TSTP Solution File: NUN067+1 by Metis---2.4
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : NUN067+1 : TPTP v8.1.0. Released v7.3.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n028.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 600s
% DateTime : Mon Jul 18 16:34:54 EDT 2022
% Result : Theorem 0.19s 0.38s
% Output : CNFRefutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 7
% Syntax : Number of formulae : 73 ( 22 unt; 0 def)
% Number of atoms : 171 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 180 ( 82 ~; 58 |; 40 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 5 ( 4 usr; 1 prp; 0-3 aty)
% Number of functors : 5 ( 5 usr; 1 con; 0-1 aty)
% Number of variables : 121 ( 19 sgn 63 !; 18 ?)
% Comments :
%------------------------------------------------------------------------------
fof(axiom_1,axiom,
? [Y24] :
! [X19] :
( ( id(X19,Y24)
& r1(X19) )
| ( ~ r1(X19)
& ~ id(X19,Y24) ) ) ).
fof(axiom_2,axiom,
! [X11] :
? [Y21] :
! [X12] :
( ( id(X12,Y21)
& r2(X11,X12) )
| ( ~ r2(X11,X12)
& ~ id(X12,Y21) ) ) ).
fof(axiom_6,axiom,
! [X21,X22] :
( ~ id(X21,X22)
| id(X22,X21) ) ).
fof(axiom_8,axiom,
! [X26,X27] :
( ~ id(X26,X27)
| ( ~ r1(X26)
& ~ r1(X27) )
| ( r1(X26)
& r1(X27) ) ) ).
fof(axiom_4a,axiom,
! [X4] :
? [Y9] :
( id(Y9,X4)
& ? [Y16] :
( r1(Y16)
& r3(X4,Y16,Y9) ) ) ).
fof(axiom_7a,axiom,
! [X7,Y10] :
( ! [Y20] :
( ~ id(Y20,Y10)
| ~ r1(Y20) )
| ~ r2(X7,Y10) ) ).
fof(nonzerosexistid,conjecture,
? [Y1] :
! [Y2] :
( ~ id(Y1,Y2)
| ~ r1(Y2) ) ).
fof(subgoal_0,plain,
? [Y1] :
! [Y2] :
( ~ id(Y1,Y2)
| ~ r1(Y2) ),
inference(strip,[],[nonzerosexistid]) ).
fof(negate_0_0,plain,
~ ? [Y1] :
! [Y2] :
( ~ id(Y1,Y2)
| ~ r1(Y2) ),
inference(negate,[],[subgoal_0]) ).
fof(normalize_0_0,plain,
! [X4] :
? [Y9] :
( id(Y9,X4)
& ? [Y16] :
( r1(Y16)
& r3(X4,Y16,Y9) ) ),
inference(canonicalize,[],[axiom_4a]) ).
fof(normalize_0_1,plain,
! [X4] :
? [Y9] :
( id(Y9,X4)
& ? [Y16] :
( r1(Y16)
& r3(X4,Y16,Y9) ) ),
inference(specialize,[],[normalize_0_0]) ).
fof(normalize_0_2,plain,
! [X4] :
( id(skolemFOFtoCNF_Y9(X4),X4)
& ? [Y16] :
( r1(Y16)
& r3(X4,Y16,skolemFOFtoCNF_Y9(X4)) ) ),
inference(skolemize,[],[normalize_0_1]) ).
fof(normalize_0_3,plain,
! [X4] :
? [Y16] :
( r1(Y16)
& r3(X4,Y16,skolemFOFtoCNF_Y9(X4)) ),
inference(conjunct,[],[normalize_0_2]) ).
fof(normalize_0_4,plain,
! [X4] :
( r1(skolemFOFtoCNF_Y16(X4))
& r3(X4,skolemFOFtoCNF_Y16(X4),skolemFOFtoCNF_Y9(X4)) ),
inference(skolemize,[],[normalize_0_3]) ).
fof(normalize_0_5,plain,
! [X4] : r1(skolemFOFtoCNF_Y16(X4)),
inference(conjunct,[],[normalize_0_4]) ).
fof(normalize_0_6,plain,
? [Y24] :
! [X19] :
( ( ~ id(X19,Y24)
& ~ r1(X19) )
| ( id(X19,Y24)
& r1(X19) ) ),
inference(canonicalize,[],[axiom_1]) ).
fof(normalize_0_7,plain,
! [X19] :
( ( ~ id(X19,skolemFOFtoCNF_Y24)
& ~ r1(X19) )
| ( id(X19,skolemFOFtoCNF_Y24)
& r1(X19) ) ),
inference(skolemize,[],[normalize_0_6]) ).
