm)],[f_7_2]) ).
fof(f_8_1,plain,
! [A] :
? [B] : element(B,A),
inference(fof_nnf,[status(thm)],[existence_m1_subset_1]) ).
fof(f_8_2,plain,
! [U_6] :
? [U_5] : element(U_5,U_6),
inference(variable_rename,[status(thm)],[f_8_1]) ).
fof(f_8_3,plain,
! [U_6] : element(sK4(U_6),U_6),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4]),skolemize(U_5,sK4(U_6))],[f_8_2]) ).
cnf(f_8_4,plain,
element(sK4(U_6),U_6),
inference(clausify,[status(thm)],[f_8_3]) ).
fof(f_9_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_m1_subset_1]) ).
cnf(f_9_2,plain,
$true,
inference(clausify,[status(thm)],[f_9_1]) ).
fof(f_10_1,plain,
! [A] :
( function(A)
| ~ empty(A) ),
inference(fof_nnf,[status(thm)],[cc1_funct_1]) ).
fof(f_10_2,plain,
! [U_7] :
( function(U_7)
| ~ empty(U_7) ),
inference(variable_rename,[status(thm)],[f_10_1]) ).
cnf(f_10_3,plain,
( function(U_7)
| ~ empty(U_7) ),
inference(clausify,[status(thm)],[f_10_2]) ).
fof(f_11_1,plain,
? [A] : empty(A),
inference(fof_nnf,[status(thm)],[rc1_xboole_0]) ).
fof(f_11_2,plain,
? [U_8] : empty(U_8),
inference(variable_rename,[status(thm)],[f_11_1]) ).
fof(f_11_3,plain,
empty(sK5),
inference(skolemize,[status(esa),new_symbols(skolem,[sK5]),skolemize(U_8,sK5)],[f_11_2]) ).
cnf(f_11_4,plain,
empty(sK5),
inference(clausify,[status(thm)],[f_11_3]) ).
fof(f_12_1,plain,
? [A] : ~ empty(A),
inference(fof_nnf,[status(thm)],[rc2_xboole_0]) ).
fof(f_12_2,plain,
? [U_9] : ~ empty(U_9),
inference(variable_rename,[status(thm)],[f_12_1]) ).
fof(f_12_3,plain,
~ empty(sK6),
inference(skolemize,[status(esa),new_symbols(skolem,[sK6]),skolemize(U_9,sK6)],[f_12_2]) ).
cnf(f_12_4,plain,
~ empty(sK6),
inference(clausify,[status(thm)],[f_12_3]) ).
fof(f_13_1,plain,
! [A,B] :
( in(A,B)
| empty(B)
| ~ element(A,B) ),
inference(fof_nnf,[status(thm)],[t2_subset]) ).
fof(f_13_2,plain,
! [U_11,U_10] :
( in(U_11,U_10)
| empty(U_10)
| ~ element(U_11,U_10) ),
inference(variable_rename,[status(thm)],[f_13_1]) ).
cnf(f_13_3,plain,
( in(U_11,U_10)
| empty(U_10)
| ~ element(U_11,U_10) ),
inference(clausify,[status(thm)],[f_13_2]) ).
fof(f_14_1,plain,
! [A] :
( A = empty_set
| ~ empty(A) ),
inference(fof_nnf,[status(thm)],[t6_boole]) ).
fof(f_14_2,plain,
! [U_12] :
( U_12 = empty_set
| ~ empty(U_12) ),
inference(variable_rename,[status(thm)],[f_14_1]) ).
cnf(f_14_3,plain,
( U_12 = empty_set
| ~ empty(U_12) ),
inference(clausify,[status(thm)],[f_14_2]) ).
fof(f_15_1,plain,
! [A,B] :
( ~ empty(B)
| A = B
| ~ empty(A) ),
inference(fof_nnf,[status(thm)],[t8_boole]) ).
