TSTP Solution File: GEO117+1 by Metis---2.4
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- Process Solution
%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : GEO117+1 : TPTP v8.1.0. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n016.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 05:24:25 EDT 2022
% Result : Theorem 3.50s 3.73s
% Output : CNFRefutation 3.50s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 5
% Syntax : Number of formulae : 33 ( 12 unt; 0 def)
% Number of atoms : 127 ( 9 equ)
% Maximal formula atoms : 18 ( 3 avg)
% Number of connectives : 168 ( 74 ~; 59 |; 23 &)
% ( 12 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 6 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 11 ( 8 usr; 1 prp; 0-4 aty)
% Number of functors : 5 ( 5 usr; 2 con; 0-4 aty)
% Number of variables : 99 ( 6 sgn 74 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(between_c_defn,axiom,
! [C,P,Q,R] :
( between_c(C,P,Q,R)
<=> ( P != R
& ? [Cpp] :
( part_of(Cpp,C)
& end_point(P,Cpp)
& end_point(R,Cpp)
& inner_point(Q,Cpp) ) ) ) ).
fof(between_o_defn,axiom,
! [O,P,Q,R] :
( between_o(O,P,Q,R)
<=> ( ( ordered_by(O,P,Q)
& ordered_by(O,Q,R) )
| ( ordered_by(O,R,Q)
& ordered_by(O,Q,P) ) ) ) ).
fof(o3,axiom,
! [P,Q,R,O] :
( between_o(O,P,Q,R)
<=> ? [C] :
( ! [P] :
( incident_o(P,O)
<=> incident_c(P,C) )
& between_c(C,P,Q,R) ) ) ).
fof(theorem_4_4,conjecture,
! [O,P] : ~ ordered_by(O,P,P) ).
fof(subgoal_0,plain,
! [O,P] : ~ ordered_by(O,P,P),
inference(strip,[],[theorem_4_4]) ).
fof(negate_0_0,plain,
~ ! [O,P] : ~ ordered_by(O,P,P),
inference(negate,[],[subgoal_0]) ).
fof(normalize_0_0,plain,
? [O,P] : ordered_by(O,P,P),
inference(canonicalize,[],[negate_0_0]) ).
fof(normalize_0_1,plain,
ordered_by(skolemFOFtoCNF_O_1,skolemFOFtoCNF_P_8,skolemFOFtoCNF_P_8),
inference(skolemize,[],[normalize_0_0]) ).
fof(normalize_0_2,plain,
! [O,P,Q,R] :
( ~ between_o(O,P,Q,R)
<=> ( ( ~ ordered_by(O,P,Q)
| ~ ordered_by(O,Q,R) )
& ( ~ ordered_by(O,Q,P)
| ~ ordered_by(O,R,Q) ) ) ),
inference(canonicalize,[],[between_o_defn]) ).
fof(normalize_0_3,plain,
! [O,P,Q,R] :
( ~ between_o(O,P,Q,R)
<=> ( ( ~ ordered_by(O,P,Q)
| ~ ordered_by(O,Q,R) )
& ( ~ ordered_by(O,Q,P)
| ~ ordered_by(O,R,Q) ) ) ),
inference(specialize,[],[normalize_0_2]) ).
fof(normalize_0_4,plain,
! [O,P,Q,R] :
( ( ~ between_o(O,P,Q,R)
| ordered_by(O,P,Q)
| ordered_by(O,Q,P) )
& ( ~ between_o(O,P,Q,R)
| ordered_by(O,P,Q)
| ordered_by(O,R,Q) )
& ( ~ between_o(O,P,Q,R)
| ordered_by(O,Q,P)
| ordered_by(O,Q,R) )
& ( ~ between_o(O,P,Q,R)
| ordered_by(O,Q,R)
| ordered_by(O,R,Q) )
& ( ~ ordered_by(O,P,Q)
| ~ ordered_by(O,Q,R)
| between_o(O,P,Q,R) )
& ( ~ ordered_by(O,Q,P)
| ~ ordered_by(O,R,Q)
| between_o(O,P,Q,R) ) ),
inference(clausify,[],[normalize_0_3]) ).
fof(normalize_0_5,plain,
! [O,P,Q,R] :
( ~ ordered_by(O,P,Q)
| ~ ordered_by(O,Q,R)
| between_o(O,P,Q,R) ),
inference(conjunct,[],[normalize_0_4]) ).
fof(normalize_0_6,plain,
! [O,P,Q,R] :
( ~ between_o(O,P,Q,R)
<=> ! [C] :
( ~ between_c(C,P,Q,R)
| ? [P] :
( ~ incident_c(P,C)
<=> incident_o(P,O) ) ) ),
inference(canonicalize,[],[o3]) ).