fof(normalize_0_8,plain,
! [X19] :
( ( ~ id(X19,skolemFOFtoCNF_Y24)
& ~ r1(X19) )
| ( id(X19,skolemFOFtoCNF_Y24)
& r1(X19) ) ),
inference(specialize,[],[normalize_0_7]) ).
fof(normalize_0_9,plain,
! [X19] :
( ( ~ id(X19,skolemFOFtoCNF_Y24)
| r1(X19) )
& ( ~ r1(X19)
| id(X19,skolemFOFtoCNF_Y24) ) ),
inference(clausify,[],[normalize_0_8]) ).
fof(normalize_0_10,plain,
! [X19] :
( ~ r1(X19)
| id(X19,skolemFOFtoCNF_Y24) ),
inference(conjunct,[],[normalize_0_9]) ).
fof(normalize_0_11,plain,
! [X7,Y10] :
( ~ r2(X7,Y10)
| ! [Y20] :
( ~ id(Y20,Y10)
| ~ r1(Y20) ) ),
inference(canonicalize,[],[axiom_7a]) ).
fof(normalize_0_12,plain,
! [X7,Y10] :
( ~ r2(X7,Y10)
| ! [Y20] :
( ~ id(Y20,Y10)
| ~ r1(Y20) ) ),
inference(specialize,[],[normalize_0_11]) ).
fof(normalize_0_13,plain,
! [X7,Y10,Y20] :
( ~ id(Y20,Y10)
| ~ r1(Y20)
| ~ r2(X7,Y10) ),
inference(clausify,[],[normalize_0_12]) ).
fof(normalize_0_14,plain,
! [Y1] :
? [Y2] :
( id(Y1,Y2)
& r1(Y2) ),
inference(canonicalize,[],[negate_0_0]) ).
fof(normalize_0_15,plain,
! [Y1] :
? [Y2] :
( id(Y1,Y2)
& r1(Y2) ),
inference(specialize,[],[normalize_0_14]) ).
fof(normalize_0_16,plain,
! [Y1] :
( id(Y1,skolemFOFtoCNF_Y2_1(Y1))
& r1(skolemFOFtoCNF_Y2_1(Y1)) ),
inference(skolemize,[],[normalize_0_15]) ).
fof(normalize_0_17,plain,
! [Y1] : id(Y1,skolemFOFtoCNF_Y2_1(Y1)),
inference(conjunct,[],[normalize_0_16]) ).
fof(normalize_0_18,plain,
! [X21,X22] :
( ~ id(X21,X22)
| id(X22,X21) ),
inference(canonicalize,[],[axiom_6]) ).
fof(normalize_0_19,plain,
! [X21,X22] :
( ~ id(X21,X22)
| id(X22,X21) ),
inference(specialize,[],[normalize_0_18]) ).
fof(normalize_0_20,plain,
! [X26,X27] :
( ~ id(X26,X27)
| ( ~ r1(X26)
& ~ r1(X27) )
| ( r1(X26)
& r1(X27) ) ),
inference(canonicalize,[],[axiom_8]) ).
fof(normalize_0_21,plain,
! [X26,X27] :
( ~ id(X26,X27)
| ( ~ r1(X26)
& ~ r1(X27) )
| ( r1(X26)
& r1(X27) ) ),
inference(specialize,[],[normalize_0_20]) ).
fof(normalize_0_22,plain,
! [X26,X27] :
( ( ~ id(X26,X27)
| ~ r1(X26)
| r1(X27) )
& ( ~ id(X26,X27)
| ~ r1(X27)
| r1(X26) ) ),
inference(clausify,[],[normalize_0_21]) ).
fof(normalize_0_23,plain,
! [X26,X27] :
( ~ id(X26,X27)
| ~ r1(X26)
| r1(X27) ),
inference(conjunct,[],[normalize_0_22]) ).
fof(normalize_0_24,plain,
! [Y1] : r1(skolemFOFtoCNF_Y2_1(Y1)),
inference(conjunct,[],[normalize_0_16]) ).
fof(normalize_0_25,plain,
! [X11] :
? [Y21] :
! [X12] :
( ( ~ id(X12,Y21)
& ~ r2(X11,X12) )
| ( id(X12,Y21)
& r2(X11,X12) ) ),
inference(canonicalize,[],[axiom_2]) ).
fof(normalize_0_26,plain,
! [X11] :
? [Y21] :
! [X12] :
( ( ~ id(X12,Y21)
& ~ r2(X11,X12) )
| ( id(X12,Y21)
& r2(X11,X12) ) ),
inference(specialize,[],[normalize_0_25]) ).
fof(normalize_0_27,plain,
! [X11,X12] :
( ( ~ id(X12,skolemFOFtoCNF_Y21(X11))
& ~ r2(X11,X12) )
| ( id(X12,skolemFOFtoCNF_Y21(X11))
& r2(X11,X12) ) ),
inference(skolemize,[],[normalize_0_26]) ).
