%------------------------------------------------------------------------------
% File : ConnectPP---0.7.2
% Problem : NUN081+1 : TPTP v9.3.1. Released v7.3.0.
% 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 : n015.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 08:53:51 AM UTC 2026
% Result : Theorem 0.22s 0.47s
% Output : Proof 0.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 4
% Syntax : Number of formulae : 41 ( 16 unt; 0 def)
% Number of atoms : 132 ( 0 equ)
% Maximal formula atoms : 6 ( 3 avg)
% Number of connectives : 122 ( 31 ~; 25 |; 66 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 5 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 6 ( 5 usr; 1 prp; 0-3 aty)
% Number of functors : 9 ( 9 usr; 0 con; 1-2 aty)
% Number of variables : 131 ( 8 sgn 46 !; 51 ?)
% Comments :
%------------------------------------------------------------------------------
fof(axiom_2a,axiom,
! [X2,X9] :
? [Y2] :
( ? [Y6] :
( r4(X2,X9,Y6)
& r3(Y6,X2,Y2) )
& ? [Y3] :
( ? [Y14] :
( r4(X2,Y14,Y3)
& r2(X9,Y14) )
& id(Y3,Y2) ) ),
file('NUM009+0.ax',axiom_2a) ).
fof(axiom_4a,axiom,
! [X4] :
? [Y9] :
( ? [Y16] :
( r3(X4,Y16,Y9)
& r1(Y16) )
& id(Y9,X4) ),
file('NUM009+0.ax',axiom_4a) ).
fof(axiom_5a,axiom,
! [X5] :
? [Y8] :
( ? [Y18] :
( r1(Y18)
& id(Y8,Y18) )
& ? [Y17] :
( r4(X5,Y17,Y8)
& r1(Y17) ) ),
file('NUM009+0.ax',axiom_5a) ).
fof(xplusyidthree,conjecture,
? [Y1,Y2,Y3] :
( ? [Y4] :
( ? [Y5] :
( ? [Y6] :
( ? [Y7] :
( r2(Y7,Y6)
& r1(Y7) )
& r2(Y6,Y5) )
& r2(Y5,Y4) )
& id(Y3,Y4) )
& r3(Y1,Y2,Y3) ),
file('theBenchmark.p',xplusyidthree) ).
fof(f_13_1,plain,
! [X2,X9] :
? [Y2] :
( ? [Y6] :
( r4(X2,X9,Y6)
& r3(Y6,X2,Y2) )
& ? [Y3] :
( ? [Y14] :
( r4(X2,Y14,Y3)
& r2(X9,Y14) )
& id(Y3,Y2) ) ),
inference(fof_nnf,[status(thm)],[axiom_2a]) ).
fof(f_13_2,plain,
! [U_48,U_47] :
? [U_46] :
( ? [U_45] :
( r4(U_48,U_47,U_45)
& r3(U_45,U_48,U_46) )
& ? [U_44] :
( ? [U_43] :
( r4(U_48,U_43,U_44)
& r2(U_47,U_43) )
& id(U_44,U_46) ) ),
inference(variable_rename,[status(thm)],[f_13_1]) ).
fof(f_13_3,plain,
! [U_48,U_47] :
( ? [U_45] :
( r4(U_48,U_47,U_45)
& r3(U_45,U_48,sK9(U_48,U_47)) )
& ? [U_44] :
( ? [U_43] :
( r4(U_48,U_43,U_44)
& r2(U_47,U_43) )
& id(U_44,sK9(U_48,U_47)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK9]),skolemize(U_46,sK9(U_48,U_47))],[f_13_2]) ).
fof(f_13_4,plain,
! [U_48,U_47] :
( ? [U_45] :
( r4(U_48,U_47,U_45)
& r3(U_45,U_48,sK9(U_48,U_47)) )
& ? [U_43] :
( r4(U_48,U_43,sK10(U_48,U_47))
& r2(U_47,U_43) )
& id(sK10(U_48,U_47),sK9(U_48,U_47)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK10]),skolemize(U_44,sK10(U_48,U_47))],[f_13_3]) ).
fof(f_13_5,plain,
! [U_48,U_47] :
( ? [U_45] :
( r4(U_48,U_47,U_45)
& r3(U_45,U_48,sK9(U_48,U_47)) )
& r4(U_48,sK11(U_48,U_47),sK10(U_48,U_47))
& r2(U_47,sK11(U_48,U_47))
& id(sK10(U_48,U_47),sK9(U_48,U_47)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK11]),skolemize(U_43,sK11(U_48,U_47))],[f_13_4]) ).
fof(f_13_6,plain,
! [U_48,U_47] :
( r4(U_48,U_47,sK12(U_48,U_47))
& r3(sK12(U_48,U_47),U_48,sK9(U_48,U_47))
& r4(U_48,sK11(U_48,U_47),sK10(U_48,U_47))
& r2(U_47,sK11(U_48,U_47))
& id(sK10(U_48,U_47),sK9(U_48,U_47)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK12]),skolemize(U_45,sK12(U_48,U_47))],[f_13_5]) ).
