%------------------------------------------------------------------------------
% File : ConnectPP---0.7.2
% Problem : SEU169+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 : n001.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 08:58:20 AM UTC 2026
% Result : Theorem 0.46s 0.77s
% Output : Proof 0.46s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 7
% Syntax : Number of formulae : 52 ( 21 unt; 0 def)
% Number of atoms : 183 ( 19 equ)
% Maximal formula atoms : 10 ( 3 avg)
% Number of connectives : 210 ( 79 ~; 69 |; 50 &)
% ( 5 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 3 con; 0-2 aty)
% Number of variables : 96 ( 1 sgn 67 !; 17 ?)
% Comments :
%------------------------------------------------------------------------------
fof(d1_zfmisc_1,axiom,
! [A,B] :
( B = powerset(A)
<=> ! [C] :
( in(C,B)
<=> subset(C,A) ) ),
file('theBenchmark.p',d1_zfmisc_1) ).
fof(d2_subset_1,axiom,
! [A,B] :
( ( empty(A)
=> ( element(B,A)
<=> empty(B) ) )
& ( ~ empty(A)
=> ( element(B,A)
<=> in(B,A) ) ) ),
file('theBenchmark.p',d2_subset_1) ).
fof(d3_tarski,axiom,
! [A,B] :
( subset(A,B)
<=> ! [C] :
( in(C,A)
=> in(C,B) ) ),
file('theBenchmark.p',d3_tarski) ).
fof(fc1_subset_1,axiom,
! [A] : ~ empty(powerset(A)),
file('theBenchmark.p',fc1_subset_1) ).
fof(l3_subset_1,conjecture,
! [A,B] :
( element(B,powerset(A))
=> ! [C] :
( in(C,B)
=> in(C,A) ) ),
file('theBenchmark.p',l3_subset_1) ).
fof(f_2_1,plain,
! [A,B] :
( ( B = powerset(A)
| ? [C] :
( ( ~ in(C,B)
& subset(C,A) )
| ( ~ subset(C,A)
& in(C,B) ) ) )
& ( ! [C] :
( ( in(C,B)
| ~ subset(C,A) )
& ( subset(C,A)
| ~ in(C,B) ) )
| B != powerset(A) ) ),
inference(fof_nnf,[status(thm)],[d1_zfmisc_1]) ).
fof(f_2_2,plain,
! [U_5,U_4] :
( ( U_4 = powerset(U_5)
| ? [U_3] :
( ( ~ in(U_3,U_4)
& subset(U_3,U_5) )
| ( ~ subset(U_3,U_5)
& in(U_3,U_4) ) ) )
& ( ! [U_2] :
( ( in(U_2,U_4)
| ~ subset(U_2,U_5) )
& ( subset(U_2,U_5)
| ~ in(U_2,U_4) ) )
| U_4 != powerset(U_5) ) ),
inference(variable_rename,[status(thm)],[f_2_1]) ).
fof(f_2_3,plain,
( ! [U_13,U_11] :
( U_11 = powerset(U_13)
| ? [U_9] :
( ~ in(U_9,U_11)
& subset(U_9,U_13) )
| ? [U_8] :
( ~ subset(U_8,U_13)
& in(U_8,U_11) ) )
& ! [U_12,U_10] :
( ( ! [U_7] :
( in(U_7,U_10)
| ~ subset(U_7,U_12) )
& ! [U_6] :
( subset(U_6,U_12)
| ~ in(U_6,U_10) ) )
| U_10 != powerset(U_12) ) ),
inference(miniscope,[status(thm)],[f_2_2]) ).
fof(f_2_4,plain,
( ! [U_13,U_11] :
( U_11 = powerset(U_13)
| ? [U_9] :
( ~ in(U_9,U_11)
& subset(U_9,U_13) )
| ( ~ subset(sK1(U_13,U_11),U_13)
& in(sK1(U_13,U_11),U_11) ) )
& ! [U_12,U_10] :
( ( ! [U_7] :
( in(U_7,U_10)
| ~ subset(U_7,U_12) )
& ! [U_6] :
( subset(U_6,U_12)
| ~ in(U_6,U_10) ) )
| U_10 != powerset(U_12) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(U_8,sK1(U_13,U_11))],[f_2_3]) ).
fof(f_2_5,plain,
( ! [U_13,U_11] :
( U_11 = powerset(U_13)
| ( ~ in(sK2(U_13,U_11),U_11)
& subset(sK2(U_13,U_11),U_13) )
| ( ~ subset(sK1(U_13,U_11),U_13)
& in(sK1(U_13,U_11),U_11) ) )
& ! [U_12,U_10] :
( ( ! [U_7] :
( in(U_7,U_10)
| ~ subset(U_7,U_12) )
& ! [U_6] :
( subset(U_6,U_12)
| ~ in(U_6,U_10) ) )
| U_10 != powerset(U_12) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2]),skolemize(U_9,sK2(U_13,U_11))],[f_2_4]) ).
