%------------------------------------------------------------------------------
% File : ConnectPP---0.7.2
% Problem : SET908+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 : n019.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 1.35s 1.69s
% Output : Proof 1.35s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 7
% Syntax : Number of formulae : 51 ( 28 unt; 0 def)
% Number of atoms : 189 ( 82 equ)
% Maximal formula atoms : 14 ( 3 avg)
% Number of connectives : 222 ( 84 ~; 79 |; 54 &)
% ( 5 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 3 con; 0-3 aty)
% Number of variables : 123 ( 5 sgn 92 !; 18 ?)
% 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(d1_tarski,axiom,
! [A,B] :
( B = singleton(A)
<=> ! [C] :
( in(C,B)
<=> C = A ) ),
file('theBenchmark.p',d1_tarski) ).
fof(d1_xboole_0,axiom,
! [A] :
( A = empty_set
<=> ! [B] : ~ in(B,A) ),
file('theBenchmark.p',d1_xboole_0) ).
fof(d2_xboole_0,axiom,
! [A,B,C] :
( C = set_union2(A,B)
<=> ! [D] :
( in(D,C)
<=> ( in(D,B)
| in(D,A) ) ) ),
file('theBenchmark.p',d2_xboole_0) ).
fof(idempotence_k2_xboole_0,axiom,
! [A,B] : set_union2(A,A) = A,
file('theBenchmark.p',idempotence_k2_xboole_0) ).
fof(t49_zfmisc_1,conjecture,
! [A,B] : set_union2(singleton(A),B) != empty_set,
file('theBenchmark.p',t49_zfmisc_1) ).
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] :
( ( B = singleton(A)
| ? [C] :
( ( ~ in(C,B)
& C = A )
| ( C != A
& in(C,B) ) ) )
& ( ! [C] :
( ( in(C,B)
| C != A )
& ( C = A
| ~ in(C,B) ) )
| B != singleton(A) ) ),
inference(fof_nnf,[status(thm)],[d1_tarski]) ).
fof(f_3_2,plain,
! [U_7,U_6] :
( ( U_6 = singleton(U_7)
| ? [U_5] :
( ( ~ in(U_5,U_6)
& U_5 = U_7 )
| ( U_5 != U_7
& in(U_5,U_6) ) ) )
& ( ! [U_4] :
( ( in(U_4,U_6)
| U_4 != U_7 )
& ( U_4 = U_7
| ~ in(U_4,U_6) ) )
| U_6 != singleton(U_7) ) ),
inference(variable_rename,[status(thm)],[f_3_1]) ).
fof(f_3_3,plain,
( ! [U_15,U_13] :
( U_13 = singleton(U_15)
| ? [U_11] :
( ~ in(U_11,U_13)
& U_11 = U_15 )
| ? [U_10] :
( U_10 != U_15
& in(U_10,U_13) ) )
& ! [U_14,U_12] :
( ( ! [U_9] :
( in(U_9,U_12)
| U_9 != U_14 )
& ! [U_8] :
( U_8 = U_14
| ~ in(U_8,U_12) ) )
| U_12 != singleton(U_14) ) ),
inference(miniscope,[status(thm)],[f_3_2]) ).
fof(f_3_4,plain,
( ! [U_15,U_13] :
( U_13 = singleton(U_15)
| ? [U_11] :
( ~ in(U_11,U_13)
& U_11 = U_15 )
| ( sK1(U_15,U_13) != U_15
& in(sK1(U_15,U_13),U_13) ) )
& ! [U_14,U_12] :
( ( ! [U_9] :
( in(U_9,U_12)
| U_9 != U_14 )
& ! [U_8] :
( U_8 = U_14
| ~ in(U_8,U_12) ) )
| U_12 != singleton(U_14) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(U_10,sK1(U_15,U_13))],[f_3_3]) ).
