%------------------------------------------------------------------------------
% File : ConnectPP---0.7.2
% Problem : SEU140+1 : TPTP v9.3.1. Released v3.3.0.
% 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 : n011.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 08:58:10 AM UTC 2026
% Result : Theorem 75.65s 75.96s
% Output : Proof 75.65s
% 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(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(reflexivity_r1_tarski,axiom,
! [A,B] : subset(A,A),
file('theBenchmark.p',reflexivity_r1_tarski) ).
fof(symmetry_r1_xboole_0,axiom,
! [A,B] :
( disjoint(A,B)
=> disjoint(B,A) ),
file('theBenchmark.p',symmetry_r1_xboole_0) ).
fof(t26_xboole_1,axiom,
! [A,B,C] :
( subset(A,B)
=> subset(set_intersection2(A,C),set_intersection2(B,C)) ),
file('theBenchmark.p',t26_xboole_1) ).
fof(t2_boole,axiom,
! [A] : set_intersection2(A,empty_set) = empty_set,
file('theBenchmark.p',t2_boole) ).
fof(t3_xboole_1,axiom,
! [A] :
( subset(A,empty_set)
=> A = empty_set ),
file('theBenchmark.p',t3_xboole_1) ).
fof(t63_xboole_1,conjecture,
! [A,B,C] :
( ( disjoint(B,C)
& subset(A,B) )
=> disjoint(A,C) ),
file('theBenchmark.p',t63_xboole_1) ).
fof(t6_boole,axiom,
! [A] :
( empty(A)
=> A = empty_set ),
file('theBenchmark.p',t6_boole) ).
fof(t7_boole,axiom,
! [A,B] :
~ ( empty(B)
& in(A,B) ),
file('theBenchmark.p',t7_boole) ).
fof(t8_boole,axiom,
! [A,B] :
~ ( empty(B)
& A != B
& empty(A) ),
file('theBenchmark.p',t8_boole) ).
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,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_3_2,plain,
! [U_5,U_4] :
( ( disjoint(U_5,U_4)
| set_intersection2(U_5,U_4) != empty_set )
& ( set_intersection2(U_5,U_4) = empty_set
| ~ disjoint(U_5,U_4) ) ),
inference(variable_rename,[status(thm)],[f_3_1]) ).
fof(f_3_3,plain,
( ! [U_9,U_7] :
( disjoint(U_9,U_7)
| set_intersection2(U_9,U_7) != empty_set )
& ! [U_8,U_6] :
( set_intersection2(U_8,U_6) = empty_set
| ~ disjoint(U_8,U_6) ) ),
inference(miniscope,[status(thm)],[f_3_2]) ).
cnf(f_3_4,plain,
( set_intersection2(U_8,U_6) = empty_set
| ~ disjoint(U_8,U_6) ),
inference(clausify,[status(thm)],[f_3_3]) ).
cnf(f_3_5,plain,
( disjoint(U_9,U_7)
| set_intersection2(U_9,U_7) != empty_set ),
inference(clausify,[status(thm)],[f_3_3]) ).
fof(f_4_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_k1_xboole_0]) ).
cnf(f_4_2,plain,
$true,
inference(clausify,[status(thm)],[f_4_1]) ).
fof(f_5_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_k3_xboole_0]) ).
cnf(f_5_2,plain,
$true,
inference(clausify,[status(thm)],[f_5_1]) ).
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,B] : set_intersection2(A,A) = A,
inference(fof_nnf,[status(thm)],[idempotence_k3_xboole_0]) ).
fof(f_7_2,plain,
! [U_11,U_10] : set_intersection2(U_11,U_11) = U_11,
inference(variable_rename,[status(thm)],[f_7_1]) ).
fof(f_7_3,plain,
! [U_11] : set_intersection2(U_11,U_11) = U_11,
inference(miniscope,[status(thm)],[f_7_2]) ).
cnf(f_7_4,plain,
set_intersection2(U_11,U_11) = U_11,
inference(clausify,[status(thm)],[f_7_3]) ).
fof(f_8_1,plain,
? [A] : empty(A),
inference(fof_nnf,[status(thm)],[rc1_xboole_0]) ).
fof(f_8_2,plain,
? [U_12] : empty(U_12),
inference(variable_rename,[status(thm)],[f_8_1]) ).
