%------------------------------------------------------------------------------
% File : ConnectPP---0.7.2
% Problem : LAT382+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 : n004.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 08:48:28 AM UTC 2026
% Result : Theorem 0.38s 0.67s
% Output : Proof 0.38s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 7
% Syntax : Number of formulae : 93 ( 66 unt; 1 def)
% Number of atoms : 207 ( 10 equ)
% Maximal formula atoms : 12 ( 2 avg)
% Number of connectives : 202 ( 88 ~; 84 |; 22 &)
% ( 1 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 3 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 9 ( 7 usr; 1 prp; 0-3 aty)
% Number of functors : 5 ( 5 usr; 4 con; 0-3 aty)
% Number of variables : 51 ( 0 sgn 34 !; 3 ?)
% 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(mDefInf,definition,
! [W0] :
( aSet0(W0)
=> ! [W1] :
( aSubsetOf0(W1,W0)
=> ! [W2] :
( aInfimumOfIn0(W2,W1,W0)
<=> ( ! [W3] :
( aLowerBoundOfIn0(W3,W1,W0)
=> sdtlseqdt0(W3,W2) )
& aLowerBoundOfIn0(W2,W1,W0)
& aElementOf0(W2,W0) ) ) ) ),
file('theBenchmark.p',mDefInf) ).
fof(m__773,hypothesis,
aSet0(xT),
file('theBenchmark.p',m__773) ).
fof(m__773_01,hypothesis,
aSubsetOf0(xS,xT),
file('theBenchmark.p',m__773_01) ).
fof(m__792,hypothesis,
( aInfimumOfIn0(xv,xS,xT)
& aInfimumOfIn0(xu,xS,xT) ),
file('theBenchmark.p',m__792) ).
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_12_1,plain,
! [W0] :
( ! [W1] :
( ! [W2] :
( ( aInfimumOfIn0(W2,W1,W0)
| ? [W3] :
( ~ sdtlseqdt0(W3,W2)
& aLowerBoundOfIn0(W3,W1,W0) )
| ~ aLowerBoundOfIn0(W2,W1,W0)
| ~ aElementOf0(W2,W0) )
& ( ( ! [W3] :
( sdtlseqdt0(W3,W2)
| ~ aLowerBoundOfIn0(W3,W1,W0) )
& aLowerBoundOfIn0(W2,W1,W0)
& aElementOf0(W2,W0) )
| ~ aInfimumOfIn0(W2,W1,W0) ) )
| ~ aSubsetOf0(W1,W0) )
| ~ aSet0(W0) ),
inference(fof_nnf,[status(thm)],[mDefInf]) ).
fof(f_12_2,plain,
! [U_39] :
( ! [U_38] :
( ! [U_37] :
( ( aInfimumOfIn0(U_37,U_38,U_39)
| ? [U_36] :
( ~ sdtlseqdt0(U_36,U_37)
& aLowerBoundOfIn0(U_36,U_38,U_39) )
| ~ aLowerBoundOfIn0(U_37,U_38,U_39)
| ~ aElementOf0(U_37,U_39) )
& ( ( ! [U_35] :
( sdtlseqdt0(U_35,U_37)
| ~ aLowerBoundOfIn0(U_35,U_38,U_39) )
& aLowerBoundOfIn0(U_37,U_38,U_39)
& aElementOf0(U_37,U_39) )
| ~ aInfimumOfIn0(U_37,U_38,U_39) ) )
| ~ aSubsetOf0(U_38,U_39) )
| ~ aSet0(U_39) ),
inference(variable_rename,[status(thm)],[f_12_1]) ).
fof(f_12_3,plain,
! [U_39] :
( ! [U_38] :
( ( ! [U_41] :
( aInfimumOfIn0(U_41,U_38,U_39)
| ? [U_36] :
( ~ sdtlseqdt0(U_36,U_41)
& aLowerBoundOfIn0(U_36,U_38,U_39) )
| ~ aLowerBoundOfIn0(U_41,U_38,U_39)
| ~ aElementOf0(U_41,U_39) )
& ! [U_40] :
( ( ! [U_35] :
( sdtlseqdt0(U_35,U_40)
| ~ aLowerBoundOfIn0(U_35,U_38,U_39) )
& aLowerBoundOfIn0(U_40,U_38,U_39)
& aElementOf0(U_40,U_39) )
| ~ aInfimumOfIn0(U_40,U_38,U_39) ) )
| ~ aSubsetOf0(U_38,U_39) )
| ~ aSet0(U_39) ),
inference(miniscope,[status(thm)],[f_12_2]) ).
