%------------------------------------------------------------------------------
% File : ConnectPP---0.7.2
% Problem : NUN069+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 08:53:49 AM UTC 2026
% Result : Theorem 0.15s 5.49s
% Output : Proof 0.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 5
% Syntax : Number of formulae : 39 ( 14 unt; 0 def)
% Number of atoms : 114 ( 32 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 106 ( 31 ~; 25 |; 50 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-3 aty)
% Number of functors : 7 ( 7 usr; 0 con; 1-2 aty)
% Number of variables : 99 ( 6 sgn 38 !; 34 ?)
% 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_3a,axiom,
! [X3,X10] :
( X3 = X10
| ! [Y12] :
( ~ r2(X10,Y12)
| ! [Y13] :
( Y13 != Y12
| ~ r2(X3,Y13) ) ) ),
file('NUM008+0.ax',axiom_3a) ).
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(oneeqone,conjecture,
? [Y1] :
( ? [Y2] :
( r2(Y2,Y1)
& r1(Y2) )
& Y1 = Y1 ),
file('theBenchmark.p',oneeqone) ).
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_7_1,plain,
! [X3,X10] :
( X3 = X10
| ! [Y12] :
( ~ r2(X10,Y12)
| ! [Y13] :
( Y13 != Y12
| ~ r2(X3,Y13) ) ) ),
inference(fof_nnf,[status(thm)],[axiom_3a]) ).
fof(f_7_2,plain,
! [U_28,U_27] :
( U_28 = U_27
| ! [U_26] :
( ~ r2(U_27,U_26)
| ! [U_25] :
( U_25 != U_26
| ~ r2(U_28,U_25) ) ) ),
inference(variable_rename,[status(thm)],[f_7_1]) ).
cnf(f_7_3,plain,
( U_28 = U_27
| ~ r2(U_27,U_26)
| U_25 != U_26
| ~ r2(U_28,U_25) ),
inference(clausify,[status(thm)],[f_7_2]) ).
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] :
( r2(Y2,Y1)
& r1(Y2) )
& Y1 = Y1 ),
inference(negate,[status(cth)],[oneeqone]) ).
fof(f_12_2,negated_conjecture,
! [Y1] :
( ! [Y2] :
( ~ r2(Y2,Y1)
| ~ r1(Y2) )
| Y1 != Y1 ),
inference(fof_nnf,[status(thm)],[f_12_1]) ).
fof(f_12_3,negated_conjecture,
! [U_44] :
( ! [U_43] :
( ~ r2(U_43,U_44)
| ~ r1(U_43) )
| U_44 != U_44 ),
inference(variable_rename,[status(thm)],[f_12_2]) ).
fof(f_12_4,negated_conjecture,
! [U_44,U_43] :
( ~ r2(U_43,U_44)
| ~ r1(U_43)
| U_44 != U_44 ),
inference(definitional_conversion,[status(esa)],[f_12_3]) ).
cnf(f_12_5,negated_conjecture,
( ~ r2(U_43,U_44)
| ~ r1(U_43)
| U_44 != U_44 ),
inference(clausify,[status(thm)],[f_12_4]) ).
cnf(equality_1,axiom,
Eq_x_0 = Eq_x_0,
theory(equality,[reflexivity]) ).
cnf(t1,plain,
( ~ r1(sK17(U_758))
| ~ r2(sK17(U_758),sK11(U_757,sK17(U_758)))
| sK11(U_757,sK17(U_758)) != sK11(U_757,sK17(U_758)) ),
inference(start,[status(thm),parent(0:0)],[f_12_5]) ).
cnf(t2,plain,
( sK11(U_752,sK11(U_757,sK17(U_758))) != sK11(U_752,sK11(U_757,sK17(U_758)))
| ~ r2(sK11(U_757,sK17(U_758)),sK11(U_752,sK11(U_757,sK17(U_758))))
| ~ r2(sK11(U_757,sK17(U_758)),sK11(U_752,sK11(U_757,sK17(U_758))))
| sK11(U_757,sK17(U_758)) = sK11(U_757,sK17(U_758)) ),
inference(extension,[status(thm),parent(t1:1)],[f_7_3]) ).
cnf(t3,plain,
$false,
inference(connection,[status(thm),parent(t2:1)],[t2:1,t1:1]) ).
cnf(t4,plain,
r2(sK11(U_757,sK17(U_758)),sK11(U_752,sK11(U_757,sK17(U_758)))),
inference(extension,[status(thm),parent(t2:2)],[f_6_7]) ).
cnf(t5,plain,
$false,
inference(connection,[status(thm),parent(t4:1)],[t4:1,t2:2]) ).
cnf(t6,plain,
r2(sK11(U_757,sK17(U_758)),sK11(U_752,sK11(U_757,sK17(U_758)))),
inference(extension,[status(thm),parent(t2:3)],[f_6_7]) ).
cnf(t7,plain,
$false,
inference(connection,[status(thm),parent(t6:1)],[t6:1,t2:3]) ).
cnf(t8,plain,
sK11(U_752,sK11(U_757,sK17(U_758))) = sK11(U_752,sK11(U_757,sK17(U_758))),
inference(extension,[status(thm),parent(t2:4)],[equality_1]) ).
cnf(t9,plain,
$false,
inference(connection,[status(thm),parent(t8:1)],[t8:1,t2:4]) ).
cnf(t10,plain,
r2(sK17(U_758),sK11(U_757,sK17(U_758))),
inference(extension,[status(thm),parent(t1:2)],[f_6_7]) ).
cnf(t11,plain,
$false,
inference(connection,[status(thm),parent(t10:1)],[t10:1,t1:2]) ).
cnf(t12,plain,
r1(sK17(U_758)),
inference(extension,[status(thm),parent(t1:3)],[f_9_8]) ).
cnf(t13,plain,
$false,
inference(connection,[status(thm),parent(t12:1)],[t12:1,t1:3]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUN069+2 : TPTP v9.3.1. Released v7.3.0.
% 0.00/0.04 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
% 0.10/5.38 % Computer : n004.cluster.edu
% 0.10/5.38 % Model : x86_64 x86_64
% 0.10/5.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/5.38 % Memory : 8046.5625MB
% 0.10/5.38 % OS : Linux 6.8.0-71-generic
% 0.10/5.38 % CPULimit : 300
% 0.10/5.38 % WCLimit : 300
% 0.10/5.38 % DateTime : Sat Sep 19 19:29:57 UTC 2026
% 0.10/5.38 % CPUTime :
% 0.15/5.49 % SZS status Theorem for theBenchmark
% 0.15/5.49 % SZS output start Proof for theBenchmark
% See solution above
%------------------------------------------------------------------------------