TSTP Solution File: GEO082+1 by Metis---2.4
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : GEO082+1 : TPTP v8.1.0. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n015.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 : Sat Jul 16 05:24:09 EDT 2022
% Result : Theorem 2.43s 2.59s
% Output : CNFRefutation 2.43s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 5
% Syntax : Number of formulae : 45 ( 12 unt; 0 def)
% Number of atoms : 110 ( 31 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 105 ( 40 ~; 42 |; 12 &)
% ( 6 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 5 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 2 con; 0-2 aty)
% Number of variables : 57 ( 0 sgn 32 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(part_of_defn,axiom,
! [C,C1] :
( part_of(C1,C)
<=> ! [P] :
( incident_c(P,C1)
=> incident_c(P,C) ) ) ).
fof(c9,axiom,
! [C,C1] :
( ! [P] :
( incident_c(P,C)
<=> incident_c(P,C1) )
=> C = C1 ) ).
fof(part_of_antisymmetry,conjecture,
! [C1,C2] :
( ( part_of(C1,C2)
& part_of(C2,C1) )
=> C1 = C2 ) ).
fof(subgoal_0,plain,
! [C1,C2] :
( ( part_of(C1,C2)
& part_of(C2,C1) )
=> C1 = C2 ),
inference(strip,[],[part_of_antisymmetry]) ).
fof(negate_0_0,plain,
~ ! [C1,C2] :
( ( part_of(C1,C2)
& part_of(C2,C1) )
=> C1 = C2 ),
inference(negate,[],[subgoal_0]) ).
fof(normalize_0_0,plain,
! [C,C1] :
( C = C1
| ? [P] :
( ~ incident_c(P,C)
<=> incident_c(P,C1) ) ),
inference(canonicalize,[],[c9]) ).
fof(normalize_0_1,plain,
! [C,C1] :
( C = C1
| ? [P] :
( ~ incident_c(P,C)
<=> incident_c(P,C1) ) ),
inference(specialize,[],[normalize_0_0]) ).
fof(normalize_0_2,plain,
! [C,C1] :
( ( ~ incident_c(skolemFOFtoCNF_P_3(C,C1),C)
| ~ incident_c(skolemFOFtoCNF_P_3(C,C1),C1)
| C = C1 )
& ( C = C1
| incident_c(skolemFOFtoCNF_P_3(C,C1),C)
| incident_c(skolemFOFtoCNF_P_3(C,C1),C1) ) ),
inference(clausify,[],[normalize_0_1]) ).
fof(normalize_0_3,plain,
! [C,C1] :
( ~ incident_c(skolemFOFtoCNF_P_3(C,C1),C)
| ~ incident_c(skolemFOFtoCNF_P_3(C,C1),C1)
| C = C1 ),
inference(conjunct,[],[normalize_0_2]) ).
fof(normalize_0_4,plain,
? [C1,C2] :
( C1 != C2
& part_of(C1,C2)
& part_of(C2,C1) ),
inference(canonicalize,[],[negate_0_0]) ).
fof(normalize_0_5,plain,
( skolemFOFtoCNF_C1_2 != skolemFOFtoCNF_C2_2
& part_of(skolemFOFtoCNF_C1_2,skolemFOFtoCNF_C2_2)
& part_of(skolemFOFtoCNF_C2_2,skolemFOFtoCNF_C1_2) ),
inference(skolemize,[],[normalize_0_4]) ).
fof(normalize_0_6,plain,
part_of(skolemFOFtoCNF_C1_2,skolemFOFtoCNF_C2_2),
inference(conjunct,[],[normalize_0_5]) ).
fof(normalize_0_7,plain,
! [C,C1] :
( ~ part_of(C1,C)
<=> ? [P] :
( ~ incident_c(P,C)
& incident_c(P,C1) ) ),
inference(canonicalize,[],[part_of_defn]) ).
