TSTP Solution File: GEO081+1 by Metis---2.4
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- Process Solution
%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : GEO081+1 : TPTP v8.1.0. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n025.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 05:24:08 EDT 2022
% Result : Theorem 1.50s 1.65s
% Output : CNFRefutation 1.50s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 2
% Syntax : Number of formulae : 35 ( 8 unt; 0 def)
% Number of atoms : 79 ( 0 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 71 ( 27 ~; 26 |; 11 &)
% ( 3 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 3 con; 0-2 aty)
% Number of variables : 48 ( 0 sgn 26 !; 5 ?)
% Comments :
%------------------------------------------------------------------------------
fof(part_of_defn,axiom,
! [C,C1] :
( part_of(C1,C)
<=> ! [P] :
( incident_c(P,C1)
=> incident_c(P,C) ) ) ).
fof(part_of_transitivity,conjecture,
! [C1,C2,C3] :
( ( part_of(C1,C2)
& part_of(C2,C3) )
=> part_of(C1,C3) ) ).
fof(subgoal_0,plain,
! [C1,C2,C3] :
( ( part_of(C1,C2)
& part_of(C2,C3) )
=> part_of(C1,C3) ),
inference(strip,[],[part_of_transitivity]) ).
fof(negate_0_0,plain,
~ ! [C1,C2,C3] :
( ( part_of(C1,C2)
& part_of(C2,C3) )
=> part_of(C1,C3) ),
inference(negate,[],[subgoal_0]) ).
fof(normalize_0_0,plain,
! [C,C1] :
( ~ part_of(C1,C)
<=> ? [P] :
( ~ incident_c(P,C)
& incident_c(P,C1) ) ),
inference(canonicalize,[],[part_of_defn]) ).
fof(normalize_0_1,plain,
! [C,C1] :
( ~ part_of(C1,C)
<=> ? [P] :
( ~ incident_c(P,C)
& incident_c(P,C1) ) ),
inference(specialize,[],[normalize_0_0]) ).
fof(normalize_0_2,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_1]) ).
fof(normalize_0_3,plain,
! [C,C1] :
( ~ incident_c(skolemFOFtoCNF_P(C,C1),C)
| part_of(C1,C) ),
inference(conjunct,[],[normalize_0_2]) ).
fof(normalize_0_4,plain,
? [C1,C2,C3] :
( ~ part_of(C1,C3)
& part_of(C1,C2)
& part_of(C2,C3) ),
inference(canonicalize,[],[negate_0_0]) ).
fof(normalize_0_5,plain,
( ~ part_of(skolemFOFtoCNF_C1_2,skolemFOFtoCNF_C3)
& part_of(skolemFOFtoCNF_C1_2,skolemFOFtoCNF_C2_2)
& part_of(skolemFOFtoCNF_C2_2,skolemFOFtoCNF_C3) ),
inference(skolemize,[],[normalize_0_4]) ).
fof(normalize_0_6,plain,
part_of(skolemFOFtoCNF_C2_2,skolemFOFtoCNF_C3),
inference(conjunct,[],[normalize_0_5]) ).
fof(normalize_0_7,plain,
! [C,C1,P] :
( ~ incident_c(P,C1)
| ~ part_of(C1,C)
| incident_c(P,C) ),
inference(conjunct,[],[normalize_0_2]) ).
fof(normalize_0_8,plain,
! [C,C1] :
( incident_c(skolemFOFtoCNF_P(C,C1),C1)
| part_of(C1,C) ),
inference(conjunct,[],[normalize_0_2]) ).
fof(normalize_0_9,plain,
part_of(skolemFOFtoCNF_C1_2,skolemFOFtoCNF_C2_2),
inference(conjunct,[],[normalize_0_5]) ).
fof(normalize_0_10,plain,
~ part_of(skolemFOFtoCNF_C1_2,skolemFOFtoCNF_C3),
inference(conjunct,[],[normalize_0_5]) ).
cnf(refute_0_0,plain,
( ~ incident_c(skolemFOFtoCNF_P(C,C1),C)
| part_of(C1,C) ),
inference(canonicalize,[],[normalize_0_3]) ).
cnf(refute_0_1,plain,
( ~ incident_c(skolemFOFtoCNF_P(skolemFOFtoCNF_C3,skolemFOFtoCNF_C1_2),skolemFOFtoCNF_C3)
| part_of(skolemFOFtoCNF_C1_2,skolemFOFtoCNF_C3) ),
inference(subst,[],[refute_0_0:[bind(C,$fot(skolemFOFtoCNF_C3)),bind(C1,$fot(skolemFOFtoCNF_C1_2))]]) ).
cnf(refute_0_2,plain,
part_of(skolemFOFtoCNF_C2_2,skolemFOFtoCNF_C3),
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_7]) ).
cnf(refute_0_4,plain,
( ~ incident_c(X_447,skolemFOFtoCNF_C2_2)
| ~ part_of(skolemFOFtoCNF_C2_2,skolemFOFtoCNF_C3)
| incident_c(X_447,skolemFOFtoCNF_C3) ),
inference(subst,[],[refute_0_3:[bind(C,$fot(skolemFOFtoCNF_C3)),bind(C1,$fot(skolemFOFtoCNF_C2_2)),bind(P,$fot(X_447))]]) ).
cnf(refute_0_5,plain,
( ~ incident_c(X_447,skolemFOFtoCNF_C2_2)
| incident_c(X_447,skolemFOFtoCNF_C3) ),
inference(resolve,[$cnf( part_of(skolemFOFtoCNF_C2_2,skolemFOFtoCNF_C3) )],[refute_0_2,refute_0_4]) ).
