%------------------------------------------------------------------------------
% File : ConnectPP---0.7.2
% Problem : NUN081+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 : n016.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 0.13s 0.41s
% Output : Proof 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 4
% Syntax : Number of formulae : 41 ( 16 unt; 0 def)
% Number of atoms : 132 ( 27 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 ( 4 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] :
( Y3 = Y2
& ? [Y14] :
( r4(X2,Y14,Y3)
& r2(X9,Y14) ) ) ),
file('NUM008+0.ax',axiom_2a) ).
fof(axiom_4a,axiom,
! [X4] :
? [Y9] :
( Y9 = X4
& ? [Y16] :
( r3(X4,Y16,Y9)
& r1(Y16) ) ),
file('NUM008+0.ax',axiom_4a) ).
fof(axiom_5a,axiom,
! [X5] :
? [Y8] :
( ? [Y18] :
( Y8 = Y18
& r1(Y18) )
& ? [Y17] :
( r4(X5,Y17,Y8)
& r1(Y17) ) ),
file('NUM008+0.ax',axiom_5a) ).
fof(xplusyeqthree,conjecture,
? [Y1,Y2,Y3] :
( ? [Y4] :
( ? [Y5] :
( ? [Y6] :
( ? [Y7] :
( r2(Y7,Y6)
& r1(Y7) )
& r2(Y6,Y5) )
& r2(Y5,Y4) )
& Y3 = Y4 )
& r3(Y1,Y2,Y3) ),
file('theBenchmark.p',xplusyeqthree) ).
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_8_1,plain,
! [X4] :
? [Y9] :
( Y9 = X4
& ? [Y16] :
( r3(X4,Y16,Y9)
& r1(Y16) ) ),
inference(fof_nnf,[status(thm)],[axiom_4a]) ).
fof(f_8_2,plain,
! [U_31] :
? [U_30] :
( U_30 = U_31
& ? [U_29] :
( r3(U_31,U_29,U_30)
& r1(U_29) ) ),
inference(variable_rename,[status(thm)],[f_8_1]) ).
fof(f_8_3,plain,
! [U_31] :
( sK13(U_31) = U_31
& ? [U_29] :
( r3(U_31,U_29,sK13(U_31))
& r1(U_29) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK13]),skolemize(U_30,sK13(U_31))],[f_8_2]) ).
fof(f_8_4,plain,
! [U_31] :
( sK13(U_31) = U_31
& r3(U_31,sK14(U_31),sK13(U_31))
& r1(sK14(U_31)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK14]),skolemize(U_29,sK14(U_31))],[f_8_3]) ).
cnf(f_8_6,plain,
r3(U_31,sK14(U_31),sK13(U_31)),
inference(clausify,[status(thm)],[f_8_4]) ).
cnf(f_8_7,plain,
sK13(U_31) = U_31,
inference(clausify,[status(thm)],[f_8_4]) ).
fof(f_9_1,plain,
! [X5] :
? [Y8] :
( ? [Y18] :
( Y8 = Y18
& r1(Y18) )
& ? [Y17] :
( r4(X5,Y17,Y8)
& r1(Y17) ) ),
inference(fof_nnf,[status(thm)],[axiom_5a]) ).
fof(f_9_2,plain,
! [U_35] :
? [U_34] :
( ? [U_33] :
( U_34 = U_33
& r1(U_33) )
& ? [U_32] :
( r4(U_35,U_32,U_34)
& r1(U_32) ) ),
inference(variable_rename,[status(thm)],[f_9_1]) ).
fof(f_9_3,plain,
! [U_35] :
( ? [U_33] :
( sK15(U_35) = U_33
& r1(U_33) )
& ? [U_32] :
( r4(U_35,U_32,sK15(U_35))
& r1(U_32) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK15]),skolemize(U_34,sK15(U_35))],[f_9_2]) ).
fof(f_9_4,plain,
! [U_35] :
( ? [U_33] :
( sK15(U_35) = U_33
& r1(U_33) )
& r4(U_35,sK16(U_35),sK15(U_35))
& r1(sK16(U_35)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK16]),skolemize(U_32,sK16(U_35))],[f_9_3]) ).
fof(f_9_5,plain,
! [U_35] :
( sK15(U_35) = sK17(U_35)
& r1(sK17(U_35))
& r4(U_35,sK16(U_35),sK15(U_35))
& r1(sK16(U_35)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK17]),skolemize(U_33,sK17(U_35))],[f_9_4]) ).
cnf(f_9_8,plain,
r1(sK17(U_35)),
inference(clausify,[status(thm)],[f_9_5]) ).
fof(f_12_1,negated_conjecture,
~ ? [Y1,Y2,Y3] :
( ? [Y4] :
( ? [Y5] :
( ? [Y6] :
( ? [Y7] :
( r2(Y7,Y6)
& r1(Y7) )
& r2(Y6,Y5) )
& r2(Y5,Y4) )
& Y3 = Y4 )
& r3(Y1,Y2,Y3) ),
inference(negate,[status(cth)],[xplusyeqthree]) ).
