%------------------------------------------------------------------------------
% File : ConnectPP---0.7.2
% Problem : LAT381+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 : n026.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 08:48:27 AM UTC 2026
% Result : Theorem 120.15s 120.46s
% Output : Proof 120.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 5
% Syntax : Number of formulae : 49 ( 29 unt; 0 def)
% Number of atoms : 190 ( 10 equ)
% Maximal formula atoms : 22 ( 3 avg)
% Number of connectives : 207 ( 66 ~; 56 |; 75 &)
% ( 0 <=>; 10 =>; 0 <=; 0 <~>)
% Maximal formula depth : 19 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 8 ( 6 usr; 1 prp; 0-3 aty)
% Number of functors : 6 ( 6 usr; 4 con; 0-1 aty)
% Number of variables : 45 ( 0 sgn 34 !; 5 ?)
% Comments :
%------------------------------------------------------------------------------
fof(mEOfElem,axiom,
! [W0] :
( aSet0(W0)
=> ! [W1] :
( aElementOf0(W1,W0)
=> aElement0(W1) ) ),
file('theBenchmark.p',mEOfElem) ).
fof(mASymm,axiom,
! [W0,W1] :
( ( aElement0(W1)
& aElement0(W0) )
=> ( ( sdtlseqdt0(W1,W0)
& sdtlseqdt0(W0,W1) )
=> W0 = W1 ) ),
file('theBenchmark.p',mASymm) ).
fof(m__725,hypothesis,
aSet0(xT),
file('theBenchmark.p',m__725) ).
fof(m__744,hypothesis,
( aSupremumOfIn0(xv,xS,xT)
& ! [W0] :
( ( aUpperBoundOfIn0(W0,xS,xT)
| ( ! [W1] :
( aElementOf0(W1,xS)
=> sdtlseqdt0(W1,W0) )
& aElementOf0(W0,xT) ) )
=> sdtlseqdt0(xv,W0) )
& aUpperBoundOfIn0(xv,xS,xT)
& ! [W0] :
( aElementOf0(W0,xS)
=> sdtlseqdt0(W0,xv) )
& aElementOf0(xv,xT)
& aElementOf0(xv,xT)
& aSupremumOfIn0(xu,xS,xT)
& ! [W0] :
( ( aUpperBoundOfIn0(W0,xS,xT)
| ( ! [W1] :
( aElementOf0(W1,xS)
=> sdtlseqdt0(W1,W0) )
& aElementOf0(W0,xT) ) )
=> sdtlseqdt0(xu,W0) )
& aUpperBoundOfIn0(xu,xS,xT)
& ! [W0] :
( aElementOf0(W0,xS)
=> sdtlseqdt0(W0,xu) )
& aElementOf0(xu,xT)
& aElementOf0(xu,xT) ),
file('theBenchmark.p',m__744) ).
fof(m__,conjecture,
xu = xv,
file('theBenchmark.p',m__) ).
fof(f_3_1,plain,
! [W0] :
( ! [W1] :
( aElement0(W1)
| ~ aElementOf0(W1,W0) )
| ~ aSet0(W0) ),
inference(fof_nnf,[status(thm)],[mEOfElem]) ).
fof(f_3_2,plain,
! [U_3] :
( ! [U_2] :
( aElement0(U_2)
| ~ aElementOf0(U_2,U_3) )
| ~ aSet0(U_3) ),
inference(variable_rename,[status(thm)],[f_3_1]) ).
cnf(f_3_3,plain,
( aElement0(U_2)
| ~ aElementOf0(U_2,U_3)
| ~ aSet0(U_3) ),
inference(clausify,[status(thm)],[f_3_2]) ).
fof(f_8_1,plain,
! [W0,W1] :
( W0 = W1
| ~ sdtlseqdt0(W1,W0)
| ~ sdtlseqdt0(W0,W1)
| ~ aElement0(W1)
| ~ aElement0(W0) ),
inference(fof_nnf,[status(thm)],[mASymm]) ).
