%------------------------------------------------------------------------------
% File : ConnectPP---0.7.2
% Problem : SEU134+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 : n005.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 08:58:08 AM UTC 2026
% Result : Theorem 0.14s 0.40s
% Output : Proof 0.14s
% 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(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(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(reflexivity_r1_tarski,axiom,
! [A,B] : subset(A,A),
file('theBenchmark.p',reflexivity_r1_tarski) ).
fof(dt_k1_xboole_0,axiom,
$true,
file('theBenchmark.p',dt_k1_xboole_0) ).
fof(dt_k4_xboole_0,axiom,
$true,
file('theBenchmark.p',dt_k4_xboole_0) ).
fof(fc1_xboole_0,axiom,
empty(empty_set),
file('theBenchmark.p',fc1_xboole_0) ).
fof(t3_boole,axiom,
! [A] : set_difference(A,empty_set) = A,
file('theBenchmark.p',t3_boole) ).
fof(t4_boole,axiom,
! [A] : set_difference(empty_set,A) = empty_set,
file('theBenchmark.p',t4_boole) ).
fof(t6_boole,axiom,
! [A] :
( empty(A)
=> A = empty_set ),
file('theBenchmark.p',t6_boole) ).
fof(t37_xboole_1,conjecture,
! [A,B] :
( set_difference(A,B) = empty_set
<=> subset(A,B) ),
file('theBenchmark.p',t37_xboole_1) ).
fof(l32_xboole_1,axiom,
! [A,B] :
( set_difference(A,B) = empty_set
<=> subset(A,B) ),
file('theBenchmark.p',l32_xboole_1) ).
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] : empty(A),
inference(fof_nnf,[status(thm)],[rc1_xboole_0]) ).
fof(f_2_2,plain,
? [U_2] : empty(U_2),
inference(variable_rename,[status(thm)],[f_2_1]) ).
fof(f_2_3,plain,
empty(sK1),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(U_2,sK1)],[f_2_2]) ).
cnf(f_2_4,plain,
empty(sK1),
inference(clausify,[status(thm)],[f_2_3]) ).
fof(f_3_1,plain,
? [A] : ~ empty(A),
inference(fof_nnf,[status(thm)],[rc2_xboole_0]) ).
fof(f_3_2,plain,
? [U_3] : ~ empty(U_3),
inference(variable_rename,[status(thm)],[f_3_1]) ).
fof(f_3_3,plain,
~ empty(sK2),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2]),skolemize(U_3,sK2)],[f_3_2]) ).
cnf(f_3_4,plain,
~ empty(sK2),
inference(clausify,[status(thm)],[f_3_3]) ).
fof(f_4_1,plain,
! [A,B] :
( ~ empty(B)
| ~ in(A,B) ),
inference(fof_nnf,[status(thm)],[t7_boole]) ).
fof(f_4_2,plain,
! [U_5,U_4] :
( ~ empty(U_4)
| ~ in(U_5,U_4) ),
inference(variable_rename,[status(thm)],[f_4_1]) ).
cnf(f_4_3,plain,
( ~ empty(U_4)
| ~ in(U_5,U_4) ),
inference(clausify,[status(thm)],[f_4_2]) ).
fof(f_5_1,plain,
! [A,B] :
( ~ empty(B)
| A = B
| ~ empty(A) ),
inference(fof_nnf,[status(thm)],[t8_boole]) ).
fof(f_5_2,plain,
! [U_7,U_6] :
( ~ empty(U_6)
| U_7 = U_6
| ~ empty(U_7) ),
inference(variable_rename,[status(thm)],[f_5_1]) ).
fof(f_5_3,plain,
! [U_7] :
( ! [U_6] :
( ~ empty(U_6)
| U_7 = U_6 )
| ~ empty(U_7) ),
inference(miniscope,[status(thm)],[f_5_2]) ).
cnf(f_5_4,plain,
( ~ empty(U_6)
| U_7 = U_6
| ~ empty(U_7) ),
inference(clausify,[status(thm)],[f_5_3]) ).
fof(f_6_1,plain,
! [A,B] : subset(A,A),
inference(fof_nnf,[status(thm)],[reflexivity_r1_tarski]) ).
