%------------------------------------------------------------------------------
% File : ConnectPP---0.7.2
% Problem : SET987+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 : n008.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 08:57:54 AM UTC 2026
% Result : Theorem 0.10s 0.39s
% Output : Proof 0.10s
% Verified :
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)
% Comments :
%------------------------------------------------------------------------------
fof(antisymmetry_r2_hidden,axiom,
! [A,B] :
( in(A,B)
=> ~ in(B,A) ),
file('theBenchmark.p',antisymmetry_r2_hidden) ).
fof(commutativity_k2_xboole_0,axiom,
! [A,B] : set_union2(A,B) = set_union2(B,A),
file('theBenchmark.p',commutativity_k2_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(t141_zfmisc_1,conjecture,
! [A,B] :
( ~ in(A,B)
=> set_difference(set_union2(B,singleton(A)),singleton(A)) = B ),
file('theBenchmark.p',t141_zfmisc_1) ).
fof(t40_xboole_1,axiom,
! [A,B] : set_difference(set_union2(A,B),B) = set_difference(A,B),
file('theBenchmark.p',t40_xboole_1) ).
fof(t65_zfmisc_1,axiom,
! [A,B] :
( set_difference(A,singleton(B)) = A
<=> ~ in(B,A) ),
file('theBenchmark.p',t65_zfmisc_1) ).
fof(f_1_1,plain,
! [A,B] :
( ~ in(B,A)
| ~ in(A,B) ),
inference(fof_nnf,[status(thm)],[antisymmetry_r2_hidden]) ).
fof(f_1_2,plain,
! [U_1,U_0] :
( ~ in(U_0,U_1)
| ~ in(U_1,U_0) ),
inference(variable_rename,[status(thm)],[f_1_1]) ).
cnf(f_1_3,plain,
( ~ in(U_0,U_1)
| ~ in(U_1,U_0) ),
inference(clausify,[status(thm)],[f_1_2]) ).
fof(f_2_1,plain,
! [A,B] : set_union2(A,B) = set_union2(B,A),
inference(fof_nnf,[status(thm)],[commutativity_k2_xboole_0]) ).
fof(f_2_2,plain,
! [U_3,U_2] : set_union2(U_3,U_2) = set_union2(U_2,U_3),
inference(variable_rename,[status(thm)],[f_2_1]) ).
cnf(f_2_3,plain,
set_union2(U_3,U_2) = set_union2(U_2,U_3),
inference(clausify,[status(thm)],[f_2_2]) ).
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_5,U_4] :
( ~ empty(set_union2(U_5,U_4))
| empty(U_5) ),
inference(variable_rename,[status(thm)],[f_3_1]) ).
fof(f_3_3,plain,
! [U_5] :
( ! [U_4] : ~ empty(set_union2(U_5,U_4))
| empty(U_5) ),
inference(miniscope,[status(thm)],[f_3_2]) ).
cnf(f_3_4,plain,
( ~ empty(set_union2(U_5,U_4))
| empty(U_5) ),
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_7,U_6] :
( ~ empty(set_union2(U_6,U_7))
| empty(U_7) ),
inference(variable_rename,[status(thm)],[f_4_1]) ).
fof(f_4_3,plain,
! [U_7] :
( ! [U_6] : ~ empty(set_union2(U_6,U_7))
| empty(U_7) ),
inference(miniscope,[status(thm)],[f_4_2]) ).
cnf(f_4_4,plain,
( ~ empty(set_union2(U_6,U_7))
| empty(U_7) ),
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_9,U_8] : set_union2(U_9,U_9) = U_9,
inference(variable_rename,[status(thm)],[f_5_1]) ).
fof(f_5_3,plain,
! [U_9] : set_union2(U_9,U_9) = U_9,
inference(miniscope,[status(thm)],[f_5_2]) ).
cnf(f_5_4,plain,
set_union2(U_9,U_9) = U_9,
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_10] : empty(U_10),
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_10,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_11] : ~ empty(U_11),
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_11,sK2)],[f_7_2]) ).
cnf(f_7_4,plain,
~ empty(sK2),
inference(clausify,[status(thm)],[f_7_3]) ).
fof(f_8_1,negated_conjecture,
~ ! [A,B] :
( ~ in(A,B)
=> set_difference(set_union2(B,singleton(A)),singleton(A)) = B ),
inference(negate,[status(cth)],[t141_zfmisc_1]) ).