fof(normalize_0_8,plain,
! [C,C1] :
( ~ part_of(C1,C)
<=> ? [P] :
( ~ incident_c(P,C)
& incident_c(P,C1) ) ),
inference(specialize,[],[normalize_0_7]) ).
fof(normalize_0_9,plain,
! [C,C1,P] :
( ( ~ incident_c(skolemFOFtoCNF_P(C,C1),C)
| part_of(C1,C) )
& ( incident_c(skolemFOFtoCNF_P(C,C1),C1)
| part_of(C1,C) )
& ( ~ incident_c(P,C1)
| ~ part_of(C1,C)
| incident_c(P,C) ) ),
inference(clausify,[],[normalize_0_8]) ).
fof(normalize_0_10,plain,
! [C,C1,P] :
( ~ incident_c(P,C1)
| ~ part_of(C1,C)
| incident_c(P,C) ),
inference(conjunct,[],[normalize_0_9]) ).
fof(normalize_0_11,plain,
! [C,C1] :
( C = C1
| incident_c(skolemFOFtoCNF_P_3(C,C1),C)
| incident_c(skolemFOFtoCNF_P_3(C,C1),C1) ),
inference(conjunct,[],[normalize_0_2]) ).
fof(normalize_0_12,plain,
skolemFOFtoCNF_C1_2 != skolemFOFtoCNF_C2_2,
inference(conjunct,[],[normalize_0_5]) ).
fof(normalize_0_13,plain,
part_of(skolemFOFtoCNF_C2_2,skolemFOFtoCNF_C1_2),
inference(conjunct,[],[normalize_0_5]) ).
cnf(refute_0_0,plain,
( ~ incident_c(skolemFOFtoCNF_P_3(C,C1),C)
| ~ incident_c(skolemFOFtoCNF_P_3(C,C1),C1)
| C = C1 ),
inference(canonicalize,[],[normalize_0_3]) ).
cnf(refute_0_1,plain,
( ~ incident_c(skolemFOFtoCNF_P_3(skolemFOFtoCNF_C2_2,skolemFOFtoCNF_C1_2),skolemFOFtoCNF_C1_2)
| ~ incident_c(skolemFOFtoCNF_P_3(skolemFOFtoCNF_C2_2,skolemFOFtoCNF_C1_2),skolemFOFtoCNF_C2_2)
| skolemFOFtoCNF_C2_2 = skolemFOFtoCNF_C1_2 ),
inference(subst,[],[refute_0_0:[bind(C,$fot(skolemFOFtoCNF_C2_2)),bind(C1,$fot(skolemFOFtoCNF_C1_2))]]) ).
cnf(refute_0_2,plain,
part_of(skolemFOFtoCNF_C1_2,skolemFOFtoCNF_C2_2),
inference(canonicalize,[],[normalize_0_6]) ).
cnf(refute_0_3,plain,
( ~ incident_c(P,C1)
| ~ part_of(C1,C)
| incident_c(P,C) ),
inference(canonicalize,[],[normalize_0_10]) ).
cnf(refute_0_4,plain,
( ~ incident_c(X_501,skolemFOFtoCNF_C1_2)
| ~ part_of(skolemFOFtoCNF_C1_2,skolemFOFtoCNF_C2_2)
| incident_c(X_501,skolemFOFtoCNF_C2_2) ),
inference(subst,[],[refute_0_3:[bind(C,$fot(skolemFOFtoCNF_C2_2)),bind(C1,$fot(skolemFOFtoCNF_C1_2)),bind(P,$fot(X_501))]]) ).
cnf(refute_0_5,plain,
( ~ incident_c(X_501,skolemFOFtoCNF_C1_2)
| incident_c(X_501,skolemFOFtoCNF_C2_2) ),
inference(resolve,[$cnf( part_of(skolemFOFtoCNF_C1_2,skolemFOFtoCNF_C2_2) )],[refute_0_2,refute_0_4]) ).