cnf(f_13_8,plain,
r2(U_47,sK11(U_48,U_47)),
inference(clausify,[status(thm)],[f_13_6]) ).
fof(f_15_1,plain,
! [X4] :
? [Y9] :
( ? [Y16] :
( r3(X4,Y16,Y9)
& r1(Y16) )
& id(Y9,X4) ),
inference(fof_nnf,[status(thm)],[axiom_4a]) ).
fof(f_15_2,plain,
! [U_55] :
? [U_54] :
( ? [U_53] :
( r3(U_55,U_53,U_54)
& r1(U_53) )
& id(U_54,U_55) ),
inference(variable_rename,[status(thm)],[f_15_1]) ).
fof(f_15_3,plain,
! [U_55] :
( ? [U_53] :
( r3(U_55,U_53,sK13(U_55))
& r1(U_53) )
& id(sK13(U_55),U_55) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK13]),skolemize(U_54,sK13(U_55))],[f_15_2]) ).
fof(f_15_4,plain,
! [U_55] :
( r3(U_55,sK14(U_55),sK13(U_55))
& r1(sK14(U_55))
& id(sK13(U_55),U_55) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK14]),skolemize(U_53,sK14(U_55))],[f_15_3]) ).
cnf(f_15_5,plain,
id(sK13(U_55),U_55),
inference(clausify,[status(thm)],[f_15_4]) ).
cnf(f_15_7,plain,
r3(U_55,sK14(U_55),sK13(U_55)),
inference(clausify,[status(thm)],[f_15_4]) ).
fof(f_16_1,plain,
! [X5] :
? [Y8] :
( ? [Y18] :
( r1(Y18)
& id(Y8,Y18) )
& ? [Y17] :
( r4(X5,Y17,Y8)
& r1(Y17) ) ),
inference(fof_nnf,[status(thm)],[axiom_5a]) ).
fof(f_16_2,plain,
! [U_59] :
? [U_58] :
( ? [U_57] :
( r1(U_57)
& id(U_58,U_57) )
& ? [U_56] :
( r4(U_59,U_56,U_58)
& r1(U_56) ) ),
inference(variable_rename,[status(thm)],[f_16_1]) ).
fof(f_16_3,plain,
! [U_59] :
( ? [U_57] :
( r1(U_57)
& id(sK15(U_59),U_57) )
& ? [U_56] :
( r4(U_59,U_56,sK15(U_59))
& r1(U_56) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK15]),skolemize(U_58,sK15(U_59))],[f_16_2]) ).
fof(f_16_4,plain,
! [U_59] :
( ? [U_57] :
( r1(U_57)
& id(sK15(U_59),U_57) )
& r4(U_59,sK16(U_59),sK15(U_59))
& r1(sK16(U_59)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK16]),skolemize(U_56,sK16(U_59))],[f_16_3]) ).
fof(f_16_5,plain,
! [U_59] :
( r1(sK17(U_59))
& id(sK15(U_59),sK17(U_59))
& r4(U_59,sK16(U_59),sK15(U_59))
& r1(sK16(U_59)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK17]),skolemize(U_57,sK17(U_59))],[f_16_4]) ).
cnf(f_16_9,plain,
r1(sK17(U_59)),
inference(clausify,[status(thm)],[f_16_5]) ).
fof(f_19_1,negated_conjecture,
~ ? [Y1,Y2,Y3] :
( ? [Y4] :
( ? [Y5] :
( ? [Y6] :
( ? [Y7] :
( r2(Y7,Y6)
& r1(Y7) )
& r2(Y6,Y5) )
& r2(Y5,Y4) )
& id(Y3,Y4) )
& r3(Y1,Y2,Y3) ),
inference(negate,[status(cth)],[xplusyidthree]) ).
fof(f_19_2,negated_conjecture,
! [Y1,Y2,Y3] :
( ! [Y4] :
( ! [Y5] :
( ! [Y6] :
( ! [Y7] :
( ~ r2(Y7,Y6)
| ~ r1(Y7) )
| ~ r2(Y6,Y5) )
| ~ r2(Y5,Y4) )
| ~ id(Y3,Y4) )
| ~ r3(Y1,Y2,Y3) ),
inference(fof_nnf,[status(thm)],[f_19_1]) ).
fof(f_19_3,negated_conjecture,
! [U_73,U_72,U_71] :
( ! [U_70] :
( ! [U_69] :
( ! [U_68] :
( ! [U_67] :
( ~ r2(U_67,U_68)
| ~ r1(U_67) )
| ~ r2(U_68,U_69) )
| ~ r2(U_69,U_70) )
| ~ id(U_71,U_70) )
| ~ r3(U_73,U_72,U_71) ),
inference(variable_rename,[status(thm)],[f_19_2]) ).
