%------------------------------------------------------------------------------
% File : ConnectPP---0.7.2
% Problem : SET891+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 : 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 08:57:45 AM UTC 2026
% Result : Theorem 0.14s 0.39s
% Output : Proof 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 5
% Syntax : Number of formulae : 27 ( 23 unt; 0 def)
% Number of atoms : 33 ( 29 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 20 ( 14 ~; 6 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 2 con; 0-2 aty)
% Number of variables : 30 ( 0 sgn 16 !; 5 ?)
% Comments :
%------------------------------------------------------------------------------
fof(l52_zfmisc_1,axiom,
! [A,B] : union(unordered_pair(A,B)) = set_union2(A,B),
file('theBenchmark.p',l52_zfmisc_1) ).
fof(t32_zfmisc_1,conjecture,
! [A,B] : union(unordered_pair(singleton(A),singleton(B))) = unordered_pair(A,B),
file('theBenchmark.p',t32_zfmisc_1) ).
fof(t41_enumset1,axiom,
! [A,B] : unordered_pair(A,B) = set_union2(singleton(A),singleton(B)),
file('theBenchmark.p',t41_enumset1) ).
fof(f_6_1,plain,
! [A,B] : union(unordered_pair(A,B)) = set_union2(A,B),
inference(fof_nnf,[status(thm)],[l52_zfmisc_1]) ).
fof(f_6_2,plain,
! [U_11,U_10] : union(unordered_pair(U_11,U_10)) = set_union2(U_11,U_10),
inference(variable_rename,[status(thm)],[f_6_1]) ).
cnf(f_6_3,plain,
union(unordered_pair(U_11,U_10)) = set_union2(U_11,U_10),
inference(clausify,[status(thm)],[f_6_2]) ).
fof(f_9_1,negated_conjecture,
~ ! [A,B] : union(unordered_pair(singleton(A),singleton(B))) = unordered_pair(A,B),
inference(negate,[status(cth)],[t32_zfmisc_1]) ).
fof(f_9_2,negated_conjecture,
? [A,B] : union(unordered_pair(singleton(A),singleton(B))) != unordered_pair(A,B),
inference(fof_nnf,[status(thm)],[f_9_1]) ).
fof(f_9_3,negated_conjecture,
? [U_15,U_14] : union(unordered_pair(singleton(U_15),singleton(U_14))) != unordered_pair(U_15,U_14),
inference(variable_rename,[status(thm)],[f_9_2]) ).
fof(f_9_4,negated_conjecture,
? [U_14] : union(unordered_pair(singleton(sK3),singleton(U_14))) != unordered_pair(sK3,U_14),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3]),skolemize(U_15,sK3)],[f_9_3]) ).
fof(f_9_5,negated_conjecture,
union(unordered_pair(singleton(sK3),singleton(sK4))) != unordered_pair(sK3,sK4),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4]),skolemize(U_14,sK4)],[f_9_4]) ).
fof(f_9_6,negated_conjecture,
union(unordered_pair(singleton(sK3),singleton(sK4))) != unordered_pair(sK3,sK4),
inference(definitional_conversion,[status(esa)],[f_9_5]) ).
cnf(f_9_7,negated_conjecture,
union(unordered_pair(singleton(sK3),singleton(sK4))) != unordered_pair(sK3,sK4),
inference(clausify,[status(thm)],[f_9_6]) ).
fof(f_10_1,plain,
! [A,B] : unordered_pair(A,B) = set_union2(singleton(A),singleton(B)),
inference(fof_nnf,[status(thm)],[t41_enumset1]) ).
fof(f_10_2,plain,
! [U_17,U_16] : unordered_pair(U_17,U_16) = set_union2(singleton(U_17),singleton(U_16)),
inference(variable_rename,[status(thm)],[f_10_1]) ).
cnf(f_10_3,plain,
unordered_pair(U_17,U_16) = set_union2(singleton(U_17),singleton(U_16)),
inference(clausify,[status(thm)],[f_10_2]) ).
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(t1,plain,
union(unordered_pair(singleton(sK3),singleton(sK4))) != unordered_pair(sK3,sK4),
inference(start,[status(thm),parent(0:0)],[f_9_7]) ).
cnf(t2,plain,
( set_union2(singleton(sK3),singleton(sK4)) != unordered_pair(sK3,sK4)
| union(unordered_pair(singleton(sK3),singleton(sK4))) != set_union2(singleton(sK3),singleton(sK4))
| union(unordered_pair(singleton(sK3),singleton(sK4))) = unordered_pair(sK3,sK4) ),
inference(extension,[status(thm),parent(t1:1)],[equality_3]) ).
cnf(t3,plain,
$false,
inference(connection,[status(thm),parent(t2:1)],[t2:1,t1:1]) ).
cnf(t4,plain,
union(unordered_pair(singleton(sK3),singleton(sK4))) = set_union2(singleton(sK3),singleton(sK4)),
inference(extension,[status(thm),parent(t2:2)],[f_6_3]) ).
cnf(t5,plain,
$false,
inference(connection,[status(thm),parent(t4:1)],[t4:1,t2:2]) ).
cnf(t6,plain,
( unordered_pair(sK3,sK4) != set_union2(singleton(sK3),singleton(sK4))
| set_union2(singleton(sK3),singleton(sK4)) = unordered_pair(sK3,sK4) ),
inference(extension,[status(thm),parent(t2:3)],[equality_2]) ).
cnf(t7,plain,
$false,
inference(connection,[status(thm),parent(t6:1)],[t6:1,t2:3]) ).
cnf(t8,plain,
unordered_pair(sK3,sK4) = set_union2(singleton(sK3),singleton(sK4)),
inference(extension,[status(thm),parent(t6:2)],[f_10_3]) ).
cnf(t9,plain,
$false,
inference(connection,[status(thm),parent(t8:1)],[t8:1,t6:2]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET891+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/sandbox2/solver/bin/connect++ --verbosity 1 --no-colour --tptp-proof --schedule default --timeout 300 /export/starexec/sandbox2/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 23:07:27 UTC 2026
% 0.14/0.36 % CPUTime :
% 0.14/0.39 % SZS status Theorem for theBenchmark
% 0.14/0.39 % SZS output start Proof for theBenchmark
% See solution above
%------------------------------------------------------------------------------