%------------------------------------------------------------------------------
% File : ConnectPP---0.7.2
% Problem : SET903+1 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/connect++ --verbosity 1 --no-colour --tptp-proof --schedule default --timeout 300 /export/starexec/sandbox/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 08:57:46 AM UTC 2026
% Result : Theorem 0.09s 0.40s
% 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(fc1_xboole_0,axiom,
empty(empty_set),
file('theBenchmark.p',fc1_xboole_0) ).
fof(fc2_xboole_0,axiom,
! [A,B] :
( ~ empty(A)
=> ~ empty(set_union2(A,B)) ),
file('theBenchmark.p',fc2_xboole_0) ).
fof(fc3_xboole_0,axiom,
! [A,B] :
( ~ empty(A)
=> ~ empty(set_union2(B,A)) ),
file('theBenchmark.p',fc3_xboole_0) ).
fof(idempotence_k2_xboole_0,axiom,
! [A,B] : set_union2(A,A) = A,
file('theBenchmark.p',idempotence_k2_xboole_0) ).
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(t43_zfmisc_1,axiom,
! [A,B,C] :
~ ( ~ ( C = empty_set
& B = singleton(A) )
& ~ ( C = singleton(A)
& B = empty_set )
& ~ ( C = singleton(A)
& B = singleton(A) )
& singleton(A) = set_union2(B,C) ),
file('theBenchmark.p',t43_zfmisc_1) ).
fof(t44_zfmisc_1,conjecture,
! [A,B,C] :
~ ( C != empty_set
& B != empty_set
& B != C
& singleton(A) = set_union2(B,C) ),
file('theBenchmark.p',t44_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,
empty(empty_set),
inference(fof_nnf,[status(thm)],[fc1_xboole_0]) ).
cnf(f_2_2,plain,
empty(empty_set),
inference(clausify,[status(thm)],[f_2_1]) ).
fof(f_3_1,plain,
! [A,B] :
( ~ empty(set_union2(A,B))
| empty(A) ),
inference(fof_nnf,[status(thm)],[fc2_xboole_0]) ).
fof(f_3_2,plain,
! [U_3,U_2] :
( ~ empty(set_union2(U_3,U_2))
| empty(U_3) ),
inference(variable_rename,[status(thm)],[f_3_1]) ).
fof(f_3_3,plain,
! [U_3] :
( ! [U_2] : ~ empty(set_union2(U_3,U_2))
| empty(U_3) ),
inference(miniscope,[status(thm)],[f_3_2]) ).
cnf(f_3_4,plain,
( ~ empty(set_union2(U_3,U_2))
| empty(U_3) ),
inference(clausify,[status(thm)],[f_3_3]) ).
fof(f_4_1,plain,
! [A,B] :
( ~ empty(set_union2(B,A))
| empty(A) ),
inference(fof_nnf,[status(thm)],[fc3_xboole_0]) ).
fof(f_4_2,plain,
! [U_5,U_4] :
( ~ empty(set_union2(U_4,U_5))
| empty(U_5) ),
inference(variable_rename,[status(thm)],[f_4_1]) ).
fof(f_4_3,plain,
! [U_5] :
( ! [U_4] : ~ empty(set_union2(U_4,U_5))
| empty(U_5) ),
inference(miniscope,[status(thm)],[f_4_2]) ).
cnf(f_4_4,plain,
( ~ empty(set_union2(U_4,U_5))
| empty(U_5) ),
inference(clausify,[status(thm)],[f_4_3]) ).
fof(f_5_1,plain,
! [A,B] : set_union2(A,A) = A,
inference(fof_nnf,[status(thm)],[idempotence_k2_xboole_0]) ).
fof(f_5_2,plain,
! [U_7,U_6] : set_union2(U_7,U_7) = U_7,
inference(variable_rename,[status(thm)],[f_5_1]) ).
fof(f_5_3,plain,
! [U_7] : set_union2(U_7,U_7) = U_7,
inference(miniscope,[status(thm)],[f_5_2]) ).
cnf(f_5_4,plain,
set_union2(U_7,U_7) = U_7,
inference(clausify,[status(thm)],[f_5_3]) ).
