%------------------------------------------------------------------------------
% File : ConnectPP---0.7.2
% Problem : NUM427+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 : n003.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 08:52:13 AM UTC 2026
% Result : Theorem 26.25s 26.53s
% Output : Proof 26.25s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 8
% Syntax : Number of formulae : 66 ( 39 unt; 2 def)
% Number of atoms : 174 ( 38 equ)
% Maximal formula atoms : 11 ( 2 avg)
% Number of connectives : 182 ( 74 ~; 69 |; 33 &)
% ( 2 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-3 aty)
% Number of functors : 9 ( 9 usr; 5 con; 0-2 aty)
% Number of variables : 47 ( 0 sgn 34 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(mIntNeg,axiom,
! [W0] :
( aInteger0(W0)
=> aInteger0(smndt0(W0)) ),
file('theBenchmark.p',mIntNeg) ).
fof(mIntPlus,axiom,
! [W0,W1] :
( ( aInteger0(W1)
& aInteger0(W0) )
=> aInteger0(sdtpldt0(W0,W1)) ),
file('theBenchmark.p',mIntPlus) ).
fof(mDivisor,definition,
! [W0] :
( aInteger0(W0)
=> ! [W1] :
( aDivisorOf0(W1,W0)
<=> ( ? [W2] :
( sdtasdt0(W1,W2) = W0
& aInteger0(W2) )
& W1 != sz00
& aInteger0(W1) ) ) ),
file('theBenchmark.p',mDivisor) ).
fof(mEquMod,definition,
! [W0,W1,W2] :
( ( W2 != sz00
& aInteger0(W2)
& aInteger0(W1)
& aInteger0(W0) )
=> ( sdteqdtlpzmzozddtrp0(W0,W1,W2)
<=> aDivisorOf0(W2,sdtpldt0(W0,smndt0(W1))) ) ),
file('theBenchmark.p',mEquMod) ).
fof(m__704,hypothesis,
( xq != sz00
& aInteger0(xq)
& aInteger0(xb)
& aInteger0(xa) ),
file('theBenchmark.p',m__704) ).
fof(m__747,hypothesis,
( sdtasdt0(xq,xn) = sdtpldt0(xa,smndt0(xb))
& aInteger0(xn) ),
file('theBenchmark.p',m__747) ).
fof(m__767,hypothesis,
sdtasdt0(xq,smndt0(xn)) = sdtpldt0(xb,smndt0(xa)),
file('theBenchmark.p',m__767) ).
fof(m__,conjecture,
sdteqdtlpzmzozddtrp0(xb,xa,xq),
file('theBenchmark.p',m__) ).
fof(f_4_1,plain,
! [W0] :
( aInteger0(smndt0(W0))
| ~ aInteger0(W0) ),
inference(fof_nnf,[status(thm)],[mIntNeg]) ).
fof(f_4_2,plain,
! [U_1] :
( aInteger0(smndt0(U_1))
| ~ aInteger0(U_1) ),
inference(variable_rename,[status(thm)],[f_4_1]) ).
cnf(f_4_3,plain,
( aInteger0(smndt0(U_1))
| ~ aInteger0(U_1) ),
inference(clausify,[status(thm)],[f_4_2]) ).
fof(f_5_1,plain,
! [W0,W1] :
( aInteger0(sdtpldt0(W0,W1))
| ~ aInteger0(W1)
| ~ aInteger0(W0) ),
inference(fof_nnf,[status(thm)],[mIntPlus]) ).
fof(f_5_2,plain,
! [U_3,U_2] :
( aInteger0(sdtpldt0(U_3,U_2))
| ~ aInteger0(U_2)
| ~ aInteger0(U_3) ),
inference(variable_rename,[status(thm)],[f_5_1]) ).
cnf(f_5_3,plain,
( aInteger0(sdtpldt0(U_3,U_2))
| ~ aInteger0(U_2)
| ~ aInteger0(U_3) ),
inference(clausify,[status(thm)],[f_5_2]) ).
