%------------------------------------------------------------------------------
% File : ConnectPP---0.7.2
% Problem : NUM557+1 : TPTP v9.3.1. Released v4.0.0.
% 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 : n012.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 08:52:37 AM UTC 2026
% Result : Theorem 120.14s 120.40s
% Output : Proof 120.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 6
% Syntax : Number of formulae : 35 ( 23 unt; 1 def)
% Number of atoms : 142 ( 44 equ)
% Maximal formula atoms : 18 ( 4 avg)
% Number of connectives : 173 ( 66 ~; 60 |; 44 &)
% ( 2 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 6 con; 0-3 aty)
% Number of variables : 40 ( 0 sgn 30 !; 5 ?)
% Comments :
%------------------------------------------------------------------------------
fof(mDefSel,definition,
! [W0,W1] :
( ( aElementOf0(W1,szNzAzT0)
& aSet0(W0) )
=> ! [W2] :
( W2 = slbdtsldtrb0(W0,W1)
<=> ( ! [W3] :
( aElementOf0(W3,W2)
<=> ( sbrdtbr0(W3) = W1
& aSubsetOf0(W3,W0) ) )
& aSet0(W2) ) ) ),
file('theBenchmark.p',mDefSel) ).
fof(m__2202,hypothesis,
aElementOf0(xk,szNzAzT0),
file('theBenchmark.p',m__2202) ).
fof(m__2202_02,hypothesis,
( xk != sz00
& aSet0(xT)
& aSet0(xS) ),
file('theBenchmark.p',m__2202_02) ).
fof(m__2431,hypothesis,
( sbrdtbr0(xP) = xk
& aSubsetOf0(xP,xS) ),
file('theBenchmark.p',m__2431) ).
fof(m__,conjecture,
aElementOf0(xP,slbdtsldtrb0(xS,xk)),
file('theBenchmark.p',m__) ).
fof(f_57_1,plain,
! [W0,W1] :
( ! [W2] :
( ( W2 = slbdtsldtrb0(W0,W1)
| ? [W3] :
( ( ~ aElementOf0(W3,W2)
& sbrdtbr0(W3) = W1
& aSubsetOf0(W3,W0) )
| ( ( sbrdtbr0(W3) != W1
| ~ aSubsetOf0(W3,W0) )
& aElementOf0(W3,W2) ) )
| ~ aSet0(W2) )
& ( ( ! [W3] :
( ( aElementOf0(W3,W2)
| sbrdtbr0(W3) != W1
| ~ aSubsetOf0(W3,W0) )
& ( ( sbrdtbr0(W3) = W1
& aSubsetOf0(W3,W0) )
| ~ aElementOf0(W3,W2) ) )
& aSet0(W2) )
| W2 != slbdtsldtrb0(W0,W1) ) )
| ~ aElementOf0(W1,szNzAzT0)
| ~ aSet0(W0) ),
inference(fof_nnf,[status(thm)],[mDefSel]) ).
fof(f_57_2,plain,
! [U_133,U_132] :
( ! [U_131] :
( ( U_131 = slbdtsldtrb0(U_133,U_132)
| ? [U_130] :
( ( ~ aElementOf0(U_130,U_131)
& sbrdtbr0(U_130) = U_132
& aSubsetOf0(U_130,U_133) )
| ( ( sbrdtbr0(U_130) != U_132
| ~ aSubsetOf0(U_130,U_133) )
& aElementOf0(U_130,U_131) ) )
| ~ aSet0(U_131) )
& ( ( ! [U_129] :
( ( aElementOf0(U_129,U_131)
| sbrdtbr0(U_129) != U_132
| ~ aSubsetOf0(U_129,U_133) )
& ( ( sbrdtbr0(U_129) = U_132
& aSubsetOf0(U_129,U_133) )
| ~ aElementOf0(U_129,U_131) ) )
& aSet0(U_131) )
| U_131 != slbdtsldtrb0(U_133,U_132) ) )
| ~ aElementOf0(U_132,szNzAzT0)
| ~ aSet0(U_133) ),
inference(variable_rename,[status(thm)],[f_57_1]) ).
