%------------------------------------------------------------------------------
% File : ConnectPP---0.7.2
% Problem : SEU118+1 : TPTP v9.3.1. Released v3.2.0.
% 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 : n016.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 08:58:04 AM UTC 2026
% Result : Theorem 6.16s 6.46s
% Output : Proof 6.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 8
% Syntax : Number of formulae : 58 ( 21 unt; 0 def)
% Number of atoms : 195 ( 19 equ)
% Maximal formula atoms : 15 ( 3 avg)
% Number of connectives : 219 ( 82 ~; 70 |; 56 &)
% ( 3 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 10 ( 8 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 2 con; 0-2 aty)
% Number of variables : 77 ( 1 sgn 54 !; 10 ?)
% Comments :
%------------------------------------------------------------------------------
fof(cc2_finset_1,axiom,
! [A] :
( finite(A)
=> ! [B] :
( element(B,powerset(A))
=> finite(B) ) ),
file('theBenchmark.p',cc2_finset_1) ).
fof(d5_finsub_1,axiom,
! [A,B] :
( preboolean(B)
=> ( B = finite_subsets(A)
<=> ! [C] :
( in(C,B)
<=> ( finite(C)
& subset(C,A) ) ) ) ),
file('theBenchmark.p',d5_finsub_1) ).
fof(fc2_finsub_1,axiom,
! [A] :
( preboolean(finite_subsets(A))
& diff_closed(finite_subsets(A))
& cup_closed(finite_subsets(A))
& ~ empty(finite_subsets(A)) ),
file('theBenchmark.p',fc2_finsub_1) ).
fof(t1_subset,axiom,
! [A,B] :
( in(A,B)
=> element(A,B) ),
file('theBenchmark.p',t1_subset) ).
fof(t34_finsub_1,conjecture,
! [A,B] :
( element(B,powerset(A))
=> ( finite(A)
=> element(B,finite_subsets(A)) ) ),
file('theBenchmark.p',t34_finsub_1) ).
fof(t3_subset,axiom,
! [A,B] :
( element(A,powerset(B))
<=> subset(A,B) ),
file('theBenchmark.p',t3_subset) ).
fof(f_4_1,plain,
! [A] :
( ! [B] :
( finite(B)
| ~ element(B,powerset(A)) )
| ~ finite(A) ),
inference(fof_nnf,[status(thm)],[cc2_finset_1]) ).
fof(f_4_2,plain,
! [U_5] :
( ! [U_4] :
( finite(U_4)
| ~ element(U_4,powerset(U_5)) )
| ~ finite(U_5) ),
inference(variable_rename,[status(thm)],[f_4_1]) ).
cnf(f_4_3,plain,
( finite(U_4)
| ~ element(U_4,powerset(U_5))
| ~ finite(U_5) ),
inference(clausify,[status(thm)],[f_4_2]) ).
fof(f_7_1,plain,
! [A,B] :
( ( ( B = finite_subsets(A)
| ? [C] :
( ( ~ in(C,B)
& finite(C)
& subset(C,A) )
| ( ( ~ finite(C)
| ~ subset(C,A) )
& in(C,B) ) ) )
& ( ! [C] :
( ( in(C,B)
| ~ finite(C)
| ~ subset(C,A) )
& ( ( finite(C)
& subset(C,A) )
| ~ in(C,B) ) )
| B != finite_subsets(A) ) )
| ~ preboolean(B) ),
inference(fof_nnf,[status(thm)],[d5_finsub_1]) ).
fof(f_7_2,plain,
! [U_12,U_11] :
( ( ( U_11 = finite_subsets(U_12)
| ? [U_10] :
( ( ~ in(U_10,U_11)
& finite(U_10)
& subset(U_10,U_12) )
| ( ( ~ finite(U_10)
| ~ subset(U_10,U_12) )
& in(U_10,U_11) ) ) )
& ( ! [U_9] :
( ( in(U_9,U_11)
| ~ finite(U_9)
| ~ subset(U_9,U_12) )
& ( ( finite(U_9)
& subset(U_9,U_12) )
| ~ in(U_9,U_11) ) )
| U_11 != finite_subsets(U_12) ) )
| ~ preboolean(U_11) ),
inference(variable_rename,[status(thm)],[f_7_1]) ).