fof(f_8_2,plain,
! [U_17,U_16] :
( U_17 = U_16
| ~ sdtlseqdt0(U_16,U_17)
| ~ sdtlseqdt0(U_17,U_16)
| ~ aElement0(U_16)
| ~ aElement0(U_17) ),
inference(variable_rename,[status(thm)],[f_8_1]) ).
cnf(f_8_3,plain,
( U_17 = U_16
| ~ sdtlseqdt0(U_16,U_17)
| ~ sdtlseqdt0(U_17,U_16)
| ~ aElement0(U_16)
| ~ aElement0(U_17) ),
inference(clausify,[status(thm)],[f_8_2]) ).
fof(f_14_1,plain,
aSet0(xT),
inference(fof_nnf,[status(thm)],[m__725]) ).
cnf(f_14_2,plain,
aSet0(xT),
inference(clausify,[status(thm)],[f_14_1]) ).
fof(f_16_1,plain,
( aSupremumOfIn0(xv,xS,xT)
& ! [W0] :
( sdtlseqdt0(xv,W0)
| ( ~ aUpperBoundOfIn0(W0,xS,xT)
& ( ? [W1] :
( ~ sdtlseqdt0(W1,W0)
& aElementOf0(W1,xS) )
| ~ aElementOf0(W0,xT) ) ) )
& aUpperBoundOfIn0(xv,xS,xT)
& ! [W0] :
( sdtlseqdt0(W0,xv)
| ~ aElementOf0(W0,xS) )
& aElementOf0(xv,xT)
& aElementOf0(xv,xT)
& aSupremumOfIn0(xu,xS,xT)
& ! [W0] :
( sdtlseqdt0(xu,W0)
| ( ~ aUpperBoundOfIn0(W0,xS,xT)
& ( ? [W1] :
( ~ sdtlseqdt0(W1,W0)
& aElementOf0(W1,xS) )
| ~ aElementOf0(W0,xT) ) ) )
& aUpperBoundOfIn0(xu,xS,xT)
& ! [W0] :
( sdtlseqdt0(W0,xu)
| ~ aElementOf0(W0,xS) )
& aElementOf0(xu,xT)
& aElementOf0(xu,xT) ),
inference(fof_nnf,[status(thm)],[m__744]) ).
fof(f_16_2,plain,
( aSupremumOfIn0(xv,xS,xT)
& ! [U_55] :
( sdtlseqdt0(xv,U_55)
| ( ~ aUpperBoundOfIn0(U_55,xS,xT)
& ( ? [U_54] :
( ~ sdtlseqdt0(U_54,U_55)
& aElementOf0(U_54,xS) )
| ~ aElementOf0(U_55,xT) ) ) )
& aUpperBoundOfIn0(xv,xS,xT)
& ! [U_53] :
( sdtlseqdt0(U_53,xv)
| ~ aElementOf0(U_53,xS) )
& aElementOf0(xv,xT)
& aElementOf0(xv,xT)
& aSupremumOfIn0(xu,xS,xT)
& ! [U_52] :
( sdtlseqdt0(xu,U_52)
| ( ~ aUpperBoundOfIn0(U_52,xS,xT)
& ( ? [U_51] :
( ~ sdtlseqdt0(U_51,U_52)
& aElementOf0(U_51,xS) )
| ~ aElementOf0(U_52,xT) ) ) )
& aUpperBoundOfIn0(xu,xS,xT)
& ! [U_50] :
( sdtlseqdt0(U_50,xu)
| ~ aElementOf0(U_50,xS) )
& aElementOf0(xu,xT)
& aElementOf0(xu,xT) ),
inference(variable_rename,[status(thm)],[f_16_1]) ).