fof(f_12_4,plain,
! [U_39] :
( ! [U_38] :
( ( ! [U_41] :
( aInfimumOfIn0(U_41,U_38,U_39)
| ( ~ sdtlseqdt0(sK5(U_39,U_38,U_41),U_41)
& aLowerBoundOfIn0(sK5(U_39,U_38,U_41),U_38,U_39) )
| ~ aLowerBoundOfIn0(U_41,U_38,U_39)
| ~ aElementOf0(U_41,U_39) )
& ! [U_40] :
( ( ! [U_35] :
( sdtlseqdt0(U_35,U_40)
| ~ aLowerBoundOfIn0(U_35,U_38,U_39) )
& aLowerBoundOfIn0(U_40,U_38,U_39)
& aElementOf0(U_40,U_39) )
| ~ aInfimumOfIn0(U_40,U_38,U_39) ) )
| ~ aSubsetOf0(U_38,U_39) )
| ~ aSet0(U_39) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK5]),skolemize(U_36,sK5(U_39,U_38,U_41))],[f_12_3]) ).
cnf(f_12_5,plain,
( aElementOf0(U_40,U_39)
| ~ aInfimumOfIn0(U_40,U_38,U_39)
| ~ aSubsetOf0(U_38,U_39)
| ~ aSet0(U_39) ),
inference(clausify,[status(thm)],[f_12_4]) ).
cnf(f_12_6,plain,
( aLowerBoundOfIn0(U_40,U_38,U_39)
| ~ aInfimumOfIn0(U_40,U_38,U_39)
| ~ aSubsetOf0(U_38,U_39)
| ~ aSet0(U_39) ),
inference(clausify,[status(thm)],[f_12_4]) ).
cnf(f_12_7,plain,
( sdtlseqdt0(U_35,U_40)
| ~ aLowerBoundOfIn0(U_35,U_38,U_39)
| ~ aInfimumOfIn0(U_40,U_38,U_39)
| ~ aSubsetOf0(U_38,U_39)
| ~ aSet0(U_39) ),
inference(clausify,[status(thm)],[f_12_4]) ).
fof(f_15_1,plain,
aSet0(xT),
inference(fof_nnf,[status(thm)],[m__773]) ).
cnf(f_15_2,plain,
aSet0(xT),
inference(clausify,[status(thm)],[f_15_1]) ).
fof(f_16_1,plain,
aSubsetOf0(xS,xT),
inference(fof_nnf,[status(thm)],[m__773_01]) ).
cnf(f_16_2,plain,
aSubsetOf0(xS,xT),
inference(clausify,[status(thm)],[f_16_1]) ).
fof(f_17_1,plain,
( aInfimumOfIn0(xv,xS,xT)
& aInfimumOfIn0(xu,xS,xT) ),
inference(fof_nnf,[status(thm)],[m__792]) ).
cnf(f_17_2,plain,
aInfimumOfIn0(xu,xS,xT),
inference(clausify,[status(thm)],[f_17_1]) ).
cnf(f_17_3,plain,
aInfimumOfIn0(xv,xS,xT),
inference(clausify,[status(thm)],[f_17_1]) ).
fof(f_18_1,negated_conjecture,
xu != xv,
inference(negate,[status(cth)],[m__]) ).
fof(f_18_2,negated_conjecture,
xu != xv,
inference(definitional_conversion,[status(esa)],[f_18_1]) ).
cnf(f_18_3,negated_conjecture,
xu != xv,
inference(clausify,[status(thm)],[f_18_2]) ).
cnf(t1,plain,
xu != xv,
inference(start,[status(thm),parent(0:0)],[f_18_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_15_2]) ).
cnf(t7,plain,
$false,
inference(connection,[status(thm),parent(t6:1)],[t6:1,t4:2]) ).
cnf(l3,lemma,
aSet0(xT),
inference(lemma,[status(cth),parent(t4:2),below(t2:2)],[t4:2]) ).
cnf(t8,plain,
( ~ aSubsetOf0(xS,xT)
| ~ aInfimumOfIn0(xu,xS,xT)
| ~ aSet0(xT)
| aElementOf0(xu,xT) ),
inference(extension,[status(thm),parent(t4:3)],[f_12_5]) ).
cnf(t9,plain,
$false,
inference(connection,[status(thm),parent(t8:1)],[t8:1,t4:3]) ).
cnf(t10,plain,
aSet0(xT),
inference(lemma_extension,[status(thm),parent(t8:2)],[l3:1]) ).