fof(f_6_2,plain,
! [U_9,U_8] : subset(U_9,U_9),
inference(variable_rename,[status(thm)],[f_6_1]) ).
fof(f_6_3,plain,
! [U_9] : subset(U_9,U_9),
inference(miniscope,[status(thm)],[f_6_2]) ).
cnf(f_6_4,plain,
subset(U_9,U_9),
inference(clausify,[status(thm)],[f_6_3]) ).
fof(f_7_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_k1_xboole_0]) ).
cnf(f_7_2,plain,
$true,
inference(clausify,[status(thm)],[f_7_1]) ).
fof(f_8_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_k4_xboole_0]) ).
cnf(f_8_2,plain,
$true,
inference(clausify,[status(thm)],[f_8_1]) ).
fof(f_9_1,plain,
empty(empty_set),
inference(fof_nnf,[status(thm)],[fc1_xboole_0]) ).
cnf(f_9_2,plain,
empty(empty_set),
inference(clausify,[status(thm)],[f_9_1]) ).
fof(f_10_1,plain,
! [A] : set_difference(A,empty_set) = A,
inference(fof_nnf,[status(thm)],[t3_boole]) ).
fof(f_10_2,plain,
! [U_10] : set_difference(U_10,empty_set) = U_10,
inference(variable_rename,[status(thm)],[f_10_1]) ).
cnf(f_10_3,plain,
set_difference(U_10,empty_set) = U_10,
inference(clausify,[status(thm)],[f_10_2]) ).
fof(f_11_1,plain,
! [A] : set_difference(empty_set,A) = empty_set,
inference(fof_nnf,[status(thm)],[t4_boole]) ).
fof(f_11_2,plain,
! [U_11] : set_difference(empty_set,U_11) = empty_set,
inference(variable_rename,[status(thm)],[f_11_1]) ).
cnf(f_11_3,plain,
set_difference(empty_set,U_11) = empty_set,
inference(clausify,[status(thm)],[f_11_2]) ).
fof(f_12_1,plain,
! [A] :
( A = empty_set
| ~ empty(A) ),
inference(fof_nnf,[status(thm)],[t6_boole]) ).
fof(f_12_2,plain,
! [U_12] :
( U_12 = empty_set
| ~ empty(U_12) ),
inference(variable_rename,[status(thm)],[f_12_1]) ).
cnf(f_12_3,plain,
( U_12 = empty_set
| ~ empty(U_12) ),
inference(clausify,[status(thm)],[f_12_2]) ).
fof(f_13_1,negated_conjecture,
~ ! [A,B] :
( set_difference(A,B) = empty_set
<=> subset(A,B) ),
inference(negate,[status(cth)],[t37_xboole_1]) ).
fof(f_13_2,negated_conjecture,
? [A,B] :
( ( set_difference(A,B) != empty_set
& subset(A,B) )
| ( ~ subset(A,B)
& set_difference(A,B) = empty_set ) ),
inference(fof_nnf,[status(thm)],[f_13_1]) ).
fof(f_13_3,negated_conjecture,
? [U_14,U_13] :
( ( set_difference(U_14,U_13) != empty_set
& subset(U_14,U_13) )
| ( ~ subset(U_14,U_13)
& set_difference(U_14,U_13) = empty_set ) ),
inference(variable_rename,[status(thm)],[f_13_2]) ).
fof(f_13_4,negated_conjecture,
( ? [U_18,U_16] :
( set_difference(U_18,U_16) != empty_set
& subset(U_18,U_16) )
| ? [U_17,U_15] :
( ~ subset(U_17,U_15)
& set_difference(U_17,U_15) = empty_set ) ),
inference(miniscope,[status(thm)],[f_13_3]) ).
fof(f_13_5,negated_conjecture,
( ? [U_18,U_16] :
( set_difference(U_18,U_16) != empty_set
& subset(U_18,U_16) )
| ? [U_15] :
( ~ subset(sK3,U_15)
& set_difference(sK3,U_15) = empty_set ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3]),skolemize(U_17,sK3)],[f_13_4]) ).