fof(f_3_5,plain,
( ! [U_15,U_13] :
( U_13 = singleton(U_15)
| ( ~ in(sK2(U_15,U_13),U_13)
& sK2(U_15,U_13) = U_15 )
| ( sK1(U_15,U_13) != U_15
& in(sK1(U_15,U_13),U_13) ) )
& ! [U_14,U_12] :
( ( ! [U_9] :
( in(U_9,U_12)
| U_9 != U_14 )
& ! [U_8] :
( U_8 = U_14
| ~ in(U_8,U_12) ) )
| U_12 != singleton(U_14) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2]),skolemize(U_11,sK2(U_15,U_13))],[f_3_4]) ).
cnf(f_3_7,plain,
( in(U_9,U_12)
| U_9 != U_14
| U_12 != singleton(U_14) ),
inference(clausify,[status(thm)],[f_3_5]) ).
fof(f_4_1,plain,
! [A] :
( ( A = empty_set
| ? [B] : in(B,A) )
& ( ! [B] : ~ in(B,A)
| A != empty_set ) ),
inference(fof_nnf,[status(thm)],[d1_xboole_0]) ).
fof(f_4_2,plain,
! [U_18] :
( ( U_18 = empty_set
| ? [U_17] : in(U_17,U_18) )
& ( ! [U_16] : ~ in(U_16,U_18)
| U_18 != empty_set ) ),
inference(variable_rename,[status(thm)],[f_4_1]) ).
fof(f_4_3,plain,
( ! [U_20] :
( U_20 = empty_set
| ? [U_17] : in(U_17,U_20) )
& ! [U_19] :
( ! [U_16] : ~ in(U_16,U_19)
| U_19 != empty_set ) ),
inference(miniscope,[status(thm)],[f_4_2]) ).
fof(f_4_4,plain,
( ! [U_20] :
( U_20 = empty_set
| in(sK3(U_20),U_20) )
& ! [U_19] :
( ! [U_16] : ~ in(U_16,U_19)
| U_19 != empty_set ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3]),skolemize(U_17,sK3(U_20))],[f_4_3]) ).
cnf(f_4_5,plain,
( ~ in(U_16,U_19)
| U_19 != empty_set ),
inference(clausify,[status(thm)],[f_4_4]) ).
fof(f_5_1,plain,
! [A,B,C] :
( ( C = set_union2(A,B)
| ? [D] :
( ( ~ in(D,C)
& ( in(D,B)
| in(D,A) ) )
| ( ~ in(D,B)
& ~ in(D,A)
& in(D,C) ) ) )
& ( ! [D] :
( ( in(D,C)
| ( ~ in(D,B)
& ~ in(D,A) ) )
& ( in(D,B)
| in(D,A)
| ~ in(D,C) ) )
| C != set_union2(A,B) ) ),
inference(fof_nnf,[status(thm)],[d2_xboole_0]) ).
fof(f_5_2,plain,
! [U_25,U_24,U_23] :
( ( U_23 = set_union2(U_25,U_24)
| ? [U_22] :
( ( ~ in(U_22,U_23)
& ( in(U_22,U_24)
| in(U_22,U_25) ) )
| ( ~ in(U_22,U_24)
& ~ in(U_22,U_25)
& in(U_22,U_23) ) ) )
& ( ! [U_21] :
( ( in(U_21,U_23)
| ( ~ in(U_21,U_24)
& ~ in(U_21,U_25) ) )
& ( in(U_21,U_24)
| in(U_21,U_25)
| ~ in(U_21,U_23) ) )
| U_23 != set_union2(U_25,U_24) ) ),
inference(variable_rename,[status(thm)],[f_5_1]) ).