fof(f_15_2,plain,
! [U_14,U_13] :
( ~ empty(U_13)
| U_14 = U_13
| ~ empty(U_14) ),
inference(variable_rename,[status(thm)],[f_15_1]) ).
fof(f_15_3,plain,
! [U_14] :
( ! [U_13] :
( ~ empty(U_13)
| U_14 = U_13 )
| ~ empty(U_14) ),
inference(miniscope,[status(thm)],[f_15_2]) ).
cnf(f_15_4,plain,
( ~ empty(U_13)
| U_14 = U_13
| ~ empty(U_14) ),
inference(clausify,[status(thm)],[f_15_3]) ).
fof(f_16_1,plain,
! [A,B] : set_intersection2(A,B) = set_intersection2(B,A),
inference(fof_nnf,[status(thm)],[commutativity_k3_xboole_0]) ).
fof(f_16_2,plain,
! [U_16,U_15] : set_intersection2(U_16,U_15) = set_intersection2(U_15,U_16),
inference(variable_rename,[status(thm)],[f_16_1]) ).
cnf(f_16_3,plain,
set_intersection2(U_16,U_15) = set_intersection2(U_15,U_16),
inference(clausify,[status(thm)],[f_16_2]) ).
fof(f_17_1,plain,
! [A,B] : set_intersection2(A,A) = A,
inference(fof_nnf,[status(thm)],[idempotence_k3_xboole_0]) ).
fof(f_17_2,plain,
! [U_18,U_17] : set_intersection2(U_18,U_18) = U_18,
inference(variable_rename,[status(thm)],[f_17_1]) ).
fof(f_17_3,plain,
! [U_18] : set_intersection2(U_18,U_18) = U_18,
inference(miniscope,[status(thm)],[f_17_2]) ).
cnf(f_17_4,plain,
set_intersection2(U_18,U_18) = U_18,
inference(clausify,[status(thm)],[f_17_3]) ).
fof(f_18_1,plain,
! [A,B] :
( ~ in(B,A)
| ~ in(A,B) ),
inference(fof_nnf,[status(thm)],[antisymmetry_r2_hidden]) ).
fof(f_18_2,plain,
! [U_20,U_19] :
( ~ in(U_19,U_20)
| ~ in(U_20,U_19) ),
inference(variable_rename,[status(thm)],[f_18_1]) ).
cnf(f_18_3,plain,
( ~ in(U_19,U_20)
| ~ in(U_20,U_19) ),
inference(clausify,[status(thm)],[f_18_2]) ).
fof(f_19_1,plain,
! [A,B] :
( relation(relation_restriction(A,B))
| ~ relation(A) ),
inference(fof_nnf,[status(thm)],[dt_k2_wellord1]) ).
fof(f_19_2,plain,
! [U_22,U_21] :
( relation(relation_restriction(U_22,U_21))
| ~ relation(U_22) ),
inference(variable_rename,[status(thm)],[f_19_1]) ).
fof(f_19_3,plain,
! [U_22] :
( ! [U_21] : relation(relation_restriction(U_22,U_21))
| ~ relation(U_22) ),
inference(miniscope,[status(thm)],[f_19_2]) ).
cnf(f_19_4,plain,
( relation(relation_restriction(U_22,U_21))
| ~ relation(U_22) ),
inference(clausify,[status(thm)],[f_19_3]) ).
fof(f_20_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_k2_zfmisc_1]) ).
cnf(f_20_2,plain,
$true,
inference(clausify,[status(thm)],[f_20_1]) ).
fof(f_21_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_k3_xboole_0]) ).
cnf(f_21_2,plain,
$true,
inference(clausify,[status(thm)],[f_21_1]) ).
fof(f_22_1,plain,
! [A,B] :
( element(A,B)
| ~ in(A,B) ),
inference(fof_nnf,[status(thm)],[t1_subset]) ).
