%------------------------------------------------------------------------------
% File : ConnectPP---0.7.2
% Problem : NUM555+1 : TPTP v9.3.1. Released v4.0.0.
% 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 : 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 08:52:37 AM UTC 2026
% Result : Theorem 2.26s 2.58s
% Output : Proof 2.26s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 6
% Syntax : Number of formulae : 32 ( 20 unt; 1 def)
% Number of atoms : 158 ( 38 equ)
% Maximal formula atoms : 22 ( 4 avg)
% Number of connectives : 200 ( 74 ~; 68 |; 55 &)
% ( 2 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 4 con; 0-3 aty)
% Number of variables : 40 ( 0 sgn 30 !; 5 ?)
% Comments :
%------------------------------------------------------------------------------
fof(mDefDiff,definition,
! [W0,W1] :
( ( aElement0(W1)
& aSet0(W0) )
=> ! [W2] :
( W2 = sdtmndt0(W0,W1)
<=> ( ! [W3] :
( aElementOf0(W3,W2)
<=> ( W3 != W1
& aElementOf0(W3,W0)
& aElement0(W3) ) )
& aSet0(W2) ) ) ),
file('theBenchmark.p',mDefDiff) ).
fof(m__2291,hypothesis,
( sbrdtbr0(xQ) = xk
& isFinite0(xQ)
& aSet0(xQ) ),
file('theBenchmark.p',m__2291) ).
fof(m__2304,hypothesis,
( aElementOf0(xy,xQ)
& aElement0(xy) ),
file('theBenchmark.p',m__2304) ).
fof(m__2323,hypothesis,
~ aElementOf0(xx,xQ),
file('theBenchmark.p',m__2323) ).
fof(m__,conjecture,
~ aElementOf0(xx,sdtmndt0(xQ,xy)),
file('theBenchmark.p',m__) ).
fof(f_16_1,plain,
! [W0,W1] :
( ! [W2] :
( ( W2 = sdtmndt0(W0,W1)
| ? [W3] :
( ( ~ aElementOf0(W3,W2)
& W3 != W1
& aElementOf0(W3,W0)
& aElement0(W3) )
| ( ( W3 = W1
| ~ aElementOf0(W3,W0)
| ~ aElement0(W3) )
& aElementOf0(W3,W2) ) )
| ~ aSet0(W2) )
& ( ( ! [W3] :
( ( aElementOf0(W3,W2)
| W3 = W1
| ~ aElementOf0(W3,W0)
| ~ aElement0(W3) )
& ( ( W3 != W1
& aElementOf0(W3,W0)
& aElement0(W3) )
| ~ aElementOf0(W3,W2) ) )
& aSet0(W2) )
| W2 != sdtmndt0(W0,W1) ) )
| ~ aElement0(W1)
| ~ aSet0(W0) ),
inference(fof_nnf,[status(thm)],[mDefDiff]) ).
fof(f_16_2,plain,
! [U_42,U_41] :
( ! [U_40] :
( ( U_40 = sdtmndt0(U_42,U_41)
| ? [U_39] :
( ( ~ aElementOf0(U_39,U_40)
& U_39 != U_41
& aElementOf0(U_39,U_42)
& aElement0(U_39) )
| ( ( U_39 = U_41
| ~ aElementOf0(U_39,U_42)
| ~ aElement0(U_39) )
& aElementOf0(U_39,U_40) ) )
| ~ aSet0(U_40) )
& ( ( ! [U_38] :
( ( aElementOf0(U_38,U_40)
| U_38 = U_41
| ~ aElementOf0(U_38,U_42)
| ~ aElement0(U_38) )
& ( ( U_38 != U_41
& aElementOf0(U_38,U_42)
& aElement0(U_38) )
| ~ aElementOf0(U_38,U_40) ) )
& aSet0(U_40) )
| U_40 != sdtmndt0(U_42,U_41) ) )
| ~ aElement0(U_41)
| ~ aSet0(U_42) ),
inference(variable_rename,[status(thm)],[f_16_1]) ).