cnf(refute_0_6,plain,
( ~ incident_c(skolemFOFtoCNF_P_3(X_1233,skolemFOFtoCNF_C1_2),skolemFOFtoCNF_C1_2)
| incident_c(skolemFOFtoCNF_P_3(X_1233,skolemFOFtoCNF_C1_2),skolemFOFtoCNF_C2_2) ),
inference(subst,[],[refute_0_5:[bind(X_501,$fot(skolemFOFtoCNF_P_3(X_1233,skolemFOFtoCNF_C1_2)))]]) ).
cnf(refute_0_7,plain,
( C = C1
| incident_c(skolemFOFtoCNF_P_3(C,C1),C)
| incident_c(skolemFOFtoCNF_P_3(C,C1),C1) ),
inference(canonicalize,[],[normalize_0_11]) ).
cnf(refute_0_8,plain,
( X_1233 = skolemFOFtoCNF_C1_2
| incident_c(skolemFOFtoCNF_P_3(X_1233,skolemFOFtoCNF_C1_2),X_1233)
| incident_c(skolemFOFtoCNF_P_3(X_1233,skolemFOFtoCNF_C1_2),skolemFOFtoCNF_C1_2) ),
inference(subst,[],[refute_0_7:[bind(C,$fot(X_1233)),bind(C1,$fot(skolemFOFtoCNF_C1_2))]]) ).
cnf(refute_0_9,plain,
( X_1233 = skolemFOFtoCNF_C1_2
| incident_c(skolemFOFtoCNF_P_3(X_1233,skolemFOFtoCNF_C1_2),X_1233)
| incident_c(skolemFOFtoCNF_P_3(X_1233,skolemFOFtoCNF_C1_2),skolemFOFtoCNF_C2_2) ),
inference(resolve,[$cnf( incident_c(skolemFOFtoCNF_P_3(X_1233,skolemFOFtoCNF_C1_2),skolemFOFtoCNF_C1_2) )],[refute_0_8,refute_0_6]) ).
cnf(refute_0_10,plain,
( skolemFOFtoCNF_C2_2 = skolemFOFtoCNF_C1_2
| incident_c(skolemFOFtoCNF_P_3(skolemFOFtoCNF_C2_2,skolemFOFtoCNF_C1_2),skolemFOFtoCNF_C2_2) ),
inference(subst,[],[refute_0_9:[bind(X_1233,$fot(skolemFOFtoCNF_C2_2))]]) ).
cnf(refute_0_11,plain,
skolemFOFtoCNF_C1_2 != skolemFOFtoCNF_C2_2,
inference(canonicalize,[],[normalize_0_12]) ).
cnf(refute_0_12,plain,
X = X,
introduced(tautology,[refl,[$fot(X)]]) ).
cnf(refute_0_13,plain,
( X != X
| X != Y
| Y = X ),
introduced(tautology,[equality,[$cnf( $equal(X,X) ),[0],$fot(Y)]]) ).
cnf(refute_0_14,plain,
( X != Y
| Y = X ),
inference(resolve,[$cnf( $equal(X,X) )],[refute_0_12,refute_0_13]) ).
cnf(refute_0_15,plain,
( skolemFOFtoCNF_C2_2 != skolemFOFtoCNF_C1_2
| skolemFOFtoCNF_C1_2 = skolemFOFtoCNF_C2_2 ),
inference(subst,[],[refute_0_14:[bind(X,$fot(skolemFOFtoCNF_C2_2)),bind(Y,$fot(skolemFOFtoCNF_C1_2))]]) ).
cnf(refute_0_16,plain,
skolemFOFtoCNF_C2_2 != skolemFOFtoCNF_C1_2,
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_C1_2,skolemFOFtoCNF_C2_2) )],[refute_0_15,refute_0_11]) ).
cnf(refute_0_17,plain,
incident_c(skolemFOFtoCNF_P_3(skolemFOFtoCNF_C2_2,skolemFOFtoCNF_C1_2),skolemFOFtoCNF_C2_2),
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_C2_2,skolemFOFtoCNF_C1_2) )],[refute_0_10,refute_0_16]) ).