fof(f_18_1,plain,
! [W0] :
( ! [W1] :
( ( aDivisorOf0(W1,W0)
| ! [W2] :
( sdtasdt0(W1,W2) != W0
| ~ aInteger0(W2) )
| W1 = sz00
| ~ aInteger0(W1) )
& ( ( ? [W2] :
( sdtasdt0(W1,W2) = W0
& aInteger0(W2) )
& W1 != sz00
& aInteger0(W1) )
| ~ aDivisorOf0(W1,W0) ) )
| ~ aInteger0(W0) ),
inference(fof_nnf,[status(thm)],[mDivisor]) ).
fof(f_18_2,plain,
! [U_29] :
( ! [U_28] :
( ( aDivisorOf0(U_28,U_29)
| ! [U_27] :
( sdtasdt0(U_28,U_27) != U_29
| ~ aInteger0(U_27) )
| U_28 = sz00
| ~ aInteger0(U_28) )
& ( ( ? [U_26] :
( sdtasdt0(U_28,U_26) = U_29
& aInteger0(U_26) )
& U_28 != sz00
& aInteger0(U_28) )
| ~ aDivisorOf0(U_28,U_29) ) )
| ~ aInteger0(U_29) ),
inference(variable_rename,[status(thm)],[f_18_1]) ).
fof(f_18_3,plain,
! [U_29] :
( ( ! [U_31] :
( aDivisorOf0(U_31,U_29)
| ! [U_27] :
( sdtasdt0(U_31,U_27) != U_29
| ~ aInteger0(U_27) )
| U_31 = sz00
| ~ aInteger0(U_31) )
& ! [U_30] :
( ( ? [U_26] :
( sdtasdt0(U_30,U_26) = U_29
& aInteger0(U_26) )
& U_30 != sz00
& aInteger0(U_30) )
| ~ aDivisorOf0(U_30,U_29) ) )
| ~ aInteger0(U_29) ),
inference(miniscope,[status(thm)],[f_18_2]) ).
fof(f_18_4,plain,
! [U_29] :
( ( ! [U_31] :
( aDivisorOf0(U_31,U_29)
| ! [U_27] :
( sdtasdt0(U_31,U_27) != U_29
| ~ aInteger0(U_27) )
| U_31 = sz00
| ~ aInteger0(U_31) )
& ! [U_30] :
( ( sdtasdt0(U_30,sK1(U_29,U_30)) = U_29
& aInteger0(sK1(U_29,U_30))
& U_30 != sz00
& aInteger0(U_30) )
| ~ aDivisorOf0(U_30,U_29) ) )
| ~ aInteger0(U_29) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(U_26,sK1(U_29,U_30))],[f_18_3]) ).
cnf(f_18_9,plain,
( aDivisorOf0(U_31,U_29)
| sdtasdt0(U_31,U_27) != U_29
| ~ aInteger0(U_27)
| U_31 = sz00
| ~ aInteger0(U_31)
| ~ aInteger0(U_29) ),
inference(clausify,[status(thm)],[f_18_4]) ).
fof(f_19_1,plain,
! [W0,W1,W2] :
( ( ( sdteqdtlpzmzozddtrp0(W0,W1,W2)
| ~ aDivisorOf0(W2,sdtpldt0(W0,smndt0(W1))) )
& ( aDivisorOf0(W2,sdtpldt0(W0,smndt0(W1)))
| ~ sdteqdtlpzmzozddtrp0(W0,W1,W2) ) )
| W2 = sz00
| ~ aInteger0(W2)
| ~ aInteger0(W1)
| ~ aInteger0(W0) ),
inference(fof_nnf,[status(thm)],[mEquMod]) ).
fof(f_19_2,plain,
! [U_34,U_33,U_32] :
( ( ( sdteqdtlpzmzozddtrp0(U_34,U_33,U_32)
| ~ aDivisorOf0(U_32,sdtpldt0(U_34,smndt0(U_33))) )
& ( aDivisorOf0(U_32,sdtpldt0(U_34,smndt0(U_33)))
| ~ sdteqdtlpzmzozddtrp0(U_34,U_33,U_32) ) )
| U_32 = sz00
| ~ aInteger0(U_32)
| ~ aInteger0(U_33)
| ~ aInteger0(U_34) ),
inference(variable_rename,[status(thm)],[f_19_1]) ).