fof(normalize_0_28,plain,
! [X11,X12] :
( ( ~ id(X12,skolemFOFtoCNF_Y21(X11))
& ~ r2(X11,X12) )
| ( id(X12,skolemFOFtoCNF_Y21(X11))
& r2(X11,X12) ) ),
inference(specialize,[],[normalize_0_27]) ).
fof(normalize_0_29,plain,
! [X11,X12] :
( ( ~ id(X12,skolemFOFtoCNF_Y21(X11))
| r2(X11,X12) )
& ( ~ r2(X11,X12)
| id(X12,skolemFOFtoCNF_Y21(X11)) ) ),
inference(clausify,[],[normalize_0_28]) ).
fof(normalize_0_30,plain,
! [X11,X12] :
( ~ id(X12,skolemFOFtoCNF_Y21(X11))
| r2(X11,X12) ),
inference(conjunct,[],[normalize_0_29]) ).
cnf(refute_0_0,plain,
r1(skolemFOFtoCNF_Y16(X4)),
inference(canonicalize,[],[normalize_0_5]) ).
cnf(refute_0_1,plain,
( ~ r1(X19)
| id(X19,skolemFOFtoCNF_Y24) ),
inference(canonicalize,[],[normalize_0_10]) ).
cnf(refute_0_2,plain,
( ~ r1(skolemFOFtoCNF_Y16(X4))
| id(skolemFOFtoCNF_Y16(X4),skolemFOFtoCNF_Y24) ),
inference(subst,[],[refute_0_1:[bind(X19,$fot(skolemFOFtoCNF_Y16(X4)))]]) ).
cnf(refute_0_3,plain,
id(skolemFOFtoCNF_Y16(X4),skolemFOFtoCNF_Y24),
inference(resolve,[$cnf( r1(skolemFOFtoCNF_Y16(X4)) )],[refute_0_0,refute_0_2]) ).
cnf(refute_0_4,plain,
( ~ id(Y20,Y10)
| ~ r1(Y20)
| ~ r2(X7,Y10) ),
inference(canonicalize,[],[normalize_0_13]) ).
cnf(refute_0_5,plain,
id(Y1,skolemFOFtoCNF_Y2_1(Y1)),
inference(canonicalize,[],[normalize_0_17]) ).
cnf(refute_0_6,plain,
id(X_39,skolemFOFtoCNF_Y2_1(X_39)),
inference(subst,[],[refute_0_5:[bind(Y1,$fot(X_39))]]) ).
cnf(refute_0_7,plain,
( ~ id(X21,X22)
| id(X22,X21) ),
inference(canonicalize,[],[normalize_0_19]) ).
cnf(refute_0_8,plain,
( ~ id(X_39,skolemFOFtoCNF_Y2_1(X_39))
| id(skolemFOFtoCNF_Y2_1(X_39),X_39) ),
inference(subst,[],[refute_0_7:[bind(X21,$fot(X_39)),bind(X22,$fot(skolemFOFtoCNF_Y2_1(X_39)))]]) ).
cnf(refute_0_9,plain,
id(skolemFOFtoCNF_Y2_1(X_39),X_39),
inference(resolve,[$cnf( id(X_39,skolemFOFtoCNF_Y2_1(X_39)) )],[refute_0_6,refute_0_8]) ).
cnf(refute_0_10,plain,
id(skolemFOFtoCNF_Y2_1(X_80),X_80),
inference(subst,[],[refute_0_9:[bind(X_39,$fot(X_80))]]) ).
cnf(refute_0_11,plain,
( ~ id(X26,X27)
| ~ r1(X26)
| r1(X27) ),
inference(canonicalize,[],[normalize_0_23]) ).
cnf(refute_0_12,plain,
( ~ id(skolemFOFtoCNF_Y2_1(X_80),X_80)
| ~ r1(skolemFOFtoCNF_Y2_1(X_80))
| r1(X_80) ),
inference(subst,[],[refute_0_11:[bind(X26,$fot(skolemFOFtoCNF_Y2_1(X_80))),bind(X27,$fot(X_80))]]) ).
cnf(refute_0_13,plain,
( ~ r1(skolemFOFtoCNF_Y2_1(X_80))
| r1(X_80) ),
inference(resolve,[$cnf( id(skolemFOFtoCNF_Y2_1(X_80),X_80) )],[refute_0_10,refute_0_12]) ).
cnf(refute_0_14,plain,
r1(skolemFOFtoCNF_Y2_1(Y1)),
inference(canonicalize,[],[normalize_0_24]) ).