cnf(refute_0_18,plain,
( ~ incident_c(skolemFOFtoCNF_P_3(skolemFOFtoCNF_C2_2,skolemFOFtoCNF_C1_2),skolemFOFtoCNF_C1_2)
| skolemFOFtoCNF_C2_2 = skolemFOFtoCNF_C1_2 ),
inference(resolve,[$cnf( incident_c(skolemFOFtoCNF_P_3(skolemFOFtoCNF_C2_2,skolemFOFtoCNF_C1_2),skolemFOFtoCNF_C2_2) )],[refute_0_17,refute_0_1]) ).
cnf(refute_0_19,plain,
part_of(skolemFOFtoCNF_C2_2,skolemFOFtoCNF_C1_2),
inference(canonicalize,[],[normalize_0_13]) ).
cnf(refute_0_20,plain,
( ~ incident_c(X_501,skolemFOFtoCNF_C2_2)
| ~ part_of(skolemFOFtoCNF_C2_2,skolemFOFtoCNF_C1_2)
| incident_c(X_501,skolemFOFtoCNF_C1_2) ),
inference(subst,[],[refute_0_3:[bind(C,$fot(skolemFOFtoCNF_C1_2)),bind(C1,$fot(skolemFOFtoCNF_C2_2)),bind(P,$fot(X_501))]]) ).
cnf(refute_0_21,plain,
( ~ incident_c(X_501,skolemFOFtoCNF_C2_2)
| incident_c(X_501,skolemFOFtoCNF_C1_2) ),
inference(resolve,[$cnf( part_of(skolemFOFtoCNF_C2_2,skolemFOFtoCNF_C1_2) )],[refute_0_19,refute_0_20]) ).
cnf(refute_0_22,plain,
( ~ incident_c(skolemFOFtoCNF_P_3(skolemFOFtoCNF_C2_2,skolemFOFtoCNF_C1_2),skolemFOFtoCNF_C2_2)
| incident_c(skolemFOFtoCNF_P_3(skolemFOFtoCNF_C2_2,skolemFOFtoCNF_C1_2),skolemFOFtoCNF_C1_2) ),
inference(subst,[],[refute_0_21:[bind(X_501,$fot(skolemFOFtoCNF_P_3(skolemFOFtoCNF_C2_2,skolemFOFtoCNF_C1_2)))]]) ).
cnf(refute_0_23,plain,
incident_c(skolemFOFtoCNF_P_3(skolemFOFtoCNF_C2_2,skolemFOFtoCNF_C1_2),skolemFOFtoCNF_C1_2),
inference(resolve,[$cnf( incident_c(skolemFOFtoCNF_P_3(skolemFOFtoCNF_C2_2,skolemFOFtoCNF_C1_2),skolemFOFtoCNF_C2_2) )],[refute_0_17,refute_0_22]) ).
cnf(refute_0_24,plain,
skolemFOFtoCNF_C2_2 = skolemFOFtoCNF_C1_2,
inference(resolve,[$cnf( incident_c(skolemFOFtoCNF_P_3(skolemFOFtoCNF_C2_2,skolemFOFtoCNF_C1_2),skolemFOFtoCNF_C1_2) )],[refute_0_23,refute_0_18]) ).
cnf(refute_0_25,plain,
$false,
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_C2_2,skolemFOFtoCNF_C1_2) )],[refute_0_24,refute_0_16]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : GEO082+1 : TPTP v8.1.0. Released v2.4.0.
% 0.12/0.12 % Command : metis --show proof --show saturation %s
% 0.12/0.33 % Computer : n015.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 600
% 0.12/0.33 % DateTime : Fri Jun 17 21:38:12 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.19/0.34 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 2.43/2.59 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 2.43/2.59
% 2.43/2.59 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 2.43/2.60
%------------------------------------------------------------------------------