%------------------------------------------------------------------------------
% File : ConnectPP---0.7.2
% Problem : SEU120+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 : n012.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 08:58:05 AM UTC 2026
% Result : Theorem 0.08s 0.34s
% Output : Proof 0.08s
% Verified :
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)
% Comments :
%------------------------------------------------------------------------------
fof(antisymmetry_r2_hidden,axiom,
! [A,B] :
( in(A,B)
=> ~ in(B,A) ),
file('theBenchmark.p',antisymmetry_r2_hidden) ).
fof(commutativity_k3_xboole_0,axiom,
! [A,B] : set_intersection2(A,B) = set_intersection2(B,A),
file('theBenchmark.p',commutativity_k3_xboole_0) ).
fof(d1_xboole_0,axiom,
! [A] :
( A = empty_set
<=> ! [B] : ~ in(B,A) ),
file('theBenchmark.p',d1_xboole_0) ).
fof(d7_xboole_0,axiom,
! [A,B] :
( disjoint(A,B)
<=> set_intersection2(A,B) = empty_set ),
file('theBenchmark.p',d7_xboole_0) ).
fof(dt_k1_xboole_0,axiom,
$true,
file('theBenchmark.p',dt_k1_xboole_0) ).
fof(dt_k3_xboole_0,axiom,
$true,
file('theBenchmark.p',dt_k3_xboole_0) ).
fof(fc1_xboole_0,axiom,
empty(empty_set),
file('theBenchmark.p',fc1_xboole_0) ).
fof(idempotence_k3_xboole_0,axiom,
! [A,B] : set_intersection2(A,A) = A,
file('theBenchmark.p',idempotence_k3_xboole_0) ).
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(symmetry_r1_xboole_0,axiom,
! [A,B] :
( disjoint(A,B)
=> disjoint(B,A) ),
file('theBenchmark.p',symmetry_r1_xboole_0) ).
fof(t4_xboole_0,conjecture,
! [A,B] :
( ~ ( disjoint(A,B)
& ? [C] : in(C,set_intersection2(A,B)) )
& ~ ( ! [C] : ~ in(C,set_intersection2(A,B))
& ~ disjoint(A,B) ) ),
file('theBenchmark.p',t4_xboole_0) ).
fof(f_1_1,plain,
! [A,B] :
( ~ in(B,A)
| ~ in(A,B) ),
inference(fof_nnf,[status(thm)],[antisymmetry_r2_hidden]) ).
fof(f_1_2,plain,
! [U_1,U_0] :
( ~ in(U_0,U_1)
| ~ in(U_1,U_0) ),
inference(variable_rename,[status(thm)],[f_1_1]) ).
cnf(f_1_3,plain,
( ~ in(U_0,U_1)
| ~ in(U_1,U_0) ),
inference(clausify,[status(thm)],[f_1_2]) ).
fof(f_2_1,plain,
! [A,B] : set_intersection2(A,B) = set_intersection2(B,A),
inference(fof_nnf,[status(thm)],[commutativity_k3_xboole_0]) ).
fof(f_2_2,plain,
! [U_3,U_2] : set_intersection2(U_3,U_2) = set_intersection2(U_2,U_3),
inference(variable_rename,[status(thm)],[f_2_1]) ).
cnf(f_2_3,plain,
set_intersection2(U_3,U_2) = set_intersection2(U_2,U_3),
inference(clausify,[status(thm)],[f_2_2]) ).
fof(f_3_1,plain,
! [A] :
( ( A = empty_set
| ? [B] : in(B,A) )
& ( ! [B] : ~ in(B,A)
| A != empty_set ) ),
inference(fof_nnf,[status(thm)],[d1_xboole_0]) ).
fof(f_3_2,plain,
! [U_6] :
( ( U_6 = empty_set
| ? [U_5] : in(U_5,U_6) )
& ( ! [U_4] : ~ in(U_4,U_6)
| U_6 != empty_set ) ),
inference(variable_rename,[status(thm)],[f_3_1]) ).