fof(f_8_3,plain,
empty(sK1),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(U_12,sK1)],[f_8_2]) ).
cnf(f_8_4,plain,
empty(sK1),
inference(clausify,[status(thm)],[f_8_3]) ).
fof(f_9_1,plain,
? [A] : ~ empty(A),
inference(fof_nnf,[status(thm)],[rc2_xboole_0]) ).
fof(f_9_2,plain,
? [U_13] : ~ empty(U_13),
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_13,sK2)],[f_9_2]) ).
cnf(f_9_4,plain,
~ empty(sK2),
inference(clausify,[status(thm)],[f_9_3]) ).
fof(f_10_1,plain,
! [A,B] : subset(A,A),
inference(fof_nnf,[status(thm)],[reflexivity_r1_tarski]) ).
fof(f_10_2,plain,
! [U_15,U_14] : subset(U_15,U_15),
inference(variable_rename,[status(thm)],[f_10_1]) ).
fof(f_10_3,plain,
! [U_15] : subset(U_15,U_15),
inference(miniscope,[status(thm)],[f_10_2]) ).
cnf(f_10_4,plain,
subset(U_15,U_15),
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_17,U_16] :
( disjoint(U_16,U_17)
| ~ disjoint(U_17,U_16) ),
inference(variable_rename,[status(thm)],[f_11_1]) ).
cnf(f_11_3,plain,
( disjoint(U_16,U_17)
| ~ disjoint(U_17,U_16) ),
inference(clausify,[status(thm)],[f_11_2]) ).
fof(f_12_1,plain,
! [A,B,C] :
( subset(set_intersection2(A,C),set_intersection2(B,C))
| ~ subset(A,B) ),
inference(fof_nnf,[status(thm)],[t26_xboole_1]) ).
fof(f_12_2,plain,
! [U_20,U_19,U_18] :
( subset(set_intersection2(U_20,U_18),set_intersection2(U_19,U_18))
| ~ subset(U_20,U_19) ),
inference(variable_rename,[status(thm)],[f_12_1]) ).
fof(f_12_3,plain,
! [U_20,U_19] :
( ! [U_18] : subset(set_intersection2(U_20,U_18),set_intersection2(U_19,U_18))
| ~ subset(U_20,U_19) ),
inference(miniscope,[status(thm)],[f_12_2]) ).
cnf(f_12_4,plain,
( subset(set_intersection2(U_20,U_18),set_intersection2(U_19,U_18))
| ~ subset(U_20,U_19) ),
inference(clausify,[status(thm)],[f_12_3]) ).
fof(f_13_1,plain,
! [A] : set_intersection2(A,empty_set) = empty_set,
inference(fof_nnf,[status(thm)],[t2_boole]) ).
fof(f_13_2,plain,
! [U_21] : set_intersection2(U_21,empty_set) = empty_set,
inference(variable_rename,[status(thm)],[f_13_1]) ).
cnf(f_13_3,plain,
set_intersection2(U_21,empty_set) = empty_set,
inference(clausify,[status(thm)],[f_13_2]) ).
fof(f_14_1,plain,
! [A] :
( A = empty_set
| ~ subset(A,empty_set) ),
inference(fof_nnf,[status(thm)],[t3_xboole_1]) ).
fof(f_14_2,plain,
! [U_22] :
( U_22 = empty_set
| ~ subset(U_22,empty_set) ),
inference(variable_rename,[status(thm)],[f_14_1]) ).
cnf(f_14_3,plain,
( U_22 = empty_set
| ~ subset(U_22,empty_set) ),
inference(clausify,[status(thm)],[f_14_2]) ).
fof(f_15_1,negated_conjecture,
~ ! [A,B,C] :
( ( disjoint(B,C)
& subset(A,B) )
=> disjoint(A,C) ),
inference(negate,[status(cth)],[t63_xboole_1]) ).
fof(f_15_2,negated_conjecture,
? [A,B,C] :
( ~ disjoint(A,C)
& disjoint(B,C)
& subset(A,B) ),
inference(fof_nnf,[status(thm)],[f_15_1]) ).
fof(f_15_3,negated_conjecture,
? [U_25,U_24,U_23] :
( ~ disjoint(U_25,U_23)
& disjoint(U_24,U_23)
& subset(U_25,U_24) ),
inference(variable_rename,[status(thm)],[f_15_2]) ).
