%------------------------------------------------------------------------------
% File : ConnectPP---0.7.2
% Problem : NUN068+1 : 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 : 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 08:53:48 AM UTC 2026
% Result : Theorem 33.95s 39.27s
% Output : Proof 33.95s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 5
% Syntax : Number of formulae : 71 ( 23 unt; 0 def)
% Number of atoms : 193 ( 0 equ)
% Maximal formula atoms : 12 ( 2 avg)
% Number of connectives : 194 ( 72 ~; 68 |; 54 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 8 ( 7 usr; 1 prp; 0-3 aty)
% Number of functors : 7 ( 7 usr; 0 con; 1-2 aty)
% Number of variables : 173 ( 14 sgn 77 !; 29 ?)
% Comments :
%------------------------------------------------------------------------------
fof(axiom_6,axiom,
! [X21,X22] :
( id(X22,X21)
| ~ id(X21,X22) ),
file('NUM009+0.ax',axiom_6) ).
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_3a,axiom,
! [X3,X10] :
( id(X3,X10)
| ! [Y12] :
( ~ r2(X10,Y12)
| ! [Y13] :
( ~ r2(X3,Y13)
| ~ id(Y13,Y12) ) ) ),
file('NUM009+0.ax',axiom_3a) ).
fof(axiom_7a,axiom,
! [X7,Y10] :
( ~ r2(X7,Y10)
| ! [Y20] :
( ~ r1(Y20)
| ~ id(Y20,Y10) ) ),
file('NUM009+0.ax',axiom_7a) ).
fof(nonzerosnononesexistid,conjecture,
? [Y1] :
( ! [Y4] :
( ~ r1(Y4)
| ~ id(Y1,Y4) )
& ! [Y2] :
( ~ id(Y1,Y2)
| ! [Y3] :
( ~ r2(Y3,Y2)
| ~ r1(Y3) ) ) ),
file('theBenchmark.p',nonzerosnononesexistid) ).
fof(f_6_1,plain,
! [X21,X22] :
( id(X22,X21)
| ~ id(X21,X22) ),
inference(fof_nnf,[status(thm)],[axiom_6]) ).
fof(f_6_2,plain,
! [U_15,U_14] :
( id(U_14,U_15)
| ~ id(U_15,U_14) ),
inference(variable_rename,[status(thm)],[f_6_1]) ).
fof(f_6_3,plain,
! [U_15,U_14] :
( id(U_14,U_15)
| ~ id(U_15,U_14) ),
inference(definitional_conversion,[status(esa)],[f_6_2]) ).
cnf(f_6_4,plain,
( id(U_14,U_15)
| ~ id(U_15,U_14) ),
inference(clausify,[status(thm)],[f_6_3]) ).
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]) ).
fof(f_13_7,plain,
( ! [U_47,U_48] : r4(U_48,U_47,sK12(U_48,U_47))
& ! [U_47,U_48] : r3(sK12(U_48,U_47),U_48,sK9(U_48,U_47))
& ! [U_47,U_48] : r4(U_48,sK11(U_48,U_47),sK10(U_48,U_47))
& ! [U_47,U_48] : r2(U_47,sK11(U_48,U_47))
& ! [U_47,U_48] : id(sK10(U_48,U_47),sK9(U_48,U_47)) ),
inference(definitional_conversion,[status(esa)],[f_13_6]) ).
cnf(f_13_9,plain,
r2(U_47,sK11(U_48,U_47)),
inference(clausify,[status(thm)],[f_13_7]) ).
fof(f_14_1,plain,
! [X3,X10] :
( id(X3,X10)
| ! [Y12] :
( ~ r2(X10,Y12)
| ! [Y13] :
( ~ r2(X3,Y13)
| ~ id(Y13,Y12) ) ) ),
inference(fof_nnf,[status(thm)],[axiom_3a]) ).
fof(f_14_2,plain,
! [U_52,U_51] :
( id(U_52,U_51)
| ! [U_50] :
( ~ r2(U_51,U_50)
| ! [U_49] :
( ~ r2(U_52,U_49)
| ~ id(U_49,U_50) ) ) ),
inference(variable_rename,[status(thm)],[f_14_1]) ).
fof(f_14_3,plain,
! [U_51,U_52,U_49,U_50] :
( id(U_52,U_51)
| ~ r2(U_51,U_50)
| ~ r2(U_52,U_49)
| ~ id(U_49,U_50) ),
inference(definitional_conversion,[status(esa)],[f_14_2]) ).