fof(f_5_3,plain,
( ! [U_35,U_33,U_31] :
( U_31 = set_union2(U_35,U_33)
| ? [U_29] :
( ~ in(U_29,U_31)
& ( in(U_29,U_33)
| in(U_29,U_35) ) )
| ? [U_28] :
( ~ in(U_28,U_33)
& ~ in(U_28,U_35)
& in(U_28,U_31) ) )
& ! [U_34,U_32,U_30] :
( ( ! [U_27] :
( in(U_27,U_30)
| ( ~ in(U_27,U_32)
& ~ in(U_27,U_34) ) )
& ! [U_26] :
( in(U_26,U_32)
| in(U_26,U_34)
| ~ in(U_26,U_30) ) )
| U_30 != set_union2(U_34,U_32) ) ),
inference(miniscope,[status(thm)],[f_5_2]) ).
fof(f_5_4,plain,
( ! [U_35,U_33,U_31] :
( U_31 = set_union2(U_35,U_33)
| ? [U_29] :
( ~ in(U_29,U_31)
& ( in(U_29,U_33)
| in(U_29,U_35) ) )
| ( ~ in(sK4(U_35,U_33,U_31),U_33)
& ~ in(sK4(U_35,U_33,U_31),U_35)
& in(sK4(U_35,U_33,U_31),U_31) ) )
& ! [U_34,U_32,U_30] :
( ( ! [U_27] :
( in(U_27,U_30)
| ( ~ in(U_27,U_32)
& ~ in(U_27,U_34) ) )
& ! [U_26] :
( in(U_26,U_32)
| in(U_26,U_34)
| ~ in(U_26,U_30) ) )
| U_30 != set_union2(U_34,U_32) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4]),skolemize(U_28,sK4(U_35,U_33,U_31))],[f_5_3]) ).
fof(f_5_5,plain,
( ! [U_35,U_33,U_31] :
( U_31 = set_union2(U_35,U_33)
| ( ~ in(sK5(U_35,U_33,U_31),U_31)
& ( in(sK5(U_35,U_33,U_31),U_33)
| in(sK5(U_35,U_33,U_31),U_35) ) )
| ( ~ in(sK4(U_35,U_33,U_31),U_33)
& ~ in(sK4(U_35,U_33,U_31),U_35)
& in(sK4(U_35,U_33,U_31),U_31) ) )
& ! [U_34,U_32,U_30] :
( ( ! [U_27] :
( in(U_27,U_30)
| ( ~ in(U_27,U_32)
& ~ in(U_27,U_34) ) )
& ! [U_26] :
( in(U_26,U_32)
| in(U_26,U_34)
| ~ in(U_26,U_30) ) )
| U_30 != set_union2(U_34,U_32) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK5]),skolemize(U_29,sK5(U_35,U_33,U_31))],[f_5_4]) ).
cnf(f_5_8,plain,
( ~ in(U_27,U_32)
| in(U_27,U_30)
| U_30 != set_union2(U_34,U_32) ),
inference(clausify,[status(thm)],[f_5_5]) ).
fof(f_9_1,plain,
! [A,B] : set_union2(A,A) = A,
inference(fof_nnf,[status(thm)],[idempotence_k2_xboole_0]) ).
fof(f_9_2,plain,
! [U_41,U_40] : set_union2(U_41,U_41) = U_41,
inference(variable_rename,[status(thm)],[f_9_1]) ).
fof(f_9_3,plain,
! [U_41] : set_union2(U_41,U_41) = U_41,
inference(miniscope,[status(thm)],[f_9_2]) ).
cnf(f_9_4,plain,
set_union2(U_41,U_41) = U_41,
inference(clausify,[status(thm)],[f_9_3]) ).
fof(f_12_1,negated_conjecture,
~ ! [A,B] : set_union2(singleton(A),B) != empty_set,
inference(negate,[status(cth)],[t49_zfmisc_1]) ).
fof(f_12_2,negated_conjecture,
? [A,B] : set_union2(singleton(A),B) = empty_set,
inference(fof_nnf,[status(thm)],[f_12_1]) ).
fof(f_12_3,negated_conjecture,
? [U_45,U_44] : set_union2(singleton(U_45),U_44) = empty_set,
inference(variable_rename,[status(thm)],[f_12_2]) ).