fof(normalize_0_7,plain,
! [O,P,Q,R] :
( ~ between_o(O,P,Q,R)
<=> ! [C] :
( ~ between_c(C,P,Q,R)
| ? [P] :
( ~ incident_c(P,C)
<=> incident_o(P,O) ) ) ),
inference(specialize,[],[normalize_0_6]) ).
fof(normalize_0_8,plain,
! [C,O,P,P0,Q,R] :
( ( ~ between_o(O,P,Q,R)
| between_c(skolemFOFtoCNF_C_2(O,P,Q,R),P,Q,R) )
& ( ~ between_o(O,P,Q,R)
| ~ incident_c(P0,skolemFOFtoCNF_C_2(O,P,Q,R))
| incident_o(P0,O) )
& ( ~ between_o(O,P,Q,R)
| ~ incident_o(P0,O)
| incident_c(P0,skolemFOFtoCNF_C_2(O,P,Q,R)) )
& ( ~ between_c(C,P,Q,R)
| ~ incident_c(skolemFOFtoCNF_P_4(C,O),C)
| ~ incident_o(skolemFOFtoCNF_P_4(C,O),O)
| between_o(O,P,Q,R) )
& ( ~ between_c(C,P,Q,R)
| between_o(O,P,Q,R)
| incident_c(skolemFOFtoCNF_P_4(C,O),C)
| incident_o(skolemFOFtoCNF_P_4(C,O),O) ) ),
inference(clausify,[],[normalize_0_7]) ).
fof(normalize_0_9,plain,
! [O,P,Q,R] :
( ~ between_o(O,P,Q,R)
| between_c(skolemFOFtoCNF_C_2(O,P,Q,R),P,Q,R) ),
inference(conjunct,[],[normalize_0_8]) ).
fof(normalize_0_10,plain,
! [C,P,Q,R] :
( ~ between_c(C,P,Q,R)
<=> ( P = R
| ! [Cpp] :
( ~ end_point(P,Cpp)
| ~ end_point(R,Cpp)
| ~ inner_point(Q,Cpp)
| ~ part_of(Cpp,C) ) ) ),
inference(canonicalize,[],[between_c_defn]) ).
fof(normalize_0_11,plain,
! [C,P,Q,R] :
( ~ between_c(C,P,Q,R)
<=> ( P = R
| ! [Cpp] :
( ~ end_point(P,Cpp)
| ~ end_point(R,Cpp)
| ~ inner_point(Q,Cpp)
| ~ part_of(Cpp,C) ) ) ),
inference(specialize,[],[normalize_0_10]) ).
fof(normalize_0_12,plain,
! [C,Cpp,P,Q,R] :
( ( P != R
| ~ between_c(C,P,Q,R) )
& ( ~ between_c(C,P,Q,R)
| end_point(P,skolemFOFtoCNF_Cpp(C,P,Q,R)) )
& ( ~ between_c(C,P,Q,R)
| end_point(R,skolemFOFtoCNF_Cpp(C,P,Q,R)) )
& ( ~ between_c(C,P,Q,R)
| inner_point(Q,skolemFOFtoCNF_Cpp(C,P,Q,R)) )
& ( ~ between_c(C,P,Q,R)
| part_of(skolemFOFtoCNF_Cpp(C,P,Q,R),C) )
& ( ~ end_point(P,Cpp)
| ~ end_point(R,Cpp)
| ~ inner_point(Q,Cpp)
| ~ part_of(Cpp,C)
| P = R
| between_c(C,P,Q,R) ) ),
inference(clausify,[],[normalize_0_11]) ).
fof(normalize_0_13,plain,
! [C,P,Q,R] :
( P != R
| ~ between_c(C,P,Q,R) ),
inference(conjunct,[],[normalize_0_12]) ).
cnf(refute_0_0,plain,
ordered_by(skolemFOFtoCNF_O_1,skolemFOFtoCNF_P_8,skolemFOFtoCNF_P_8),
inference(canonicalize,[],[normalize_0_1]) ).
cnf(refute_0_1,plain,
( ~ ordered_by(O,P,Q)
| ~ ordered_by(O,Q,R)
| between_o(O,P,Q,R) ),
inference(canonicalize,[],[normalize_0_5]) ).
cnf(refute_0_2,plain,
( ~ ordered_by(skolemFOFtoCNF_O_1,skolemFOFtoCNF_P_8,skolemFOFtoCNF_P_8)
| between_o(skolemFOFtoCNF_O_1,skolemFOFtoCNF_P_8,skolemFOFtoCNF_P_8,skolemFOFtoCNF_P_8) ),
inference(subst,[],[refute_0_1:[bind(O,$fot(skolemFOFtoCNF_O_1)),bind(P,$fot(skolemFOFtoCNF_P_8)),bind(Q,$fot(skolemFOFtoCNF_P_8)),bind(R,$fot(skolemFOFtoCNF_P_8))]]) ).