fof(f_19_4,negated_conjecture,
! [U_68,U_67,U_69,U_70,U_71,U_72,U_73] :
( ~ r2(U_67,U_68)
| ~ r1(U_67)
| ~ r2(U_68,U_69)
| ~ r2(U_69,U_70)
| ~ id(U_71,U_70)
| ~ r3(U_73,U_72,U_71) ),
inference(definitional_conversion,[status(esa)],[f_19_3]) ).
cnf(f_19_5,negated_conjecture,
( ~ r2(U_67,U_68)
| ~ r1(U_67)
| ~ r2(U_68,U_69)
| ~ r2(U_69,U_70)
| ~ id(U_71,U_70)
| ~ r3(U_73,U_72,U_71) ),
inference(clausify,[status(thm)],[f_19_4]) ).
cnf(t1,plain,
( ~ id(sK13(sK11(U_613,sK11(U_611,sK11(U_608,sK17(U_609))))),sK11(U_613,sK11(U_611,sK11(U_608,sK17(U_609)))))
| ~ r2(sK11(U_611,sK11(U_608,sK17(U_609))),sK11(U_613,sK11(U_611,sK11(U_608,sK17(U_609)))))
| ~ r2(sK11(U_608,sK17(U_609)),sK11(U_611,sK11(U_608,sK17(U_609))))
| ~ r1(sK17(U_609))
| ~ r2(sK17(U_609),sK11(U_608,sK17(U_609)))
| ~ r3(sK11(U_613,sK11(U_611,sK11(U_608,sK17(U_609)))),sK14(sK11(U_613,sK11(U_611,sK11(U_608,sK17(U_609))))),sK13(sK11(U_613,sK11(U_611,sK11(U_608,sK17(U_609)))))) ),
inference(start,[status(thm),parent(0:0)],[f_19_5]) ).
cnf(t2,plain,
r3(sK11(U_613,sK11(U_611,sK11(U_608,sK17(U_609)))),sK14(sK11(U_613,sK11(U_611,sK11(U_608,sK17(U_609))))),sK13(sK11(U_613,sK11(U_611,sK11(U_608,sK17(U_609)))))),
inference(extension,[status(thm),parent(t1:1)],[f_15_7]) ).
cnf(t3,plain,
$false,
inference(connection,[status(thm),parent(t2:1)],[t2:1,t1:1]) ).
cnf(t4,plain,
r2(sK17(U_609),sK11(U_608,sK17(U_609))),
inference(extension,[status(thm),parent(t1:2)],[f_13_8]) ).
cnf(t5,plain,
$false,
inference(connection,[status(thm),parent(t4:1)],[t4:1,t1:2]) ).
cnf(t6,plain,
r1(sK17(U_609)),
inference(extension,[status(thm),parent(t1:3)],[f_16_9]) ).
cnf(t7,plain,
$false,
inference(connection,[status(thm),parent(t6:1)],[t6:1,t1:3]) ).
cnf(t8,plain,
r2(sK11(U_608,sK17(U_609)),sK11(U_611,sK11(U_608,sK17(U_609)))),
inference(extension,[status(thm),parent(t1:4)],[f_13_8]) ).
cnf(t9,plain,
$false,
inference(connection,[status(thm),parent(t8:1)],[t8:1,t1:4]) ).
cnf(t10,plain,
r2(sK11(U_611,sK11(U_608,sK17(U_609))),sK11(U_613,sK11(U_611,sK11(U_608,sK17(U_609))))),
inference(extension,[status(thm),parent(t1:5)],[f_13_8]) ).
cnf(t11,plain,
$false,
inference(connection,[status(thm),parent(t10:1)],[t10:1,t1:5]) ).
cnf(t12,plain,
id(sK13(sK11(U_613,sK11(U_611,sK11(U_608,sK17(U_609))))),sK11(U_613,sK11(U_611,sK11(U_608,sK17(U_609))))),
inference(extension,[status(thm),parent(t1:6)],[f_15_5]) ).
cnf(t13,plain,
$false,
inference(connection,[status(thm),parent(t12:1)],[t12:1,t1:6]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUN081+1 : TPTP v9.3.1. Released v7.3.0.
% 0.00/0.03 This is a FOF_THM_RFO_NEQ 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
% 0.09/0.37 % Computer : n015.cluster.edu
% 0.09/0.37 % Model : x86_64 x86_64
% 0.09/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.37 % Memory : 8046.5625MB
% 0.09/0.37 % OS : Linux 6.8.0-71-generic
% 0.09/0.37 % CPULimit : 300
% 0.09/0.37 % WCLimit : 300
% 0.09/0.37 % DateTime : Sat Sep 19 19:37:34 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.22/0.47 % SZS status Theorem for theBenchmark
% 0.22/0.47 % SZS output start Proof for theBenchmark
% See solution above
%------------------------------------------------------------------------------