%------------------------------------------------------------------------------
% File : ConnectPP---0.7.2
% Problem : NUN070+2 : 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 : n018.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 246.45s 246.72s
% Output : Proof 246.45s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 4
% Syntax : Number of formulae : 47 ( 19 unt; 0 def)
% Number of atoms : 154 ( 30 equ)
% Maximal formula atoms : 7 ( 3 avg)
% Number of connectives : 143 ( 36 ~; 30 |; 77 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 5 avg)
% Maximal term depth : 4 ( 1 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 : 135 ( 9 sgn 60 !; 49 ?)
% Comments :
%------------------------------------------------------------------------------
fof(axiom_1a,axiom,
! [X1,X8] :
? [Y4] :
( ? [Y7] :
( r3(X1,X8,Y7)
& r2(Y7,Y4) )
& ? [Y5] :
( Y5 = Y4
& ? [Y15] :
( r3(X1,Y15,Y5)
& r2(X8,Y15) ) ) ),
file('NUM008+0.ax',axiom_1a) ).
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(onepluszeroeqone,conjecture,
? [Y1] :
( ? [Y3] :
( ? [Y6] :
( r2(Y6,Y3)
& r1(Y6) )
& Y1 = Y3 )
& ? [Y2] :
( ? [Y5] :
( r2(Y5,Y2)
& r1(Y5) )
& ? [Y4] :
( r3(Y2,Y4,Y1)
& r1(Y4) ) ) ),
file('theBenchmark.p',onepluszeroeqone) ).
fof(f_5_1,plain,
! [X1,X8] :
? [Y4] :
( ? [Y7] :
( r3(X1,X8,Y7)
& r2(Y7,Y4) )
& ? [Y5] :
( Y5 = Y4
& ? [Y15] :
( r3(X1,Y15,Y5)
& r2(X8,Y15) ) ) ),
inference(fof_nnf,[status(thm)],[axiom_1a]) ).
fof(f_5_2,plain,
! [U_18,U_17] :
? [U_16] :
( ? [U_15] :
( r3(U_18,U_17,U_15)
& r2(U_15,U_16) )
& ? [U_14] :
( U_14 = U_16
& ? [U_13] :
( r3(U_18,U_13,U_14)
& r2(U_17,U_13) ) ) ),
inference(variable_rename,[status(thm)],[f_5_1]) ).
fof(f_5_3,plain,
! [U_18,U_17] :
( ? [U_15] :
( r3(U_18,U_17,U_15)
& r2(U_15,sK5(U_18,U_17)) )
& ? [U_14] :
( U_14 = sK5(U_18,U_17)
& ? [U_13] :
( r3(U_18,U_13,U_14)
& r2(U_17,U_13) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK5]),skolemize(U_16,sK5(U_18,U_17))],[f_5_2]) ).
fof(f_5_4,plain,
! [U_18,U_17] :
( ? [U_15] :
( r3(U_18,U_17,U_15)
& r2(U_15,sK5(U_18,U_17)) )
& sK6(U_18,U_17) = sK5(U_18,U_17)
& ? [U_13] :
( r3(U_18,U_13,sK6(U_18,U_17))
& r2(U_17,U_13) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK6]),skolemize(U_14,sK6(U_18,U_17))],[f_5_3]) ).
fof(f_5_5,plain,
! [U_18,U_17] :
( ? [U_15] :
( r3(U_18,U_17,U_15)
& r2(U_15,sK5(U_18,U_17)) )
& sK6(U_18,U_17) = sK5(U_18,U_17)
& r3(U_18,sK7(U_18,U_17),sK6(U_18,U_17))
& r2(U_17,sK7(U_18,U_17)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK7]),skolemize(U_13,sK7(U_18,U_17))],[f_5_4]) ).
fof(f_5_6,plain,
! [U_18,U_17] :
( r3(U_18,U_17,sK8(U_18,U_17))
& r2(sK8(U_18,U_17),sK5(U_18,U_17))
& sK6(U_18,U_17) = sK5(U_18,U_17)
& r3(U_18,sK7(U_18,U_17),sK6(U_18,U_17))
& r2(U_17,sK7(U_18,U_17)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK8]),skolemize(U_15,sK8(U_18,U_17))],[f_5_5]) ).