fof(f_16_3,plain,
! [U_42,U_41] :
( ( ! [U_48] :
( U_48 = sdtmndt0(U_42,U_41)
| ? [U_46] :
( ~ aElementOf0(U_46,U_48)
& U_46 != U_41
& aElementOf0(U_46,U_42)
& aElement0(U_46) )
| ? [U_45] :
( ( U_45 = U_41
| ~ aElementOf0(U_45,U_42)
| ~ aElement0(U_45) )
& aElementOf0(U_45,U_48) )
| ~ aSet0(U_48) )
& ! [U_47] :
( ( ! [U_44] :
( aElementOf0(U_44,U_47)
| U_44 = U_41
| ~ aElementOf0(U_44,U_42)
| ~ aElement0(U_44) )
& ! [U_43] :
( ( U_43 != U_41
& aElementOf0(U_43,U_42)
& aElement0(U_43) )
| ~ aElementOf0(U_43,U_47) )
& aSet0(U_47) )
| U_47 != sdtmndt0(U_42,U_41) ) )
| ~ aElement0(U_41)
| ~ aSet0(U_42) ),
inference(miniscope,[status(thm)],[f_16_2]) ).
fof(f_16_4,plain,
! [U_42,U_41] :
( ( ! [U_48] :
( U_48 = sdtmndt0(U_42,U_41)
| ? [U_46] :
( ~ aElementOf0(U_46,U_48)
& U_46 != U_41
& aElementOf0(U_46,U_42)
& aElement0(U_46) )
| ( ( sK5(U_42,U_41,U_48) = U_41
| ~ aElementOf0(sK5(U_42,U_41,U_48),U_42)
| ~ aElement0(sK5(U_42,U_41,U_48)) )
& aElementOf0(sK5(U_42,U_41,U_48),U_48) )
| ~ aSet0(U_48) )
& ! [U_47] :
( ( ! [U_44] :
( aElementOf0(U_44,U_47)
| U_44 = U_41
| ~ aElementOf0(U_44,U_42)
| ~ aElement0(U_44) )
& ! [U_43] :
( ( U_43 != U_41
& aElementOf0(U_43,U_42)
& aElement0(U_43) )
| ~ aElementOf0(U_43,U_47) )
& aSet0(U_47) )
| U_47 != sdtmndt0(U_42,U_41) ) )
| ~ aElement0(U_41)
| ~ aSet0(U_42) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK5]),skolemize(U_45,sK5(U_42,U_41,U_48))],[f_16_3]) ).
fof(f_16_5,plain,
! [U_42,U_41] :
( ( ! [U_48] :
( U_48 = sdtmndt0(U_42,U_41)
| ( ~ aElementOf0(sK6(U_42,U_41,U_48),U_48)
& sK6(U_42,U_41,U_48) != U_41
& aElementOf0(sK6(U_42,U_41,U_48),U_42)
& aElement0(sK6(U_42,U_41,U_48)) )
| ( ( sK5(U_42,U_41,U_48) = U_41
| ~ aElementOf0(sK5(U_42,U_41,U_48),U_42)
| ~ aElement0(sK5(U_42,U_41,U_48)) )
& aElementOf0(sK5(U_42,U_41,U_48),U_48) )
| ~ aSet0(U_48) )
& ! [U_47] :
( ( ! [U_44] :
( aElementOf0(U_44,U_47)
| U_44 = U_41
| ~ aElementOf0(U_44,U_42)
| ~ aElement0(U_44) )
& ! [U_43] :
( ( U_43 != U_41
& aElementOf0(U_43,U_42)
& aElement0(U_43) )
| ~ aElementOf0(U_43,U_47) )
& aSet0(U_47) )
| U_47 != sdtmndt0(U_42,U_41) ) )
| ~ aElement0(U_41)
| ~ aSet0(U_42) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK6]),skolemize(U_46,sK6(U_42,U_41,U_48))],[f_16_4]) ).
cnf(f_16_8,plain,
( aElementOf0(U_43,U_42)
| ~ aElementOf0(U_43,U_47)
| U_47 != sdtmndt0(U_42,U_41)
| ~ aElement0(U_41)
| ~ aSet0(U_42) ),
inference(clausify,[status(thm)],[f_16_5]) ).
