%------------------------------------------------------------------------------
% File : ConnectPP---0.7.2
% Problem : NUM523+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 : n008.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 08:52:30 AM UTC 2026
% Result : Theorem 17.55s 17.82s
% Output : Proof 17.55s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 8
% Syntax : Number of formulae : 68 ( 41 unt; 1 def)
% Number of atoms : 161 ( 23 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 163 ( 70 ~; 64 |; 24 &)
% ( 1 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 4 con; 0-2 aty)
% Number of variables : 39 ( 0 sgn 26 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(mSortsB_02,axiom,
! [W0,W1] :
( ( aNaturalNumber0(W1)
& aNaturalNumber0(W0) )
=> aNaturalNumber0(sdtasdt0(W0,W1)) ),
file('theBenchmark.p',mSortsB_02) ).
fof(mDefDiv,definition,
! [W0,W1] :
( ( aNaturalNumber0(W1)
& aNaturalNumber0(W0) )
=> ( doDivides0(W0,W1)
<=> ? [W2] :
( W1 = sdtasdt0(W0,W2)
& aNaturalNumber0(W2) ) ) ),
file('theBenchmark.p',mDefDiv) ).
fof(mPDP,axiom,
! [W0,W1,W2] :
( ( aNaturalNumber0(W2)
& aNaturalNumber0(W1)
& aNaturalNumber0(W0) )
=> ( ( doDivides0(W2,sdtasdt0(W0,W1))
& isPrime0(W2) )
=> ( doDivides0(W2,W1)
| doDivides0(W2,W0) ) ) ),
file('theBenchmark.p',mPDP) ).
fof(m__2987,hypothesis,
( xp != sz00
& xm != sz00
& xn != sz00
& aNaturalNumber0(xp)
& aNaturalNumber0(xm)
& aNaturalNumber0(xn) ),
file('theBenchmark.p',m__2987) ).
fof(m__3014,hypothesis,
sdtasdt0(xp,sdtasdt0(xm,xm)) = sdtasdt0(xn,xn),
file('theBenchmark.p',m__3014) ).
fof(m__3025,hypothesis,
isPrime0(xp),
file('theBenchmark.p',m__3025) ).
fof(m__,conjecture,
( doDivides0(xp,xn)
& doDivides0(xp,sdtasdt0(xn,xn)) ),
file('theBenchmark.p',m__) ).
fof(f_5_1,plain,
! [W0,W1] :
( aNaturalNumber0(sdtasdt0(W0,W1))
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) ),
inference(fof_nnf,[status(thm)],[mSortsB_02]) ).
fof(f_5_2,plain,
! [U_4,U_3] :
( aNaturalNumber0(sdtasdt0(U_4,U_3))
| ~ aNaturalNumber0(U_3)
| ~ aNaturalNumber0(U_4) ),
inference(variable_rename,[status(thm)],[f_5_1]) ).
cnf(f_5_3,plain,
( aNaturalNumber0(sdtasdt0(U_4,U_3))
| ~ aNaturalNumber0(U_3)
| ~ aNaturalNumber0(U_4) ),
inference(clausify,[status(thm)],[f_5_2]) ).
fof(f_30_1,plain,
! [W0,W1] :
( ( ( doDivides0(W0,W1)
| ! [W2] :
( W1 != sdtasdt0(W0,W2)
| ~ aNaturalNumber0(W2) ) )
& ( ? [W2] :
( W1 = sdtasdt0(W0,W2)
& aNaturalNumber0(W2) )
| ~ doDivides0(W0,W1) ) )
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) ),
inference(fof_nnf,[status(thm)],[mDefDiv]) ).
fof(f_30_2,plain,
! [U_64,U_63] :
( ( ( doDivides0(U_64,U_63)
| ! [U_62] :
( U_63 != sdtasdt0(U_64,U_62)
| ~ aNaturalNumber0(U_62) ) )
& ( ? [U_61] :
( U_63 = sdtasdt0(U_64,U_61)
& aNaturalNumber0(U_61) )
| ~ doDivides0(U_64,U_63) ) )
| ~ aNaturalNumber0(U_63)
| ~ aNaturalNumber0(U_64) ),
inference(variable_rename,[status(thm)],[f_30_1]) ).