cnf(f_2_6,plain,
( subset(U_6,U_12)
| ~ in(U_6,U_10)
| U_10 != powerset(U_12) ),
inference(clausify,[status(thm)],[f_2_5]) ).
fof(f_3_1,plain,
! [A,B] :
( ( ( ( element(B,A)
| ~ empty(B) )
& ( empty(B)
| ~ element(B,A) ) )
| ~ empty(A) )
& ( ( ( element(B,A)
| ~ in(B,A) )
& ( in(B,A)
| ~ element(B,A) ) )
| empty(A) ) ),
inference(fof_nnf,[status(thm)],[d2_subset_1]) ).
fof(f_3_2,plain,
! [U_15,U_14] :
( ( ( ( element(U_14,U_15)
| ~ empty(U_14) )
& ( empty(U_14)
| ~ element(U_14,U_15) ) )
| ~ empty(U_15) )
& ( ( ( element(U_14,U_15)
| ~ in(U_14,U_15) )
& ( in(U_14,U_15)
| ~ element(U_14,U_15) ) )
| empty(U_15) ) ),
inference(variable_rename,[status(thm)],[f_3_1]) ).
fof(f_3_3,plain,
( ! [U_23] :
( ( ! [U_21] :
( element(U_21,U_23)
| ~ empty(U_21) )
& ! [U_20] :
( empty(U_20)
| ~ element(U_20,U_23) ) )
| ~ empty(U_23) )
& ! [U_22] :
( ( ! [U_19] :
( element(U_19,U_22)
| ~ in(U_19,U_22) )
& ! [U_18] :
( in(U_18,U_22)
| ~ element(U_18,U_22) ) )
| empty(U_22) ) ),
inference(miniscope,[status(thm)],[f_3_2]) ).
cnf(f_3_4,plain,
( in(U_18,U_22)
| ~ element(U_18,U_22)
| empty(U_22) ),
inference(clausify,[status(thm)],[f_3_3]) ).
fof(f_4_1,plain,
! [A,B] :
( ( subset(A,B)
| ? [C] :
( ~ in(C,B)
& in(C,A) ) )
& ( ! [C] :
( in(C,B)
| ~ in(C,A) )
| ~ subset(A,B) ) ),
inference(fof_nnf,[status(thm)],[d3_tarski]) ).
fof(f_4_2,plain,
! [U_27,U_26] :
( ( subset(U_27,U_26)
| ? [U_25] :
( ~ in(U_25,U_26)
& in(U_25,U_27) ) )
& ( ! [U_24] :
( in(U_24,U_26)
| ~ in(U_24,U_27) )
| ~ subset(U_27,U_26) ) ),
inference(variable_rename,[status(thm)],[f_4_1]) ).
fof(f_4_3,plain,
( ! [U_31,U_29] :
( subset(U_31,U_29)
| ? [U_25] :
( ~ in(U_25,U_29)
& in(U_25,U_31) ) )
& ! [U_30,U_28] :
( ! [U_24] :
( in(U_24,U_28)
| ~ in(U_24,U_30) )
| ~ subset(U_30,U_28) ) ),
inference(miniscope,[status(thm)],[f_4_2]) ).
fof(f_4_4,plain,
( ! [U_31,U_29] :
( subset(U_31,U_29)
| ( ~ in(sK3(U_31,U_29),U_29)
& in(sK3(U_31,U_29),U_31) ) )
& ! [U_30,U_28] :
( ! [U_24] :
( in(U_24,U_28)
| ~ in(U_24,U_30) )
| ~ subset(U_30,U_28) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3]),skolemize(U_25,sK3(U_31,U_29))],[f_4_3]) ).
cnf(f_4_5,plain,
( in(U_24,U_28)
| ~ in(U_24,U_30)
| ~ subset(U_30,U_28) ),
inference(clausify,[status(thm)],[f_4_4]) ).
fof(f_9_1,plain,
! [A] : ~ empty(powerset(A)),
inference(fof_nnf,[status(thm)],[fc1_subset_1]) ).
fof(f_9_2,plain,
! [U_34] : ~ empty(powerset(U_34)),
inference(variable_rename,[status(thm)],[f_9_1]) ).
cnf(f_9_3,plain,
~ empty(powerset(U_34)),
inference(clausify,[status(thm)],[f_9_2]) ).
fof(f_11_1,negated_conjecture,
~ ! [A,B] :
( element(B,powerset(A))
=> ! [C] :
( in(C,B)
=> in(C,A) ) ),
inference(negate,[status(cth)],[l3_subset_1]) ).
fof(f_11_2,negated_conjecture,
? [A,B] :
( ? [C] :
( ~ in(C,A)
& in(C,B) )
& element(B,powerset(A)) ),
inference(fof_nnf,[status(thm)],[f_11_1]) ).
fof(f_11_3,negated_conjecture,
? [U_37,U_36] :
( ? [U_35] :
( ~ in(U_35,U_37)
& in(U_35,U_36) )
& element(U_36,powerset(U_37)) ),
inference(variable_rename,[status(thm)],[f_11_2]) ).