fof(f_3_3,plain,
( ! [U_8] :
( U_8 = empty_set
| ? [U_5] : in(U_5,U_8) )
& ! [U_7] :
( ! [U_4] : ~ in(U_4,U_7)
| U_7 != empty_set ) ),
inference(miniscope,[status(thm)],[f_3_2]) ).
fof(f_3_4,plain,
( ! [U_8] :
( U_8 = empty_set
| in(sK1(U_8),U_8) )
& ! [U_7] :
( ! [U_4] : ~ in(U_4,U_7)
| U_7 != empty_set ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(U_5,sK1(U_8))],[f_3_3]) ).
cnf(f_3_5,plain,
( ~ in(U_4,U_7)
| U_7 != empty_set ),
inference(clausify,[status(thm)],[f_3_4]) ).
cnf(f_3_6,plain,
( U_8 = empty_set
| in(sK1(U_8),U_8) ),
inference(clausify,[status(thm)],[f_3_4]) ).
fof(f_4_1,plain,
! [A,B] :
( ( disjoint(A,B)
| set_intersection2(A,B) != empty_set )
& ( set_intersection2(A,B) = empty_set
| ~ disjoint(A,B) ) ),
inference(fof_nnf,[status(thm)],[d7_xboole_0]) ).
fof(f_4_2,plain,
! [U_10,U_9] :
( ( disjoint(U_10,U_9)
| set_intersection2(U_10,U_9) != empty_set )
& ( set_intersection2(U_10,U_9) = empty_set
| ~ disjoint(U_10,U_9) ) ),
inference(variable_rename,[status(thm)],[f_4_1]) ).
fof(f_4_3,plain,
( ! [U_14,U_12] :
( disjoint(U_14,U_12)
| set_intersection2(U_14,U_12) != empty_set )
& ! [U_13,U_11] :
( set_intersection2(U_13,U_11) = empty_set
| ~ disjoint(U_13,U_11) ) ),
inference(miniscope,[status(thm)],[f_4_2]) ).
cnf(f_4_4,plain,
( set_intersection2(U_13,U_11) = empty_set
| ~ disjoint(U_13,U_11) ),
inference(clausify,[status(thm)],[f_4_3]) ).
cnf(f_4_5,plain,
( disjoint(U_14,U_12)
| set_intersection2(U_14,U_12) != empty_set ),
inference(clausify,[status(thm)],[f_4_3]) ).
fof(f_5_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_k1_xboole_0]) ).
cnf(f_5_2,plain,
$true,
inference(clausify,[status(thm)],[f_5_1]) ).
fof(f_6_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_k3_xboole_0]) ).
cnf(f_6_2,plain,
$true,
inference(clausify,[status(thm)],[f_6_1]) ).
fof(f_7_1,plain,
empty(empty_set),
inference(fof_nnf,[status(thm)],[fc1_xboole_0]) ).
cnf(f_7_2,plain,
empty(empty_set),
inference(clausify,[status(thm)],[f_7_1]) ).
fof(f_8_1,plain,
! [A,B] : set_intersection2(A,A) = A,
inference(fof_nnf,[status(thm)],[idempotence_k3_xboole_0]) ).
fof(f_8_2,plain,
! [U_16,U_15] : set_intersection2(U_16,U_16) = U_16,
inference(variable_rename,[status(thm)],[f_8_1]) ).
fof(f_8_3,plain,
! [U_16] : set_intersection2(U_16,U_16) = U_16,
inference(miniscope,[status(thm)],[f_8_2]) ).
cnf(f_8_4,plain,
set_intersection2(U_16,U_16) = U_16,
inference(clausify,[status(thm)],[f_8_3]) ).
fof(f_9_1,plain,
? [A] : empty(A),
inference(fof_nnf,[status(thm)],[rc1_xboole_0]) ).
fof(f_9_2,plain,
? [U_17] : empty(U_17),
inference(variable_rename,[status(thm)],[f_9_1]) ).
