%------------------------------------------------------------------------------
% File : ConnectPP---0.7.2
% Problem : NUM623+3 : 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 : n005.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 08:52:53 AM UTC 2026
% Result : Theorem 30.78s 31.04s
% Output : Proof 30.78s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 8
% Syntax : Number of formulae : 56 ( 24 unt; 0 def)
% Number of atoms : 123 ( 20 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 106 ( 39 ~; 35 |; 27 &)
% ( 0 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 13 ( 13 usr; 9 con; 0-2 aty)
% Number of variables : 28 ( 0 sgn 20 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(mLessASymm,axiom,
! [W0,W1] :
( ( aElementOf0(W1,szNzAzT0)
& aElementOf0(W0,szNzAzT0) )
=> ( ( sdtlseqdt0(W1,W0)
& sdtlseqdt0(W0,W1) )
=> W0 = W1 ) ),
file('theBenchmark.p',mLessASymm) ).
fof(m__5106,hypothesis,
( aSubsetOf0(xQ,szNzAzT0)
& ! [W0] :
( aElementOf0(W0,xQ)
=> aElementOf0(W0,szNzAzT0) ) ),
file('theBenchmark.p',m__5106) ).
fof(m__5147,hypothesis,
( xp = szmzizndt0(xQ)
& ! [W0] :
( aElementOf0(W0,xQ)
=> sdtlseqdt0(xp,W0) )
& aElementOf0(xp,xQ) ),
file('theBenchmark.p',m__5147) ).
fof(m__5173,hypothesis,
aElementOf0(xp,xQ),
file('theBenchmark.p',m__5173) ).
fof(m__5365,hypothesis,
( ? [W0] :
( sdtlpdtrp0(xe,W0) = xx
& aElementOf0(W0,sdtlbdtrb0(xd,szDzizrdt0(xd))) )
& aElementOf0(xx,szNzAzT0) ),
file('theBenchmark.p',m__5365) ).
fof(m__5401,hypothesis,
! [W0] :
( aElementOf0(W0,sdtlpdtrp0(xN,xm))
=> sdtlseqdt0(xx,W0) ),
file('theBenchmark.p',m__5401) ).
fof(m__5481,hypothesis,
( aElementOf0(xx,xQ)
& aElementOf0(xp,sdtlpdtrp0(xN,xm)) ),
file('theBenchmark.p',m__5481) ).
fof(m__,conjecture,
xp = xx,
file('theBenchmark.p',m__) ).
fof(f_35_1,plain,
! [W0,W1] :
( W0 = W1
| ~ sdtlseqdt0(W1,W0)
| ~ sdtlseqdt0(W0,W1)
| ~ aElementOf0(W1,szNzAzT0)
| ~ aElementOf0(W0,szNzAzT0) ),
inference(fof_nnf,[status(thm)],[mLessASymm]) ).
fof(f_35_2,plain,
! [U_76,U_75] :
( U_76 = U_75
| ~ sdtlseqdt0(U_75,U_76)
| ~ sdtlseqdt0(U_76,U_75)
| ~ aElementOf0(U_75,szNzAzT0)
| ~ aElementOf0(U_76,szNzAzT0) ),
inference(variable_rename,[status(thm)],[f_35_1]) ).
fof(f_35_3,plain,
! [U_76,U_75] :
( U_76 = U_75
| ~ sdtlseqdt0(U_75,U_76)
| ~ sdtlseqdt0(U_76,U_75)
| ~ aElementOf0(U_75,szNzAzT0)
| ~ aElementOf0(U_76,szNzAzT0) ),
inference(definitional_conversion,[status(esa)],[f_35_2]) ).
cnf(f_35_4,plain,
( U_76 = U_75
| ~ sdtlseqdt0(U_75,U_76)
| ~ sdtlseqdt0(U_76,U_75)
| ~ aElementOf0(U_75,szNzAzT0)
| ~ aElementOf0(U_76,szNzAzT0) ),
inference(clausify,[status(thm)],[f_35_3]) ).
fof(f_101_1,plain,
( aSubsetOf0(xQ,szNzAzT0)
& ! [W0] :
( aElementOf0(W0,szNzAzT0)
| ~ aElementOf0(W0,xQ) ) ),
inference(fof_nnf,[status(thm)],[m__5106]) ).
fof(f_101_2,plain,
( aSubsetOf0(xQ,szNzAzT0)
& ! [U_343] :
( aElementOf0(U_343,szNzAzT0)
| ~ aElementOf0(U_343,xQ) ) ),
inference(variable_rename,[status(thm)],[f_101_1]) ).