fof(f_30_3,plain,
! [U_64,U_63] :
( ( ( doDivides0(U_64,U_63)
| ! [U_62] :
( U_63 != sdtasdt0(U_64,U_62)
| ~ aNaturalNumber0(U_62) ) )
& ( ( U_63 = sdtasdt0(U_64,sK2(U_64,U_63))
& aNaturalNumber0(sK2(U_64,U_63)) )
| ~ doDivides0(U_64,U_63) ) )
| ~ aNaturalNumber0(U_63)
| ~ aNaturalNumber0(U_64) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2]),skolemize(U_61,sK2(U_64,U_63))],[f_30_2]) ).
cnf(f_30_6,plain,
( doDivides0(U_64,U_63)
| U_63 != sdtasdt0(U_64,U_62)
| ~ aNaturalNumber0(U_62)
| ~ aNaturalNumber0(U_63)
| ~ aNaturalNumber0(U_64) ),
inference(clausify,[status(thm)],[f_30_3]) ).
fof(f_39_1,plain,
! [W0,W1,W2] :
( doDivides0(W2,W1)
| doDivides0(W2,W0)
| ~ doDivides0(W2,sdtasdt0(W0,W1))
| ~ isPrime0(W2)
| ~ aNaturalNumber0(W2)
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) ),
inference(fof_nnf,[status(thm)],[mPDP]) ).
fof(f_39_2,plain,
! [U_91,U_90,U_89] :
( doDivides0(U_89,U_90)
| doDivides0(U_89,U_91)
| ~ doDivides0(U_89,sdtasdt0(U_91,U_90))
| ~ isPrime0(U_89)
| ~ aNaturalNumber0(U_89)
| ~ aNaturalNumber0(U_90)
| ~ aNaturalNumber0(U_91) ),
inference(variable_rename,[status(thm)],[f_39_1]) ).
cnf(f_39_3,plain,
( doDivides0(U_89,U_90)
| doDivides0(U_89,U_91)
| ~ doDivides0(U_89,sdtasdt0(U_91,U_90))
| ~ isPrime0(U_89)
| ~ aNaturalNumber0(U_89)
| ~ aNaturalNumber0(U_90)
| ~ aNaturalNumber0(U_91) ),
inference(clausify,[status(thm)],[f_39_2]) ).
fof(f_40_1,plain,
( xp != sz00
& xm != sz00
& xn != sz00
& aNaturalNumber0(xp)
& aNaturalNumber0(xm)
& aNaturalNumber0(xn) ),
inference(fof_nnf,[status(thm)],[m__2987]) ).
cnf(f_40_2,plain,
aNaturalNumber0(xn),
inference(clausify,[status(thm)],[f_40_1]) ).
cnf(f_40_3,plain,
aNaturalNumber0(xm),
inference(clausify,[status(thm)],[f_40_1]) ).
cnf(f_40_4,plain,
aNaturalNumber0(xp),
inference(clausify,[status(thm)],[f_40_1]) ).
fof(f_42_1,plain,
sdtasdt0(xp,sdtasdt0(xm,xm)) = sdtasdt0(xn,xn),
inference(fof_nnf,[status(thm)],[m__3014]) ).
cnf(f_42_2,plain,
sdtasdt0(xp,sdtasdt0(xm,xm)) = sdtasdt0(xn,xn),
inference(clausify,[status(thm)],[f_42_1]) ).
fof(f_43_1,plain,
isPrime0(xp),
inference(fof_nnf,[status(thm)],[m__3025]) ).
cnf(f_43_2,plain,
isPrime0(xp),
inference(clausify,[status(thm)],[f_43_1]) ).
