%------------------------------------------------------------------------------
% File : ConnectPP---0.7.2
% Problem : NUN067+2 : TPTP v9.3.1. Released v7.3.0.
% 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 : 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 08:53:48 AM UTC 2026
% Result : Theorem 0.21s 0.46s
% Output : Proof 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 4
% Syntax : Number of formulae : 30 ( 10 unt; 0 def)
% Number of atoms : 76 ( 24 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 68 ( 22 ~; 14 |; 32 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-3 aty)
% Number of functors : 5 ( 5 usr; 0 con; 1-2 aty)
% Number of variables : 71 ( 6 sgn 30 !; 22 ?)
% Comments :
%------------------------------------------------------------------------------
fof(axiom_2a,axiom,
! [X2,X9] :
? [Y2] :
( ? [Y6] :
( r4(X2,X9,Y6)
& r3(Y6,X2,Y2) )
& ? [Y3] :
( Y3 = Y2
& ? [Y14] :
( r4(X2,Y14,Y3)
& r2(X9,Y14) ) ) ),
file('NUM008+0.ax',axiom_2a) ).
fof(axiom_7a,axiom,
! [X7,Y10] :
( ~ r2(X7,Y10)
| ! [Y20] :
( Y20 != Y10
| ~ r1(Y20) ) ),
file('NUM008+0.ax',axiom_7a) ).
fof(nonzerosexist,conjecture,
? [Y1] :
! [Y2] :
( Y1 != Y2
| ~ r1(Y2) ),
file('theBenchmark.p',nonzerosexist) ).
fof(f_6_1,plain,
! [X2,X9] :
? [Y2] :
( ? [Y6] :
( r4(X2,X9,Y6)
& r3(Y6,X2,Y2) )
& ? [Y3] :
( Y3 = Y2
& ? [Y14] :
( r4(X2,Y14,Y3)
& r2(X9,Y14) ) ) ),
inference(fof_nnf,[status(thm)],[axiom_2a]) ).
fof(f_6_2,plain,
! [U_24,U_23] :
? [U_22] :
( ? [U_21] :
( r4(U_24,U_23,U_21)
& r3(U_21,U_24,U_22) )
& ? [U_20] :
( U_20 = U_22
& ? [U_19] :
( r4(U_24,U_19,U_20)
& r2(U_23,U_19) ) ) ),
inference(variable_rename,[status(thm)],[f_6_1]) ).
fof(f_6_3,plain,
! [U_24,U_23] :
( ? [U_21] :
( r4(U_24,U_23,U_21)
& r3(U_21,U_24,sK9(U_24,U_23)) )
& ? [U_20] :
( U_20 = sK9(U_24,U_23)
& ? [U_19] :
( r4(U_24,U_19,U_20)
& r2(U_23,U_19) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK9]),skolemize(U_22,sK9(U_24,U_23))],[f_6_2]) ).
fof(f_6_4,plain,
! [U_24,U_23] :
( ? [U_21] :
( r4(U_24,U_23,U_21)
& r3(U_21,U_24,sK9(U_24,U_23)) )
& sK10(U_24,U_23) = sK9(U_24,U_23)
& ? [U_19] :
( r4(U_24,U_19,sK10(U_24,U_23))
& r2(U_23,U_19) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK10]),skolemize(U_20,sK10(U_24,U_23))],[f_6_3]) ).
fof(f_6_5,plain,
! [U_24,U_23] :
( ? [U_21] :
( r4(U_24,U_23,U_21)
& r3(U_21,U_24,sK9(U_24,U_23)) )
& sK10(U_24,U_23) = sK9(U_24,U_23)
& r4(U_24,sK11(U_24,U_23),sK10(U_24,U_23))
& r2(U_23,sK11(U_24,U_23)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK11]),skolemize(U_19,sK11(U_24,U_23))],[f_6_4]) ).
fof(f_6_6,plain,
! [U_24,U_23] :
( r4(U_24,U_23,sK12(U_24,U_23))
& r3(sK12(U_24,U_23),U_24,sK9(U_24,U_23))
& sK10(U_24,U_23) = sK9(U_24,U_23)
& r4(U_24,sK11(U_24,U_23),sK10(U_24,U_23))
& r2(U_23,sK11(U_24,U_23)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK12]),skolemize(U_21,sK12(U_24,U_23))],[f_6_5]) ).
cnf(f_6_7,plain,
r2(U_23,sK11(U_24,U_23)),
inference(clausify,[status(thm)],[f_6_6]) ).