fof(f_9_3,plain,
empty(sK2),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2]),skolemize(U_17,sK2)],[f_9_2]) ).
cnf(f_9_4,plain,
empty(sK2),
inference(clausify,[status(thm)],[f_9_3]) ).
fof(f_10_1,plain,
? [A] : ~ empty(A),
inference(fof_nnf,[status(thm)],[rc2_xboole_0]) ).
fof(f_10_2,plain,
? [U_18] : ~ empty(U_18),
inference(variable_rename,[status(thm)],[f_10_1]) ).
fof(f_10_3,plain,
~ empty(sK3),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3]),skolemize(U_18,sK3)],[f_10_2]) ).
cnf(f_10_4,plain,
~ empty(sK3),
inference(clausify,[status(thm)],[f_10_3]) ).
fof(f_11_1,plain,
! [A,B] :
( disjoint(B,A)
| ~ disjoint(A,B) ),
inference(fof_nnf,[status(thm)],[symmetry_r1_xboole_0]) ).
fof(f_11_2,plain,
! [U_20,U_19] :
( disjoint(U_19,U_20)
| ~ disjoint(U_20,U_19) ),
inference(variable_rename,[status(thm)],[f_11_1]) ).
cnf(f_11_3,plain,
( disjoint(U_19,U_20)
| ~ disjoint(U_20,U_19) ),
inference(clausify,[status(thm)],[f_11_2]) ).
fof(f_12_1,negated_conjecture,
~ ! [A,B] :
( ~ ( disjoint(A,B)
& ? [C] : in(C,set_intersection2(A,B)) )
& ~ ( ! [C] : ~ in(C,set_intersection2(A,B))
& ~ disjoint(A,B) ) ),
inference(negate,[status(cth)],[t4_xboole_0]) ).
fof(f_12_2,negated_conjecture,
? [A,B] :
( ( disjoint(A,B)
& ? [C] : in(C,set_intersection2(A,B)) )
| ( ! [C] : ~ in(C,set_intersection2(A,B))
& ~ disjoint(A,B) ) ),
inference(fof_nnf,[status(thm)],[f_12_1]) ).
fof(f_12_3,negated_conjecture,
? [U_24,U_23] :
( ( disjoint(U_24,U_23)
& ? [U_22] : in(U_22,set_intersection2(U_24,U_23)) )
| ( ! [U_21] : ~ in(U_21,set_intersection2(U_24,U_23))
& ~ disjoint(U_24,U_23) ) ),
inference(variable_rename,[status(thm)],[f_12_2]) ).
fof(f_12_4,negated_conjecture,
( ? [U_28,U_26] :
( disjoint(U_28,U_26)
& ? [U_22] : in(U_22,set_intersection2(U_28,U_26)) )
| ? [U_27,U_25] :
( ! [U_21] : ~ in(U_21,set_intersection2(U_27,U_25))
& ~ disjoint(U_27,U_25) ) ),
inference(miniscope,[status(thm)],[f_12_3]) ).
fof(f_12_5,negated_conjecture,
( ? [U_28,U_26] :
( disjoint(U_28,U_26)
& ? [U_22] : in(U_22,set_intersection2(U_28,U_26)) )
| ? [U_25] :
( ! [U_21] : ~ in(U_21,set_intersection2(sK4,U_25))
& ~ disjoint(sK4,U_25) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4]),skolemize(U_27,sK4)],[f_12_4]) ).
fof(f_12_6,negated_conjecture,
( ? [U_28,U_26] :
( disjoint(U_28,U_26)
& ? [U_22] : in(U_22,set_intersection2(U_28,U_26)) )
| ( ! [U_21] : ~ in(U_21,set_intersection2(sK4,sK5))
& ~ disjoint(sK4,sK5) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK5]),skolemize(U_25,sK5)],[f_12_5]) ).