fof(f_44_1,negated_conjecture,
~ ( doDivides0(xp,xn)
& doDivides0(xp,sdtasdt0(xn,xn)) ),
inference(negate,[status(cth)],[m__]) ).
fof(f_44_2,negated_conjecture,
( ~ doDivides0(xp,xn)
| ~ doDivides0(xp,sdtasdt0(xn,xn)) ),
inference(fof_nnf,[status(thm)],[f_44_1]) ).
fof(f_44_3,negated_conjecture,
( ~ doDivides0(xp,xn)
| ~ doDivides0(xp,sdtasdt0(xn,xn)) ),
inference(definitional_conversion,[status(esa)],[f_44_2]) ).
cnf(f_44_4,negated_conjecture,
( ~ doDivides0(xp,xn)
| ~ doDivides0(xp,sdtasdt0(xn,xn)) ),
inference(clausify,[status(thm)],[f_44_3]) ).
cnf(equality_2,axiom,
( Eq_x_1 = Eq_x_0
| Eq_x_0 != Eq_x_1 ),
theory(equality,[symmetry]) ).
cnf(t1,plain,
( ~ doDivides0(xp,xn)
| ~ doDivides0(xp,sdtasdt0(xn,xn)) ),
inference(start,[status(thm),parent(0:0)],[f_44_4]) ).
cnf(t2,plain,
( ~ aNaturalNumber0(sdtasdt0(xn,xn))
| ~ aNaturalNumber0(sdtasdt0(xm,xm))
| sdtasdt0(xn,xn) != sdtasdt0(xp,sdtasdt0(xm,xm))
| ~ aNaturalNumber0(xp)
| doDivides0(xp,sdtasdt0(xn,xn)) ),
inference(extension,[status(thm),parent(t1:1)],[f_30_6]) ).
cnf(t3,plain,
$false,
inference(connection,[status(thm),parent(t2:1)],[t2:1,t1:1]) ).
cnf(t4,plain,
aNaturalNumber0(xp),
inference(extension,[status(thm),parent(t2:2)],[f_40_4]) ).
cnf(t5,plain,
$false,
inference(connection,[status(thm),parent(t4:1)],[t4:1,t2:2]) ).
cnf(t6,plain,
( sdtasdt0(xp,sdtasdt0(xm,xm)) != sdtasdt0(xn,xn)
| sdtasdt0(xn,xn) = sdtasdt0(xp,sdtasdt0(xm,xm)) ),
inference(extension,[status(thm),parent(t2:3)],[equality_2]) ).
cnf(t7,plain,
$false,
inference(connection,[status(thm),parent(t6:1)],[t6:1,t2:3]) ).
cnf(t8,plain,
sdtasdt0(xp,sdtasdt0(xm,xm)) = sdtasdt0(xn,xn),
inference(extension,[status(thm),parent(t6:2)],[f_42_2]) ).
cnf(t9,plain,
$false,
inference(connection,[status(thm),parent(t8:1)],[t8:1,t6:2]) ).
cnf(t10,plain,
( ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(xm)
| aNaturalNumber0(sdtasdt0(xm,xm)) ),
inference(extension,[status(thm),parent(t2:4)],[f_5_3]) ).
cnf(t11,plain,
$false,
inference(connection,[status(thm),parent(t10:1)],[t10:1,t2:4]) ).
cnf(t12,plain,
aNaturalNumber0(xm),
inference(extension,[status(thm),parent(t10:2)],[f_40_3]) ).
cnf(t13,plain,
$false,
inference(connection,[status(thm),parent(t12:1)],[t12:1,t10:2]) ).
cnf(l6,lemma,
aNaturalNumber0(xm),
inference(lemma,[status(cth),parent(t10:2),below(t2:4)],[t10:2]) ).
cnf(t14,plain,
aNaturalNumber0(xm),
inference(lemma_extension,[status(thm),parent(t10:3)],[l6:1]) ).
