%------------------------------------------------------------------------------
% File : ConnectPP---0.7.2
% Problem : NUM482+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 08:52:22 AM UTC 2026
% Result : Theorem 20.87s 21.19s
% Output : Proof 20.87s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 5
% Syntax : Number of formulae : 39 ( 17 unt; 0 def)
% Number of atoms : 210 ( 79 equ)
% Maximal formula atoms : 36 ( 5 avg)
% Number of connectives : 263 ( 92 ~; 83 |; 82 &)
% ( 0 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 18 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 9 ( 7 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 64 ( 1 sgn 43 !; 13 ?)
% Comments :
%------------------------------------------------------------------------------
fof(mSortsC_01,axiom,
( sz10 != sz00
& aNaturalNumber0(sz10) ),
file('theBenchmark.p',mSortsC_01) ).
fof(m_MulUnit,axiom,
! [W0] :
( aNaturalNumber0(W0)
=> ( W0 = sdtasdt0(sz10,W0)
& sdtasdt0(W0,sz10) = W0 ) ),
file('theBenchmark.p',m_MulUnit) ).
fof(m__1716,hypothesis,
aNaturalNumber0(xk),
file('theBenchmark.p',m__1716) ).
fof(m__,conjecture,
( ( isPrime0(xk)
& ! [W0] :
( ( ( doDivides0(W0,xk)
| ? [W1] :
( xk = sdtasdt0(W0,W1)
& aNaturalNumber0(W1) ) )
& aNaturalNumber0(W0) )
=> ( W0 = xk
| W0 = sz10 ) ) )
=> ? [W0] :
( ( isPrime0(W0)
| ( ! [W1] :
( ( doDivides0(W1,W0)
& ? [W2] :
( W0 = sdtasdt0(W1,W2)
& aNaturalNumber0(W2) )
& aNaturalNumber0(W1) )
=> ( W1 = W0
| W1 = sz10 ) )
& W0 != sz10
& W0 != sz00 ) )
& ( doDivides0(W0,xk)
| ? [W1] :
( xk = sdtasdt0(W0,W1)
& aNaturalNumber0(W1) ) )
& aNaturalNumber0(W0) ) ),
file('theBenchmark.p',m__) ).
fof(f_3_1,plain,
( sz10 != sz00
& aNaturalNumber0(sz10) ),
inference(fof_nnf,[status(thm)],[mSortsC_01]) ).
cnf(f_3_2,plain,
aNaturalNumber0(sz10),
inference(clausify,[status(thm)],[f_3_1]) ).
fof(f_11_1,plain,
! [W0] :
( ( W0 = sdtasdt0(sz10,W0)
& sdtasdt0(W0,sz10) = W0 )
| ~ aNaturalNumber0(W0) ),
inference(fof_nnf,[status(thm)],[m_MulUnit]) ).
fof(f_11_2,plain,
! [U_16] :
( ( U_16 = sdtasdt0(sz10,U_16)
& sdtasdt0(U_16,sz10) = U_16 )
| ~ aNaturalNumber0(U_16) ),
inference(variable_rename,[status(thm)],[f_11_1]) ).
cnf(f_11_3,plain,
( sdtasdt0(U_16,sz10) = U_16
| ~ aNaturalNumber0(U_16) ),
inference(clausify,[status(thm)],[f_11_2]) ).
fof(f_38_1,plain,
aNaturalNumber0(xk),
inference(fof_nnf,[status(thm)],[m__1716]) ).
cnf(f_38_2,plain,
aNaturalNumber0(xk),
inference(clausify,[status(thm)],[f_38_1]) ).
fof(f_41_1,negated_conjecture,
( ~ ? [W0] :
( ( isPrime0(W0)
| ( ! [W1] :
( ( doDivides0(W1,W0)
& ? [W2] :
( W0 = sdtasdt0(W1,W2)
& aNaturalNumber0(W2) )
& aNaturalNumber0(W1) )
=> ( W1 = W0
| W1 = sz10 ) )
& W0 != sz10
& W0 != sz00 ) )
& ( doDivides0(W0,xk)
| ? [W1] :
( xk = sdtasdt0(W0,W1)
& aNaturalNumber0(W1) ) )
& aNaturalNumber0(W0) )
& isPrime0(xk)
& ! [W0] :
( ( ( doDivides0(W0,xk)
| ? [W1] :
( xk = sdtasdt0(W0,W1)
& aNaturalNumber0(W1) ) )
& aNaturalNumber0(W0) )
=> ( W0 = xk
| W0 = sz10 ) ) ),
inference(negate,[status(cth)],[m__]) ).