fof(f_101_3,plain,
( aSubsetOf0(xQ,szNzAzT0)
& ! [U_343] :
( aElementOf0(U_343,szNzAzT0)
| ~ aElementOf0(U_343,xQ) ) ),
inference(definitional_conversion,[status(esa)],[f_101_2]) ).
cnf(f_101_4,plain,
( aElementOf0(U_343,szNzAzT0)
| ~ aElementOf0(U_343,xQ) ),
inference(clausify,[status(thm)],[f_101_3]) ).
fof(f_103_1,plain,
( xp = szmzizndt0(xQ)
& ! [W0] :
( sdtlseqdt0(xp,W0)
| ~ aElementOf0(W0,xQ) )
& aElementOf0(xp,xQ) ),
inference(fof_nnf,[status(thm)],[m__5147]) ).
fof(f_103_2,plain,
( xp = szmzizndt0(xQ)
& ! [U_346] :
( sdtlseqdt0(xp,U_346)
| ~ aElementOf0(U_346,xQ) )
& aElementOf0(xp,xQ) ),
inference(variable_rename,[status(thm)],[f_103_1]) ).
fof(f_103_3,plain,
( xp = szmzizndt0(xQ)
& ! [U_346] :
( sdtlseqdt0(xp,U_346)
| ~ aElementOf0(U_346,xQ) )
& aElementOf0(xp,xQ) ),
inference(definitional_conversion,[status(esa)],[f_103_2]) ).
cnf(f_103_5,plain,
( sdtlseqdt0(xp,U_346)
| ~ aElementOf0(U_346,xQ) ),
inference(clausify,[status(thm)],[f_103_3]) ).
fof(f_105_1,plain,
aElementOf0(xp,xQ),
inference(fof_nnf,[status(thm)],[m__5173]) ).
fof(f_105_2,plain,
aElementOf0(xp,xQ),
inference(definitional_conversion,[status(esa)],[f_105_1]) ).
cnf(f_105_3,plain,
aElementOf0(xp,xQ),
inference(clausify,[status(thm)],[f_105_2]) ).
fof(f_114_1,plain,
( ? [W0] :
( sdtlpdtrp0(xe,W0) = xx
& aElementOf0(W0,sdtlbdtrb0(xd,szDzizrdt0(xd))) )
& aElementOf0(xx,szNzAzT0) ),
inference(fof_nnf,[status(thm)],[m__5365]) ).
fof(f_114_2,plain,
( ? [U_354] :
( sdtlpdtrp0(xe,U_354) = xx
& aElementOf0(U_354,sdtlbdtrb0(xd,szDzizrdt0(xd))) )
& aElementOf0(xx,szNzAzT0) ),
inference(variable_rename,[status(thm)],[f_114_1]) ).
fof(f_114_3,plain,
( sdtlpdtrp0(xe,sK56) = xx
& aElementOf0(sK56,sdtlbdtrb0(xd,szDzizrdt0(xd)))
& aElementOf0(xx,szNzAzT0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK56]),skolemize(U_354,sK56)],[f_114_2]) ).
fof(f_114_4,plain,
( sdtlpdtrp0(xe,sK56) = xx
& aElementOf0(sK56,sdtlbdtrb0(xd,szDzizrdt0(xd)))
& aElementOf0(xx,szNzAzT0) ),
inference(definitional_conversion,[status(esa)],[f_114_3]) ).
cnf(f_114_5,plain,
aElementOf0(xx,szNzAzT0),
inference(clausify,[status(thm)],[f_114_4]) ).
fof(f_116_1,plain,
! [W0] :
( sdtlseqdt0(xx,W0)
| ~ aElementOf0(W0,sdtlpdtrp0(xN,xm)) ),
inference(fof_nnf,[status(thm)],[m__5401]) ).
fof(f_116_2,plain,
! [U_355] :
( sdtlseqdt0(xx,U_355)
| ~ aElementOf0(U_355,sdtlpdtrp0(xN,xm)) ),
inference(variable_rename,[status(thm)],[f_116_1]) ).
fof(f_116_3,plain,
! [U_355] :
( sdtlseqdt0(xx,U_355)
| ~ aElementOf0(U_355,sdtlpdtrp0(xN,xm)) ),
inference(definitional_conversion,[status(esa)],[f_116_2]) ).
cnf(f_116_4,plain,
( sdtlseqdt0(xx,U_355)
| ~ aElementOf0(U_355,sdtlpdtrp0(xN,xm)) ),
inference(clausify,[status(thm)],[f_116_3]) ).