fof(f_57_3,plain,
! [U_133,U_132] :
( ( ! [U_139] :
( U_139 = slbdtsldtrb0(U_133,U_132)
| ? [U_137] :
( ~ aElementOf0(U_137,U_139)
& sbrdtbr0(U_137) = U_132
& aSubsetOf0(U_137,U_133) )
| ? [U_136] :
( ( sbrdtbr0(U_136) != U_132
| ~ aSubsetOf0(U_136,U_133) )
& aElementOf0(U_136,U_139) )
| ~ aSet0(U_139) )
& ! [U_138] :
( ( ! [U_135] :
( aElementOf0(U_135,U_138)
| sbrdtbr0(U_135) != U_132
| ~ aSubsetOf0(U_135,U_133) )
& ! [U_134] :
( ( sbrdtbr0(U_134) = U_132
& aSubsetOf0(U_134,U_133) )
| ~ aElementOf0(U_134,U_138) )
& aSet0(U_138) )
| U_138 != slbdtsldtrb0(U_133,U_132) ) )
| ~ aElementOf0(U_132,szNzAzT0)
| ~ aSet0(U_133) ),
inference(miniscope,[status(thm)],[f_57_2]) ).
fof(f_57_4,plain,
! [U_133,U_132] :
( ( ! [U_139] :
( U_139 = slbdtsldtrb0(U_133,U_132)
| ? [U_137] :
( ~ aElementOf0(U_137,U_139)
& sbrdtbr0(U_137) = U_132
& aSubsetOf0(U_137,U_133) )
| ( ( sbrdtbr0(sK14(U_133,U_132,U_139)) != U_132
| ~ aSubsetOf0(sK14(U_133,U_132,U_139),U_133) )
& aElementOf0(sK14(U_133,U_132,U_139),U_139) )
| ~ aSet0(U_139) )
& ! [U_138] :
( ( ! [U_135] :
( aElementOf0(U_135,U_138)
| sbrdtbr0(U_135) != U_132
| ~ aSubsetOf0(U_135,U_133) )
& ! [U_134] :
( ( sbrdtbr0(U_134) = U_132
& aSubsetOf0(U_134,U_133) )
| ~ aElementOf0(U_134,U_138) )
& aSet0(U_138) )
| U_138 != slbdtsldtrb0(U_133,U_132) ) )
| ~ aElementOf0(U_132,szNzAzT0)
| ~ aSet0(U_133) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK14]),skolemize(U_136,sK14(U_133,U_132,U_139))],[f_57_3]) ).
fof(f_57_5,plain,
! [U_133,U_132] :
( ( ! [U_139] :
( U_139 = slbdtsldtrb0(U_133,U_132)
| ( ~ aElementOf0(sK15(U_133,U_132,U_139),U_139)
& sbrdtbr0(sK15(U_133,U_132,U_139)) = U_132
& aSubsetOf0(sK15(U_133,U_132,U_139),U_133) )
| ( ( sbrdtbr0(sK14(U_133,U_132,U_139)) != U_132
| ~ aSubsetOf0(sK14(U_133,U_132,U_139),U_133) )
& aElementOf0(sK14(U_133,U_132,U_139),U_139) )
| ~ aSet0(U_139) )
& ! [U_138] :
( ( ! [U_135] :
( aElementOf0(U_135,U_138)
| sbrdtbr0(U_135) != U_132
| ~ aSubsetOf0(U_135,U_133) )
& ! [U_134] :
( ( sbrdtbr0(U_134) = U_132
& aSubsetOf0(U_134,U_133) )
| ~ aElementOf0(U_134,U_138) )
& aSet0(U_138) )
| U_138 != slbdtsldtrb0(U_133,U_132) ) )
| ~ aElementOf0(U_132,szNzAzT0)
| ~ aSet0(U_133) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK15]),skolemize(U_137,sK15(U_133,U_132,U_139))],[f_57_4]) ).
cnf(f_57_9,plain,
( aElementOf0(U_135,U_138)
| sbrdtbr0(U_135) != U_132
| ~ aSubsetOf0(U_135,U_133)
| U_138 != slbdtsldtrb0(U_133,U_132)
| ~ aElementOf0(U_132,szNzAzT0)
| ~ aSet0(U_133) ),
inference(clausify,[status(thm)],[f_57_5]) ).
fof(f_61_1,plain,
aElementOf0(xk,szNzAzT0),
inference(fof_nnf,[status(thm)],[m__2202]) ).
cnf(f_61_2,plain,
aElementOf0(xk,szNzAzT0),
inference(clausify,[status(thm)],[f_61_1]) ).
fof(f_62_1,plain,
( xk != sz00
& aSet0(xT)
& aSet0(xS) ),
inference(fof_nnf,[status(thm)],[m__2202_02]) ).