fof(f_16_3,plain,
( aSupremumOfIn0(xv,xS,xT)
& ! [U_55] :
( sdtlseqdt0(xv,U_55)
| ( ~ aUpperBoundOfIn0(U_55,xS,xT)
& ( ? [U_54] :
( ~ sdtlseqdt0(U_54,U_55)
& aElementOf0(U_54,xS) )
| ~ aElementOf0(U_55,xT) ) ) )
& aUpperBoundOfIn0(xv,xS,xT)
& ! [U_53] :
( sdtlseqdt0(U_53,xv)
| ~ aElementOf0(U_53,xS) )
& aElementOf0(xv,xT)
& aElementOf0(xv,xT)
& aSupremumOfIn0(xu,xS,xT)
& ! [U_52] :
( sdtlseqdt0(xu,U_52)
| ( ~ aUpperBoundOfIn0(U_52,xS,xT)
& ( ( ~ sdtlseqdt0(sK7(U_52),U_52)
& aElementOf0(sK7(U_52),xS) )
| ~ aElementOf0(U_52,xT) ) ) )
& aUpperBoundOfIn0(xu,xS,xT)
& ! [U_50] :
( sdtlseqdt0(U_50,xu)
| ~ aElementOf0(U_50,xS) )
& aElementOf0(xu,xT)
& aElementOf0(xu,xT) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK7]),skolemize(U_51,sK7(U_52))],[f_16_2]) ).
fof(f_16_4,plain,
( aSupremumOfIn0(xv,xS,xT)
& ! [U_55] :
( sdtlseqdt0(xv,U_55)
| ( ~ aUpperBoundOfIn0(U_55,xS,xT)
& ( ( ~ sdtlseqdt0(sK8(U_55),U_55)
& aElementOf0(sK8(U_55),xS) )
| ~ aElementOf0(U_55,xT) ) ) )
& aUpperBoundOfIn0(xv,xS,xT)
& ! [U_53] :
( sdtlseqdt0(U_53,xv)
| ~ aElementOf0(U_53,xS) )
& aElementOf0(xv,xT)
& aElementOf0(xv,xT)
& aSupremumOfIn0(xu,xS,xT)
& ! [U_52] :
( sdtlseqdt0(xu,U_52)
| ( ~ aUpperBoundOfIn0(U_52,xS,xT)
& ( ( ~ sdtlseqdt0(sK7(U_52),U_52)
& aElementOf0(sK7(U_52),xS) )
| ~ aElementOf0(U_52,xT) ) ) )
& aUpperBoundOfIn0(xu,xS,xT)
& ! [U_50] :
( sdtlseqdt0(U_50,xu)
| ~ aElementOf0(U_50,xS) )
& aElementOf0(xu,xT)
& aElementOf0(xu,xT) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK8]),skolemize(U_54,sK8(U_55))],[f_16_3]) ).
cnf(f_16_6,plain,
aElementOf0(xu,xT),
inference(clausify,[status(thm)],[f_16_4]) ).
cnf(f_16_8,plain,
aUpperBoundOfIn0(xu,xS,xT),
inference(clausify,[status(thm)],[f_16_4]) ).
cnf(f_16_11,plain,
( ~ aUpperBoundOfIn0(U_52,xS,xT)
| sdtlseqdt0(xu,U_52) ),
inference(clausify,[status(thm)],[f_16_4]) ).
cnf(f_16_14,plain,
aElementOf0(xv,xT),
inference(clausify,[status(thm)],[f_16_4]) ).
cnf(f_16_16,plain,
aUpperBoundOfIn0(xv,xS,xT),
inference(clausify,[status(thm)],[f_16_4]) ).
cnf(f_16_19,plain,
( ~ aUpperBoundOfIn0(U_55,xS,xT)
| sdtlseqdt0(xv,U_55) ),
inference(clausify,[status(thm)],[f_16_4]) ).
fof(f_17_1,negated_conjecture,
xu != xv,
inference(negate,[status(cth)],[m__]) ).
fof(f_17_2,negated_conjecture,
xu != xv,
inference(definitional_conversion,[status(esa)],[f_17_1]) ).
cnf(f_17_3,negated_conjecture,
xu != xv,
inference(clausify,[status(thm)],[f_17_2]) ).
cnf(t1,plain,
xu != xv,
inference(start,[status(thm),parent(0:0)],[f_17_3]) ).
cnf(t2,plain,
( ~ aElement0(xv)
| ~ sdtlseqdt0(xu,xv)
| ~ sdtlseqdt0(xv,xu)
| ~ aElement0(xu)
| xu = xv ),
inference(extension,[status(thm),parent(t1:1)],[f_8_3]) ).