cnf(f_14_4,plain,
( id(U_52,U_51)
| ~ r2(U_51,U_50)
| ~ r2(U_52,U_49)
| ~ id(U_49,U_50) ),
inference(clausify,[status(thm)],[f_14_3]) ).
fof(f_18_1,plain,
! [X7,Y10] :
( ~ r2(X7,Y10)
| ! [Y20] :
( ~ r1(Y20)
| ~ id(Y20,Y10) ) ),
inference(fof_nnf,[status(thm)],[axiom_7a]) ).
fof(f_18_2,plain,
! [U_66,U_65] :
( ~ r2(U_66,U_65)
| ! [U_64] :
( ~ r1(U_64)
| ~ id(U_64,U_65) ) ),
inference(variable_rename,[status(thm)],[f_18_1]) ).
fof(f_18_3,plain,
! [U_64,U_66,U_65] :
( ~ r2(U_66,U_65)
| ~ r1(U_64)
| ~ id(U_64,U_65) ),
inference(definitional_conversion,[status(esa)],[f_18_2]) ).
cnf(f_18_4,plain,
( ~ r2(U_66,U_65)
| ~ r1(U_64)
| ~ id(U_64,U_65) ),
inference(clausify,[status(thm)],[f_18_3]) ).
fof(f_19_1,negated_conjecture,
~ ? [Y1] :
( ! [Y4] :
( ~ r1(Y4)
| ~ id(Y1,Y4) )
& ! [Y2] :
( ~ id(Y1,Y2)
| ! [Y3] :
( ~ r2(Y3,Y2)
| ~ r1(Y3) ) ) ),
inference(negate,[status(cth)],[nonzerosnononesexistid]) ).
fof(f_19_2,negated_conjecture,
! [Y1] :
( ? [Y4] :
( r1(Y4)
& id(Y1,Y4) )
| ? [Y2] :
( id(Y1,Y2)
& ? [Y3] :
( r2(Y3,Y2)
& r1(Y3) ) ) ),
inference(fof_nnf,[status(thm)],[f_19_1]) ).
fof(f_19_3,negated_conjecture,
! [U_70] :
( ? [U_69] :
( r1(U_69)
& id(U_70,U_69) )
| ? [U_68] :
( id(U_70,U_68)
& ? [U_67] :
( r2(U_67,U_68)
& r1(U_67) ) ) ),
inference(variable_rename,[status(thm)],[f_19_2]) ).
fof(f_19_4,negated_conjecture,
! [U_70] :
( ? [U_69] :
( r1(U_69)
& id(U_70,U_69) )
| ( id(U_70,sK21(U_70))
& ? [U_67] :
( r2(U_67,sK21(U_70))
& r1(U_67) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK21]),skolemize(U_68,sK21(U_70))],[f_19_3]) ).
fof(f_19_5,negated_conjecture,
! [U_70] :
( ? [U_69] :
( r1(U_69)
& id(U_70,U_69) )
| ( id(U_70,sK21(U_70))
& r2(sK22(U_70),sK21(U_70))
& r1(sK22(U_70)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK22]),skolemize(U_67,sK22(U_70))],[f_19_4]) ).
fof(f_19_6,negated_conjecture,
! [U_70] :
( ( r1(sK23(U_70))
& id(U_70,sK23(U_70)) )
| ( id(U_70,sK21(U_70))
& r2(sK22(U_70),sK21(U_70))
& r1(sK22(U_70)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK23]),skolemize(U_69,sK23(U_70))],[f_19_5]) ).
fof(f_19_7,negated_conjecture,
( ! [U_70] :
( r1(sK23(U_70))
| ~ sP19(U_70) )
& ! [U_70] :
( id(U_70,sK23(U_70))
| ~ sP19(U_70) )
& ! [U_70] :
( id(U_70,sK21(U_70))
| ~ sP18(U_70) )
& ! [U_70] :
( r2(sK22(U_70),sK21(U_70))
| ~ sP18(U_70) )
& ! [U_70] :
( r1(sK22(U_70))
| ~ sP18(U_70) )
& ! [U_70] :
( sP19(U_70)
| sP18(U_70) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP18,sP19])],[f_19_6]) ).
cnf(f_19_8,negated_conjecture,
( sP19(U_70)
| sP18(U_70) ),
inference(clausify,[status(thm)],[f_19_7]) ).
cnf(f_19_9,negated_conjecture,
( r1(sK22(U_70))
| ~ sP18(U_70) ),
inference(clausify,[status(thm)],[f_19_7]) ).