fof(f_22_2,plain,
! [U_24,U_23] :
( element(U_24,U_23)
| ~ in(U_24,U_23) ),
inference(variable_rename,[status(thm)],[f_22_1]) ).
cnf(f_22_3,plain,
( element(U_24,U_23)
| ~ in(U_24,U_23) ),
inference(clausify,[status(thm)],[f_22_2]) ).
fof(f_23_1,plain,
! [A,B] :
( ~ empty(B)
| ~ in(A,B) ),
inference(fof_nnf,[status(thm)],[t7_boole]) ).
fof(f_23_2,plain,
! [U_26,U_25] :
( ~ empty(U_25)
| ~ in(U_26,U_25) ),
inference(variable_rename,[status(thm)],[f_23_1]) ).
cnf(f_23_3,plain,
( ~ empty(U_25)
| ~ in(U_26,U_25) ),
inference(clausify,[status(thm)],[f_23_2]) ).
fof(f_24_1,plain,
! [A] :
( ! [B] : relation_restriction(A,B) = set_intersection2(A,cartesian_product2(B,B))
| ~ relation(A) ),
inference(fof_nnf,[status(thm)],[d6_wellord1]) ).
fof(f_24_2,plain,
! [U_28] :
( ! [U_27] : relation_restriction(U_28,U_27) = set_intersection2(U_28,cartesian_product2(U_27,U_27))
| ~ relation(U_28) ),
inference(variable_rename,[status(thm)],[f_24_1]) ).
cnf(f_24_3,plain,
( relation_restriction(U_28,U_27) = set_intersection2(U_28,cartesian_product2(U_27,U_27))
| ~ relation(U_28) ),
inference(clausify,[status(thm)],[f_24_2]) ).
fof(f_25_1,negated_conjecture,
~ ! [A,B,C] :
( relation(C)
=> ( in(A,relation_restriction(C,B))
<=> ( in(A,cartesian_product2(B,B))
& in(A,C) ) ) ),
inference(negate,[status(cth)],[t16_wellord1]) ).
fof(f_25_2,negated_conjecture,
? [A,B,C] :
( ( ( ~ in(A,relation_restriction(C,B))
& in(A,cartesian_product2(B,B))
& in(A,C) )
| ( ( ~ in(A,cartesian_product2(B,B))
| ~ in(A,C) )
& in(A,relation_restriction(C,B)) ) )
& relation(C) ),
inference(fof_nnf,[status(thm)],[f_25_1]) ).
fof(f_25_3,negated_conjecture,
? [U_31,U_30,U_29] :
( ( ( ~ in(U_31,relation_restriction(U_29,U_30))
& in(U_31,cartesian_product2(U_30,U_30))
& in(U_31,U_29) )
| ( ( ~ in(U_31,cartesian_product2(U_30,U_30))
| ~ in(U_31,U_29) )
& in(U_31,relation_restriction(U_29,U_30)) ) )
& relation(U_29) ),
inference(variable_rename,[status(thm)],[f_25_2]) ).
fof(f_25_4,negated_conjecture,
? [U_30,U_29] :
( ( ( ~ in(sK7,relation_restriction(U_29,U_30))
& in(sK7,cartesian_product2(U_30,U_30))
& in(sK7,U_29) )
| ( ( ~ in(sK7,cartesian_product2(U_30,U_30))
| ~ in(sK7,U_29) )
& in(sK7,relation_restriction(U_29,U_30)) ) )
& relation(U_29) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK7]),skolemize(U_31,sK7)],[f_25_3]) ).
fof(f_25_5,negated_conjecture,
? [U_29] :
( ( ( ~ in(sK7,relation_restriction(U_29,sK8))
& in(sK7,cartesian_product2(sK8,sK8))
& in(sK7,U_29) )
| ( ( ~ in(sK7,cartesian_product2(sK8,sK8))
| ~ in(sK7,U_29) )
& in(sK7,relation_restriction(U_29,sK8)) ) )
& relation(U_29) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK8]),skolemize(U_30,sK8)],[f_25_4]) ).