fof(f_12_7,negated_conjecture,
( ? [U_26] :
( disjoint(sK6,U_26)
& ? [U_22] : in(U_22,set_intersection2(sK6,U_26)) )
| ( ! [U_21] : ~ in(U_21,set_intersection2(sK4,sK5))
& ~ disjoint(sK4,sK5) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK6]),skolemize(U_28,sK6)],[f_12_6]) ).
fof(f_12_8,negated_conjecture,
( ( disjoint(sK6,sK7)
& ? [U_22] : in(U_22,set_intersection2(sK6,sK7)) )
| ( ! [U_21] : ~ in(U_21,set_intersection2(sK4,sK5))
& ~ disjoint(sK4,sK5) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK7]),skolemize(U_26,sK7)],[f_12_7]) ).
fof(f_12_9,negated_conjecture,
( ( disjoint(sK6,sK7)
& in(sK8,set_intersection2(sK6,sK7)) )
| ( ! [U_21] : ~ in(U_21,set_intersection2(sK4,sK5))
& ~ disjoint(sK4,sK5) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK8]),skolemize(U_22,sK8)],[f_12_8]) ).
fof(f_12_10,negated_conjecture,
( ( disjoint(sK6,sK7)
| ~ sP1 )
& ( in(sK8,set_intersection2(sK6,sK7))
| ~ sP1 )
& ! [U_21] :
( ~ in(U_21,set_intersection2(sK4,sK5))
| ~ sP0(U_21) )
& ! [U_21] :
( ~ disjoint(sK4,sK5)
| ~ sP0(U_21) )
& ! [U_21] :
( sP1
| sP0(U_21) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP0,sP1])],[f_12_9]) ).
cnf(f_12_11,negated_conjecture,
( sP1
| sP0(U_21) ),
inference(clausify,[status(thm)],[f_12_10]) ).
cnf(f_12_12,negated_conjecture,
( ~ disjoint(sK4,sK5)
| ~ sP0(U_21) ),
inference(clausify,[status(thm)],[f_12_10]) ).
cnf(f_12_13,negated_conjecture,
( ~ in(U_21,set_intersection2(sK4,sK5))
| ~ sP0(U_21) ),
inference(clausify,[status(thm)],[f_12_10]) ).
cnf(f_12_14,negated_conjecture,
( in(sK8,set_intersection2(sK6,sK7))
| ~ sP1 ),
inference(clausify,[status(thm)],[f_12_10]) ).
cnf(f_12_15,negated_conjecture,
( disjoint(sK6,sK7)
| ~ sP1 ),
inference(clausify,[status(thm)],[f_12_10]) ).
cnf(f_5_2_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_5_2]) ).
cnf(f_6_2_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_6_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,
( sK1(Eq_x_0) = sK1(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_6,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(equality_7,axiom,
( disjoint(Eq_y_0,Eq_y_1)
| ~ disjoint(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_8,axiom,
( empty(Eq_y_0)
| ~ empty(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_9,axiom,
( sP0(Eq_y_0)
| ~ sP0(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
% 0.00/0.01 % Problem : SEU120+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.01 This is a FOF_THM_RFO_SEQ problem
% 0.00/0.02 % Command : /export/starexec/sandbox2/solver/bin/connect++ --verbosity 1 --no-colour --tptp-proof --schedule default --timeout 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.03/0.30 % Computer : n012.cluster.edu
% 0.03/0.30 % Model : x86_64 x86_64
% 0.03/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.03/0.30 % Memory : 8046.5625MB
% 0.03/0.30 % OS : Linux 6.8.0-71-generic
% 0.03/0.30 % CPULimit : 300
% 0.03/0.30 % WCLimit : 300
% 0.03/0.30 % DateTime : Sat Sep 19 23:19:52 UTC 2026
% 0.03/0.31 % CPUTime :
% 0.08/0.34 % SZS status Theorem for theBenchmark
% 0.08/0.34 % SZS output start Proof for theBenchmark
% See solution above
%------------------------------------------------------------------------------