TSTP Solution File: GEO258+1 by Metis---2.4
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : GEO258+1 : TPTP v8.1.0. Bugfixed v6.4.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n012.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 05:25:57 EDT 2022
% Result : Theorem 0.21s 0.39s
% Output : CNFRefutation 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 2
% Syntax : Number of formulae : 51 ( 9 unt; 0 def)
% Number of atoms : 140 ( 0 equ)
% Maximal formula atoms : 18 ( 2 avg)
% Number of connectives : 144 ( 55 ~; 72 |; 11 &)
% ( 3 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 4 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-4 aty)
% Number of functors : 4 ( 4 usr; 4 con; 0-0 aty)
% Number of variables : 86 ( 2 sgn 52 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(bet_def,axiom,
! [L,A,B,C] :
( between_on_line(L,A,B,C)
<=> ( ( before_on_line(L,A,B)
& before_on_line(L,B,C) )
| ( before_on_line(L,C,B)
& before_on_line(L,B,A) ) ) ) ).
fof(con,conjecture,
! [L,A,B,C] :
( between_on_line(L,A,B,C)
=> between_on_line(L,C,B,A) ) ).
fof(subgoal_0,plain,
! [L,A,B,C] :
( between_on_line(L,A,B,C)
=> between_on_line(L,C,B,A) ),
inference(strip,[],[con]) ).
fof(negate_0_0,plain,
~ ! [L,A,B,C] :
( between_on_line(L,A,B,C)
=> between_on_line(L,C,B,A) ),
inference(negate,[],[subgoal_0]) ).
fof(normalize_0_0,plain,
! [A,B,C,L] :
( ~ between_on_line(L,A,B,C)
<=> ( ( ~ before_on_line(L,A,B)
| ~ before_on_line(L,B,C) )
& ( ~ before_on_line(L,B,A)
| ~ before_on_line(L,C,B) ) ) ),
inference(canonicalize,[],[bet_def]) ).
fof(normalize_0_1,plain,
! [A,B,C,L] :
( ~ between_on_line(L,A,B,C)
<=> ( ( ~ before_on_line(L,A,B)
| ~ before_on_line(L,B,C) )
& ( ~ before_on_line(L,B,A)
| ~ before_on_line(L,C,B) ) ) ),
inference(specialize,[],[normalize_0_0]) ).
fof(normalize_0_2,plain,
! [A,B,C,L] :
( ( ~ before_on_line(L,A,B)
| ~ before_on_line(L,B,C)
| between_on_line(L,A,B,C) )
& ( ~ before_on_line(L,B,A)
| ~ before_on_line(L,C,B)
| between_on_line(L,A,B,C) )
& ( ~ between_on_line(L,A,B,C)
| before_on_line(L,A,B)
| before_on_line(L,B,A) )
& ( ~ between_on_line(L,A,B,C)
| before_on_line(L,A,B)
| before_on_line(L,C,B) )
& ( ~ between_on_line(L,A,B,C)
| before_on_line(L,B,A)
| before_on_line(L,B,C) )
& ( ~ between_on_line(L,A,B,C)
| before_on_line(L,B,C)
| before_on_line(L,C,B) ) ),
inference(clausify,[],[normalize_0_1]) ).
fof(normalize_0_3,plain,
! [A,B,C,L] :
( ~ before_on_line(L,A,B)
| ~ before_on_line(L,B,C)
| between_on_line(L,A,B,C) ),
inference(conjunct,[],[normalize_0_2]) ).
fof(normalize_0_4,plain,
? [A,B,C,L] :
( ~ between_on_line(L,C,B,A)
& between_on_line(L,A,B,C) ),
inference(canonicalize,[],[negate_0_0]) ).
fof(normalize_0_5,plain,
( ~ between_on_line(skolemFOFtoCNF_L,skolemFOFtoCNF_C,skolemFOFtoCNF_B,skolemFOFtoCNF_A)
& between_on_line(skolemFOFtoCNF_L,skolemFOFtoCNF_A,skolemFOFtoCNF_B,skolemFOFtoCNF_C) ),
inference(skolemize,[],[normalize_0_4]) ).
fof(normalize_0_6,plain,
between_on_line(skolemFOFtoCNF_L,skolemFOFtoCNF_A,skolemFOFtoCNF_B,skolemFOFtoCNF_C),
inference(conjunct,[],[normalize_0_5]) ).
fof(normalize_0_7,plain,
! [A,B,C,L] :
( ~ between_on_line(L,A,B,C)
| before_on_line(L,A,B)
| before_on_line(L,B,A) ),
inference(conjunct,[],[normalize_0_2]) ).
fof(normalize_0_8,plain,
! [A,B,C,L] :
( ~ between_on_line(L,A,B,C)
| before_on_line(L,A,B)
| before_on_line(L,C,B) ),
inference(conjunct,[],[normalize_0_2]) ).