fof(f_7_3,plain,
! [U_12,U_11] :
( ( ( U_11 = finite_subsets(U_12)
| ? [U_16] :
( ~ in(U_16,U_11)
& finite(U_16)
& subset(U_16,U_12) )
| ? [U_15] :
( ( ~ finite(U_15)
| ~ subset(U_15,U_12) )
& in(U_15,U_11) ) )
& ( ( ! [U_14] :
( in(U_14,U_11)
| ~ finite(U_14)
| ~ subset(U_14,U_12) )
& ! [U_13] :
( ( finite(U_13)
& subset(U_13,U_12) )
| ~ in(U_13,U_11) ) )
| U_11 != finite_subsets(U_12) ) )
| ~ preboolean(U_11) ),
inference(miniscope,[status(thm)],[f_7_2]) ).
fof(f_7_4,plain,
! [U_12,U_11] :
( ( ( U_11 = finite_subsets(U_12)
| ? [U_16] :
( ~ in(U_16,U_11)
& finite(U_16)
& subset(U_16,U_12) )
| ( ( ~ finite(sK1(U_12,U_11))
| ~ subset(sK1(U_12,U_11),U_12) )
& in(sK1(U_12,U_11),U_11) ) )
& ( ( ! [U_14] :
( in(U_14,U_11)
| ~ finite(U_14)
| ~ subset(U_14,U_12) )
& ! [U_13] :
( ( finite(U_13)
& subset(U_13,U_12) )
| ~ in(U_13,U_11) ) )
| U_11 != finite_subsets(U_12) ) )
| ~ preboolean(U_11) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(U_15,sK1(U_12,U_11))],[f_7_3]) ).
fof(f_7_5,plain,
! [U_12,U_11] :
( ( ( U_11 = finite_subsets(U_12)
| ( ~ in(sK2(U_12,U_11),U_11)
& finite(sK2(U_12,U_11))
& subset(sK2(U_12,U_11),U_12) )
| ( ( ~ finite(sK1(U_12,U_11))
| ~ subset(sK1(U_12,U_11),U_12) )
& in(sK1(U_12,U_11),U_11) ) )
& ( ( ! [U_14] :
( in(U_14,U_11)
| ~ finite(U_14)
| ~ subset(U_14,U_12) )
& ! [U_13] :
( ( finite(U_13)
& subset(U_13,U_12) )
| ~ in(U_13,U_11) ) )
| U_11 != finite_subsets(U_12) ) )
| ~ preboolean(U_11) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2]),skolemize(U_16,sK2(U_12,U_11))],[f_7_4]) ).
cnf(f_7_8,plain,
( in(U_14,U_11)
| ~ finite(U_14)
| ~ subset(U_14,U_12)
| U_11 != finite_subsets(U_12)
| ~ preboolean(U_11) ),
inference(clausify,[status(thm)],[f_7_5]) ).
fof(f_13_1,plain,
! [A] :
( preboolean(finite_subsets(A))
& diff_closed(finite_subsets(A))
& cup_closed(finite_subsets(A))
& ~ empty(finite_subsets(A)) ),
inference(fof_nnf,[status(thm)],[fc2_finsub_1]) ).
fof(f_13_2,plain,
! [U_26] :
( preboolean(finite_subsets(U_26))
& diff_closed(finite_subsets(U_26))
& cup_closed(finite_subsets(U_26))
& ~ empty(finite_subsets(U_26)) ),
inference(variable_rename,[status(thm)],[f_13_1]) ).
fof(f_13_3,plain,
( ! [U_30] : preboolean(finite_subsets(U_30))
& ! [U_29] : diff_closed(finite_subsets(U_29))
& ! [U_28] : cup_closed(finite_subsets(U_28))
& ! [U_27] : ~ empty(finite_subsets(U_27)) ),
inference(miniscope,[status(thm)],[f_13_2]) ).