cnf(refute_0_3,plain,
between_o(skolemFOFtoCNF_O_1,skolemFOFtoCNF_P_8,skolemFOFtoCNF_P_8,skolemFOFtoCNF_P_8),
inference(resolve,[$cnf( ordered_by(skolemFOFtoCNF_O_1,skolemFOFtoCNF_P_8,skolemFOFtoCNF_P_8) )],[refute_0_0,refute_0_2]) ).
cnf(refute_0_4,plain,
( ~ between_o(O,P,Q,R)
| between_c(skolemFOFtoCNF_C_2(O,P,Q,R),P,Q,R) ),
inference(canonicalize,[],[normalize_0_9]) ).
cnf(refute_0_5,plain,
( ~ between_o(skolemFOFtoCNF_O_1,skolemFOFtoCNF_P_8,skolemFOFtoCNF_P_8,skolemFOFtoCNF_P_8)
| between_c(skolemFOFtoCNF_C_2(skolemFOFtoCNF_O_1,skolemFOFtoCNF_P_8,skolemFOFtoCNF_P_8,skolemFOFtoCNF_P_8),skolemFOFtoCNF_P_8,skolemFOFtoCNF_P_8,skolemFOFtoCNF_P_8) ),
inference(subst,[],[refute_0_4:[bind(O,$fot(skolemFOFtoCNF_O_1)),bind(P,$fot(skolemFOFtoCNF_P_8)),bind(Q,$fot(skolemFOFtoCNF_P_8)),bind(R,$fot(skolemFOFtoCNF_P_8))]]) ).
cnf(refute_0_6,plain,
between_c(skolemFOFtoCNF_C_2(skolemFOFtoCNF_O_1,skolemFOFtoCNF_P_8,skolemFOFtoCNF_P_8,skolemFOFtoCNF_P_8),skolemFOFtoCNF_P_8,skolemFOFtoCNF_P_8,skolemFOFtoCNF_P_8),
inference(resolve,[$cnf( between_o(skolemFOFtoCNF_O_1,skolemFOFtoCNF_P_8,skolemFOFtoCNF_P_8,skolemFOFtoCNF_P_8) )],[refute_0_3,refute_0_5]) ).
cnf(refute_0_7,plain,
( P != R
| ~ between_c(C,P,Q,R) ),
inference(canonicalize,[],[normalize_0_13]) ).
cnf(refute_0_8,plain,
( R != R
| ~ between_c(C,R,Q,R) ),
inference(subst,[],[refute_0_7:[bind(P,$fot(R))]]) ).
cnf(refute_0_9,plain,
R = R,
introduced(tautology,[refl,[$fot(R)]]) ).
cnf(refute_0_10,plain,
~ between_c(C,R,Q,R),
inference(resolve,[$cnf( $equal(R,R) )],[refute_0_9,refute_0_8]) ).
cnf(refute_0_11,plain,
~ between_c(skolemFOFtoCNF_C_2(skolemFOFtoCNF_O_1,skolemFOFtoCNF_P_8,skolemFOFtoCNF_P_8,skolemFOFtoCNF_P_8),skolemFOFtoCNF_P_8,skolemFOFtoCNF_P_8,skolemFOFtoCNF_P_8),
inference(subst,[],[refute_0_10:[bind(C,$fot(skolemFOFtoCNF_C_2(skolemFOFtoCNF_O_1,skolemFOFtoCNF_P_8,skolemFOFtoCNF_P_8,skolemFOFtoCNF_P_8))),bind(Q,$fot(skolemFOFtoCNF_P_8)),bind(R,$fot(skolemFOFtoCNF_P_8))]]) ).
cnf(refute_0_12,plain,
$false,
inference(resolve,[$cnf( between_c(skolemFOFtoCNF_C_2(skolemFOFtoCNF_O_1,skolemFOFtoCNF_P_8,skolemFOFtoCNF_P_8,skolemFOFtoCNF_P_8),skolemFOFtoCNF_P_8,skolemFOFtoCNF_P_8,skolemFOFtoCNF_P_8) )],[refute_0_6,refute_0_11]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.13 % Problem : GEO117+1 : TPTP v8.1.0. Released v2.4.0.
% 0.04/0.14 % Command : metis --show proof --show saturation %s
% 0.14/0.36 % Computer : n016.cluster.edu
% 0.14/0.36 % Model : x86_64 x86_64
% 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36 % Memory : 8042.1875MB
% 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36 % CPULimit : 300
% 0.14/0.36 % WCLimit : 600
% 0.14/0.36 % DateTime : Sat Jun 18 15:14:52 EDT 2022
% 0.14/0.36 % CPUTime :
% 0.14/0.36 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 3.50/3.73 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 3.50/3.73
% 3.50/3.73 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 3.50/3.74
%------------------------------------------------------------------------------