fof(f_11_4,negated_conjecture,
? [U_36] :
( ? [U_35] :
( ~ in(U_35,sK5)
& in(U_35,U_36) )
& element(U_36,powerset(sK5)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK5]),skolemize(U_37,sK5)],[f_11_3]) ).
fof(f_11_5,negated_conjecture,
( ? [U_35] :
( ~ in(U_35,sK5)
& in(U_35,sK6) )
& element(sK6,powerset(sK5)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK6]),skolemize(U_36,sK6)],[f_11_4]) ).
fof(f_11_6,negated_conjecture,
( ~ in(sK7,sK5)
& in(sK7,sK6)
& element(sK6,powerset(sK5)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK7]),skolemize(U_35,sK7)],[f_11_5]) ).
fof(f_11_7,negated_conjecture,
( ~ in(sK7,sK5)
& in(sK7,sK6)
& element(sK6,powerset(sK5)) ),
inference(definitional_conversion,[status(esa)],[f_11_6]) ).
cnf(f_11_8,negated_conjecture,
element(sK6,powerset(sK5)),
inference(clausify,[status(thm)],[f_11_7]) ).
cnf(f_11_9,negated_conjecture,
in(sK7,sK6),
inference(clausify,[status(thm)],[f_11_7]) ).
cnf(f_11_10,negated_conjecture,
~ in(sK7,sK5),
inference(clausify,[status(thm)],[f_11_7]) ).
cnf(equality_1,axiom,
Eq_x_0 = Eq_x_0,
theory(equality,[reflexivity]) ).
cnf(equality_4,axiom,
( powerset(Eq_x_0) = powerset(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(t1,plain,
~ empty(powerset(sK5)),
inference(start,[status(thm),parent(0:0)],[f_9_3]) ).
cnf(t2,plain,
( ~ element(sK6,powerset(sK5))
| in(sK6,powerset(sK5))
| empty(powerset(sK5)) ),
inference(extension,[status(thm),parent(t1:1)],[f_3_4]) ).
cnf(t3,plain,
$false,
inference(connection,[status(thm),parent(t2:1)],[t2:1,t1:1]) ).
cnf(t4,plain,
( subset(sK6,sK5)
| powerset(sK5) != powerset(sK5)
| ~ in(sK6,powerset(sK5)) ),
inference(extension,[status(thm),parent(t2:2)],[f_2_6]) ).
cnf(t5,plain,
$false,
inference(connection,[status(thm),parent(t4:1)],[t4:1,t2:2]) ).
cnf(t6,plain,
( sK5 != sK5
| powerset(sK5) = powerset(sK5) ),
inference(extension,[status(thm),parent(t4:2)],[equality_4]) ).
cnf(t7,plain,
$false,
inference(connection,[status(thm),parent(t6:1)],[t6:1,t4:2]) ).
cnf(t8,plain,
sK5 = sK5,
inference(extension,[status(thm),parent(t6:2)],[equality_1]) ).
cnf(t9,plain,
$false,
inference(connection,[status(thm),parent(t8:1)],[t8:1,t6:2]) ).
cnf(t10,plain,
( ~ in(sK7,sK6)
| in(sK7,sK5)
| ~ subset(sK6,sK5) ),
inference(extension,[status(thm),parent(t4:3)],[f_4_5]) ).
cnf(t11,plain,
$false,
inference(connection,[status(thm),parent(t10:1)],[t10:1,t4:3]) ).
cnf(t12,plain,
~ in(sK7,sK5),
inference(extension,[status(thm),parent(t10:2)],[f_11_10]) ).
cnf(t13,plain,
$false,
inference(connection,[status(thm),parent(t12:1)],[t12:1,t10:2]) ).
cnf(t14,plain,
in(sK7,sK6),
inference(extension,[status(thm),parent(t10:3)],[f_11_9]) ).
cnf(t15,plain,
$false,
inference(connection,[status(thm),parent(t14:1)],[t14:1,t10:3]) ).
cnf(t16,plain,
element(sK6,powerset(sK5)),
inference(extension,[status(thm),parent(t2:3)],[f_11_8]) ).
cnf(t17,plain,
$false,
inference(connection,[status(thm),parent(t16:1)],[t16:1,t2:3]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU169+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
% 0.11/0.36 % Computer : n001.cluster.edu
% 0.11/0.36 % Model : x86_64 x86_64
% 0.11/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.36 % Memory : 8046.5625MB
% 0.11/0.36 % OS : Linux 6.8.0-71-generic
% 0.11/0.36 % CPULimit : 300
% 0.11/0.36 % WCLimit : 300
% 0.11/0.36 % DateTime : Sat Sep 19 23:30:40 UTC 2026
% 0.11/0.36 % CPUTime :
% 0.46/0.77 % SZS status Theorem for theBenchmark
% 0.46/0.77 % SZS output start Proof for theBenchmark
% See solution above
%------------------------------------------------------------------------------