cnf(f_13_7,plain,
preboolean(finite_subsets(U_30)),
inference(clausify,[status(thm)],[f_13_3]) ).
fof(f_25_1,plain,
! [A,B] :
( element(A,B)
| ~ in(A,B) ),
inference(fof_nnf,[status(thm)],[t1_subset]) ).
fof(f_25_2,plain,
! [U_50,U_49] :
( element(U_50,U_49)
| ~ in(U_50,U_49) ),
inference(variable_rename,[status(thm)],[f_25_1]) ).
cnf(f_25_3,plain,
( element(U_50,U_49)
| ~ in(U_50,U_49) ),
inference(clausify,[status(thm)],[f_25_2]) ).
fof(f_27_1,negated_conjecture,
~ ! [A,B] :
( element(B,powerset(A))
=> ( finite(A)
=> element(B,finite_subsets(A)) ) ),
inference(negate,[status(cth)],[t34_finsub_1]) ).
fof(f_27_2,negated_conjecture,
? [A,B] :
( ~ element(B,finite_subsets(A))
& finite(A)
& element(B,powerset(A)) ),
inference(fof_nnf,[status(thm)],[f_27_1]) ).
fof(f_27_3,negated_conjecture,
? [U_54,U_53] :
( ~ element(U_53,finite_subsets(U_54))
& finite(U_54)
& element(U_53,powerset(U_54)) ),
inference(variable_rename,[status(thm)],[f_27_2]) ).
fof(f_27_4,negated_conjecture,
? [U_53] :
( ~ element(U_53,finite_subsets(sK13))
& finite(sK13)
& element(U_53,powerset(sK13)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK13]),skolemize(U_54,sK13)],[f_27_3]) ).
fof(f_27_5,negated_conjecture,
( ~ element(sK14,finite_subsets(sK13))
& finite(sK13)
& element(sK14,powerset(sK13)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK14]),skolemize(U_53,sK14)],[f_27_4]) ).
fof(f_27_6,negated_conjecture,
( ~ element(sK14,finite_subsets(sK13))
& finite(sK13)
& element(sK14,powerset(sK13)) ),
inference(definitional_conversion,[status(esa)],[f_27_5]) ).
cnf(f_27_7,negated_conjecture,
element(sK14,powerset(sK13)),
inference(clausify,[status(thm)],[f_27_6]) ).
cnf(f_27_8,negated_conjecture,
finite(sK13),
inference(clausify,[status(thm)],[f_27_6]) ).
cnf(f_27_9,negated_conjecture,
~ element(sK14,finite_subsets(sK13)),
inference(clausify,[status(thm)],[f_27_6]) ).
fof(f_28_1,plain,
! [A,B] :
( ( element(A,powerset(B))
| ~ subset(A,B) )
& ( subset(A,B)
| ~ element(A,powerset(B)) ) ),
inference(fof_nnf,[status(thm)],[t3_subset]) ).
fof(f_28_2,plain,
! [U_56,U_55] :
( ( element(U_56,powerset(U_55))
| ~ subset(U_56,U_55) )
& ( subset(U_56,U_55)
| ~ element(U_56,powerset(U_55)) ) ),
inference(variable_rename,[status(thm)],[f_28_1]) ).
fof(f_28_3,plain,
( ! [U_60,U_58] :
( element(U_60,powerset(U_58))
| ~ subset(U_60,U_58) )
& ! [U_59,U_57] :
( subset(U_59,U_57)
| ~ element(U_59,powerset(U_57)) ) ),
inference(miniscope,[status(thm)],[f_28_2]) ).
cnf(f_28_4,plain,
( subset(U_59,U_57)
| ~ element(U_59,powerset(U_57)) ),
inference(clausify,[status(thm)],[f_28_3]) ).
cnf(equality_1,axiom,
Eq_x_0 = Eq_x_0,
theory(equality,[reflexivity]) ).
cnf(equality_5,axiom,
( finite_subsets(Eq_x_0) = finite_subsets(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(t1,plain,
~ element(sK14,finite_subsets(sK13)),
inference(start,[status(thm),parent(0:0)],[f_27_9]) ).
