%------------------------------------------------------------------------------
% File : ConnectPP---0.7.2
% Problem : NUM490+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 : n006.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 08:52:23 AM UTC 2026
% Result : Theorem 84.15s 84.43s
% Output : Proof 84.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 9
% Syntax : Number of formulae : 84 ( 57 unt; 2 def)
% Number of atoms : 187 ( 48 equ)
% Maximal formula atoms : 9 ( 2 avg)
% Number of connectives : 182 ( 79 ~; 76 |; 21 &)
% ( 2 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 4 con; 0-2 aty)
% Number of variables : 46 ( 0 sgn 30 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(mSortsB_02,axiom,
! [W0,W1] :
( ( aNaturalNumber0(W1)
& aNaturalNumber0(W0) )
=> aNaturalNumber0(sdtasdt0(W0,W1)) ),
file('theBenchmark.p',mSortsB_02) ).
fof(mDefLE,definition,
! [W0,W1] :
( ( aNaturalNumber0(W1)
& aNaturalNumber0(W0) )
=> ( sdtlseqdt0(W0,W1)
<=> ? [W2] :
( sdtpldt0(W0,W2) = W1
& aNaturalNumber0(W2) ) ) ),
file('theBenchmark.p',mDefLE) ).
fof(mDefDiff,definition,
! [W0,W1] :
( ( aNaturalNumber0(W1)
& aNaturalNumber0(W0) )
=> ( sdtlseqdt0(W0,W1)
=> ! [W2] :
( W2 = sdtmndt0(W1,W0)
<=> ( sdtpldt0(W0,W2) = W1
& aNaturalNumber0(W2) ) ) ) ),
file('theBenchmark.p',mDefDiff) ).
fof(m__1837,hypothesis,
( aNaturalNumber0(xp)
& aNaturalNumber0(xm)
& aNaturalNumber0(xn) ),
file('theBenchmark.p',m__1837) ).
fof(m__1870,hypothesis,
sdtlseqdt0(xp,xn),
file('theBenchmark.p',m__1870) ).
fof(m__1883,hypothesis,
xr = sdtmndt0(xn,xp),
file('theBenchmark.p',m__1883) ).
fof(m__1951,hypothesis,
sdtasdt0(xn,xm) = sdtpldt0(sdtasdt0(xp,xm),sdtasdt0(xr,xm)),
file('theBenchmark.p',m__1951) ).
fof(m__,conjecture,
sdtasdt0(xr,xm) = sdtmndt0(sdtasdt0(xn,xm),sdtasdt0(xp,xm)),
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_18_1,plain,
! [W0,W1] :
( ( ( sdtlseqdt0(W0,W1)
| ! [W2] :
( sdtpldt0(W0,W2) != W1
| ~ aNaturalNumber0(W2) ) )
& ( ? [W2] :
( sdtpldt0(W0,W2) = W1
& aNaturalNumber0(W2) )
| ~ sdtlseqdt0(W0,W1) ) )
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) ),
inference(fof_nnf,[status(thm)],[mDefLE]) ).
fof(f_18_2,plain,
! [U_34,U_33] :
( ( ( sdtlseqdt0(U_34,U_33)
| ! [U_32] :
( sdtpldt0(U_34,U_32) != U_33
| ~ aNaturalNumber0(U_32) ) )
& ( ? [U_31] :
( sdtpldt0(U_34,U_31) = U_33
& aNaturalNumber0(U_31) )
| ~ sdtlseqdt0(U_34,U_33) ) )
| ~ aNaturalNumber0(U_33)
| ~ aNaturalNumber0(U_34) ),
inference(variable_rename,[status(thm)],[f_18_1]) ).
fof(f_18_3,plain,
! [U_34,U_33] :
( ( ( sdtlseqdt0(U_34,U_33)
| ! [U_32] :
( sdtpldt0(U_34,U_32) != U_33
| ~ aNaturalNumber0(U_32) ) )
& ( ( sdtpldt0(U_34,sK1(U_34,U_33)) = U_33
& aNaturalNumber0(sK1(U_34,U_33)) )
| ~ sdtlseqdt0(U_34,U_33) ) )
| ~ aNaturalNumber0(U_33)
| ~ aNaturalNumber0(U_34) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(U_31,sK1(U_34,U_33))],[f_18_2]) ).
cnf(f_18_6,plain,
( sdtlseqdt0(U_34,U_33)
| sdtpldt0(U_34,U_32) != U_33
| ~ aNaturalNumber0(U_32)
| ~ aNaturalNumber0(U_33)
| ~ aNaturalNumber0(U_34) ),
inference(clausify,[status(thm)],[f_18_3]) ).