fof(f_5_7,plain,
( ! [U_18,U_17] : r3(U_18,U_17,sK8(U_18,U_17))
& ! [U_18,U_17] : r2(sK8(U_18,U_17),sK5(U_18,U_17))
& ! [U_18,U_17] : sK6(U_18,U_17) = sK5(U_18,U_17)
& ! [U_18,U_17] : r3(U_18,sK7(U_18,U_17),sK6(U_18,U_17))
& ! [U_18,U_17] : r2(U_17,sK7(U_18,U_17)) ),
inference(definitional_conversion,[status(esa)],[f_5_6]) ).
cnf(f_5_8,plain,
r2(U_17,sK7(U_18,U_17)),
inference(clausify,[status(thm)],[f_5_7]) ).
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]) ).
fof(f_8_5,plain,
( ! [U_31] : sK13(U_31) = U_31
& ! [U_31] : r3(U_31,sK14(U_31),sK13(U_31))
& ! [U_31] : r1(sK14(U_31)) ),
inference(definitional_conversion,[status(esa)],[f_8_4]) ).
cnf(f_8_6,plain,
r1(sK14(U_31)),
inference(clausify,[status(thm)],[f_8_5]) ).
cnf(f_8_7,plain,
r3(U_31,sK14(U_31),sK13(U_31)),
inference(clausify,[status(thm)],[f_8_5]) ).
cnf(f_8_8,plain,
sK13(U_31) = U_31,
inference(clausify,[status(thm)],[f_8_5]) ).
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]) ).
fof(f_9_6,plain,
( ! [U_35] : sK15(U_35) = sK17(U_35)
& ! [U_35] : r1(sK17(U_35))
& ! [U_35] : r4(U_35,sK16(U_35),sK15(U_35))
& ! [U_35] : r1(sK16(U_35)) ),
inference(definitional_conversion,[status(esa)],[f_9_5]) ).
cnf(f_9_9,plain,
r1(sK17(U_35)),
inference(clausify,[status(thm)],[f_9_6]) ).
fof(f_12_1,negated_conjecture,
~ ? [Y1] :
( ? [Y3] :
( ? [Y6] :
( r2(Y6,Y3)
& r1(Y6) )
& Y1 = Y3 )
& ? [Y2] :
( ? [Y5] :
( r2(Y5,Y2)
& r1(Y5) )
& ? [Y4] :
( r3(Y2,Y4,Y1)
& r1(Y4) ) ) ),
inference(negate,[status(cth)],[onepluszeroeqone]) ).
fof(f_12_2,negated_conjecture,
! [Y1] :
( ! [Y3] :
( ! [Y6] :
( ~ r2(Y6,Y3)
| ~ r1(Y6) )
| Y1 != Y3 )
| ! [Y2] :
( ! [Y5] :
( ~ r2(Y5,Y2)
| ~ r1(Y5) )
| ! [Y4] :
( ~ r3(Y2,Y4,Y1)
| ~ r1(Y4) ) ) ),
inference(fof_nnf,[status(thm)],[f_12_1]) ).
fof(f_12_3,negated_conjecture,
! [U_48] :
( ! [U_47] :
( ! [U_46] :
( ~ r2(U_46,U_47)
| ~ r1(U_46) )
| U_48 != U_47 )
| ! [U_45] :
( ! [U_44] :
( ~ r2(U_44,U_45)
| ~ r1(U_44) )
| ! [U_43] :
( ~ r3(U_45,U_43,U_48)
| ~ r1(U_43) ) ) ),
inference(variable_rename,[status(thm)],[f_12_2]) ).
fof(f_12_4,negated_conjecture,
! [U_46,U_45,U_43,U_44,U_47,U_48] :
( ~ r2(U_46,U_47)
| ~ r1(U_46)
| U_48 != U_47
| ~ r2(U_44,U_45)
| ~ r1(U_44)
| ~ r3(U_45,U_43,U_48)
| ~ r1(U_43) ),
inference(definitional_conversion,[status(esa)],[f_12_3]) ).