cnf(refute_0_6,plain,
( ~ incident_c(skolemFOFtoCNF_P(X_585,skolemFOFtoCNF_C1_2),skolemFOFtoCNF_C2_2)
| incident_c(skolemFOFtoCNF_P(X_585,skolemFOFtoCNF_C1_2),skolemFOFtoCNF_C3) ),
inference(subst,[],[refute_0_5:[bind(X_447,$fot(skolemFOFtoCNF_P(X_585,skolemFOFtoCNF_C1_2)))]]) ).
cnf(refute_0_7,plain,
( incident_c(skolemFOFtoCNF_P(C,C1),C1)
| part_of(C1,C) ),
inference(canonicalize,[],[normalize_0_8]) ).
cnf(refute_0_8,plain,
( incident_c(skolemFOFtoCNF_P(C,skolemFOFtoCNF_C1_2),skolemFOFtoCNF_C1_2)
| part_of(skolemFOFtoCNF_C1_2,C) ),
inference(subst,[],[refute_0_7:[bind(C1,$fot(skolemFOFtoCNF_C1_2))]]) ).
cnf(refute_0_9,plain,
part_of(skolemFOFtoCNF_C1_2,skolemFOFtoCNF_C2_2),
inference(canonicalize,[],[normalize_0_9]) ).
cnf(refute_0_10,plain,
( ~ incident_c(X_447,skolemFOFtoCNF_C1_2)
| ~ part_of(skolemFOFtoCNF_C1_2,skolemFOFtoCNF_C2_2)
| incident_c(X_447,skolemFOFtoCNF_C2_2) ),
inference(subst,[],[refute_0_3:[bind(C,$fot(skolemFOFtoCNF_C2_2)),bind(C1,$fot(skolemFOFtoCNF_C1_2)),bind(P,$fot(X_447))]]) ).
cnf(refute_0_11,plain,
( ~ incident_c(X_447,skolemFOFtoCNF_C1_2)
| incident_c(X_447,skolemFOFtoCNF_C2_2) ),
inference(resolve,[$cnf( part_of(skolemFOFtoCNF_C1_2,skolemFOFtoCNF_C2_2) )],[refute_0_9,refute_0_10]) ).
cnf(refute_0_12,plain,
( ~ incident_c(skolemFOFtoCNF_P(C,skolemFOFtoCNF_C1_2),skolemFOFtoCNF_C1_2)
| incident_c(skolemFOFtoCNF_P(C,skolemFOFtoCNF_C1_2),skolemFOFtoCNF_C2_2) ),
inference(subst,[],[refute_0_11:[bind(X_447,$fot(skolemFOFtoCNF_P(C,skolemFOFtoCNF_C1_2)))]]) ).
cnf(refute_0_13,plain,
( incident_c(skolemFOFtoCNF_P(C,skolemFOFtoCNF_C1_2),skolemFOFtoCNF_C2_2)
| part_of(skolemFOFtoCNF_C1_2,C) ),
inference(resolve,[$cnf( incident_c(skolemFOFtoCNF_P(C,skolemFOFtoCNF_C1_2),skolemFOFtoCNF_C1_2) )],[refute_0_8,refute_0_12]) ).
cnf(refute_0_14,plain,
( incident_c(skolemFOFtoCNF_P(X_585,skolemFOFtoCNF_C1_2),skolemFOFtoCNF_C2_2)
| part_of(skolemFOFtoCNF_C1_2,X_585) ),
inference(subst,[],[refute_0_13:[bind(C,$fot(X_585))]]) ).
cnf(refute_0_15,plain,
( incident_c(skolemFOFtoCNF_P(X_585,skolemFOFtoCNF_C1_2),skolemFOFtoCNF_C3)
| part_of(skolemFOFtoCNF_C1_2,X_585) ),
inference(resolve,[$cnf( incident_c(skolemFOFtoCNF_P(X_585,skolemFOFtoCNF_C1_2),skolemFOFtoCNF_C2_2) )],[refute_0_14,refute_0_6]) ).
cnf(refute_0_16,plain,
( incident_c(skolemFOFtoCNF_P(skolemFOFtoCNF_C3,skolemFOFtoCNF_C1_2),skolemFOFtoCNF_C3)
| part_of(skolemFOFtoCNF_C1_2,skolemFOFtoCNF_C3) ),
inference(subst,[],[refute_0_15:[bind(X_585,$fot(skolemFOFtoCNF_C3))]]) ).
cnf(refute_0_17,plain,
part_of(skolemFOFtoCNF_C1_2,skolemFOFtoCNF_C3),
inference(resolve,[$cnf( incident_c(skolemFOFtoCNF_P(skolemFOFtoCNF_C3,skolemFOFtoCNF_C1_2),skolemFOFtoCNF_C3) )],[refute_0_16,refute_0_1]) ).
cnf(refute_0_18,plain,
~ part_of(skolemFOFtoCNF_C1_2,skolemFOFtoCNF_C3),
inference(canonicalize,[],[normalize_0_10]) ).
cnf(refute_0_19,plain,
$false,
inference(resolve,[$cnf( part_of(skolemFOFtoCNF_C1_2,skolemFOFtoCNF_C3) )],[refute_0_17,refute_0_18]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : GEO081+1 : TPTP v8.1.0. Released v2.4.0.
% 0.06/0.12 % Command : metis --show proof --show saturation %s
% 0.13/0.33 % Computer : n025.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 : Sat Jun 18 01:08:27 EDT 2022
% 0.13/0.33 % CPUTime :
% 0.13/0.34 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 1.50/1.65 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 1.50/1.65
% 1.50/1.65 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 1.50/1.66
%------------------------------------------------------------------------------