cnf(t2,plain,
( ~ in(sK14,finite_subsets(sK13))
| element(sK14,finite_subsets(sK13)) ),
inference(extension,[status(thm),parent(t1:1)],[f_25_3]) ).
cnf(t3,plain,
$false,
inference(connection,[status(thm),parent(t2:1)],[t2:1,t1:1]) ).
cnf(t4,plain,
( finite_subsets(sK13) != finite_subsets(sK13)
| ~ subset(sK14,sK13)
| ~ finite(sK14)
| ~ preboolean(finite_subsets(sK13))
| in(sK14,finite_subsets(sK13)) ),
inference(extension,[status(thm),parent(t2:2)],[f_7_8]) ).
cnf(t5,plain,
$false,
inference(connection,[status(thm),parent(t4:1)],[t4:1,t2:2]) ).
cnf(t6,plain,
preboolean(finite_subsets(sK13)),
inference(extension,[status(thm),parent(t4:2)],[f_13_7]) ).
cnf(t7,plain,
$false,
inference(connection,[status(thm),parent(t6:1)],[t6:1,t4:2]) ).
cnf(t8,plain,
( ~ element(sK14,powerset(sK13))
| ~ finite(sK13)
| finite(sK14) ),
inference(extension,[status(thm),parent(t4:3)],[f_4_3]) ).
cnf(t9,plain,
$false,
inference(connection,[status(thm),parent(t8:1)],[t8:1,t4:3]) ).
cnf(t10,plain,
finite(sK13),
inference(extension,[status(thm),parent(t8:2)],[f_27_8]) ).
cnf(t11,plain,
$false,
inference(connection,[status(thm),parent(t10:1)],[t10:1,t8:2]) ).
cnf(t12,plain,
element(sK14,powerset(sK13)),
inference(extension,[status(thm),parent(t8:3)],[f_27_7]) ).
cnf(t13,plain,
$false,
inference(connection,[status(thm),parent(t12:1)],[t12:1,t8:3]) ).
cnf(t14,plain,
( ~ element(sK14,powerset(sK13))
| subset(sK14,sK13) ),
inference(extension,[status(thm),parent(t4:4)],[f_28_4]) ).
cnf(t15,plain,
$false,
inference(connection,[status(thm),parent(t14:1)],[t14:1,t4:4]) ).
cnf(t16,plain,
element(sK14,powerset(sK13)),
inference(extension,[status(thm),parent(t14:2)],[f_27_7]) ).
cnf(t17,plain,
$false,
inference(connection,[status(thm),parent(t16:1)],[t16:1,t14:2]) ).
cnf(t18,plain,
( sK13 != sK13
| finite_subsets(sK13) = finite_subsets(sK13) ),
inference(extension,[status(thm),parent(t4:5)],[equality_5]) ).
cnf(t19,plain,
$false,
inference(connection,[status(thm),parent(t18:1)],[t18:1,t4:5]) ).
cnf(t20,plain,
sK13 = sK13,
inference(extension,[status(thm),parent(t18:2)],[equality_1]) ).
cnf(t21,plain,
$false,
inference(connection,[status(thm),parent(t20:1)],[t20:1,t18:2]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU118+1 : TPTP v9.3.1. Released v3.2.0.
% 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
% 0.12/0.36 % Computer : n016.cluster.edu
% 0.12/0.36 % Model : x86_64 x86_64
% 0.12/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.36 % Memory : 8046.5625MB
% 0.12/0.36 % OS : Linux 6.8.0-71-generic
% 0.12/0.36 % CPULimit : 300
% 0.12/0.36 % WCLimit : 300
% 0.12/0.36 % DateTime : Sat Sep 19 23:24:21 UTC 2026
% 0.12/0.36 % CPUTime :
% 6.16/6.46 % SZS status Theorem for theBenchmark
% 6.16/6.46 % SZS output start Proof for theBenchmark
% See solution above
%------------------------------------------------------------------------------