fof(f_8_2,negated_conjecture,
? [A,B] :
( set_difference(set_union2(B,singleton(A)),singleton(A)) != B
& ~ in(A,B) ),
inference(fof_nnf,[status(thm)],[f_8_1]) ).
fof(f_8_3,negated_conjecture,
? [U_13,U_12] :
( set_difference(set_union2(U_12,singleton(U_13)),singleton(U_13)) != U_12
& ~ in(U_13,U_12) ),
inference(variable_rename,[status(thm)],[f_8_2]) ).
fof(f_8_4,negated_conjecture,
? [U_12] :
( set_difference(set_union2(U_12,singleton(sK3)),singleton(sK3)) != U_12
& ~ in(sK3,U_12) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3]),skolemize(U_13,sK3)],[f_8_3]) ).
fof(f_8_5,negated_conjecture,
( set_difference(set_union2(sK4,singleton(sK3)),singleton(sK3)) != sK4
& ~ in(sK3,sK4) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4]),skolemize(U_12,sK4)],[f_8_4]) ).
fof(f_8_6,negated_conjecture,
( set_difference(set_union2(sK4,singleton(sK3)),singleton(sK3)) != sK4
& ~ in(sK3,sK4) ),
inference(definitional_conversion,[status(esa)],[f_8_5]) ).
cnf(f_8_7,negated_conjecture,
~ in(sK3,sK4),
inference(clausify,[status(thm)],[f_8_6]) ).
cnf(f_8_8,negated_conjecture,
set_difference(set_union2(sK4,singleton(sK3)),singleton(sK3)) != sK4,
inference(clausify,[status(thm)],[f_8_6]) ).
fof(f_9_1,plain,
! [A,B] : set_difference(set_union2(A,B),B) = set_difference(A,B),
inference(fof_nnf,[status(thm)],[t40_xboole_1]) ).
fof(f_9_2,plain,
! [U_15,U_14] : set_difference(set_union2(U_15,U_14),U_14) = set_difference(U_15,U_14),
inference(variable_rename,[status(thm)],[f_9_1]) ).
cnf(f_9_3,plain,
set_difference(set_union2(U_15,U_14),U_14) = set_difference(U_15,U_14),
inference(clausify,[status(thm)],[f_9_2]) ).
fof(f_10_1,plain,
! [A,B] :
( ( set_difference(A,singleton(B)) = A
| in(B,A) )
& ( ~ in(B,A)
| set_difference(A,singleton(B)) != A ) ),
inference(fof_nnf,[status(thm)],[t65_zfmisc_1]) ).
fof(f_10_2,plain,
! [U_17,U_16] :
( ( set_difference(U_17,singleton(U_16)) = U_17
| in(U_16,U_17) )
& ( ~ in(U_16,U_17)
| set_difference(U_17,singleton(U_16)) != U_17 ) ),
inference(variable_rename,[status(thm)],[f_10_1]) ).
fof(f_10_3,plain,
( ! [U_21,U_19] :
( set_difference(U_21,singleton(U_19)) = U_21
| in(U_19,U_21) )
& ! [U_20,U_18] :
( ~ in(U_18,U_20)
| set_difference(U_20,singleton(U_18)) != U_20 ) ),
inference(miniscope,[status(thm)],[f_10_2]) ).
cnf(f_10_4,plain,
( ~ in(U_18,U_20)
| set_difference(U_20,singleton(U_18)) != U_20 ),
inference(clausify,[status(thm)],[f_10_3]) ).
cnf(f_10_5,plain,
( set_difference(U_21,singleton(U_19)) = U_21
| in(U_19,U_21) ),
inference(clausify,[status(thm)],[f_10_3]) ).
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,
( set_difference(Eq_x_0,Eq_x_1) = set_difference(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_7,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(equality_8,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
% 0.00/0.03 % Problem : SET987+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/sandbox/solver/bin/connect++ --verbosity 1 --no-colour --tptp-proof --schedule default --timeout 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.36 % Computer : n008.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Sat Sep 19 23:11:08 UTC 2026
% 0.10/0.36 % CPUTime :
% 0.10/0.39 % SZS status Theorem for theBenchmark
% 0.10/0.39 % SZS output start Proof for theBenchmark
% See solution above
%------------------------------------------------------------------------------