cnf(t3,plain,
$false,
inference(connection,[status(thm),parent(t2:1)],[t2:1,t1:1]) ).
cnf(t4,plain,
( ~ aElementOf0(xu,xT)
| ~ aSet0(xT)
| aElement0(xu) ),
inference(extension,[status(thm),parent(t2:2)],[f_3_3]) ).
cnf(t5,plain,
$false,
inference(connection,[status(thm),parent(t4:1)],[t4:1,t2:2]) ).
cnf(t6,plain,
aSet0(xT),
inference(extension,[status(thm),parent(t4:2)],[f_14_2]) ).
cnf(t7,plain,
$false,
inference(connection,[status(thm),parent(t6:1)],[t6:1,t4:2]) ).
cnf(t8,plain,
aElementOf0(xu,xT),
inference(extension,[status(thm),parent(t4:3)],[f_16_6]) ).
cnf(t9,plain,
$false,
inference(connection,[status(thm),parent(t8:1)],[t8:1,t4:3]) ).
cnf(t10,plain,
( ~ aUpperBoundOfIn0(xu,xS,xT)
| sdtlseqdt0(xv,xu) ),
inference(extension,[status(thm),parent(t2:3)],[f_16_19]) ).
cnf(t11,plain,
$false,
inference(connection,[status(thm),parent(t10:1)],[t10:1,t2:3]) ).
cnf(t12,plain,
aUpperBoundOfIn0(xu,xS,xT),
inference(extension,[status(thm),parent(t10:2)],[f_16_8]) ).
cnf(t13,plain,
$false,
inference(connection,[status(thm),parent(t12:1)],[t12:1,t10:2]) ).
cnf(t14,plain,
( ~ aUpperBoundOfIn0(xv,xS,xT)
| sdtlseqdt0(xu,xv) ),
inference(extension,[status(thm),parent(t2:4)],[f_16_11]) ).
cnf(t15,plain,
$false,
inference(connection,[status(thm),parent(t14:1)],[t14:1,t2:4]) ).
cnf(t16,plain,
aUpperBoundOfIn0(xv,xS,xT),
inference(extension,[status(thm),parent(t14:2)],[f_16_16]) ).
cnf(t17,plain,
$false,
inference(connection,[status(thm),parent(t16:1)],[t16:1,t14:2]) ).
cnf(t18,plain,
( ~ aElementOf0(xv,xT)
| ~ aSet0(xT)
| aElement0(xv) ),
inference(extension,[status(thm),parent(t2:5)],[f_3_3]) ).
cnf(t19,plain,
$false,
inference(connection,[status(thm),parent(t18:1)],[t18:1,t2:5]) ).
cnf(t20,plain,
aSet0(xT),
inference(extension,[status(thm),parent(t18:2)],[f_14_2]) ).
cnf(t21,plain,
$false,
inference(connection,[status(thm),parent(t20:1)],[t20:1,t18:2]) ).
cnf(t22,plain,
aElementOf0(xv,xT),
inference(extension,[status(thm),parent(t18:3)],[f_16_14]) ).
cnf(t23,plain,
$false,
inference(connection,[status(thm),parent(t22:1)],[t22:1,t18:3]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : LAT381+3 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.03 This is a FOF_THM_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
% 0.08/0.35 % Computer : n026.cluster.edu
% 0.08/0.35 % Model : x86_64 x86_64
% 0.08/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.35 % Memory : 8046.5625MB
% 0.08/0.35 % OS : Linux 6.8.0-71-generic
% 0.08/0.35 % CPULimit : 300
% 0.08/0.35 % WCLimit : 300
% 0.08/0.35 % DateTime : Sat Sep 19 13:52:51 UTC 2026
% 0.08/0.36 % CPUTime :
% 120.15/120.46 % SZS status Theorem for theBenchmark
% 120.15/120.46 % SZS output start Proof for theBenchmark
% See solution above
%------------------------------------------------------------------------------