cnf(t11,plain,
$false,
inference(connection,[status(thm),parent(t10:1)],[t10:1,t8:2]) ).
cnf(t12,plain,
aInfimumOfIn0(xu,xS,xT),
inference(extension,[status(thm),parent(t8:3)],[f_17_2]) ).
cnf(t13,plain,
$false,
inference(connection,[status(thm),parent(t12:1)],[t12:1,t8:3]) ).
cnf(t14,plain,
aSubsetOf0(xS,xT),
inference(extension,[status(thm),parent(t8:4)],[f_16_2]) ).
cnf(t15,plain,
$false,
inference(connection,[status(thm),parent(t14:1)],[t14:1,t8:4]) ).
cnf(t16,plain,
( ~ aSubsetOf0(xS,xT)
| ~ aInfimumOfIn0(xu,xS,xT)
| ~ aLowerBoundOfIn0(xv,xS,xT)
| ~ aSet0(xT)
| sdtlseqdt0(xv,xu) ),
inference(extension,[status(thm),parent(t2:3)],[f_12_7]) ).
cnf(t17,plain,
$false,
inference(connection,[status(thm),parent(t16:1)],[t16:1,t2:3]) ).
cnf(t18,plain,
aSet0(xT),
inference(extension,[status(thm),parent(t16:2)],[f_15_2]) ).
cnf(t19,plain,
$false,
inference(connection,[status(thm),parent(t18:1)],[t18:1,t16:2]) ).
cnf(l8,lemma,
aSet0(xT),
inference(lemma,[status(cth),parent(t16:2),below(t2:3)],[t16:2]) ).
cnf(t20,plain,
( ~ aSubsetOf0(xS,xT)
| ~ aInfimumOfIn0(xv,xS,xT)
| ~ aSet0(xT)
| aLowerBoundOfIn0(xv,xS,xT) ),
inference(extension,[status(thm),parent(t16:3)],[f_12_6]) ).
cnf(t21,plain,
$false,
inference(connection,[status(thm),parent(t20:1)],[t20:1,t16:3]) ).
cnf(t22,plain,
aSet0(xT),
inference(lemma_extension,[status(thm),parent(t20:2)],[l8:1]) ).
cnf(t23,plain,
$false,
inference(connection,[status(thm),parent(t22:1)],[t22:1,t20:2]) ).
cnf(t24,plain,
aInfimumOfIn0(xv,xS,xT),
inference(extension,[status(thm),parent(t20:3)],[f_17_3]) ).
cnf(t25,plain,
$false,
inference(connection,[status(thm),parent(t24:1)],[t24:1,t20:3]) ).
cnf(t26,plain,
aSubsetOf0(xS,xT),
inference(extension,[status(thm),parent(t20:4)],[f_16_2]) ).
cnf(t27,plain,
$false,
inference(connection,[status(thm),parent(t26:1)],[t26:1,t20:4]) ).
cnf(t28,plain,
aInfimumOfIn0(xu,xS,xT),
inference(extension,[status(thm),parent(t16:4)],[f_17_2]) ).
cnf(t29,plain,
$false,
inference(connection,[status(thm),parent(t28:1)],[t28:1,t16:4]) ).
cnf(t30,plain,
aSubsetOf0(xS,xT),
inference(extension,[status(thm),parent(t16:5)],[f_16_2]) ).
cnf(t31,plain,
$false,
inference(connection,[status(thm),parent(t30:1)],[t30:1,t16:5]) ).
cnf(t32,plain,
( ~ aSubsetOf0(xS,xT)
| ~ aInfimumOfIn0(xv,xS,xT)
| ~ aLowerBoundOfIn0(xu,xS,xT)
| ~ aSet0(xT)
| sdtlseqdt0(xu,xv) ),
inference(extension,[status(thm),parent(t2:4)],[f_12_7]) ).
cnf(t33,plain,
$false,
inference(connection,[status(thm),parent(t32:1)],[t32:1,t2:4]) ).
cnf(t34,plain,
aSet0(xT),
inference(extension,[status(thm),parent(t32:2)],[f_15_2]) ).
cnf(t35,plain,
$false,
inference(connection,[status(thm),parent(t34:1)],[t34:1,t32:2]) ).
cnf(l15,lemma,
aSet0(xT),
inference(lemma,[status(cth),parent(t32:2),below(t2:4)],[t32:2]) ).
