%------------------------------------------------------------------------------
% File : ConnectPP---0.7.2
% Problem : SEU150+1 : TPTP v9.3.1. Released v3.3.0.
% 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 : n016.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 08:58:13 AM UTC 2026
% Result : Theorem 0.08s 0.38s
% Output : Proof 0.08s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 5
% Syntax : Number of formulae : 38 ( 18 unt; 0 def)
% Number of atoms : 61 ( 53 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 46 ( 23 ~; 14 |; 6 &)
% ( 0 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 43 ( 1 sgn 24 !; 9 ?)
% Comments :
%------------------------------------------------------------------------------
fof(commutativity_k2_tarski,axiom,
! [A,B] : unordered_pair(A,B) = unordered_pair(B,A),
file('theBenchmark.p',commutativity_k2_tarski) ).
fof(t8_zfmisc_1,axiom,
! [A,B,C] :
( singleton(A) = unordered_pair(B,C)
=> A = B ),
file('theBenchmark.p',t8_zfmisc_1) ).
fof(t9_zfmisc_1,conjecture,
! [A,B,C] :
( singleton(A) = unordered_pair(B,C)
=> B = C ),
file('theBenchmark.p',t9_zfmisc_1) ).
fof(f_1_1,plain,
! [A,B] : unordered_pair(A,B) = unordered_pair(B,A),
inference(fof_nnf,[status(thm)],[commutativity_k2_tarski]) ).
fof(f_1_2,plain,
! [U_1,U_0] : unordered_pair(U_1,U_0) = unordered_pair(U_0,U_1),
inference(variable_rename,[status(thm)],[f_1_1]) ).
cnf(f_1_3,plain,
unordered_pair(U_1,U_0) = unordered_pair(U_0,U_1),
inference(clausify,[status(thm)],[f_1_2]) ).
fof(f_4_1,plain,
! [A,B,C] :
( A = B
| singleton(A) != unordered_pair(B,C) ),
inference(fof_nnf,[status(thm)],[t8_zfmisc_1]) ).
fof(f_4_2,plain,
! [U_4,U_3,U_2] :
( U_4 = U_3
| singleton(U_4) != unordered_pair(U_3,U_2) ),
inference(variable_rename,[status(thm)],[f_4_1]) ).
fof(f_4_3,plain,
! [U_4,U_3] :
( ! [U_2] : singleton(U_4) != unordered_pair(U_3,U_2)
| U_4 = U_3 ),
inference(miniscope,[status(thm)],[f_4_2]) ).
cnf(f_4_4,plain,
( singleton(U_4) != unordered_pair(U_3,U_2)
| U_4 = U_3 ),
inference(clausify,[status(thm)],[f_4_3]) ).
fof(f_5_1,negated_conjecture,
~ ! [A,B,C] :
( singleton(A) = unordered_pair(B,C)
=> B = C ),
inference(negate,[status(cth)],[t9_zfmisc_1]) ).
fof(f_5_2,negated_conjecture,
? [A,B,C] :
( B != C
& singleton(A) = unordered_pair(B,C) ),
inference(fof_nnf,[status(thm)],[f_5_1]) ).
fof(f_5_3,negated_conjecture,
? [U_7,U_6,U_5] :
( U_6 != U_5
& singleton(U_7) = unordered_pair(U_6,U_5) ),
inference(variable_rename,[status(thm)],[f_5_2]) ).
fof(f_5_4,negated_conjecture,
? [U_6,U_5] :
( U_6 != U_5
& singleton(sK1) = unordered_pair(U_6,U_5) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(U_7,sK1)],[f_5_3]) ).
fof(f_5_5,negated_conjecture,
? [U_5] :
( sK2 != U_5
& singleton(sK1) = unordered_pair(sK2,U_5) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2]),skolemize(U_6,sK2)],[f_5_4]) ).
