%------------------------------------------------------------------------------
% File : ConnectPP---0.7.2
% Problem : SEU112+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 08:58:03 AM UTC 2026
% Result : Theorem 126.35s 126.69s
% Output : Proof 126.35s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 7
% Syntax : Number of formulae : 43 ( 30 unt; 0 def)
% Number of atoms : 65 ( 11 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 49 ( 27 ~; 19 |; 1 &)
% ( 0 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 2 con; 0-2 aty)
% Number of variables : 50 ( 1 sgn 31 !; 5 ?)
% Comments :
%------------------------------------------------------------------------------
fof(commutativity_k2_xboole_0,axiom,
! [A,B] : set_union2(A,B) = set_union2(B,A),
file('theBenchmark.p',commutativity_k2_xboole_0) ).
fof(t23_finsub_1,axiom,
! [A,B] :
( subset(A,B)
=> subset(finite_subsets(A),finite_subsets(B)) ),
file('theBenchmark.p',t23_finsub_1) ).
fof(t25_finsub_1,conjecture,
! [A,B] : subset(set_union2(finite_subsets(A),finite_subsets(B)),finite_subsets(set_union2(A,B))),
file('theBenchmark.p',t25_finsub_1) ).
fof(t7_xboole_1,axiom,
! [A,B] : subset(A,set_union2(A,B)),
file('theBenchmark.p',t7_xboole_1) ).
fof(t8_xboole_1,axiom,
! [A,B,C] :
( ( subset(C,B)
& subset(A,B) )
=> subset(set_union2(A,C),B) ),
file('theBenchmark.p',t8_xboole_1) ).
fof(f_7_1,plain,
! [A,B] : set_union2(A,B) = set_union2(B,A),
inference(fof_nnf,[status(thm)],[commutativity_k2_xboole_0]) ).
fof(f_7_2,plain,
! [U_10,U_9] : set_union2(U_10,U_9) = set_union2(U_9,U_10),
inference(variable_rename,[status(thm)],[f_7_1]) ).
cnf(f_7_3,plain,
set_union2(U_10,U_9) = set_union2(U_9,U_10),
inference(clausify,[status(thm)],[f_7_2]) ).
fof(f_30_1,plain,
! [A,B] :
( subset(finite_subsets(A),finite_subsets(B))
| ~ subset(A,B) ),
inference(fof_nnf,[status(thm)],[t23_finsub_1]) ).
fof(f_30_2,plain,
! [U_53,U_52] :
( subset(finite_subsets(U_53),finite_subsets(U_52))
| ~ subset(U_53,U_52) ),
inference(variable_rename,[status(thm)],[f_30_1]) ).
cnf(f_30_3,plain,
( subset(finite_subsets(U_53),finite_subsets(U_52))
| ~ subset(U_53,U_52) ),
inference(clausify,[status(thm)],[f_30_2]) ).
fof(f_31_1,negated_conjecture,
~ ! [A,B] : subset(set_union2(finite_subsets(A),finite_subsets(B)),finite_subsets(set_union2(A,B))),
inference(negate,[status(cth)],[t25_finsub_1]) ).
fof(f_31_2,negated_conjecture,
? [A,B] : ~ subset(set_union2(finite_subsets(A),finite_subsets(B)),finite_subsets(set_union2(A,B))),
inference(fof_nnf,[status(thm)],[f_31_1]) ).
fof(f_31_3,negated_conjecture,
? [U_55,U_54] : ~ subset(set_union2(finite_subsets(U_55),finite_subsets(U_54)),finite_subsets(set_union2(U_55,U_54))),
inference(variable_rename,[status(thm)],[f_31_2]) ).
fof(f_31_4,negated_conjecture,
? [U_54] : ~ subset(set_union2(finite_subsets(sK11),finite_subsets(U_54)),finite_subsets(set_union2(sK11,U_54))),
inference(skolemize,[status(esa),new_symbols(skolem,[sK11]),skolemize(U_55,sK11)],[f_31_3]) ).
fof(f_31_5,negated_conjecture,
~ subset(set_union2(finite_subsets(sK11),finite_subsets(sK12)),finite_subsets(set_union2(sK11,sK12))),
inference(skolemize,[status(esa),new_symbols(skolem,[sK12]),skolemize(U_54,sK12)],[f_31_4]) ).
fof(f_31_6,negated_conjecture,
~ subset(set_union2(finite_subsets(sK11),finite_subsets(sK12)),finite_subsets(set_union2(sK11,sK12))),
inference(definitional_conversion,[status(esa)],[f_31_5]) ).
cnf(f_31_7,negated_conjecture,
~ subset(set_union2(finite_subsets(sK11),finite_subsets(sK12)),finite_subsets(set_union2(sK11,sK12))),
inference(clausify,[status(thm)],[f_31_6]) ).
fof(f_38_1,plain,
! [A,B] : subset(A,set_union2(A,B)),
inference(fof_nnf,[status(thm)],[t7_xboole_1]) ).