fof(f_6_1,plain,
? [A] : empty(A),
inference(fof_nnf,[status(thm)],[rc1_xboole_0]) ).
fof(f_6_2,plain,
? [U_8] : empty(U_8),
inference(variable_rename,[status(thm)],[f_6_1]) ).
fof(f_6_3,plain,
empty(sK1),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(U_8,sK1)],[f_6_2]) ).
cnf(f_6_4,plain,
empty(sK1),
inference(clausify,[status(thm)],[f_6_3]) ).
fof(f_7_1,plain,
? [A] : ~ empty(A),
inference(fof_nnf,[status(thm)],[rc2_xboole_0]) ).
fof(f_7_2,plain,
? [U_9] : ~ empty(U_9),
inference(variable_rename,[status(thm)],[f_7_1]) ).
fof(f_7_3,plain,
~ empty(sK2),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2]),skolemize(U_9,sK2)],[f_7_2]) ).
cnf(f_7_4,plain,
~ empty(sK2),
inference(clausify,[status(thm)],[f_7_3]) ).
fof(f_8_1,plain,
! [A,B,C] :
( ( C = empty_set
& B = singleton(A) )
| ( C = singleton(A)
& B = empty_set )
| ( C = singleton(A)
& B = singleton(A) )
| singleton(A) != set_union2(B,C) ),
inference(fof_nnf,[status(thm)],[t43_zfmisc_1]) ).
fof(f_8_2,plain,
! [U_12,U_11,U_10] :
( ( U_10 = empty_set
& U_11 = singleton(U_12) )
| ( U_10 = singleton(U_12)
& U_11 = empty_set )
| ( U_10 = singleton(U_12)
& U_11 = singleton(U_12) )
| singleton(U_12) != set_union2(U_11,U_10) ),
inference(variable_rename,[status(thm)],[f_8_1]) ).
cnf(f_8_3,plain,
( U_11 = empty_set
| U_11 = singleton(U_12)
| U_11 = singleton(U_12)
| singleton(U_12) != set_union2(U_11,U_10) ),
inference(clausify,[status(thm)],[f_8_2]) ).
cnf(f_8_4,plain,
( U_10 = singleton(U_12)
| U_11 = singleton(U_12)
| U_11 = singleton(U_12)
| singleton(U_12) != set_union2(U_11,U_10) ),
inference(clausify,[status(thm)],[f_8_2]) ).
cnf(f_8_5,plain,
( U_11 = empty_set
| U_10 = singleton(U_12)
| U_11 = singleton(U_12)
| singleton(U_12) != set_union2(U_11,U_10) ),
inference(clausify,[status(thm)],[f_8_2]) ).
cnf(f_8_6,plain,
( U_10 = singleton(U_12)
| U_10 = singleton(U_12)
| U_11 = singleton(U_12)
| singleton(U_12) != set_union2(U_11,U_10) ),
inference(clausify,[status(thm)],[f_8_2]) ).
cnf(f_8_7,plain,
( U_11 = empty_set
| U_11 = singleton(U_12)
| U_10 = empty_set
| singleton(U_12) != set_union2(U_11,U_10) ),
inference(clausify,[status(thm)],[f_8_2]) ).
cnf(f_8_8,plain,
( U_10 = singleton(U_12)
| U_11 = singleton(U_12)
| U_10 = empty_set
| singleton(U_12) != set_union2(U_11,U_10) ),
inference(clausify,[status(thm)],[f_8_2]) ).
cnf(f_8_9,plain,
( U_11 = empty_set
| U_10 = singleton(U_12)
| U_10 = empty_set
| singleton(U_12) != set_union2(U_11,U_10) ),
inference(clausify,[status(thm)],[f_8_2]) ).
cnf(f_8_10,plain,
( U_10 = singleton(U_12)
| U_10 = singleton(U_12)
| U_10 = empty_set
| singleton(U_12) != set_union2(U_11,U_10) ),
inference(clausify,[status(thm)],[f_8_2]) ).
fof(f_9_1,negated_conjecture,
~ ! [A,B,C] :
~ ( C != empty_set
& B != empty_set
& B != C
& singleton(A) = set_union2(B,C) ),
inference(negate,[status(cth)],[t44_zfmisc_1]) ).