fof(f_19_1,plain,
! [W0,W1] :
( ! [W2] :
( ( W2 = sdtmndt0(W1,W0)
| sdtpldt0(W0,W2) != W1
| ~ aNaturalNumber0(W2) )
& ( ( sdtpldt0(W0,W2) = W1
& aNaturalNumber0(W2) )
| W2 != sdtmndt0(W1,W0) ) )
| ~ sdtlseqdt0(W0,W1)
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) ),
inference(fof_nnf,[status(thm)],[mDefDiff]) ).
fof(f_19_2,plain,
! [U_37,U_36] :
( ! [U_35] :
( ( U_35 = sdtmndt0(U_36,U_37)
| sdtpldt0(U_37,U_35) != U_36
| ~ aNaturalNumber0(U_35) )
& ( ( sdtpldt0(U_37,U_35) = U_36
& aNaturalNumber0(U_35) )
| U_35 != sdtmndt0(U_36,U_37) ) )
| ~ sdtlseqdt0(U_37,U_36)
| ~ aNaturalNumber0(U_36)
| ~ aNaturalNumber0(U_37) ),
inference(variable_rename,[status(thm)],[f_19_1]) ).
fof(f_19_3,plain,
! [U_37,U_36] :
( ( ! [U_39] :
( U_39 = sdtmndt0(U_36,U_37)
| sdtpldt0(U_37,U_39) != U_36
| ~ aNaturalNumber0(U_39) )
& ! [U_38] :
( ( sdtpldt0(U_37,U_38) = U_36
& aNaturalNumber0(U_38) )
| U_38 != sdtmndt0(U_36,U_37) ) )
| ~ sdtlseqdt0(U_37,U_36)
| ~ aNaturalNumber0(U_36)
| ~ aNaturalNumber0(U_37) ),
inference(miniscope,[status(thm)],[f_19_2]) ).
cnf(f_19_4,plain,
( aNaturalNumber0(U_38)
| U_38 != sdtmndt0(U_36,U_37)
| ~ sdtlseqdt0(U_37,U_36)
| ~ aNaturalNumber0(U_36)
| ~ aNaturalNumber0(U_37) ),
inference(clausify,[status(thm)],[f_19_3]) ).
cnf(f_19_6,plain,
( U_39 = sdtmndt0(U_36,U_37)
| sdtpldt0(U_37,U_39) != U_36
| ~ aNaturalNumber0(U_39)
| ~ sdtlseqdt0(U_37,U_36)
| ~ aNaturalNumber0(U_36)
| ~ aNaturalNumber0(U_37) ),
inference(clausify,[status(thm)],[f_19_3]) ).
fof(f_39_1,plain,
( aNaturalNumber0(xp)
& aNaturalNumber0(xm)
& aNaturalNumber0(xn) ),
inference(fof_nnf,[status(thm)],[m__1837]) ).
cnf(f_39_2,plain,
aNaturalNumber0(xn),
inference(clausify,[status(thm)],[f_39_1]) ).
cnf(f_39_3,plain,
aNaturalNumber0(xm),
inference(clausify,[status(thm)],[f_39_1]) ).
cnf(f_39_4,plain,
aNaturalNumber0(xp),
inference(clausify,[status(thm)],[f_39_1]) ).
fof(f_42_1,plain,
sdtlseqdt0(xp,xn),
inference(fof_nnf,[status(thm)],[m__1870]) ).
cnf(f_42_2,plain,
sdtlseqdt0(xp,xn),
inference(clausify,[status(thm)],[f_42_1]) ).
fof(f_43_1,plain,
xr = sdtmndt0(xn,xp),
inference(fof_nnf,[status(thm)],[m__1883]) ).
cnf(f_43_2,plain,
xr = sdtmndt0(xn,xp),
inference(clausify,[status(thm)],[f_43_1]) ).
fof(f_46_1,plain,
sdtasdt0(xn,xm) = sdtpldt0(sdtasdt0(xp,xm),sdtasdt0(xr,xm)),
inference(fof_nnf,[status(thm)],[m__1951]) ).
cnf(f_46_2,plain,
sdtasdt0(xn,xm) = sdtpldt0(sdtasdt0(xp,xm),sdtasdt0(xr,xm)),
inference(clausify,[status(thm)],[f_46_1]) ).
fof(f_47_1,negated_conjecture,
sdtasdt0(xr,xm) != sdtmndt0(sdtasdt0(xn,xm),sdtasdt0(xp,xm)),
inference(negate,[status(cth)],[m__]) ).
cnf(f_47_2,negated_conjecture,
sdtasdt0(xr,xm) != sdtmndt0(sdtasdt0(xn,xm),sdtasdt0(xp,xm)),
inference(clausify,[status(thm)],[f_47_1]) ).
cnf(equality_2,axiom,
( Eq_x_1 = Eq_x_0
| Eq_x_0 != Eq_x_1 ),
theory(equality,[symmetry]) ).