cnf(t36,plain,
( ~ aSubsetOf0(xS,xT)
| ~ aInfimumOfIn0(xu,xS,xT)
| ~ aSet0(xT)
| aLowerBoundOfIn0(xu,xS,xT) ),
inference(extension,[status(thm),parent(t32:3)],[f_12_6]) ).
cnf(t37,plain,
$false,
inference(connection,[status(thm),parent(t36:1)],[t36:1,t32:3]) ).
cnf(t38,plain,
aSet0(xT),
inference(lemma_extension,[status(thm),parent(t36:2)],[l15:1]) ).
cnf(t39,plain,
$false,
inference(connection,[status(thm),parent(t38:1)],[t38:1,t36:2]) ).
cnf(t40,plain,
aInfimumOfIn0(xu,xS,xT),
inference(extension,[status(thm),parent(t36:3)],[f_17_2]) ).
cnf(t41,plain,
$false,
inference(connection,[status(thm),parent(t40:1)],[t40:1,t36:3]) ).
cnf(t42,plain,
aSubsetOf0(xS,xT),
inference(extension,[status(thm),parent(t36:4)],[f_16_2]) ).
cnf(t43,plain,
$false,
inference(connection,[status(thm),parent(t42:1)],[t42:1,t36:4]) ).
cnf(t44,plain,
aInfimumOfIn0(xv,xS,xT),
inference(extension,[status(thm),parent(t32:4)],[f_17_3]) ).
cnf(t45,plain,
$false,
inference(connection,[status(thm),parent(t44:1)],[t44:1,t32:4]) ).
cnf(t46,plain,
aSubsetOf0(xS,xT),
inference(extension,[status(thm),parent(t32:5)],[f_16_2]) ).
cnf(t47,plain,
$false,
inference(connection,[status(thm),parent(t46:1)],[t46:1,t32:5]) ).
cnf(t48,plain,
( ~ aElementOf0(xv,xT)
| ~ aSet0(xT)
| aElement0(xv) ),
inference(extension,[status(thm),parent(t2:5)],[f_3_3]) ).
cnf(t49,plain,
$false,
inference(connection,[status(thm),parent(t48:1)],[t48:1,t2:5]) ).
cnf(t50,plain,
aSet0(xT),
inference(extension,[status(thm),parent(t48:2)],[f_15_2]) ).
cnf(t51,plain,
$false,
inference(connection,[status(thm),parent(t50:1)],[t50:1,t48:2]) ).
cnf(l22,lemma,
aSet0(xT),
inference(lemma,[status(cth),parent(t48:2),below(t2:5)],[t48:2]) ).
cnf(t52,plain,
( ~ aSubsetOf0(xS,xT)
| ~ aInfimumOfIn0(xv,xS,xT)
| ~ aSet0(xT)
| aElementOf0(xv,xT) ),
inference(extension,[status(thm),parent(t48:3)],[f_12_5]) ).
cnf(t53,plain,
$false,
inference(connection,[status(thm),parent(t52:1)],[t52:1,t48:3]) ).
cnf(t54,plain,
aSet0(xT),
inference(lemma_extension,[status(thm),parent(t52:2)],[l22:1]) ).
cnf(t55,plain,
$false,
inference(connection,[status(thm),parent(t54:1)],[t54:1,t52:2]) ).
cnf(t56,plain,
aInfimumOfIn0(xv,xS,xT),
inference(extension,[status(thm),parent(t52:3)],[f_17_3]) ).
cnf(t57,plain,
$false,
inference(connection,[status(thm),parent(t56:1)],[t56:1,t52:3]) ).
cnf(t58,plain,
aSubsetOf0(xS,xT),
inference(extension,[status(thm),parent(t52:4)],[f_16_2]) ).
cnf(t59,plain,
$false,
inference(connection,[status(thm),parent(t58:1)],[t58:1,t52:4]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : LAT382+1 : 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/sandbox2/solver/bin/connect++ --verbosity 1 --no-colour --tptp-proof --schedule default --timeout 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.35 % Computer : n004.cluster.edu
% 0.09/0.35 % Model : x86_64 x86_64
% 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.35 % Memory : 8046.5625MB
% 0.09/0.35 % OS : Linux 6.8.0-71-generic
% 0.09/0.35 % CPULimit : 300
% 0.09/0.35 % WCLimit : 300
% 0.09/0.35 % DateTime : Sat Sep 19 13:50:21 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.38/0.67 % SZS status Theorem for theBenchmark
% 0.38/0.67 % SZS output start Proof for theBenchmark
% See solution above
%------------------------------------------------------------------------------