fof(f_41_2,negated_conjecture,
( ! [W0] :
( ( ~ isPrime0(W0)
& ( ? [W1] :
( W1 != W0
& W1 != sz10
& doDivides0(W1,W0)
& ? [W2] :
( W0 = sdtasdt0(W1,W2)
& aNaturalNumber0(W2) )
& aNaturalNumber0(W1) )
| W0 = sz10
| W0 = sz00 ) )
| ( ~ doDivides0(W0,xk)
& ! [W1] :
( xk != sdtasdt0(W0,W1)
| ~ aNaturalNumber0(W1) ) )
| ~ aNaturalNumber0(W0) )
& isPrime0(xk)
& ! [W0] :
( W0 = xk
| W0 = sz10
| ( ~ doDivides0(W0,xk)
& ! [W1] :
( xk != sdtasdt0(W0,W1)
| ~ aNaturalNumber0(W1) ) )
| ~ aNaturalNumber0(W0) ) ),
inference(fof_nnf,[status(thm)],[f_41_1]) ).
fof(f_41_3,negated_conjecture,
( ! [U_97] :
( ( ~ isPrime0(U_97)
& ( ? [U_96] :
( U_96 != U_97
& U_96 != sz10
& doDivides0(U_96,U_97)
& ? [U_95] :
( U_97 = sdtasdt0(U_96,U_95)
& aNaturalNumber0(U_95) )
& aNaturalNumber0(U_96) )
| U_97 = sz10
| U_97 = sz00 ) )
| ( ~ doDivides0(U_97,xk)
& ! [U_94] :
( xk != sdtasdt0(U_97,U_94)
| ~ aNaturalNumber0(U_94) ) )
| ~ aNaturalNumber0(U_97) )
& isPrime0(xk)
& ! [U_93] :
( U_93 = xk
| U_93 = sz10
| ( ~ doDivides0(U_93,xk)
& ! [U_92] :
( xk != sdtasdt0(U_93,U_92)
| ~ aNaturalNumber0(U_92) ) )
| ~ aNaturalNumber0(U_93) ) ),
inference(variable_rename,[status(thm)],[f_41_2]) ).
fof(f_41_4,negated_conjecture,
( ! [U_97] :
( ( ~ isPrime0(U_97)
& ( ( sK6(U_97) != U_97
& sK6(U_97) != sz10
& doDivides0(sK6(U_97),U_97)
& ? [U_95] :
( U_97 = sdtasdt0(sK6(U_97),U_95)
& aNaturalNumber0(U_95) )
& aNaturalNumber0(sK6(U_97)) )
| U_97 = sz10
| U_97 = sz00 ) )
| ( ~ doDivides0(U_97,xk)
& ! [U_94] :
( xk != sdtasdt0(U_97,U_94)
| ~ aNaturalNumber0(U_94) ) )
| ~ aNaturalNumber0(U_97) )
& isPrime0(xk)
& ! [U_93] :
( U_93 = xk
| U_93 = sz10
| ( ~ doDivides0(U_93,xk)
& ! [U_92] :
( xk != sdtasdt0(U_93,U_92)
| ~ aNaturalNumber0(U_92) ) )
| ~ aNaturalNumber0(U_93) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK6]),skolemize(U_96,sK6(U_97))],[f_41_3]) ).
fof(f_41_5,negated_conjecture,
( ! [U_97] :
( ( ~ isPrime0(U_97)
& ( ( sK6(U_97) != U_97
& sK6(U_97) != sz10
& doDivides0(sK6(U_97),U_97)
& U_97 = sdtasdt0(sK6(U_97),sK7(U_97))
& aNaturalNumber0(sK7(U_97))
& aNaturalNumber0(sK6(U_97)) )
| U_97 = sz10
| U_97 = sz00 ) )
| ( ~ doDivides0(U_97,xk)
& ! [U_94] :
( xk != sdtasdt0(U_97,U_94)
| ~ aNaturalNumber0(U_94) ) )
| ~ aNaturalNumber0(U_97) )
& isPrime0(xk)
& ! [U_93] :
( U_93 = xk
| U_93 = sz10
| ( ~ doDivides0(U_93,xk)
& ! [U_92] :
( xk != sdtasdt0(U_93,U_92)
| ~ aNaturalNumber0(U_92) ) )
| ~ aNaturalNumber0(U_93) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK7]),skolemize(U_95,sK7(U_97))],[f_41_4]) ).
