%------------------------------------------------------------------------------
% File : ConnectPP---0.7.2
% Problem : SET881+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 : n006.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 08:57:43 AM UTC 2026
% Result : Theorem 0.46s 1.16s
% Output : Proof 0.46s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 5
% Syntax : Number of formulae : 34 ( 20 unt; 0 def)
% Number of atoms : 118 ( 82 equ)
% Maximal formula atoms : 14 ( 3 avg)
% Number of connectives : 139 ( 55 ~; 48 |; 33 &)
% ( 3 <=>; 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 : 8 ( 8 usr; 3 con; 0-3 aty)
% Number of variables : 75 ( 1 sgn 56 !; 10 ?)
% Comments :
%------------------------------------------------------------------------------
fof(commutativity_k2_tarski,axiom,
! [A,B] : unordered_pair(A,B) = unordered_pair(B,A),
file('theBenchmark.p',commutativity_k2_tarski) ).
fof(d2_tarski,axiom,
! [A,B,C] :
( C = unordered_pair(A,B)
<=> ! [D] :
( in(D,C)
<=> ( D = B
| D = A ) ) ),
file('theBenchmark.p',d2_tarski) ).
fof(l36_zfmisc_1,axiom,
! [A,B] :
( set_difference(singleton(A),B) = empty_set
<=> in(A,B) ),
file('theBenchmark.p',l36_zfmisc_1) ).
fof(t22_zfmisc_1,conjecture,
! [A,B] : set_difference(singleton(A),unordered_pair(A,B)) = empty_set,
file('theBenchmark.p',t22_zfmisc_1) ).
fof(f_2_1,plain,
! [A,B] : unordered_pair(A,B) = unordered_pair(B,A),
inference(fof_nnf,[status(thm)],[commutativity_k2_tarski]) ).
fof(f_2_2,plain,
! [U_3,U_2] : unordered_pair(U_3,U_2) = unordered_pair(U_2,U_3),
inference(variable_rename,[status(thm)],[f_2_1]) ).
cnf(f_2_3,plain,
unordered_pair(U_3,U_2) = unordered_pair(U_2,U_3),
inference(clausify,[status(thm)],[f_2_2]) ).
fof(f_3_1,plain,
! [A,B,C] :
( ( C = unordered_pair(A,B)
| ? [D] :
( ( ~ in(D,C)
& ( D = B
| D = A ) )
| ( D != B
& D != A
& in(D,C) ) ) )
& ( ! [D] :
( ( in(D,C)
| ( D != B
& D != A ) )
& ( D = B
| D = A
| ~ in(D,C) ) )
| C != unordered_pair(A,B) ) ),
inference(fof_nnf,[status(thm)],[d2_tarski]) ).
fof(f_3_2,plain,
! [U_8,U_7,U_6] :
( ( U_6 = unordered_pair(U_8,U_7)
| ? [U_5] :
( ( ~ in(U_5,U_6)
& ( U_5 = U_7
| U_5 = U_8 ) )
| ( U_5 != U_7
& U_5 != U_8
& in(U_5,U_6) ) ) )
& ( ! [U_4] :
( ( in(U_4,U_6)
| ( U_4 != U_7
& U_4 != U_8 ) )
& ( U_4 = U_7
| U_4 = U_8
| ~ in(U_4,U_6) ) )
| U_6 != unordered_pair(U_8,U_7) ) ),
inference(variable_rename,[status(thm)],[f_3_1]) ).
fof(f_3_3,plain,
( ! [U_18,U_16,U_14] :
( U_14 = unordered_pair(U_18,U_16)
| ? [U_12] :
( ~ in(U_12,U_14)
& ( U_12 = U_16
| U_12 = U_18 ) )
| ? [U_11] :
( U_11 != U_16
& U_11 != U_18
& in(U_11,U_14) ) )
& ! [U_17,U_15,U_13] :
( ( ! [U_10] :
( in(U_10,U_13)
| ( U_10 != U_15
& U_10 != U_17 ) )
& ! [U_9] :
( U_9 = U_15
| U_9 = U_17
| ~ in(U_9,U_13) ) )
| U_13 != unordered_pair(U_17,U_15) ) ),
inference(miniscope,[status(thm)],[f_3_2]) ).
fof(f_3_4,plain,
( ! [U_18,U_16,U_14] :
( U_14 = unordered_pair(U_18,U_16)
| ? [U_12] :
( ~ in(U_12,U_14)
& ( U_12 = U_16
| U_12 = U_18 ) )
| ( sK1(U_18,U_16,U_14) != U_16
& sK1(U_18,U_16,U_14) != U_18
& in(sK1(U_18,U_16,U_14),U_14) ) )
& ! [U_17,U_15,U_13] :
( ( ! [U_10] :
( in(U_10,U_13)
| ( U_10 != U_15
& U_10 != U_17 ) )
& ! [U_9] :
( U_9 = U_15
| U_9 = U_17
| ~ in(U_9,U_13) ) )
| U_13 != unordered_pair(U_17,U_15) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(U_11,sK1(U_18,U_16,U_14))],[f_3_3]) ).
fof(f_3_5,plain,
( ! [U_18,U_16,U_14] :
( U_14 = unordered_pair(U_18,U_16)
| ( ~ in(sK2(U_18,U_16,U_14),U_14)
& ( sK2(U_18,U_16,U_14) = U_16
| sK2(U_18,U_16,U_14) = U_18 ) )
| ( sK1(U_18,U_16,U_14) != U_16
& sK1(U_18,U_16,U_14) != U_18
& in(sK1(U_18,U_16,U_14),U_14) ) )
& ! [U_17,U_15,U_13] :
( ( ! [U_10] :
( in(U_10,U_13)
| ( U_10 != U_15
& U_10 != U_17 ) )
& ! [U_9] :
( U_9 = U_15
| U_9 = U_17
| ~ in(U_9,U_13) ) )
| U_13 != unordered_pair(U_17,U_15) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2]),skolemize(U_12,sK2(U_18,U_16,U_14))],[f_3_4]) ).