fof(f_25_6,negated_conjecture,
( ( ( ~ in(sK7,relation_restriction(sK9,sK8))
& in(sK7,cartesian_product2(sK8,sK8))
& in(sK7,sK9) )
| ( ( ~ in(sK7,cartesian_product2(sK8,sK8))
| ~ in(sK7,sK9) )
& in(sK7,relation_restriction(sK9,sK8)) ) )
& relation(sK9) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK9]),skolemize(U_29,sK9)],[f_25_5]) ).
fof(f_25_7,negated_conjecture,
( ( ~ in(sK7,relation_restriction(sK9,sK8))
| ~ sP1 )
& ( in(sK7,cartesian_product2(sK8,sK8))
| ~ sP1 )
& ( in(sK7,sK9)
| ~ sP1 )
& ( ~ in(sK7,cartesian_product2(sK8,sK8))
| ~ in(sK7,sK9)
| ~ sP0 )
& ( in(sK7,relation_restriction(sK9,sK8))
| ~ sP0 )
& ( sP1
| sP0 )
& relation(sK9) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP0,sP1])],[f_25_6]) ).
cnf(f_25_8,negated_conjecture,
relation(sK9),
inference(clausify,[status(thm)],[f_25_7]) ).
cnf(f_25_9,negated_conjecture,
( sP1
| sP0 ),
inference(clausify,[status(thm)],[f_25_7]) ).
cnf(f_25_10,negated_conjecture,
( in(sK7,relation_restriction(sK9,sK8))
| ~ sP0 ),
inference(clausify,[status(thm)],[f_25_7]) ).
cnf(f_25_11,negated_conjecture,
( ~ in(sK7,cartesian_product2(sK8,sK8))
| ~ in(sK7,sK9)
| ~ sP0 ),
inference(clausify,[status(thm)],[f_25_7]) ).
cnf(f_25_12,negated_conjecture,
( in(sK7,sK9)
| ~ sP1 ),
inference(clausify,[status(thm)],[f_25_7]) ).
cnf(f_25_13,negated_conjecture,
( in(sK7,cartesian_product2(sK8,sK8))
| ~ sP1 ),
inference(clausify,[status(thm)],[f_25_7]) ).
cnf(f_25_14,negated_conjecture,
( ~ in(sK7,relation_restriction(sK9,sK8))
| ~ sP1 ),
inference(clausify,[status(thm)],[f_25_7]) ).
fof(f_26_1,plain,
! [A,B,C] :
( ( C = set_intersection2(A,B)
| ? [D] :
( ( ~ in(D,C)
& in(D,B)
& in(D,A) )
| ( ( ~ in(D,B)
| ~ in(D,A) )
& in(D,C) ) ) )
& ( ! [D] :
( ( in(D,C)
| ~ in(D,B)
| ~ in(D,A) )
& ( ( in(D,B)
& in(D,A) )
| ~ in(D,C) ) )
| C != set_intersection2(A,B) ) ),
inference(fof_nnf,[status(thm)],[d3_xboole_0]) ).
fof(f_26_2,plain,
! [U_36,U_35,U_34] :
( ( U_34 = set_intersection2(U_36,U_35)
| ? [U_33] :
( ( ~ in(U_33,U_34)
& in(U_33,U_35)
& in(U_33,U_36) )
| ( ( ~ in(U_33,U_35)
| ~ in(U_33,U_36) )
& in(U_33,U_34) ) ) )
& ( ! [U_32] :
( ( in(U_32,U_34)
| ~ in(U_32,U_35)
| ~ in(U_32,U_36) )
& ( ( in(U_32,U_35)
& in(U_32,U_36) )
| ~ in(U_32,U_34) ) )
| U_34 != set_intersection2(U_36,U_35) ) ),
inference(variable_rename,[status(thm)],[f_26_1]) ).