cnf(t1,plain,
sdtasdt0(xr,xm) != sdtmndt0(sdtasdt0(xn,xm),sdtasdt0(xp,xm)),
inference(start,[status(thm),parent(0:0)],[f_47_2]) ).
cnf(t2,plain,
( ~ aNaturalNumber0(sdtasdt0(xn,xm))
| ~ sdtlseqdt0(sdtasdt0(xp,xm),sdtasdt0(xn,xm))
| ~ aNaturalNumber0(sdtasdt0(xr,xm))
| sdtpldt0(sdtasdt0(xp,xm),sdtasdt0(xr,xm)) != sdtasdt0(xn,xm)
| ~ aNaturalNumber0(sdtasdt0(xp,xm))
| sdtasdt0(xr,xm) = sdtmndt0(sdtasdt0(xn,xm),sdtasdt0(xp,xm)) ),
inference(extension,[status(thm),parent(t1:1)],[f_19_6]) ).
cnf(t3,plain,
$false,
inference(connection,[status(thm),parent(t2:1)],[t2:1,t1:1]) ).
cnf(t4,plain,
( ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(xp)
| aNaturalNumber0(sdtasdt0(xp,xm)) ),
inference(extension,[status(thm),parent(t2:2)],[f_5_3]) ).
cnf(t5,plain,
$false,
inference(connection,[status(thm),parent(t4:1)],[t4:1,t2:2]) ).
cnf(t6,plain,
aNaturalNumber0(xp),
inference(extension,[status(thm),parent(t4:2)],[f_39_4]) ).
cnf(t7,plain,
$false,
inference(connection,[status(thm),parent(t6:1)],[t6:1,t4:2]) ).
cnf(t8,plain,
aNaturalNumber0(xm),
inference(extension,[status(thm),parent(t4:3)],[f_39_3]) ).
cnf(t9,plain,
$false,
inference(connection,[status(thm),parent(t8:1)],[t8:1,t4:3]) ).
cnf(l2,lemma,
aNaturalNumber0(sdtasdt0(xp,xm)),
inference(lemma,[status(cth),parent(t2:2),below(t1:1)],[t2:2]) ).
cnf(t10,plain,
( sdtasdt0(xn,xm) != sdtpldt0(sdtasdt0(xp,xm),sdtasdt0(xr,xm))
| sdtpldt0(sdtasdt0(xp,xm),sdtasdt0(xr,xm)) = sdtasdt0(xn,xm) ),
inference(extension,[status(thm),parent(t2:3)],[equality_2]) ).
cnf(t11,plain,
$false,
inference(connection,[status(thm),parent(t10:1)],[t10:1,t2:3]) ).
cnf(t12,plain,
sdtasdt0(xn,xm) = sdtpldt0(sdtasdt0(xp,xm),sdtasdt0(xr,xm)),
inference(extension,[status(thm),parent(t10:2)],[f_46_2]) ).
cnf(t13,plain,
$false,
inference(connection,[status(thm),parent(t12:1)],[t12:1,t10:2]) ).
cnf(t14,plain,
( ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(xr)
| aNaturalNumber0(sdtasdt0(xr,xm)) ),
inference(extension,[status(thm),parent(t2:4)],[f_5_3]) ).
cnf(t15,plain,
$false,
inference(connection,[status(thm),parent(t14:1)],[t14:1,t2:4]) ).
cnf(t16,plain,
( ~ aNaturalNumber0(xn)
| ~ sdtlseqdt0(xp,xn)
| xr != sdtmndt0(xn,xp)
| ~ aNaturalNumber0(xp)
| aNaturalNumber0(xr) ),
inference(extension,[status(thm),parent(t14:2)],[f_19_4]) ).
cnf(t17,plain,
$false,
inference(connection,[status(thm),parent(t16:1)],[t16:1,t14:2]) ).
cnf(t18,plain,
aNaturalNumber0(xp),
inference(extension,[status(thm),parent(t16:2)],[f_39_4]) ).
cnf(t19,plain,
$false,
inference(connection,[status(thm),parent(t18:1)],[t18:1,t16:2]) ).
cnf(t20,plain,
xr = sdtmndt0(xn,xp),
inference(extension,[status(thm),parent(t16:3)],[f_43_2]) ).
cnf(t21,plain,
$false,
inference(connection,[status(thm),parent(t20:1)],[t20:1,t16:3]) ).
cnf(t22,plain,
sdtlseqdt0(xp,xn),
inference(extension,[status(thm),parent(t16:4)],[f_42_2]) ).
cnf(t23,plain,
$false,
inference(connection,[status(thm),parent(t22:1)],[t22:1,t16:4]) ).
cnf(t24,plain,
aNaturalNumber0(xn),
inference(extension,[status(thm),parent(t16:5)],[f_39_2]) ).