cnf(f_19_4,plain,
( sdteqdtlpzmzozddtrp0(U_34,U_33,U_32)
| ~ aDivisorOf0(U_32,sdtpldt0(U_34,smndt0(U_33)))
| U_32 = sz00
| ~ aInteger0(U_32)
| ~ aInteger0(U_33)
| ~ aInteger0(U_34) ),
inference(clausify,[status(thm)],[f_19_2]) ).
fof(f_21_1,plain,
( xq != sz00
& aInteger0(xq)
& aInteger0(xb)
& aInteger0(xa) ),
inference(fof_nnf,[status(thm)],[m__704]) ).
cnf(f_21_2,plain,
aInteger0(xa),
inference(clausify,[status(thm)],[f_21_1]) ).
cnf(f_21_3,plain,
aInteger0(xb),
inference(clausify,[status(thm)],[f_21_1]) ).
cnf(f_21_4,plain,
aInteger0(xq),
inference(clausify,[status(thm)],[f_21_1]) ).
cnf(f_21_5,plain,
xq != sz00,
inference(clausify,[status(thm)],[f_21_1]) ).
fof(f_23_1,plain,
( sdtasdt0(xq,xn) = sdtpldt0(xa,smndt0(xb))
& aInteger0(xn) ),
inference(fof_nnf,[status(thm)],[m__747]) ).
cnf(f_23_2,plain,
aInteger0(xn),
inference(clausify,[status(thm)],[f_23_1]) ).
fof(f_24_1,plain,
sdtasdt0(xq,smndt0(xn)) = sdtpldt0(xb,smndt0(xa)),
inference(fof_nnf,[status(thm)],[m__767]) ).
cnf(f_24_2,plain,
sdtasdt0(xq,smndt0(xn)) = sdtpldt0(xb,smndt0(xa)),
inference(clausify,[status(thm)],[f_24_1]) ).
fof(f_25_1,negated_conjecture,
~ sdteqdtlpzmzozddtrp0(xb,xa,xq),
inference(negate,[status(cth)],[m__]) ).
fof(f_25_2,negated_conjecture,
~ sdteqdtlpzmzozddtrp0(xb,xa,xq),
inference(definitional_conversion,[status(esa)],[f_25_1]) ).
cnf(f_25_3,negated_conjecture,
~ sdteqdtlpzmzozddtrp0(xb,xa,xq),
inference(clausify,[status(thm)],[f_25_2]) ).
cnf(t1,plain,
~ sdteqdtlpzmzozddtrp0(xb,xa,xq),
inference(start,[status(thm),parent(0:0)],[f_25_3]) ).
cnf(t2,plain,
( ~ aInteger0(xa)
| ~ aInteger0(xq)
| xq = sz00
| ~ aDivisorOf0(xq,sdtpldt0(xb,smndt0(xa)))
| ~ aInteger0(xb)
| sdteqdtlpzmzozddtrp0(xb,xa,xq) ),
inference(extension,[status(thm),parent(t1:1)],[f_19_4]) ).
cnf(t3,plain,
$false,
inference(connection,[status(thm),parent(t2:1)],[t2:1,t1:1]) ).
cnf(t4,plain,
aInteger0(xb),
inference(extension,[status(thm),parent(t2:2)],[f_21_3]) ).
cnf(t5,plain,
$false,
inference(connection,[status(thm),parent(t4:1)],[t4:1,t2:2]) ).
cnf(l2,lemma,
aInteger0(xb),
inference(lemma,[status(cth),parent(t2:2),below(t1:1)],[t2:2]) ).
cnf(t6,plain,
( ~ aInteger0(xq)
| xq = sz00
| ~ aInteger0(smndt0(xn))
| sdtasdt0(xq,smndt0(xn)) != sdtpldt0(xb,smndt0(xa))
| ~ aInteger0(sdtpldt0(xb,smndt0(xa)))
| aDivisorOf0(xq,sdtpldt0(xb,smndt0(xa))) ),
inference(extension,[status(thm),parent(t2:3)],[f_18_9]) ).