fof(f_13_6,negated_conjecture,
( ? [U_18,U_16] :
( set_difference(U_18,U_16) != empty_set
& subset(U_18,U_16) )
| ( ~ subset(sK3,sK4)
& set_difference(sK3,sK4) = empty_set ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4]),skolemize(U_15,sK4)],[f_13_5]) ).
fof(f_13_7,negated_conjecture,
( ? [U_16] :
( set_difference(sK5,U_16) != empty_set
& subset(sK5,U_16) )
| ( ~ subset(sK3,sK4)
& set_difference(sK3,sK4) = empty_set ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK5]),skolemize(U_18,sK5)],[f_13_6]) ).
fof(f_13_8,negated_conjecture,
( ( set_difference(sK5,sK6) != empty_set
& subset(sK5,sK6) )
| ( ~ subset(sK3,sK4)
& set_difference(sK3,sK4) = empty_set ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK6]),skolemize(U_16,sK6)],[f_13_7]) ).
fof(f_13_9,negated_conjecture,
( ( set_difference(sK5,sK6) != empty_set
| ~ sP1 )
& ( subset(sK5,sK6)
| ~ sP1 )
& ( ~ subset(sK3,sK4)
| ~ sP0 )
& ( set_difference(sK3,sK4) = empty_set
| ~ sP0 )
& ( sP1
| sP0 ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP0,sP1])],[f_13_8]) ).
cnf(f_13_10,negated_conjecture,
( sP1
| sP0 ),
inference(clausify,[status(thm)],[f_13_9]) ).
cnf(f_13_11,negated_conjecture,
( set_difference(sK3,sK4) = empty_set
| ~ sP0 ),
inference(clausify,[status(thm)],[f_13_9]) ).
cnf(f_13_12,negated_conjecture,
( ~ subset(sK3,sK4)
| ~ sP0 ),
inference(clausify,[status(thm)],[f_13_9]) ).
cnf(f_13_13,negated_conjecture,
( subset(sK5,sK6)
| ~ sP1 ),
inference(clausify,[status(thm)],[f_13_9]) ).
cnf(f_13_14,negated_conjecture,
( set_difference(sK5,sK6) != empty_set
| ~ sP1 ),
inference(clausify,[status(thm)],[f_13_9]) ).
fof(f_14_1,plain,
! [A,B] :
( ( set_difference(A,B) = empty_set
| ~ subset(A,B) )
& ( subset(A,B)
| set_difference(A,B) != empty_set ) ),
inference(fof_nnf,[status(thm)],[l32_xboole_1]) ).
fof(f_14_2,plain,
! [U_20,U_19] :
( ( set_difference(U_20,U_19) = empty_set
| ~ subset(U_20,U_19) )
& ( subset(U_20,U_19)
| set_difference(U_20,U_19) != empty_set ) ),
inference(variable_rename,[status(thm)],[f_14_1]) ).
fof(f_14_3,plain,
( ! [U_24,U_22] :
( set_difference(U_24,U_22) = empty_set
| ~ subset(U_24,U_22) )
& ! [U_23,U_21] :
( subset(U_23,U_21)
| set_difference(U_23,U_21) != empty_set ) ),
inference(miniscope,[status(thm)],[f_14_2]) ).
cnf(f_14_4,plain,
( subset(U_23,U_21)
| set_difference(U_23,U_21) != empty_set ),
inference(clausify,[status(thm)],[f_14_3]) ).
cnf(f_14_5,plain,
( set_difference(U_24,U_22) = empty_set
| ~ subset(U_24,U_22) ),
inference(clausify,[status(thm)],[f_14_3]) ).
cnf(f_7_2_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_7_2]) ).
cnf(f_8_2_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_8_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_difference(Eq_x_0,Eq_x_1) = set_difference(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,
( empty(Eq_y_0)
| ~ empty(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_7,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 : SEU134+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/sandbox2/solver/bin/connect++ --verbosity 1 --no-colour --tptp-proof --schedule default --timeout 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.11/0.37 % Computer : n005.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Sat Sep 19 23:21:19 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.14/0.40 % SZS status Theorem for theBenchmark
% 0.14/0.40 % SZS output start Proof for theBenchmark
% See solution above
%------------------------------------------------------------------------------