fof(f_9_2,negated_conjecture,
? [A,B,C] :
( C != empty_set
& B != empty_set
& B != C
& singleton(A) = set_union2(B,C) ),
inference(fof_nnf,[status(thm)],[f_9_1]) ).
fof(f_9_3,negated_conjecture,
? [U_15,U_14,U_13] :
( U_13 != empty_set
& U_14 != empty_set
& U_14 != U_13
& singleton(U_15) = set_union2(U_14,U_13) ),
inference(variable_rename,[status(thm)],[f_9_2]) ).
fof(f_9_4,negated_conjecture,
? [U_15,U_14] :
( ? [U_13] :
( U_13 != empty_set
& U_14 != U_13
& singleton(U_15) = set_union2(U_14,U_13) )
& U_14 != empty_set ),
inference(miniscope,[status(thm)],[f_9_3]) ).
fof(f_9_5,negated_conjecture,
? [U_14] :
( ? [U_13] :
( U_13 != empty_set
& U_14 != U_13
& singleton(sK3) = set_union2(U_14,U_13) )
& U_14 != empty_set ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3]),skolemize(U_15,sK3)],[f_9_4]) ).
fof(f_9_6,negated_conjecture,
( ? [U_13] :
( U_13 != empty_set
& sK4 != U_13
& singleton(sK3) = set_union2(sK4,U_13) )
& sK4 != empty_set ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4]),skolemize(U_14,sK4)],[f_9_5]) ).
fof(f_9_7,negated_conjecture,
( sK5 != empty_set
& sK4 != sK5
& singleton(sK3) = set_union2(sK4,sK5)
& sK4 != empty_set ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK5]),skolemize(U_13,sK5)],[f_9_6]) ).
fof(f_9_8,negated_conjecture,
( sK5 != empty_set
& sK4 != sK5
& singleton(sK3) = set_union2(sK4,sK5)
& sK4 != empty_set ),
inference(definitional_conversion,[status(esa)],[f_9_7]) ).
cnf(f_9_9,negated_conjecture,
sK4 != empty_set,
inference(clausify,[status(thm)],[f_9_8]) ).
cnf(f_9_10,negated_conjecture,
singleton(sK3) = set_union2(sK4,sK5),
inference(clausify,[status(thm)],[f_9_8]) ).
cnf(f_9_11,negated_conjecture,
sK4 != sK5,
inference(clausify,[status(thm)],[f_9_8]) ).
cnf(f_9_12,negated_conjecture,
sK5 != empty_set,
inference(clausify,[status(thm)],[f_9_8]) ).
cnf(f_8_3_simplified,plain,
( U_11 = empty_set
| U_11 = singleton(U_12)
| singleton(U_12) != set_union2(U_11,U_10) ),
inference(simplify_clause,[status(thm)],[f_8_3]) ).
cnf(f_8_4_simplified,plain,
( U_10 = singleton(U_12)
| U_11 = singleton(U_12)
| singleton(U_12) != set_union2(U_11,U_10) ),
inference(simplify_clause,[status(thm)],[f_8_4]) ).
cnf(f_8_6_simplified,plain,
( U_10 = singleton(U_12)
| U_11 = singleton(U_12)
| singleton(U_12) != set_union2(U_11,U_10) ),
inference(simplify_clause,[status(thm)],[f_8_6]) ).
cnf(f_8_10_simplified,plain,
( U_10 = singleton(U_12)
| U_10 = empty_set
| singleton(U_12) != set_union2(U_11,U_10) ),
inference(simplify_clause,[status(thm)],[f_8_10]) ).
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,
( empty(Eq_y_0)
| ~ empty(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(sat_proved,plain,
$false,
inference(cadical,[status(thm)],[]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET903+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.03 This is a FOF_THM_RFO_SEQ problem
% 0.00/0.03 % Command : /export/starexec/sandbox/solver/bin/connect++ --verbosity 1 --no-colour --tptp-proof --schedule default --timeout 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n001.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 23:12:27 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.40 % SZS status Theorem for theBenchmark
% 0.09/0.40 % SZS output start Proof for theBenchmark
% See solution above
%------------------------------------------------------------------------------