%------------------------------------------------------------------------------
% File : ConnectPP---0.7.2
% Problem : SEU161+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 : n014.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 08:58:16 AM UTC 2026
% Result : Theorem 0.09s 0.39s
% Output : Proof 0.09s
% Verified :
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)
% 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(idempotence_k2_xboole_0,axiom,
! [A,B] : set_union2(A,A) = A,
file('theBenchmark.p',idempotence_k2_xboole_0) ).
fof(antisymmetry_r2_hidden,axiom,
! [A,B] :
( in(A,B)
=> ~ in(B,A) ),
file('theBenchmark.p',antisymmetry_r2_hidden) ).
fof(dt_k1_tarski,axiom,
$true,
file('theBenchmark.p',dt_k1_tarski) ).
fof(dt_k2_xboole_0,axiom,
$true,
file('theBenchmark.p',dt_k2_xboole_0) ).
fof(t46_zfmisc_1,conjecture,
! [A,B] :
( in(A,B)
=> set_union2(singleton(A),B) = B ),
file('theBenchmark.p',t46_zfmisc_1) ).
fof(l23_zfmisc_1,axiom,
! [A,B] :
( in(A,B)
=> set_union2(singleton(A),B) = B ),
file('theBenchmark.p',l23_zfmisc_1) ).
fof(f_1_1,plain,
! [A,B] : set_union2(A,B) = set_union2(B,A),
inference(fof_nnf,[status(thm)],[commutativity_k2_xboole_0]) ).
fof(f_1_2,plain,
! [U_1,U_0] : set_union2(U_1,U_0) = set_union2(U_0,U_1),
inference(variable_rename,[status(thm)],[f_1_1]) ).
cnf(f_1_3,plain,
set_union2(U_1,U_0) = set_union2(U_0,U_1),
inference(clausify,[status(thm)],[f_1_2]) ).
fof(f_2_1,plain,
! [A,B] : set_union2(A,A) = A,
inference(fof_nnf,[status(thm)],[idempotence_k2_xboole_0]) ).
fof(f_2_2,plain,
! [U_3,U_2] : set_union2(U_3,U_3) = U_3,
inference(variable_rename,[status(thm)],[f_2_1]) ).
fof(f_2_3,plain,
! [U_3] : set_union2(U_3,U_3) = U_3,
inference(miniscope,[status(thm)],[f_2_2]) ).
cnf(f_2_4,plain,
set_union2(U_3,U_3) = U_3,
inference(clausify,[status(thm)],[f_2_3]) ).
fof(f_3_1,plain,
! [A,B] :
( ~ in(B,A)
| ~ in(A,B) ),
inference(fof_nnf,[status(thm)],[antisymmetry_r2_hidden]) ).
fof(f_3_2,plain,
! [U_5,U_4] :
( ~ in(U_4,U_5)
| ~ in(U_5,U_4) ),
inference(variable_rename,[status(thm)],[f_3_1]) ).
cnf(f_3_3,plain,
( ~ in(U_4,U_5)
| ~ in(U_5,U_4) ),
inference(clausify,[status(thm)],[f_3_2]) ).
fof(f_4_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_k1_tarski]) ).
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_k2_xboole_0]) ).
cnf(f_5_2,plain,
$true,
inference(clausify,[status(thm)],[f_5_1]) ).
fof(f_6_1,negated_conjecture,
~ ! [A,B] :
( in(A,B)
=> set_union2(singleton(A),B) = B ),
inference(negate,[status(cth)],[t46_zfmisc_1]) ).
fof(f_6_2,negated_conjecture,
? [A,B] :
( set_union2(singleton(A),B) != B
& in(A,B) ),
inference(fof_nnf,[status(thm)],[f_6_1]) ).
fof(f_6_3,negated_conjecture,
? [U_7,U_6] :
( set_union2(singleton(U_7),U_6) != U_6
& in(U_7,U_6) ),
inference(variable_rename,[status(thm)],[f_6_2]) ).
fof(f_6_4,negated_conjecture,
? [U_6] :
( set_union2(singleton(sK1),U_6) != U_6
& in(sK1,U_6) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(U_7,sK1)],[f_6_3]) ).
fof(f_6_5,negated_conjecture,
( set_union2(singleton(sK1),sK2) != sK2
& in(sK1,sK2) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2]),skolemize(U_6,sK2)],[f_6_4]) ).
fof(f_6_6,negated_conjecture,
( set_union2(singleton(sK1),sK2) != sK2
& in(sK1,sK2) ),
inference(definitional_conversion,[status(esa)],[f_6_5]) ).
cnf(f_6_7,negated_conjecture,
in(sK1,sK2),
inference(clausify,[status(thm)],[f_6_6]) ).
cnf(f_6_8,negated_conjecture,
set_union2(singleton(sK1),sK2) != sK2,
inference(clausify,[status(thm)],[f_6_6]) ).
fof(f_7_1,plain,
! [A,B] :
( set_union2(singleton(A),B) = B
| ~ in(A,B) ),
inference(fof_nnf,[status(thm)],[l23_zfmisc_1]) ).
fof(f_7_2,plain,
! [U_9,U_8] :
( set_union2(singleton(U_9),U_8) = U_8
| ~ in(U_9,U_8) ),
inference(variable_rename,[status(thm)],[f_7_1]) ).
cnf(f_7_3,plain,
( set_union2(singleton(U_9),U_8) = U_8
| ~ in(U_9,U_8) ),
inference(clausify,[status(thm)],[f_7_2]) ).
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_union2(Eq_x_0,Eq_x_1) = set_union2(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,
( singleton(Eq_x_0) = singleton(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_6,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(sat_proved,plain,
$false,
inference(cadical,[status(thm)],[]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU161+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
% 0.09/0.36 % Computer : n014.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Sat Sep 19 23:24:20 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.39 % SZS status Theorem for theBenchmark
% 0.09/0.39 % SZS output start Proof for theBenchmark
% See solution above
%------------------------------------------------------------------------------