cnf(f_62_2,plain,
aSet0(xS),
inference(clausify,[status(thm)],[f_62_1]) ).
fof(f_72_1,plain,
( sbrdtbr0(xP) = xk
& aSubsetOf0(xP,xS) ),
inference(fof_nnf,[status(thm)],[m__2431]) ).
cnf(f_72_2,plain,
aSubsetOf0(xP,xS),
inference(clausify,[status(thm)],[f_72_1]) ).
cnf(f_72_3,plain,
sbrdtbr0(xP) = xk,
inference(clausify,[status(thm)],[f_72_1]) ).
fof(f_73_1,negated_conjecture,
~ aElementOf0(xP,slbdtsldtrb0(xS,xk)),
inference(negate,[status(cth)],[m__]) ).
fof(f_73_2,negated_conjecture,
~ aElementOf0(xP,slbdtsldtrb0(xS,xk)),
inference(definitional_conversion,[status(esa)],[f_73_1]) ).
cnf(f_73_3,negated_conjecture,
~ aElementOf0(xP,slbdtsldtrb0(xS,xk)),
inference(clausify,[status(thm)],[f_73_2]) ).
cnf(equality_1,axiom,
Eq_x_0 = Eq_x_0,
theory(equality,[reflexivity]) ).
cnf(t1,plain,
~ aElementOf0(xP,slbdtsldtrb0(xS,xk)),
inference(start,[status(thm),parent(0:0)],[f_73_3]) ).
cnf(t2,plain,
( ~ aElementOf0(xk,szNzAzT0)
| slbdtsldtrb0(xS,xk) != slbdtsldtrb0(xS,xk)
| ~ aSubsetOf0(xP,xS)
| sbrdtbr0(xP) != xk
| ~ aSet0(xS)
| aElementOf0(xP,slbdtsldtrb0(xS,xk)) ),
inference(extension,[status(thm),parent(t1:1)],[f_57_9]) ).
cnf(t3,plain,
$false,
inference(connection,[status(thm),parent(t2:1)],[t2:1,t1:1]) ).
cnf(t4,plain,
aSet0(xS),
inference(extension,[status(thm),parent(t2:2)],[f_62_2]) ).
cnf(t5,plain,
$false,
inference(connection,[status(thm),parent(t4:1)],[t4:1,t2:2]) ).
cnf(t6,plain,
sbrdtbr0(xP) = xk,
inference(extension,[status(thm),parent(t2:3)],[f_72_3]) ).
cnf(t7,plain,
$false,
inference(connection,[status(thm),parent(t6:1)],[t6:1,t2:3]) ).
cnf(t8,plain,
aSubsetOf0(xP,xS),
inference(extension,[status(thm),parent(t2:4)],[f_72_2]) ).
cnf(t9,plain,
$false,
inference(connection,[status(thm),parent(t8:1)],[t8:1,t2:4]) ).
cnf(t10,plain,
slbdtsldtrb0(xS,xk) = slbdtsldtrb0(xS,xk),
inference(extension,[status(thm),parent(t2:5)],[equality_1]) ).
cnf(t11,plain,
$false,
inference(connection,[status(thm),parent(t10:1)],[t10:1,t2:5]) ).
cnf(t12,plain,
aElementOf0(xk,szNzAzT0),
inference(extension,[status(thm),parent(t2:6)],[f_61_2]) ).
cnf(t13,plain,
$false,
inference(connection,[status(thm),parent(t12:1)],[t12:1,t2:6]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : NUM557+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.01 This is a FOF_THM_RFO_SEQ problem
% 0.00/0.02 % Command : /export/starexec/sandbox2/solver/bin/connect++ --verbosity 1 --no-colour --tptp-proof --schedule default --timeout 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.04/0.30 % Computer : n012.cluster.edu
% 0.04/0.30 % Model : x86_64 x86_64
% 0.04/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.04/0.30 % Memory : 8046.5625MB
% 0.04/0.30 % OS : Linux 6.8.0-71-generic
% 0.04/0.30 % CPULimit : 300
% 0.04/0.30 % WCLimit : 300
% 0.04/0.30 % DateTime : Sat Sep 19 18:47:52 UTC 2026
% 0.04/0.30 % CPUTime :
% 120.14/120.40 % SZS status Theorem for theBenchmark
% 120.14/120.40 % SZS output start Proof for theBenchmark
% See solution above
%------------------------------------------------------------------------------