cnf(f_3_8,plain,
( U_10 != U_15
| in(U_10,U_13)
| U_13 != unordered_pair(U_17,U_15) ),
inference(clausify,[status(thm)],[f_3_5]) ).
fof(f_5_1,plain,
! [A,B] :
( ( set_difference(singleton(A),B) = empty_set
| ~ in(A,B) )
& ( in(A,B)
| set_difference(singleton(A),B) != empty_set ) ),
inference(fof_nnf,[status(thm)],[l36_zfmisc_1]) ).
fof(f_5_2,plain,
! [U_20,U_19] :
( ( set_difference(singleton(U_20),U_19) = empty_set
| ~ in(U_20,U_19) )
& ( in(U_20,U_19)
| set_difference(singleton(U_20),U_19) != empty_set ) ),
inference(variable_rename,[status(thm)],[f_5_1]) ).
fof(f_5_3,plain,
( ! [U_24,U_22] :
( set_difference(singleton(U_24),U_22) = empty_set
| ~ in(U_24,U_22) )
& ! [U_23,U_21] :
( in(U_23,U_21)
| set_difference(singleton(U_23),U_21) != empty_set ) ),
inference(miniscope,[status(thm)],[f_5_2]) ).
cnf(f_5_5,plain,
( set_difference(singleton(U_24),U_22) = empty_set
| ~ in(U_24,U_22) ),
inference(clausify,[status(thm)],[f_5_3]) ).
fof(f_8_1,negated_conjecture,
~ ! [A,B] : set_difference(singleton(A),unordered_pair(A,B)) = empty_set,
inference(negate,[status(cth)],[t22_zfmisc_1]) ).
fof(f_8_2,negated_conjecture,
? [A,B] : set_difference(singleton(A),unordered_pair(A,B)) != empty_set,
inference(fof_nnf,[status(thm)],[f_8_1]) ).
fof(f_8_3,negated_conjecture,
? [U_28,U_27] : set_difference(singleton(U_28),unordered_pair(U_28,U_27)) != empty_set,
inference(variable_rename,[status(thm)],[f_8_2]) ).
fof(f_8_4,negated_conjecture,
? [U_27] : set_difference(singleton(sK5),unordered_pair(sK5,U_27)) != empty_set,
inference(skolemize,[status(esa),new_symbols(skolem,[sK5]),skolemize(U_28,sK5)],[f_8_3]) ).
fof(f_8_5,negated_conjecture,
set_difference(singleton(sK5),unordered_pair(sK5,sK6)) != empty_set,
inference(skolemize,[status(esa),new_symbols(skolem,[sK6]),skolemize(U_27,sK6)],[f_8_4]) ).
fof(f_8_6,negated_conjecture,
set_difference(singleton(sK5),unordered_pair(sK5,sK6)) != empty_set,
inference(definitional_conversion,[status(esa)],[f_8_5]) ).
cnf(f_8_7,negated_conjecture,
set_difference(singleton(sK5),unordered_pair(sK5,sK6)) != empty_set,
inference(clausify,[status(thm)],[f_8_6]) ).
cnf(equality_1,axiom,
Eq_x_0 = Eq_x_0,
theory(equality,[reflexivity]) ).
cnf(t1,plain,
set_difference(singleton(sK5),unordered_pair(sK5,sK6)) != empty_set,
inference(start,[status(thm),parent(0:0)],[f_8_7]) ).
cnf(t2,plain,
( ~ in(sK5,unordered_pair(sK5,sK6))
| set_difference(singleton(sK5),unordered_pair(sK5,sK6)) = empty_set ),
inference(extension,[status(thm),parent(t1:1)],[f_5_5]) ).
cnf(t3,plain,
$false,
inference(connection,[status(thm),parent(t2:1)],[t2:1,t1:1]) ).
cnf(t4,plain,
( sK5 != sK5
| unordered_pair(sK5,sK6) != unordered_pair(sK6,sK5)
| in(sK5,unordered_pair(sK5,sK6)) ),
inference(extension,[status(thm),parent(t2:2)],[f_3_8]) ).
cnf(t5,plain,
$false,
inference(connection,[status(thm),parent(t4:1)],[t4:1,t2:2]) ).
cnf(t6,plain,
unordered_pair(sK5,sK6) = unordered_pair(sK6,sK5),
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,
sK5 = sK5,
inference(extension,[status(thm),parent(t4:3)],[equality_1]) ).
cnf(t9,plain,
$false,
inference(connection,[status(thm),parent(t8:1)],[t8:1,t4:3]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET881+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
% 0.09/0.79 % Computer : n006.cluster.edu
% 0.09/0.79 % Model : x86_64 x86_64
% 0.09/0.79 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.79 % Memory : 8046.5625MB
% 0.09/0.79 % OS : Linux 6.8.0-71-generic
% 0.09/0.79 % CPULimit : 300
% 0.09/0.79 % WCLimit : 300
% 0.09/0.79 % DateTime : Sat Sep 19 23:06:16 UTC 2026
% 0.09/0.79 % CPUTime :
% 0.46/1.16 % SZS status Theorem for theBenchmark
% 0.46/1.16 % SZS output start Proof for theBenchmark
% See solution above
%------------------------------------------------------------------------------