fof(f_11_1,plain,
! [X7,Y10] :
( ~ r2(X7,Y10)
| ! [Y20] :
( Y20 != Y10
| ~ r1(Y20) ) ),
inference(fof_nnf,[status(thm)],[axiom_7a]) ).
fof(f_11_2,plain,
! [U_42,U_41] :
( ~ r2(U_42,U_41)
| ! [U_40] :
( U_40 != U_41
| ~ r1(U_40) ) ),
inference(variable_rename,[status(thm)],[f_11_1]) ).
cnf(f_11_3,plain,
( ~ r2(U_42,U_41)
| U_40 != U_41
| ~ r1(U_40) ),
inference(clausify,[status(thm)],[f_11_2]) ).
fof(f_12_1,negated_conjecture,
~ ? [Y1] :
! [Y2] :
( Y1 != Y2
| ~ r1(Y2) ),
inference(negate,[status(cth)],[nonzerosexist]) ).
fof(f_12_2,negated_conjecture,
! [Y1] :
? [Y2] :
( Y1 = Y2
& r1(Y2) ),
inference(fof_nnf,[status(thm)],[f_12_1]) ).
fof(f_12_3,negated_conjecture,
! [U_44] :
? [U_43] :
( U_44 = U_43
& r1(U_43) ),
inference(variable_rename,[status(thm)],[f_12_2]) ).
fof(f_12_4,negated_conjecture,
! [U_44] :
( U_44 = sK21(U_44)
& r1(sK21(U_44)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK21]),skolemize(U_43,sK21(U_44))],[f_12_3]) ).
fof(f_12_5,negated_conjecture,
( ! [U_44] : U_44 = sK21(U_44)
& ! [U_44] : r1(sK21(U_44)) ),
inference(definitional_conversion,[status(esa)],[f_12_4]) ).
cnf(f_12_6,negated_conjecture,
r1(sK21(U_44)),
inference(clausify,[status(thm)],[f_12_5]) ).
cnf(f_12_7,negated_conjecture,
U_44 = sK21(U_44),
inference(clausify,[status(thm)],[f_12_5]) ).
cnf(equality_2,axiom,
( Eq_x_1 = Eq_x_0
| Eq_x_0 != Eq_x_1 ),
theory(equality,[symmetry]) ).
cnf(t1,plain,
( sK21(sK11(U_760,U_759)) != sK11(U_760,U_759)
| ~ r2(U_759,sK11(U_760,U_759))
| ~ r1(sK21(sK11(U_760,U_759))) ),
inference(start,[status(thm),parent(0:0)],[f_11_3]) ).
cnf(t2,plain,
r1(sK21(sK11(U_760,U_759))),
inference(extension,[status(thm),parent(t1:1)],[f_12_6]) ).
cnf(t3,plain,
$false,
inference(connection,[status(thm),parent(t2:1)],[t2:1,t1:1]) ).
cnf(t4,plain,
r2(U_759,sK11(U_760,U_759)),
inference(extension,[status(thm),parent(t1:2)],[f_6_7]) ).
cnf(t5,plain,
$false,
inference(connection,[status(thm),parent(t4:1)],[t4:1,t1:2]) ).
cnf(t6,plain,
( sK11(U_760,U_759) != sK21(sK11(U_760,U_759))
| sK21(sK11(U_760,U_759)) = sK11(U_760,U_759) ),
inference(extension,[status(thm),parent(t1:3)],[equality_2]) ).
cnf(t7,plain,
$false,
inference(connection,[status(thm),parent(t6:1)],[t6:1,t1:3]) ).
cnf(t8,plain,
sK11(U_760,U_759) = sK21(sK11(U_760,U_759)),
inference(extension,[status(thm),parent(t6:2)],[f_12_7]) ).
cnf(t9,plain,
$false,
inference(connection,[status(thm),parent(t8:1)],[t8:1,t6:2]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUN067+2 : TPTP v9.3.1. Released v7.3.0.
% 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
% 0.10/0.37 % Computer : n004.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
% 0.10/0.38 % CPULimit : 300
% 0.10/0.38 % WCLimit : 300
% 0.10/0.38 % DateTime : Sat Sep 19 19:29:39 UTC 2026
% 0.10/0.38 % CPUTime :
% 0.21/0.46 % SZS status Theorem for theBenchmark
% 0.21/0.46 % SZS output start Proof for theBenchmark
% See solution above
%------------------------------------------------------------------------------