cnf(t25,plain,
$false,
inference(connection,[status(thm),parent(t24:1)],[t24:1,t16:5]) ).
cnf(t26,plain,
aNaturalNumber0(xm),
inference(extension,[status(thm),parent(t14:3)],[f_39_3]) ).
cnf(t27,plain,
$false,
inference(connection,[status(thm),parent(t26:1)],[t26:1,t14:3]) ).
cnf(l7,lemma,
aNaturalNumber0(sdtasdt0(xr,xm)),
inference(lemma,[status(cth),parent(t2:4),below(t1:1)],[t2:4]) ).
cnf(t28,plain,
( ~ aNaturalNumber0(sdtasdt0(xn,xm))
| ~ aNaturalNumber0(sdtasdt0(xr,xm))
| sdtpldt0(sdtasdt0(xp,xm),sdtasdt0(xr,xm)) != sdtasdt0(xn,xm)
| ~ aNaturalNumber0(sdtasdt0(xp,xm))
| sdtlseqdt0(sdtasdt0(xp,xm),sdtasdt0(xn,xm)) ),
inference(extension,[status(thm),parent(t2:5)],[f_18_6]) ).
cnf(t29,plain,
$false,
inference(connection,[status(thm),parent(t28:1)],[t28:1,t2:5]) ).
cnf(t30,plain,
aNaturalNumber0(sdtasdt0(xp,xm)),
inference(lemma_extension,[status(thm),parent(t28:2)],[l2:1]) ).
cnf(t31,plain,
$false,
inference(connection,[status(thm),parent(t30:1)],[t30:1,t28:2]) ).
cnf(t32,plain,
( sdtasdt0(xn,xm) != sdtpldt0(sdtasdt0(xp,xm),sdtasdt0(xr,xm))
| sdtpldt0(sdtasdt0(xp,xm),sdtasdt0(xr,xm)) = sdtasdt0(xn,xm) ),
inference(extension,[status(thm),parent(t28:3)],[equality_2]) ).
cnf(t33,plain,
$false,
inference(connection,[status(thm),parent(t32:1)],[t32:1,t28:3]) ).
cnf(t34,plain,
sdtasdt0(xn,xm) = sdtpldt0(sdtasdt0(xp,xm),sdtasdt0(xr,xm)),
inference(extension,[status(thm),parent(t32:2)],[f_46_2]) ).
cnf(t35,plain,
$false,
inference(connection,[status(thm),parent(t34:1)],[t34:1,t32:2]) ).
cnf(t36,plain,
aNaturalNumber0(sdtasdt0(xr,xm)),
inference(lemma_extension,[status(thm),parent(t28:4)],[l7:1]) ).
cnf(t37,plain,
$false,
inference(connection,[status(thm),parent(t36:1)],[t36:1,t28:4]) ).
cnf(t38,plain,
( ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(xn)
| aNaturalNumber0(sdtasdt0(xn,xm)) ),
inference(extension,[status(thm),parent(t28:5)],[f_5_3]) ).
cnf(t39,plain,
$false,
inference(connection,[status(thm),parent(t38:1)],[t38:1,t28:5]) ).
cnf(t40,plain,
aNaturalNumber0(xn),
inference(extension,[status(thm),parent(t38:2)],[f_39_2]) ).
cnf(t41,plain,
$false,
inference(connection,[status(thm),parent(t40:1)],[t40:1,t38:2]) ).
cnf(t42,plain,
aNaturalNumber0(xm),
inference(extension,[status(thm),parent(t38:3)],[f_39_3]) ).
cnf(t43,plain,
$false,
inference(connection,[status(thm),parent(t42:1)],[t42:1,t38:3]) ).
cnf(t44,plain,
( ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(xn)
| aNaturalNumber0(sdtasdt0(xn,xm)) ),
inference(extension,[status(thm),parent(t2:6)],[f_5_3]) ).
cnf(t45,plain,
$false,
inference(connection,[status(thm),parent(t44:1)],[t44:1,t2:6]) ).
cnf(t46,plain,
aNaturalNumber0(xn),
inference(extension,[status(thm),parent(t44:2)],[f_39_2]) ).
cnf(t47,plain,
$false,
inference(connection,[status(thm),parent(t46:1)],[t46:1,t44:2]) ).
cnf(t48,plain,
aNaturalNumber0(xm),
inference(extension,[status(thm),parent(t44:3)],[f_39_3]) ).
cnf(t49,plain,
$false,
inference(connection,[status(thm),parent(t48:1)],[t48:1,t44:3]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : NUM490+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
% 0.08/0.35 % Computer : n006.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 18:36:12 UTC 2026
% 0.08/0.35 % CPUTime :
% 84.15/84.43 % SZS status Theorem for theBenchmark
% 84.15/84.43 % SZS output start Proof for theBenchmark
% See solution above
%------------------------------------------------------------------------------