fof(f_38_2,plain,
! [U_74,U_73] : subset(U_74,set_union2(U_74,U_73)),
inference(variable_rename,[status(thm)],[f_38_1]) ).
cnf(f_38_3,plain,
subset(U_74,set_union2(U_74,U_73)),
inference(clausify,[status(thm)],[f_38_2]) ).
fof(f_40_1,plain,
! [A,B,C] :
( subset(set_union2(A,C),B)
| ~ subset(C,B)
| ~ subset(A,B) ),
inference(fof_nnf,[status(thm)],[t8_xboole_1]) ).
fof(f_40_2,plain,
! [U_79,U_78,U_77] :
( subset(set_union2(U_79,U_77),U_78)
| ~ subset(U_77,U_78)
| ~ subset(U_79,U_78) ),
inference(variable_rename,[status(thm)],[f_40_1]) ).
cnf(f_40_3,plain,
( subset(set_union2(U_79,U_77),U_78)
| ~ subset(U_77,U_78)
| ~ subset(U_79,U_78) ),
inference(clausify,[status(thm)],[f_40_2]) ).
cnf(equality_1,axiom,
Eq_x_0 = Eq_x_0,
theory(equality,[reflexivity]) ).
cnf(equality_28,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(t1,plain,
~ subset(set_union2(finite_subsets(sK11),finite_subsets(sK12)),finite_subsets(set_union2(sK11,sK12))),
inference(start,[status(thm),parent(0:0)],[f_31_7]) ).
cnf(t2,plain,
( ~ subset(finite_subsets(sK12),finite_subsets(set_union2(sK11,sK12)))
| ~ subset(finite_subsets(sK11),finite_subsets(set_union2(sK11,sK12)))
| subset(set_union2(finite_subsets(sK11),finite_subsets(sK12)),finite_subsets(set_union2(sK11,sK12))) ),
inference(extension,[status(thm),parent(t1:1)],[f_40_3]) ).
cnf(t3,plain,
$false,
inference(connection,[status(thm),parent(t2:1)],[t2:1,t1:1]) ).
cnf(t4,plain,
( ~ subset(sK11,set_union2(sK11,sK12))
| subset(finite_subsets(sK11),finite_subsets(set_union2(sK11,sK12))) ),
inference(extension,[status(thm),parent(t2:2)],[f_30_3]) ).
cnf(t5,plain,
$false,
inference(connection,[status(thm),parent(t4:1)],[t4:1,t2:2]) ).
cnf(t6,plain,
subset(sK11,set_union2(sK11,sK12)),
inference(extension,[status(thm),parent(t4:2)],[f_38_3]) ).
cnf(t7,plain,
$false,
inference(connection,[status(thm),parent(t6:1)],[t6:1,t4:2]) ).
cnf(t8,plain,
( ~ subset(sK12,set_union2(sK11,sK12))
| subset(finite_subsets(sK12),finite_subsets(set_union2(sK11,sK12))) ),
inference(extension,[status(thm),parent(t2:3)],[f_30_3]) ).
cnf(t9,plain,
$false,
inference(connection,[status(thm),parent(t8:1)],[t8:1,t2:3]) ).
cnf(t10,plain,
( set_union2(sK12,sK11) != set_union2(sK11,sK12)
| ~ subset(sK12,set_union2(sK12,sK11))
| sK12 != sK12
| subset(sK12,set_union2(sK11,sK12)) ),
inference(extension,[status(thm),parent(t8:2)],[equality_28]) ).
cnf(t11,plain,
$false,
inference(connection,[status(thm),parent(t10:1)],[t10:1,t8:2]) ).
cnf(t12,plain,
sK12 = sK12,
inference(extension,[status(thm),parent(t10:2)],[equality_1]) ).
cnf(t13,plain,
$false,
inference(connection,[status(thm),parent(t12:1)],[t12:1,t10:2]) ).
cnf(t14,plain,
subset(sK12,set_union2(sK12,sK11)),
inference(extension,[status(thm),parent(t10:3)],[f_38_3]) ).
cnf(t15,plain,
$false,
inference(connection,[status(thm),parent(t14:1)],[t14:1,t10:3]) ).
cnf(t16,plain,
set_union2(sK12,sK11) = set_union2(sK11,sK12),
inference(extension,[status(thm),parent(t10:4)],[f_7_3]) ).
cnf(t17,plain,
$false,
inference(connection,[status(thm),parent(t16:1)],[t16:1,t10:4]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU112+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
% 0.07/0.35 % Computer : n016.cluster.edu
% 0.07/0.35 % Model : x86_64 x86_64
% 0.07/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.35 % Memory : 8046.5625MB
% 0.07/0.35 % OS : Linux 6.8.0-71-generic
% 0.07/0.35 % CPULimit : 300
% 0.07/0.35 % WCLimit : 300
% 0.07/0.35 % DateTime : Sat Sep 19 23:24:35 UTC 2026
% 0.07/0.35 % CPUTime :
% 126.35/126.69 % SZS status Theorem for theBenchmark
% 126.35/126.69 % SZS output start Proof for theBenchmark
% See solution above
%------------------------------------------------------------------------------