cnf(t7,plain,
$false,
inference(connection,[status(thm),parent(t6:1)],[t6:1,t2:3]) ).
cnf(t8,plain,
( ~ aInteger0(smndt0(xa))
| ~ aInteger0(xb)
| aInteger0(sdtpldt0(xb,smndt0(xa))) ),
inference(extension,[status(thm),parent(t6:2)],[f_5_3]) ).
cnf(t9,plain,
$false,
inference(connection,[status(thm),parent(t8:1)],[t8:1,t6:2]) ).
cnf(t10,plain,
aInteger0(xb),
inference(lemma_extension,[status(thm),parent(t8:2)],[l2:1]) ).
cnf(t11,plain,
$false,
inference(connection,[status(thm),parent(t10:1)],[t10:1,t8:2]) ).
cnf(t12,plain,
( ~ aInteger0(xa)
| aInteger0(smndt0(xa)) ),
inference(extension,[status(thm),parent(t8:3)],[f_4_3]) ).
cnf(t13,plain,
$false,
inference(connection,[status(thm),parent(t12:1)],[t12:1,t8:3]) ).
cnf(t14,plain,
aInteger0(xa),
inference(extension,[status(thm),parent(t12:2)],[f_21_2]) ).
cnf(t15,plain,
$false,
inference(connection,[status(thm),parent(t14:1)],[t14:1,t12:2]) ).
cnf(t16,plain,
sdtasdt0(xq,smndt0(xn)) = sdtpldt0(xb,smndt0(xa)),
inference(extension,[status(thm),parent(t6:3)],[f_24_2]) ).
cnf(t17,plain,
$false,
inference(connection,[status(thm),parent(t16:1)],[t16:1,t6:3]) ).
cnf(t18,plain,
( ~ aInteger0(xn)
| aInteger0(smndt0(xn)) ),
inference(extension,[status(thm),parent(t6:4)],[f_4_3]) ).
cnf(t19,plain,
$false,
inference(connection,[status(thm),parent(t18:1)],[t18:1,t6:4]) ).
cnf(t20,plain,
aInteger0(xn),
inference(extension,[status(thm),parent(t18:2)],[f_23_2]) ).
cnf(t21,plain,
$false,
inference(connection,[status(thm),parent(t20:1)],[t20:1,t18:2]) ).
cnf(t22,plain,
xq != sz00,
inference(extension,[status(thm),parent(t6:5)],[f_21_5]) ).
cnf(t23,plain,
$false,
inference(connection,[status(thm),parent(t22:1)],[t22:1,t6:5]) ).
cnf(t24,plain,
aInteger0(xq),
inference(extension,[status(thm),parent(t6:6)],[f_21_4]) ).
cnf(t25,plain,
$false,
inference(connection,[status(thm),parent(t24:1)],[t24:1,t6:6]) ).
cnf(t26,plain,
xq != sz00,
inference(extension,[status(thm),parent(t2:4)],[f_21_5]) ).
cnf(t27,plain,
$false,
inference(connection,[status(thm),parent(t26:1)],[t26:1,t2:4]) ).
cnf(t28,plain,
aInteger0(xq),
inference(extension,[status(thm),parent(t2:5)],[f_21_4]) ).
cnf(t29,plain,
$false,
inference(connection,[status(thm),parent(t28:1)],[t28:1,t2:5]) ).
cnf(t30,plain,
aInteger0(xa),
inference(extension,[status(thm),parent(t2:6)],[f_21_2]) ).
cnf(t31,plain,
$false,
inference(connection,[status(thm),parent(t30:1)],[t30:1,t2:6]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM427+1 : 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/sandbox2/solver/bin/connect++ --verbosity 1 --no-colour --tptp-proof --schedule default --timeout 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.37 % Computer : n003.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Sat Sep 19 18:25:28 UTC 2026
% 0.03/0.37 % CPUTime :
% 26.25/26.53 % SZS status Theorem for theBenchmark
% 26.25/26.53 % SZS output start Proof for theBenchmark
% See solution above
%------------------------------------------------------------------------------