cnf(t15,plain,
$false,
inference(connection,[status(thm),parent(t14:1)],[t14:1,t10:3]) ).
cnf(t16,plain,
( ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(xn)
| aNaturalNumber0(sdtasdt0(xn,xn)) ),
inference(extension,[status(thm),parent(t2:5)],[f_5_3]) ).
cnf(t17,plain,
$false,
inference(connection,[status(thm),parent(t16:1)],[t16:1,t2:5]) ).
cnf(t18,plain,
aNaturalNumber0(xn),
inference(extension,[status(thm),parent(t16:2)],[f_40_2]) ).
cnf(t19,plain,
$false,
inference(connection,[status(thm),parent(t18:1)],[t18:1,t16:2]) ).
cnf(l8,lemma,
aNaturalNumber0(xn),
inference(lemma,[status(cth),parent(t16:2),below(t2:5)],[t16:2]) ).
cnf(t20,plain,
aNaturalNumber0(xn),
inference(lemma_extension,[status(thm),parent(t16:3)],[l8:1]) ).
cnf(t21,plain,
$false,
inference(connection,[status(thm),parent(t20:1)],[t20:1,t16:3]) ).
cnf(l1,lemma,
doDivides0(xp,sdtasdt0(xn,xn)),
inference(lemma,[status(cth),parent(t1:1),below(0:0)],[t1:1]) ).
cnf(t22,plain,
( ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(xp)
| ~ isPrime0(xp)
| ~ doDivides0(xp,sdtasdt0(xn,xn))
| doDivides0(xp,xn)
| ~ aNaturalNumber0(xn)
| doDivides0(xp,xn) ),
inference(extension,[status(thm),parent(t1:2)],[f_39_3]) ).
cnf(t23,plain,
$false,
inference(connection,[status(thm),parent(t22:1)],[t22:1,t1:2]) ).
cnf(t24,plain,
aNaturalNumber0(xn),
inference(extension,[status(thm),parent(t22:2)],[f_40_2]) ).
cnf(t25,plain,
$false,
inference(connection,[status(thm),parent(t24:1)],[t24:1,t22:2]) ).
cnf(l10,lemma,
aNaturalNumber0(xn),
inference(lemma,[status(cth),parent(t22:2),below(t1:2)],[t22:2]) ).
cnf(t26,plain,
$false,
inference(reduction,[status(thm),parent(t22:3)],[t22:3,t1:2]) ).
cnf(t27,plain,
doDivides0(xp,sdtasdt0(xn,xn)),
inference(lemma_extension,[status(thm),parent(t22:4)],[l1:1]) ).
cnf(t28,plain,
$false,
inference(connection,[status(thm),parent(t27:1)],[t27:1,t22:4]) ).
cnf(t29,plain,
isPrime0(xp),
inference(extension,[status(thm),parent(t22:5)],[f_43_2]) ).
cnf(t30,plain,
$false,
inference(connection,[status(thm),parent(t29:1)],[t29:1,t22:5]) ).
cnf(t31,plain,
aNaturalNumber0(xp),
inference(extension,[status(thm),parent(t22:6)],[f_40_4]) ).
cnf(t32,plain,
$false,
inference(connection,[status(thm),parent(t31:1)],[t31:1,t22:6]) ).
cnf(t33,plain,
aNaturalNumber0(xn),
inference(lemma_extension,[status(thm),parent(t22:7)],[l10:1]) ).
cnf(t34,plain,
$false,
inference(connection,[status(thm),parent(t33:1)],[t33:1,t22:7]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : NUM523+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/sandbox/solver/bin/connect++ --verbosity 1 --no-colour --tptp-proof --schedule default --timeout 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.36 % Computer : n008.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Sat Sep 19 18:43:38 UTC 2026
% 0.10/0.37 % CPUTime :
% 17.55/17.82 % SZS status Theorem for theBenchmark
% 17.55/17.82 % SZS output start Proof for theBenchmark
% See solution above
%------------------------------------------------------------------------------