cnf(f_19_10,negated_conjecture,
( r2(sK22(U_70),sK21(U_70))
| ~ sP18(U_70) ),
inference(clausify,[status(thm)],[f_19_7]) ).
cnf(f_19_11,negated_conjecture,
( id(U_70,sK21(U_70))
| ~ sP18(U_70) ),
inference(clausify,[status(thm)],[f_19_7]) ).
cnf(f_19_12,negated_conjecture,
( id(U_70,sK23(U_70))
| ~ sP19(U_70) ),
inference(clausify,[status(thm)],[f_19_7]) ).
cnf(f_19_13,negated_conjecture,
( r1(sK23(U_70))
| ~ sP19(U_70) ),
inference(clausify,[status(thm)],[f_19_7]) ).
cnf(t1,plain,
( r2(sK22(sK11(U_1025,sK11(U_1030,U_1029))),sK21(sK11(U_1025,sK11(U_1030,U_1029))))
| ~ sP18(sK11(U_1025,sK11(U_1030,U_1029))) ),
inference(start,[status(thm),parent(0:0)],[f_19_10]) ).
cnf(t2,plain,
( sP19(sK11(U_1025,sK11(U_1030,U_1029)))
| sP18(sK11(U_1025,sK11(U_1030,U_1029))) ),
inference(extension,[status(thm),parent(t1:1)],[f_19_8]) ).
cnf(t3,plain,
$false,
inference(connection,[status(thm),parent(t2:1)],[t2:1,t1:1]) ).
cnf(t4,plain,
( id(sK11(U_1025,sK11(U_1030,U_1029)),sK23(sK11(U_1025,sK11(U_1030,U_1029))))
| ~ sP19(sK11(U_1025,sK11(U_1030,U_1029))) ),
inference(extension,[status(thm),parent(t2:2)],[f_19_12]) ).
cnf(t5,plain,
$false,
inference(connection,[status(thm),parent(t4:1)],[t4:1,t2:2]) ).
cnf(t6,plain,
( id(sK23(sK11(U_1025,sK11(U_1030,U_1029))),sK11(U_1025,sK11(U_1030,U_1029)))
| ~ id(sK11(U_1025,sK11(U_1030,U_1029)),sK23(sK11(U_1025,sK11(U_1030,U_1029)))) ),
inference(extension,[status(thm),parent(t4:2)],[f_6_4]) ).
cnf(t7,plain,
$false,
inference(connection,[status(thm),parent(t6:1)],[t6:1,t4:2]) ).
cnf(t8,plain,
( ~ r1(sK23(sK11(U_1025,sK11(U_1030,U_1029))))
| ~ r2(sK11(U_1030,U_1029),sK11(U_1025,sK11(U_1030,U_1029)))
| ~ id(sK23(sK11(U_1025,sK11(U_1030,U_1029))),sK11(U_1025,sK11(U_1030,U_1029))) ),
inference(extension,[status(thm),parent(t6:2)],[f_18_4]) ).
cnf(t9,plain,
$false,
inference(connection,[status(thm),parent(t8:1)],[t8:1,t6:2]) ).
cnf(t10,plain,
r2(sK11(U_1030,U_1029),sK11(U_1025,sK11(U_1030,U_1029))),
inference(extension,[status(thm),parent(t8:2)],[f_13_9]) ).
cnf(t11,plain,
$false,
inference(connection,[status(thm),parent(t10:1)],[t10:1,t8:2]) ).
cnf(t12,plain,
( ~ sP19(sK11(U_1025,sK11(U_1030,U_1029)))
| r1(sK23(sK11(U_1025,sK11(U_1030,U_1029)))) ),
inference(extension,[status(thm),parent(t8:3)],[f_19_13]) ).
cnf(t13,plain,
$false,
inference(connection,[status(thm),parent(t12:1)],[t12:1,t8:3]) ).
cnf(t14,plain,
$false,
inference(reduction,[status(thm),parent(t12:2)],[t12:2,t2:2]) ).
cnf(l1,lemma,
sP18(sK11(U_1025,sK11(U_1030,U_1029))),
inference(lemma,[status(cth),parent(t1:1),below(0:0)],[t1:1]) ).