cnf(refute_0_15,plain,
r1(skolemFOFtoCNF_Y2_1(X_80)),
inference(subst,[],[refute_0_14:[bind(Y1,$fot(X_80))]]) ).
cnf(refute_0_16,plain,
r1(X_80),
inference(resolve,[$cnf( r1(skolemFOFtoCNF_Y2_1(X_80)) )],[refute_0_15,refute_0_13]) ).
cnf(refute_0_17,plain,
r1(Y20),
inference(subst,[],[refute_0_16:[bind(X_80,$fot(Y20))]]) ).
cnf(refute_0_18,plain,
( ~ id(Y20,Y10)
| ~ r2(X7,Y10) ),
inference(resolve,[$cnf( r1(Y20) )],[refute_0_17,refute_0_4]) ).
cnf(refute_0_19,plain,
( ~ id(skolemFOFtoCNF_Y16(X4),skolemFOFtoCNF_Y24)
| ~ r2(X_152,skolemFOFtoCNF_Y24) ),
inference(subst,[],[refute_0_18:[bind(X7,$fot(X_152)),bind(Y10,$fot(skolemFOFtoCNF_Y24)),bind(Y20,$fot(skolemFOFtoCNF_Y16(X4)))]]) ).
cnf(refute_0_20,plain,
~ r2(X_152,skolemFOFtoCNF_Y24),
inference(resolve,[$cnf( id(skolemFOFtoCNF_Y16(X4),skolemFOFtoCNF_Y24) )],[refute_0_3,refute_0_19]) ).
cnf(refute_0_21,plain,
( ~ id(X12,skolemFOFtoCNF_Y21(X11))
| r2(X11,X12) ),
inference(canonicalize,[],[normalize_0_30]) ).
cnf(refute_0_22,plain,
( ~ id(skolemFOFtoCNF_Y24,skolemFOFtoCNF_Y21(X11))
| r2(X11,skolemFOFtoCNF_Y24) ),
inference(subst,[],[refute_0_21:[bind(X12,$fot(skolemFOFtoCNF_Y24))]]) ).
cnf(refute_0_23,plain,
( ~ id(X_82,skolemFOFtoCNF_Y24)
| id(skolemFOFtoCNF_Y24,X_82) ),
inference(subst,[],[refute_0_7:[bind(X21,$fot(X_82)),bind(X22,$fot(skolemFOFtoCNF_Y24))]]) ).
cnf(refute_0_24,plain,
( ~ r1(X_81)
| id(X_81,skolemFOFtoCNF_Y24) ),
inference(subst,[],[refute_0_1:[bind(X19,$fot(X_81))]]) ).
cnf(refute_0_25,plain,
r1(X_81),
inference(subst,[],[refute_0_16:[bind(X_80,$fot(X_81))]]) ).
cnf(refute_0_26,plain,
id(X_81,skolemFOFtoCNF_Y24),
inference(resolve,[$cnf( r1(X_81) )],[refute_0_25,refute_0_24]) ).
cnf(refute_0_27,plain,
id(X_82,skolemFOFtoCNF_Y24),
inference(subst,[],[refute_0_26:[bind(X_81,$fot(X_82))]]) ).
cnf(refute_0_28,plain,
id(skolemFOFtoCNF_Y24,X_82),
inference(resolve,[$cnf( id(X_82,skolemFOFtoCNF_Y24) )],[refute_0_27,refute_0_23]) ).
cnf(refute_0_29,plain,
id(skolemFOFtoCNF_Y24,skolemFOFtoCNF_Y21(X11)),
inference(subst,[],[refute_0_28:[bind(X_82,$fot(skolemFOFtoCNF_Y21(X11)))]]) ).
cnf(refute_0_30,plain,
r2(X11,skolemFOFtoCNF_Y24),
inference(resolve,[$cnf( id(skolemFOFtoCNF_Y24,skolemFOFtoCNF_Y21(X11)) )],[refute_0_29,refute_0_22]) ).
cnf(refute_0_31,plain,
r2(X_152,skolemFOFtoCNF_Y24),
inference(subst,[],[refute_0_30:[bind(X11,$fot(X_152))]]) ).
cnf(refute_0_32,plain,
$false,
inference(resolve,[$cnf( r2(X_152,skolemFOFtoCNF_Y24) )],[refute_0_31,refute_0_20]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : NUN067+1 : TPTP v8.1.0. Released v7.3.0.
% 0.03/0.13 % Command : metis --show proof --show saturation %s
% 0.13/0.33 % Computer : n028.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 600
% 0.13/0.33 % DateTime : Thu Jun 2 08:10:38 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.13/0.34 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.19/0.38 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.19/0.38
% 0.19/0.38 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 0.19/0.39
%------------------------------------------------------------------------------