cnf(f_12_5,negated_conjecture,
( ~ r2(U_46,U_47)
| ~ r1(U_46)
| U_48 != U_47
| ~ r2(U_44,U_45)
| ~ r1(U_44)
| ~ r3(U_45,U_43,U_48)
| ~ r1(U_43) ),
inference(clausify,[status(thm)],[f_12_4]) ).
cnf(t1,plain,
( ~ r1(sK14(sK7(U_11875,sK17(U_11872))))
| ~ r2(sK17(U_11872),sK7(U_11875,sK17(U_11872)))
| sK13(sK7(U_11875,sK17(U_11872))) != sK7(U_11875,sK17(U_11872))
| ~ r1(sK17(U_11872))
| ~ r3(sK7(U_11875,sK17(U_11872)),sK14(sK7(U_11875,sK17(U_11872))),sK13(sK7(U_11875,sK17(U_11872))))
| ~ r2(sK17(U_11872),sK7(U_11875,sK17(U_11872)))
| ~ r1(sK17(U_11872)) ),
inference(start,[status(thm),parent(0:0)],[f_12_5]) ).
cnf(t2,plain,
r1(sK17(U_11872)),
inference(extension,[status(thm),parent(t1:1)],[f_9_9]) ).
cnf(t3,plain,
$false,
inference(connection,[status(thm),parent(t2:1)],[t2:1,t1:1]) ).
cnf(t4,plain,
r2(sK17(U_11872),sK7(U_11875,sK17(U_11872))),
inference(extension,[status(thm),parent(t1:2)],[f_5_8]) ).
cnf(t5,plain,
$false,
inference(connection,[status(thm),parent(t4:1)],[t4:1,t1:2]) ).
cnf(t6,plain,
r3(sK7(U_11875,sK17(U_11872)),sK14(sK7(U_11875,sK17(U_11872))),sK13(sK7(U_11875,sK17(U_11872)))),
inference(extension,[status(thm),parent(t1:3)],[f_8_7]) ).
cnf(t7,plain,
$false,
inference(connection,[status(thm),parent(t6:1)],[t6:1,t1:3]) ).
cnf(t8,plain,
r1(sK17(U_11872)),
inference(extension,[status(thm),parent(t1:4)],[f_9_9]) ).
cnf(t9,plain,
$false,
inference(connection,[status(thm),parent(t8:1)],[t8:1,t1:4]) ).
cnf(t10,plain,
sK13(sK7(U_11875,sK17(U_11872))) = sK7(U_11875,sK17(U_11872)),
inference(extension,[status(thm),parent(t1:5)],[f_8_8]) ).
cnf(t11,plain,
$false,
inference(connection,[status(thm),parent(t10:1)],[t10:1,t1:5]) ).
cnf(t12,plain,
r2(sK17(U_11872),sK7(U_11875,sK17(U_11872))),
inference(extension,[status(thm),parent(t1:6)],[f_5_8]) ).
cnf(t13,plain,
$false,
inference(connection,[status(thm),parent(t12:1)],[t12:1,t1:6]) ).
cnf(t14,plain,
r1(sK14(sK7(U_11875,sK17(U_11872)))),
inference(extension,[status(thm),parent(t1:7)],[f_8_6]) ).
cnf(t15,plain,
$false,
inference(connection,[status(thm),parent(t14:1)],[t14:1,t1:7]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : NUN070+2 : TPTP v9.3.1. Released v7.3.0.
% 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
% 0.07/0.34 % Computer : n018.cluster.edu
% 0.07/0.34 % Model : x86_64 x86_64
% 0.07/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.34 % Memory : 8046.5625MB
% 0.07/0.34 % OS : Linux 6.8.0-71-generic
% 0.07/0.34 % CPULimit : 300
% 0.07/0.34 % WCLimit : 300
% 0.07/0.34 % DateTime : Sat Sep 19 19:31:57 UTC 2026
% 0.07/0.35 % CPUTime :
% 246.45/246.72 % SZS status Theorem for theBenchmark
% 246.45/246.72 % SZS output start Proof for theBenchmark
% See solution above
%------------------------------------------------------------------------------