cnf(t15,plain,
( id(sK22(sK11(U_1025,sK11(U_1030,U_1029))),sK11(U_1030,U_1029))
| ~ r2(sK11(U_1030,U_1029),sK11(U_1025,sK11(U_1030,U_1029)))
| ~ id(sK21(sK11(U_1025,sK11(U_1030,U_1029))),sK11(U_1025,sK11(U_1030,U_1029)))
| ~ r2(sK22(sK11(U_1025,sK11(U_1030,U_1029))),sK21(sK11(U_1025,sK11(U_1030,U_1029)))) ),
inference(extension,[status(thm),parent(t1:2)],[f_14_4]) ).
cnf(t16,plain,
$false,
inference(connection,[status(thm),parent(t15:1)],[t15:1,t1:2]) ).
cnf(t17,plain,
( ~ id(sK11(U_1025,sK11(U_1030,U_1029)),sK21(sK11(U_1025,sK11(U_1030,U_1029))))
| id(sK21(sK11(U_1025,sK11(U_1030,U_1029))),sK11(U_1025,sK11(U_1030,U_1029))) ),
inference(extension,[status(thm),parent(t15:2)],[f_6_4]) ).
cnf(t18,plain,
$false,
inference(connection,[status(thm),parent(t17:1)],[t17:1,t15:2]) ).
cnf(t19,plain,
( ~ sP18(sK11(U_1025,sK11(U_1030,U_1029)))
| id(sK11(U_1025,sK11(U_1030,U_1029)),sK21(sK11(U_1025,sK11(U_1030,U_1029)))) ),
inference(extension,[status(thm),parent(t17:2)],[f_19_11]) ).
cnf(t20,plain,
$false,
inference(connection,[status(thm),parent(t19:1)],[t19:1,t17:2]) ).
cnf(t21,plain,
sP18(sK11(U_1025,sK11(U_1030,U_1029))),
inference(lemma_extension,[status(thm),parent(t19:2)],[l1:1]) ).
cnf(t22,plain,
$false,
inference(connection,[status(thm),parent(t21:1)],[t21:1,t19:2]) ).
cnf(t23,plain,
r2(sK11(U_1030,U_1029),sK11(U_1025,sK11(U_1030,U_1029))),
inference(extension,[status(thm),parent(t15:3)],[f_13_9]) ).
cnf(t24,plain,
$false,
inference(connection,[status(thm),parent(t23:1)],[t23:1,t15:3]) ).
cnf(t25,plain,
( ~ r1(sK22(sK11(U_1025,sK11(U_1030,U_1029))))
| ~ r2(U_1029,sK11(U_1030,U_1029))
| ~ id(sK22(sK11(U_1025,sK11(U_1030,U_1029))),sK11(U_1030,U_1029)) ),
inference(extension,[status(thm),parent(t15:4)],[f_18_4]) ).
cnf(t26,plain,
$false,
inference(connection,[status(thm),parent(t25:1)],[t25:1,t15:4]) ).
cnf(t27,plain,
r2(U_1029,sK11(U_1030,U_1029)),
inference(extension,[status(thm),parent(t25:2)],[f_13_9]) ).
cnf(t28,plain,
$false,
inference(connection,[status(thm),parent(t27:1)],[t27:1,t25:2]) ).
cnf(t29,plain,
( ~ sP18(sK11(U_1025,sK11(U_1030,U_1029)))
| r1(sK22(sK11(U_1025,sK11(U_1030,U_1029)))) ),
inference(extension,[status(thm),parent(t25:3)],[f_19_9]) ).
cnf(t30,plain,
$false,
inference(connection,[status(thm),parent(t29:1)],[t29:1,t25:3]) ).
cnf(t31,plain,
sP18(sK11(U_1025,sK11(U_1030,U_1029))),
inference(lemma_extension,[status(thm),parent(t29:2)],[l1:1]) ).
cnf(t32,plain,
$false,
inference(connection,[status(thm),parent(t31:1)],[t31:1,t29:2]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUN068+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/sandbox/solver/bin/connect++ --verbosity 1 --no-colour --tptp-proof --schedule default --timeout 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/5.37 % Computer : n018.cluster.edu
% 0.10/5.37 % Model : x86_64 x86_64
% 0.10/5.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/5.37 % Memory : 8046.5625MB
% 0.10/5.37 % OS : Linux 6.8.0-71-generic
% 0.10/5.37 % CPULimit : 300
% 0.10/5.37 % WCLimit : 300
% 0.10/5.37 % DateTime : Sat Sep 19 19:31:48 UTC 2026
% 0.10/5.38 % CPUTime :
% 33.95/39.27 % SZS status Theorem for theBenchmark
% 33.95/39.27 % SZS output start Proof for theBenchmark
% See solution above
%------------------------------------------------------------------------------