fof(f_41_6,negated_conjecture,
( ! [U_97] :
( sK6(U_97) != U_97
| ~ sP2(U_97) )
& ! [U_97] :
( sK6(U_97) != sz10
| ~ sP2(U_97) )
& ! [U_97] :
( doDivides0(sK6(U_97),U_97)
| ~ sP2(U_97) )
& ! [U_97] :
( U_97 = sdtasdt0(sK6(U_97),sK7(U_97))
| ~ sP2(U_97) )
& ! [U_97] :
( aNaturalNumber0(sK7(U_97))
| ~ sP2(U_97) )
& ! [U_97] :
( aNaturalNumber0(sK6(U_97))
| ~ sP2(U_97) )
& ! [U_97] :
( ~ isPrime0(U_97)
| ~ sP3(U_97) )
& ! [U_97] :
( sP2(U_97)
| U_97 = sz10
| U_97 = sz00
| ~ sP3(U_97) )
& ! [U_94,U_97] :
( ~ doDivides0(U_97,xk)
| ~ sP1(U_94,U_97) )
& ! [U_94,U_97] :
( xk != sdtasdt0(U_97,U_94)
| ~ aNaturalNumber0(U_94)
| ~ sP1(U_94,U_97) )
& ! [U_92,U_93] :
( ~ doDivides0(U_93,xk)
| ~ sP0(U_92,U_93) )
& ! [U_92,U_93] :
( xk != sdtasdt0(U_93,U_92)
| ~ aNaturalNumber0(U_92)
| ~ sP0(U_92,U_93) )
& ! [U_94,U_97] :
( sP3(U_97)
| sP1(U_94,U_97)
| ~ aNaturalNumber0(U_97) )
& isPrime0(xk)
& ! [U_92,U_93] :
( U_93 = xk
| U_93 = sz10
| sP0(U_92,U_93)
| ~ aNaturalNumber0(U_93) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP0,sP1,sP2,sP3])],[f_41_5]) ).
cnf(f_41_8,negated_conjecture,
isPrime0(xk),
inference(clausify,[status(thm)],[f_41_6]) ).
cnf(f_41_9,negated_conjecture,
( sP3(U_97)
| sP1(U_94,U_97)
| ~ aNaturalNumber0(U_97) ),
inference(clausify,[status(thm)],[f_41_6]) ).
cnf(f_41_12,negated_conjecture,
( xk != sdtasdt0(U_97,U_94)
| ~ aNaturalNumber0(U_94)
| ~ sP1(U_94,U_97) ),
inference(clausify,[status(thm)],[f_41_6]) ).
cnf(f_41_15,negated_conjecture,
( ~ isPrime0(U_97)
| ~ sP3(U_97) ),
inference(clausify,[status(thm)],[f_41_6]) ).
cnf(equality_2,axiom,
( Eq_x_1 = Eq_x_0
| Eq_x_0 != Eq_x_1 ),
theory(equality,[symmetry]) ).
cnf(t1,plain,
( ~ aNaturalNumber0(sz10)
| xk != sdtasdt0(xk,sz10)
| ~ sP1(sz10,xk) ),
inference(start,[status(thm),parent(0:0)],[f_41_12]) ).
cnf(t2,plain,
( sP3(xk)
| ~ aNaturalNumber0(xk)
| sP1(sz10,xk) ),
inference(extension,[status(thm),parent(t1:1)],[f_41_9]) ).
cnf(t3,plain,
$false,
inference(connection,[status(thm),parent(t2:1)],[t2:1,t1:1]) ).
cnf(t4,plain,
aNaturalNumber0(xk),
inference(extension,[status(thm),parent(t2:2)],[f_38_2]) ).
cnf(t5,plain,
$false,
inference(connection,[status(thm),parent(t4:1)],[t4:1,t2:2]) ).
cnf(t6,plain,
( ~ isPrime0(xk)
| ~ sP3(xk) ),
inference(extension,[status(thm),parent(t2:3)],[f_41_15]) ).
cnf(t7,plain,
$false,
inference(connection,[status(thm),parent(t6:1)],[t6:1,t2:3]) ).
cnf(t8,plain,
isPrime0(xk),
inference(extension,[status(thm),parent(t6:2)],[f_41_8]) ).
cnf(t9,plain,
$false,
inference(connection,[status(thm),parent(t8:1)],[t8:1,t6:2]) ).
cnf(t10,plain,
( sdtasdt0(xk,sz10) != xk
| xk = sdtasdt0(xk,sz10) ),
inference(extension,[status(thm),parent(t1:2)],[equality_2]) ).
cnf(t11,plain,
$false,
inference(connection,[status(thm),parent(t10:1)],[t10:1,t1:2]) ).
cnf(t12,plain,
( ~ aNaturalNumber0(xk)
| sdtasdt0(xk,sz10) = xk ),
inference(extension,[status(thm),parent(t10:2)],[f_11_3]) ).
cnf(t13,plain,
$false,
inference(connection,[status(thm),parent(t12:1)],[t12:1,t10:2]) ).
cnf(t14,plain,
aNaturalNumber0(xk),
inference(extension,[status(thm),parent(t12:2)],[f_38_2]) ).
cnf(t15,plain,
$false,
inference(connection,[status(thm),parent(t14:1)],[t14:1,t12:2]) ).
cnf(t16,plain,
aNaturalNumber0(sz10),
inference(extension,[status(thm),parent(t1:3)],[f_3_2]) ).
cnf(t17,plain,
$false,
inference(connection,[status(thm),parent(t16:1)],[t16:1,t1:3]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM482+3 : 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
% 0.10/0.36 % Computer : n026.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 18:37:22 UTC 2026
% 0.10/0.36 % CPUTime :
% 20.87/21.19 % SZS status Theorem for theBenchmark
% 20.87/21.19 % SZS output start Proof for theBenchmark
% See solution above
%------------------------------------------------------------------------------