fof(f_26_3,plain,
( ! [U_46,U_44,U_42] :
( U_42 = set_intersection2(U_46,U_44)
| ? [U_40] :
( ~ in(U_40,U_42)
& in(U_40,U_44)
& in(U_40,U_46) )
| ? [U_39] :
( ( ~ in(U_39,U_44)
| ~ in(U_39,U_46) )
& in(U_39,U_42) ) )
& ! [U_45,U_43,U_41] :
( ( ! [U_38] :
( in(U_38,U_41)
| ~ in(U_38,U_43)
| ~ in(U_38,U_45) )
& ! [U_37] :
( ( in(U_37,U_43)
& in(U_37,U_45) )
| ~ in(U_37,U_41) ) )
| U_41 != set_intersection2(U_45,U_43) ) ),
inference(miniscope,[status(thm)],[f_26_2]) ).
fof(f_26_4,plain,
( ! [U_46,U_44,U_42] :
( U_42 = set_intersection2(U_46,U_44)
| ? [U_40] :
( ~ in(U_40,U_42)
& in(U_40,U_44)
& in(U_40,U_46) )
| ( ( ~ in(sK10(U_46,U_44,U_42),U_44)
| ~ in(sK10(U_46,U_44,U_42),U_46) )
& in(sK10(U_46,U_44,U_42),U_42) ) )
& ! [U_45,U_43,U_41] :
( ( ! [U_38] :
( in(U_38,U_41)
| ~ in(U_38,U_43)
| ~ in(U_38,U_45) )
& ! [U_37] :
( ( in(U_37,U_43)
& in(U_37,U_45) )
| ~ in(U_37,U_41) ) )
| U_41 != set_intersection2(U_45,U_43) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK10]),skolemize(U_39,sK10(U_46,U_44,U_42))],[f_26_3]) ).
fof(f_26_5,plain,
( ! [U_46,U_44,U_42] :
( U_42 = set_intersection2(U_46,U_44)
| ( ~ in(sK11(U_46,U_44,U_42),U_42)
& in(sK11(U_46,U_44,U_42),U_44)
& in(sK11(U_46,U_44,U_42),U_46) )
| ( ( ~ in(sK10(U_46,U_44,U_42),U_44)
| ~ in(sK10(U_46,U_44,U_42),U_46) )
& in(sK10(U_46,U_44,U_42),U_42) ) )
& ! [U_45,U_43,U_41] :
( ( ! [U_38] :
( in(U_38,U_41)
| ~ in(U_38,U_43)
| ~ in(U_38,U_45) )
& ! [U_37] :
( ( in(U_37,U_43)
& in(U_37,U_45) )
| ~ in(U_37,U_41) ) )
| U_41 != set_intersection2(U_45,U_43) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK11]),skolemize(U_40,sK11(U_46,U_44,U_42))],[f_26_4]) ).
cnf(f_26_6,plain,
( in(U_37,U_45)
| ~ in(U_37,U_41)
| U_41 != set_intersection2(U_45,U_43) ),
inference(clausify,[status(thm)],[f_26_5]) ).
cnf(f_26_7,plain,
( in(U_37,U_43)
| ~ in(U_37,U_41)
| U_41 != set_intersection2(U_45,U_43) ),
inference(clausify,[status(thm)],[f_26_5]) ).
cnf(f_26_8,plain,
( in(U_38,U_41)
| ~ in(U_38,U_43)
| ~ in(U_38,U_45)
| U_41 != set_intersection2(U_45,U_43) ),
inference(clausify,[status(thm)],[f_26_5]) ).
cnf(f_26_9,plain,
( in(sK11(U_46,U_44,U_42),U_46)
| in(sK10(U_46,U_44,U_42),U_42)
| U_42 = set_intersection2(U_46,U_44) ),
inference(clausify,[status(thm)],[f_26_5]) ).