fof(f_12_4,negated_conjecture,
? [U_44] : set_union2(singleton(sK8),U_44) = empty_set,
inference(skolemize,[status(esa),new_symbols(skolem,[sK8]),skolemize(U_45,sK8)],[f_12_3]) ).
fof(f_12_5,negated_conjecture,
set_union2(singleton(sK8),sK9) = empty_set,
inference(skolemize,[status(esa),new_symbols(skolem,[sK9]),skolemize(U_44,sK9)],[f_12_4]) ).
fof(f_12_6,negated_conjecture,
set_union2(singleton(sK8),sK9) = empty_set,
inference(definitional_conversion,[status(esa)],[f_12_5]) ).
cnf(f_12_7,negated_conjecture,
set_union2(singleton(sK8),sK9) = empty_set,
inference(clausify,[status(thm)],[f_12_6]) ).
cnf(equality_1,axiom,
Eq_x_0 = Eq_x_0,
theory(equality,[reflexivity]) ).
cnf(t1,plain,
( ~ in(set_union2(sK8,sK8),set_union2(singleton(sK8),sK9))
| set_union2(singleton(sK8),sK9) != empty_set ),
inference(start,[status(thm),parent(0:0)],[f_4_5]) ).
cnf(t2,plain,
set_union2(singleton(sK8),sK9) = empty_set,
inference(extension,[status(thm),parent(t1:1)],[f_12_7]) ).
cnf(t3,plain,
$false,
inference(connection,[status(thm),parent(t2:1)],[t2:1,t1:1]) ).
cnf(t4,plain,
( ~ in(set_union2(sK8,sK8),singleton(sK8))
| set_union2(singleton(sK8),sK9) != set_union2(sK9,singleton(sK8))
| in(set_union2(sK8,sK8),set_union2(singleton(sK8),sK9)) ),
inference(extension,[status(thm),parent(t1:2)],[f_5_8]) ).
cnf(t5,plain,
$false,
inference(connection,[status(thm),parent(t4:1)],[t4:1,t1:2]) ).
cnf(t6,plain,
set_union2(singleton(sK8),sK9) = set_union2(sK9,singleton(sK8)),
inference(extension,[status(thm),parent(t4:2)],[f_2_3]) ).
cnf(t7,plain,
$false,
inference(connection,[status(thm),parent(t6:1)],[t6:1,t4:2]) ).
cnf(t8,plain,
( set_union2(sK8,sK8) != sK8
| singleton(sK8) != singleton(sK8)
| in(set_union2(sK8,sK8),singleton(sK8)) ),
inference(extension,[status(thm),parent(t4:3)],[f_3_7]) ).
cnf(t9,plain,
$false,
inference(connection,[status(thm),parent(t8:1)],[t8:1,t4:3]) ).
cnf(t10,plain,
singleton(sK8) = singleton(sK8),
inference(extension,[status(thm),parent(t8:2)],[equality_1]) ).
cnf(t11,plain,
$false,
inference(connection,[status(thm),parent(t10:1)],[t10:1,t8:2]) ).
cnf(t12,plain,
set_union2(sK8,sK8) = sK8,
inference(extension,[status(thm),parent(t8:3)],[f_9_4]) ).
cnf(t13,plain,
$false,
inference(connection,[status(thm),parent(t12:1)],[t12:1,t8:3]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET908+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
% 0.09/0.35 % Computer : n019.cluster.edu
% 0.09/0.35 % Model : x86_64 x86_64
% 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.35 % Memory : 8046.5625MB
% 0.09/0.35 % OS : Linux 6.8.0-71-generic
% 0.09/0.35 % CPULimit : 300
% 0.09/0.35 % WCLimit : 300
% 0.09/0.35 % DateTime : Sat Sep 19 23:07:22 UTC 2026
% 0.09/0.35 % CPUTime :
% 1.35/1.69 % SZS status Theorem for theBenchmark
% 1.35/1.69 % SZS output start Proof for theBenchmark
% See solution above
%------------------------------------------------------------------------------