fof(f_12_2,negated_conjecture,
! [Y1,Y2,Y3] :
( ! [Y4] :
( ! [Y5] :
( ! [Y6] :
( ! [Y7] :
( ~ r2(Y7,Y6)
| ~ r1(Y7) )
| ~ r2(Y6,Y5) )
| ~ r2(Y5,Y4) )
| Y3 != Y4 )
| ~ r3(Y1,Y2,Y3) ),
inference(fof_nnf,[status(thm)],[f_12_1]) ).
fof(f_12_3,negated_conjecture,
! [U_49,U_48,U_47] :
( ! [U_46] :
( ! [U_45] :
( ! [U_44] :
( ! [U_43] :
( ~ r2(U_43,U_44)
| ~ r1(U_43) )
| ~ r2(U_44,U_45) )
| ~ r2(U_45,U_46) )
| U_47 != U_46 )
| ~ r3(U_49,U_48,U_47) ),
inference(variable_rename,[status(thm)],[f_12_2]) ).
fof(f_12_4,negated_conjecture,
! [U_44,U_43,U_47,U_45,U_46,U_48,U_49] :
( ~ r2(U_43,U_44)
| ~ r1(U_43)
| ~ r2(U_44,U_45)
| ~ r2(U_45,U_46)
| U_47 != U_46
| ~ r3(U_49,U_48,U_47) ),
inference(definitional_conversion,[status(esa)],[f_12_3]) ).
cnf(f_12_5,negated_conjecture,
( ~ r2(U_43,U_44)
| ~ r1(U_43)
| ~ r2(U_44,U_45)
| ~ r2(U_45,U_46)
| U_47 != U_46
| ~ r3(U_49,U_48,U_47) ),
inference(clausify,[status(thm)],[f_12_4]) ).
cnf(t1,plain,
( sK13(sK11(U_789,sK11(U_787,sK11(U_784,sK17(U_785))))) != sK11(U_789,sK11(U_787,sK11(U_784,sK17(U_785))))
| ~ r2(sK11(U_787,sK11(U_784,sK17(U_785))),sK11(U_789,sK11(U_787,sK11(U_784,sK17(U_785)))))
| ~ r2(sK11(U_784,sK17(U_785)),sK11(U_787,sK11(U_784,sK17(U_785))))
| ~ r1(sK17(U_785))
| ~ r2(sK17(U_785),sK11(U_784,sK17(U_785)))
| ~ r3(sK11(U_789,sK11(U_787,sK11(U_784,sK17(U_785)))),sK14(sK11(U_789,sK11(U_787,sK11(U_784,sK17(U_785))))),sK13(sK11(U_789,sK11(U_787,sK11(U_784,sK17(U_785)))))) ),
inference(start,[status(thm),parent(0:0)],[f_12_5]) ).
cnf(t2,plain,
r3(sK11(U_789,sK11(U_787,sK11(U_784,sK17(U_785)))),sK14(sK11(U_789,sK11(U_787,sK11(U_784,sK17(U_785))))),sK13(sK11(U_789,sK11(U_787,sK11(U_784,sK17(U_785)))))),
inference(extension,[status(thm),parent(t1:1)],[f_8_6]) ).
cnf(t3,plain,
$false,
inference(connection,[status(thm),parent(t2:1)],[t2:1,t1:1]) ).
cnf(t4,plain,
r2(sK17(U_785),sK11(U_784,sK17(U_785))),
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,
r1(sK17(U_785)),
inference(extension,[status(thm),parent(t1:3)],[f_9_8]) ).
cnf(t7,plain,
$false,
inference(connection,[status(thm),parent(t6:1)],[t6:1,t1:3]) ).
cnf(t8,plain,
r2(sK11(U_784,sK17(U_785)),sK11(U_787,sK11(U_784,sK17(U_785)))),
inference(extension,[status(thm),parent(t1:4)],[f_6_7]) ).
cnf(t9,plain,
$false,
inference(connection,[status(thm),parent(t8:1)],[t8:1,t1:4]) ).
cnf(t10,plain,
r2(sK11(U_787,sK11(U_784,sK17(U_785))),sK11(U_789,sK11(U_787,sK11(U_784,sK17(U_785))))),
inference(extension,[status(thm),parent(t1:5)],[f_6_7]) ).
cnf(t11,plain,
$false,
inference(connection,[status(thm),parent(t10:1)],[t10:1,t1:5]) ).
cnf(t12,plain,
sK13(sK11(U_789,sK11(U_787,sK11(U_784,sK17(U_785))))) = sK11(U_789,sK11(U_787,sK11(U_784,sK17(U_785)))),
inference(extension,[status(thm),parent(t1:6)],[f_8_7]) ).
cnf(t13,plain,
$false,
inference(connection,[status(thm),parent(t12:1)],[t12:1,t1:6]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUN081+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
% 0.10/0.35 % Computer : n016.cluster.edu
% 0.10/0.35 % Model : x86_64 x86_64
% 0.10/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.35 % Memory : 8046.5625MB
% 0.10/0.35 % OS : Linux 6.8.0-71-generic
% 0.10/0.35 % CPULimit : 300
% 0.10/0.35 % WCLimit : 300
% 0.10/0.35 % DateTime : Sat Sep 19 19:39:20 UTC 2026
% 0.10/0.35 % CPUTime :
% 0.13/0.41 % SZS status Theorem for theBenchmark
% 0.13/0.41 % SZS output start Proof for theBenchmark
% See solution above
%------------------------------------------------------------------------------