cnf(f_26_10,plain,
( in(sK11(U_46,U_44,U_42),U_44)
| in(sK10(U_46,U_44,U_42),U_42)
| U_42 = set_intersection2(U_46,U_44) ),
inference(clausify,[status(thm)],[f_26_5]) ).
cnf(f_26_11,plain,
( ~ in(sK11(U_46,U_44,U_42),U_42)
| in(sK10(U_46,U_44,U_42),U_42)
| U_42 = set_intersection2(U_46,U_44) ),
inference(clausify,[status(thm)],[f_26_5]) ).
cnf(f_26_12,plain,
( in(sK11(U_46,U_44,U_42),U_46)
| ~ in(sK10(U_46,U_44,U_42),U_44)
| ~ in(sK10(U_46,U_44,U_42),U_46)
| U_42 = set_intersection2(U_46,U_44) ),
inference(clausify,[status(thm)],[f_26_5]) ).
cnf(f_26_13,plain,
( in(sK11(U_46,U_44,U_42),U_44)
| ~ in(sK10(U_46,U_44,U_42),U_44)
| ~ in(sK10(U_46,U_44,U_42),U_46)
| U_42 = set_intersection2(U_46,U_44) ),
inference(clausify,[status(thm)],[f_26_5]) ).
cnf(f_26_14,plain,
( ~ in(sK11(U_46,U_44,U_42),U_42)
| ~ in(sK10(U_46,U_44,U_42),U_44)
| ~ in(sK10(U_46,U_44,U_42),U_46)
| U_42 = set_intersection2(U_46,U_44) ),
inference(clausify,[status(thm)],[f_26_5]) ).
cnf(f_2_2_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_2_2]) ).
cnf(f_5_3_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_5_3]) ).
cnf(f_5_4_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_5_4]) ).
cnf(f_9_2_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_9_2]) ).
cnf(f_20_2_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_20_2]) ).
cnf(f_21_2_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_21_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,
( set_intersection2(Eq_x_0,Eq_x_1) = set_intersection2(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,
( relation_restriction(Eq_x_0,Eq_x_1) = relation_restriction(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,
( cartesian_product2(Eq_x_0,Eq_x_1) = cartesian_product2(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_7,axiom,
( sK4(Eq_x_0) = sK4(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_8,axiom,
( sK10(Eq_x_0,Eq_x_1,Eq_x_2) = sK10(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_9,axiom,
( sK11(Eq_x_0,Eq_x_1,Eq_x_2) = sK11(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,
( relation(Eq_y_0)
| ~ relation(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_11,axiom,
( function(Eq_y_0)
| ~ function(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_12,axiom,
( one_to_one(Eq_y_0)
| ~ one_to_one(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_13,axiom,
( empty(Eq_y_0)
| ~ empty(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_14,axiom,
( element(Eq_y_0,Eq_y_1)
| ~ element(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_15,axiom,
( in(Eq_y_0,Eq_y_1)
| ~ in(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(sat_proved,plain,
$false,
inference(cadical,[status(thm)],[]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU245+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.03 This is a FOF_THM_RFO_SEQ problem
% 0.00/0.03 % Command : /export/starexec/sandbox2/solver/bin/connect++ --verbosity 1 --no-colour --tptp-proof --schedule default --timeout 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.07/0.35 % Computer : n003.cluster.edu
% 0.07/0.35 % Model : x86_64 x86_64
% 0.07/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.35 % Memory : 8046.5625MB
% 0.07/0.35 % OS : Linux 6.8.0-71-generic
% 0.07/0.35 % CPULimit : 300
% 0.07/0.35 % WCLimit : 300
% 0.07/0.35 % DateTime : Sat Sep 19 23:40:58 UTC 2026
% 0.07/0.35 % CPUTime :
% 9.36/9.70 % SZS status Theorem for theBenchmark
% 9.36/9.70 % SZS output start Proof for theBenchmark
% See solution above
%------------------------------------------------------------------------------