fof(f_5_6,negated_conjecture,
( sK2 != sK3
& singleton(sK1) = unordered_pair(sK2,sK3) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3]),skolemize(U_5,sK3)],[f_5_5]) ).
fof(f_5_7,negated_conjecture,
( sK2 != sK3
& singleton(sK1) = unordered_pair(sK2,sK3) ),
inference(definitional_conversion,[status(esa)],[f_5_6]) ).
cnf(f_5_8,negated_conjecture,
singleton(sK1) = unordered_pair(sK2,sK3),
inference(clausify,[status(thm)],[f_5_7]) ).
cnf(f_5_9,negated_conjecture,
sK2 != sK3,
inference(clausify,[status(thm)],[f_5_7]) ).
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,
sK2 != sK3,
inference(start,[status(thm),parent(0:0)],[f_5_9]) ).
cnf(t2,plain,
( sK1 != sK3
| sK2 != sK1
| sK2 = sK3 ),
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,
( sK1 != sK2
| sK2 = sK1 ),
inference(extension,[status(thm),parent(t2:2)],[equality_2]) ).
cnf(t5,plain,
$false,
inference(connection,[status(thm),parent(t4:1)],[t4:1,t2:2]) ).
cnf(t6,plain,
( singleton(sK1) != unordered_pair(sK2,sK3)
| sK1 = sK2 ),
inference(extension,[status(thm),parent(t4:2)],[f_4_4]) ).
cnf(t7,plain,
$false,
inference(connection,[status(thm),parent(t6:1)],[t6:1,t4:2]) ).
cnf(t8,plain,
singleton(sK1) = unordered_pair(sK2,sK3),
inference(extension,[status(thm),parent(t6:2)],[f_5_8]) ).
cnf(t9,plain,
$false,
inference(connection,[status(thm),parent(t8:1)],[t8:1,t6:2]) ).
cnf(t10,plain,
( singleton(sK1) != unordered_pair(sK3,sK2)
| sK1 = sK3 ),
inference(extension,[status(thm),parent(t2:3)],[f_4_4]) ).
cnf(t11,plain,
$false,
inference(connection,[status(thm),parent(t10:1)],[t10:1,t2:3]) ).
cnf(t12,plain,
( unordered_pair(sK2,sK3) != unordered_pair(sK3,sK2)
| singleton(sK1) != unordered_pair(sK2,sK3)
| singleton(sK1) = unordered_pair(sK3,sK2) ),
inference(extension,[status(thm),parent(t10:2)],[equality_3]) ).
cnf(t13,plain,
$false,
inference(connection,[status(thm),parent(t12:1)],[t12:1,t10:2]) ).
cnf(t14,plain,
singleton(sK1) = unordered_pair(sK2,sK3),
inference(extension,[status(thm),parent(t12:2)],[f_5_8]) ).
cnf(t15,plain,
$false,
inference(connection,[status(thm),parent(t14:1)],[t14:1,t12:2]) ).
cnf(t16,plain,
unordered_pair(sK2,sK3) = unordered_pair(sK3,sK2),
inference(extension,[status(thm),parent(t12:3)],[f_1_3]) ).
cnf(t17,plain,
$false,
inference(connection,[status(thm),parent(t16:1)],[t16:1,t12:3]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU150+1 : TPTP v9.3.1. Released v3.3.0.
% 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
% 0.08/0.36 % Computer : n016.cluster.edu
% 0.08/0.36 % Model : x86_64 x86_64
% 0.08/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.36 % Memory : 8046.5625MB
% 0.08/0.36 % OS : Linux 6.8.0-71-generic
% 0.08/0.36 % CPULimit : 300
% 0.08/0.36 % WCLimit : 300
% 0.08/0.36 % DateTime : Sat Sep 19 23:27:37 UTC 2026
% 0.08/0.37 % CPUTime :
% 0.08/0.38 % SZS status Theorem for theBenchmark
% 0.08/0.38 % SZS output start Proof for theBenchmark
% See solution above
%------------------------------------------------------------------------------