fof(f_119_1,plain,
( aElementOf0(xx,xQ)
& aElementOf0(xp,sdtlpdtrp0(xN,xm)) ),
inference(fof_nnf,[status(thm)],[m__5481]) ).
fof(f_119_2,plain,
( aElementOf0(xx,xQ)
& aElementOf0(xp,sdtlpdtrp0(xN,xm)) ),
inference(definitional_conversion,[status(esa)],[f_119_1]) ).
cnf(f_119_3,plain,
aElementOf0(xp,sdtlpdtrp0(xN,xm)),
inference(clausify,[status(thm)],[f_119_2]) ).
cnf(f_119_4,plain,
aElementOf0(xx,xQ),
inference(clausify,[status(thm)],[f_119_2]) ).
fof(f_120_1,negated_conjecture,
xp != xx,
inference(negate,[status(cth)],[m__]) ).
fof(f_120_2,negated_conjecture,
xp != xx,
inference(definitional_conversion,[status(esa)],[f_120_1]) ).
cnf(f_120_3,negated_conjecture,
xp != xx,
inference(clausify,[status(thm)],[f_120_2]) ).
cnf(t1,plain,
xp != xx,
inference(start,[status(thm),parent(0:0)],[f_120_3]) ).
cnf(t2,plain,
( ~ aElementOf0(xx,szNzAzT0)
| ~ sdtlseqdt0(xp,xx)
| ~ sdtlseqdt0(xx,xp)
| ~ aElementOf0(xp,szNzAzT0)
| xp = xx ),
inference(extension,[status(thm),parent(t1:1)],[f_35_4]) ).
cnf(t3,plain,
$false,
inference(connection,[status(thm),parent(t2:1)],[t2:1,t1:1]) ).
cnf(t4,plain,
( ~ aElementOf0(xp,xQ)
| aElementOf0(xp,szNzAzT0) ),
inference(extension,[status(thm),parent(t2:2)],[f_101_4]) ).
cnf(t5,plain,
$false,
inference(connection,[status(thm),parent(t4:1)],[t4:1,t2:2]) ).
cnf(t6,plain,
aElementOf0(xp,xQ),
inference(extension,[status(thm),parent(t4:2)],[f_105_3]) ).
cnf(t7,plain,
$false,
inference(connection,[status(thm),parent(t6:1)],[t6:1,t4:2]) ).
cnf(t8,plain,
( ~ aElementOf0(xp,sdtlpdtrp0(xN,xm))
| sdtlseqdt0(xx,xp) ),
inference(extension,[status(thm),parent(t2:3)],[f_116_4]) ).
cnf(t9,plain,
$false,
inference(connection,[status(thm),parent(t8:1)],[t8:1,t2:3]) ).
cnf(t10,plain,
aElementOf0(xp,sdtlpdtrp0(xN,xm)),
inference(extension,[status(thm),parent(t8:2)],[f_119_3]) ).
cnf(t11,plain,
$false,
inference(connection,[status(thm),parent(t10:1)],[t10:1,t8:2]) ).
cnf(t12,plain,
( ~ aElementOf0(xx,xQ)
| sdtlseqdt0(xp,xx) ),
inference(extension,[status(thm),parent(t2:4)],[f_103_5]) ).
cnf(t13,plain,
$false,
inference(connection,[status(thm),parent(t12:1)],[t12:1,t2:4]) ).
cnf(t14,plain,
aElementOf0(xx,xQ),
inference(extension,[status(thm),parent(t12:2)],[f_119_4]) ).
cnf(t15,plain,
$false,
inference(connection,[status(thm),parent(t14:1)],[t14:1,t12:2]) ).
cnf(t16,plain,
aElementOf0(xx,szNzAzT0),
inference(extension,[status(thm),parent(t2:5)],[f_114_5]) ).
cnf(t17,plain,
$false,
inference(connection,[status(thm),parent(t16:1)],[t16:1,t2:5]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : NUM623+3 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.03 This is a FOF_CAX_RFO_SEQ problem
% 0.00/0.03 % Command : /export/starexec/sandbox/solver/bin/connect++ --verbosity 1 --no-colour --tptp-proof --schedule default --timeout 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.11/0.37 % Computer : n005.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Sat Sep 19 19:00:03 UTC 2026
% 0.11/0.37 % CPUTime :
% 30.78/31.04 % SZS status Theorem for theBenchmark
% 30.78/31.04 % SZS output start Proof for theBenchmark
% See solution above
%------------------------------------------------------------------------------