fof(f_15_4,negated_conjecture,
? [U_24,U_23] :
( ~ disjoint(sK3,U_23)
& disjoint(U_24,U_23)
& subset(sK3,U_24) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3]),skolemize(U_25,sK3)],[f_15_3]) ).
fof(f_15_5,negated_conjecture,
? [U_23] :
( ~ disjoint(sK3,U_23)
& disjoint(sK4,U_23)
& subset(sK3,sK4) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4]),skolemize(U_24,sK4)],[f_15_4]) ).
fof(f_15_6,negated_conjecture,
( ~ disjoint(sK3,sK5)
& disjoint(sK4,sK5)
& subset(sK3,sK4) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK5]),skolemize(U_23,sK5)],[f_15_5]) ).
cnf(f_15_7,negated_conjecture,
subset(sK3,sK4),
inference(clausify,[status(thm)],[f_15_6]) ).
cnf(f_15_8,negated_conjecture,
disjoint(sK4,sK5),
inference(clausify,[status(thm)],[f_15_6]) ).
cnf(f_15_9,negated_conjecture,
~ disjoint(sK3,sK5),
inference(clausify,[status(thm)],[f_15_6]) ).
fof(f_16_1,plain,
! [A] :
( A = empty_set
| ~ empty(A) ),
inference(fof_nnf,[status(thm)],[t6_boole]) ).
fof(f_16_2,plain,
! [U_26] :
( U_26 = empty_set
| ~ empty(U_26) ),
inference(variable_rename,[status(thm)],[f_16_1]) ).
cnf(f_16_3,plain,
( U_26 = empty_set
| ~ empty(U_26) ),
inference(clausify,[status(thm)],[f_16_2]) ).
fof(f_17_1,plain,
! [A,B] :
( ~ empty(B)
| ~ in(A,B) ),
inference(fof_nnf,[status(thm)],[t7_boole]) ).
fof(f_17_2,plain,
! [U_28,U_27] :
( ~ empty(U_27)
| ~ in(U_28,U_27) ),
inference(variable_rename,[status(thm)],[f_17_1]) ).
cnf(f_17_3,plain,
( ~ empty(U_27)
| ~ in(U_28,U_27) ),
inference(clausify,[status(thm)],[f_17_2]) ).
fof(f_18_1,plain,
! [A,B] :
( ~ empty(B)
| A = B
| ~ empty(A) ),
inference(fof_nnf,[status(thm)],[t8_boole]) ).
fof(f_18_2,plain,
! [U_30,U_29] :
( ~ empty(U_29)
| U_30 = U_29
| ~ empty(U_30) ),
inference(variable_rename,[status(thm)],[f_18_1]) ).
fof(f_18_3,plain,
! [U_30] :
( ! [U_29] :
( ~ empty(U_29)
| U_30 = U_29 )
| ~ empty(U_30) ),
inference(miniscope,[status(thm)],[f_18_2]) ).
cnf(f_18_4,plain,
( ~ empty(U_29)
| U_30 = U_29
| ~ empty(U_30) ),
inference(clausify,[status(thm)],[f_18_3]) ).
cnf(f_4_2_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_4_2]) ).
cnf(f_5_2_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_5_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,
( 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_6,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_7,axiom,
( empty(Eq_y_0)
| ~ empty(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_8,axiom,
( subset(Eq_y_0,Eq_y_1)
| ~ subset(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
% 0.00/0.03 % Problem : SEU140+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.03 This is a FOF_THM_RFO_SEQ problem
% 0.00/0.04 % Command : /export/starexec/sandbox/solver/bin/connect++ --verbosity 1 --no-colour --tptp-proof --schedule default --timeout 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.35 % Computer : n011.cluster.edu
% 0.08/0.35 % Model : x86_64 x86_64
% 0.08/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.35 % Memory : 8046.5625MB
% 0.08/0.35 % OS : Linux 6.8.0-71-generic
% 0.08/0.35 % CPULimit : 300
% 0.08/0.35 % WCLimit : 300
% 0.08/0.35 % DateTime : Sat Sep 19 23:21:54 UTC 2026
% 0.08/0.35 % CPUTime :
% 75.65/75.96 % SZS status Theorem for theBenchmark
% 75.65/75.96 % SZS output start Proof for theBenchmark
% See solution above
%------------------------------------------------------------------------------