fof(f_66_1,plain,
( sbrdtbr0(xQ) = xk
& isFinite0(xQ)
& aSet0(xQ) ),
inference(fof_nnf,[status(thm)],[m__2291]) ).
cnf(f_66_2,plain,
aSet0(xQ),
inference(clausify,[status(thm)],[f_66_1]) ).
fof(f_67_1,plain,
( aElementOf0(xy,xQ)
& aElement0(xy) ),
inference(fof_nnf,[status(thm)],[m__2304]) ).
cnf(f_67_2,plain,
aElement0(xy),
inference(clausify,[status(thm)],[f_67_1]) ).
fof(f_68_1,plain,
~ aElementOf0(xx,xQ),
inference(fof_nnf,[status(thm)],[m__2323]) ).
cnf(f_68_2,plain,
~ aElementOf0(xx,xQ),
inference(clausify,[status(thm)],[f_68_1]) ).
fof(f_71_1,negated_conjecture,
aElementOf0(xx,sdtmndt0(xQ,xy)),
inference(negate,[status(cth)],[m__]) ).
fof(f_71_2,negated_conjecture,
aElementOf0(xx,sdtmndt0(xQ,xy)),
inference(definitional_conversion,[status(esa)],[f_71_1]) ).
cnf(f_71_3,negated_conjecture,
aElementOf0(xx,sdtmndt0(xQ,xy)),
inference(clausify,[status(thm)],[f_71_2]) ).
cnf(equality_1,axiom,
Eq_x_0 = Eq_x_0,
theory(equality,[reflexivity]) ).
cnf(t1,plain,
~ aElementOf0(xx,xQ),
inference(start,[status(thm),parent(0:0)],[f_68_2]) ).
cnf(t2,plain,
( ~ aElement0(xy)
| sdtmndt0(xQ,xy) != sdtmndt0(xQ,xy)
| ~ aElementOf0(xx,sdtmndt0(xQ,xy))
| ~ aSet0(xQ)
| aElementOf0(xx,xQ) ),
inference(extension,[status(thm),parent(t1:1)],[f_16_8]) ).
cnf(t3,plain,
$false,
inference(connection,[status(thm),parent(t2:1)],[t2:1,t1:1]) ).
cnf(t4,plain,
aSet0(xQ),
inference(extension,[status(thm),parent(t2:2)],[f_66_2]) ).
cnf(t5,plain,
$false,
inference(connection,[status(thm),parent(t4:1)],[t4:1,t2:2]) ).
cnf(t6,plain,
aElementOf0(xx,sdtmndt0(xQ,xy)),
inference(extension,[status(thm),parent(t2:3)],[f_71_3]) ).
cnf(t7,plain,
$false,
inference(connection,[status(thm),parent(t6:1)],[t6:1,t2:3]) ).
cnf(t8,plain,
sdtmndt0(xQ,xy) = sdtmndt0(xQ,xy),
inference(extension,[status(thm),parent(t2:4)],[equality_1]) ).
cnf(t9,plain,
$false,
inference(connection,[status(thm),parent(t8:1)],[t8:1,t2:4]) ).
cnf(t10,plain,
aElement0(xy),
inference(extension,[status(thm),parent(t2:5)],[f_67_2]) ).
cnf(t11,plain,
$false,
inference(connection,[status(thm),parent(t10:1)],[t10:1,t2:5]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : NUM555+1 : TPTP v9.3.1. Released v4.0.0.
% 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
% 0.07/0.34 % Computer : n006.cluster.edu
% 0.07/0.34 % Model : x86_64 x86_64
% 0.07/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.34 % Memory : 8046.5625MB
% 0.07/0.34 % OS : Linux 6.8.0-71-generic
% 0.07/0.34 % CPULimit : 300
% 0.07/0.34 % WCLimit : 300
% 0.07/0.34 % DateTime : Sat Sep 19 18:47:42 UTC 2026
% 0.07/0.34 % CPUTime :
% 2.26/2.58 % SZS status Theorem for theBenchmark
% 2.26/2.58 % SZS output start Proof for theBenchmark
% See solution above
%------------------------------------------------------------------------------