fof(normalize_0_9,plain,
~ between_on_line(skolemFOFtoCNF_L,skolemFOFtoCNF_C,skolemFOFtoCNF_B,skolemFOFtoCNF_A),
inference(conjunct,[],[normalize_0_5]) ).
fof(normalize_0_10,plain,
! [A,B,C,L] :
( ~ before_on_line(L,B,A)
| ~ before_on_line(L,C,B)
| between_on_line(L,A,B,C) ),
inference(conjunct,[],[normalize_0_2]) ).
fof(normalize_0_11,plain,
! [A,B,C,L] :
( ~ between_on_line(L,A,B,C)
| before_on_line(L,B,A)
| before_on_line(L,B,C) ),
inference(conjunct,[],[normalize_0_2]) ).
fof(normalize_0_12,plain,
! [A,B,C,L] :
( ~ between_on_line(L,A,B,C)
| before_on_line(L,B,C)
| before_on_line(L,C,B) ),
inference(conjunct,[],[normalize_0_2]) ).
cnf(refute_0_0,plain,
( ~ before_on_line(L,A,B)
| ~ before_on_line(L,B,C)
| between_on_line(L,A,B,C) ),
inference(canonicalize,[],[normalize_0_3]) ).
cnf(refute_0_1,plain,
( ~ before_on_line(skolemFOFtoCNF_L,A,skolemFOFtoCNF_B)
| ~ before_on_line(skolemFOFtoCNF_L,skolemFOFtoCNF_B,skolemFOFtoCNF_A)
| between_on_line(skolemFOFtoCNF_L,A,skolemFOFtoCNF_B,skolemFOFtoCNF_A) ),
inference(subst,[],[refute_0_0:[bind(B,$fot(skolemFOFtoCNF_B)),bind(C,$fot(skolemFOFtoCNF_A)),bind(L,$fot(skolemFOFtoCNF_L))]]) ).
cnf(refute_0_2,plain,
between_on_line(skolemFOFtoCNF_L,skolemFOFtoCNF_A,skolemFOFtoCNF_B,skolemFOFtoCNF_C),
inference(canonicalize,[],[normalize_0_6]) ).
cnf(refute_0_3,plain,
( ~ between_on_line(L,A,B,C)
| before_on_line(L,A,B)
| before_on_line(L,B,A) ),
inference(canonicalize,[],[normalize_0_7]) ).
cnf(refute_0_4,plain,
( ~ between_on_line(skolemFOFtoCNF_L,skolemFOFtoCNF_A,skolemFOFtoCNF_B,skolemFOFtoCNF_C)
| before_on_line(skolemFOFtoCNF_L,skolemFOFtoCNF_A,skolemFOFtoCNF_B)
| before_on_line(skolemFOFtoCNF_L,skolemFOFtoCNF_B,skolemFOFtoCNF_A) ),
inference(subst,[],[refute_0_3:[bind(A,$fot(skolemFOFtoCNF_A)),bind(B,$fot(skolemFOFtoCNF_B)),bind(C,$fot(skolemFOFtoCNF_C)),bind(L,$fot(skolemFOFtoCNF_L))]]) ).
cnf(refute_0_5,plain,
( before_on_line(skolemFOFtoCNF_L,skolemFOFtoCNF_A,skolemFOFtoCNF_B)
| before_on_line(skolemFOFtoCNF_L,skolemFOFtoCNF_B,skolemFOFtoCNF_A) ),
inference(resolve,[$cnf( between_on_line(skolemFOFtoCNF_L,skolemFOFtoCNF_A,skolemFOFtoCNF_B,skolemFOFtoCNF_C) )],[refute_0_2,refute_0_4]) ).
cnf(refute_0_6,plain,
( ~ before_on_line(skolemFOFtoCNF_L,A,skolemFOFtoCNF_B)
| before_on_line(skolemFOFtoCNF_L,skolemFOFtoCNF_A,skolemFOFtoCNF_B)
| between_on_line(skolemFOFtoCNF_L,A,skolemFOFtoCNF_B,skolemFOFtoCNF_A) ),
inference(resolve,[$cnf( before_on_line(skolemFOFtoCNF_L,skolemFOFtoCNF_B,skolemFOFtoCNF_A) )],[refute_0_5,refute_0_1]) ).
cnf(refute_0_7,plain,
( ~ before_on_line(skolemFOFtoCNF_L,skolemFOFtoCNF_C,skolemFOFtoCNF_B)
| before_on_line(skolemFOFtoCNF_L,skolemFOFtoCNF_A,skolemFOFtoCNF_B)
| between_on_line(skolemFOFtoCNF_L,skolemFOFtoCNF_C,skolemFOFtoCNF_B,skolemFOFtoCNF_A) ),
inference(subst,[],[refute_0_6:[bind(A,$fot(skolemFOFtoCNF_C))]]) ).
cnf(refute_0_8,plain,
( ~ between_on_line(L,A,B,C)
| before_on_line(L,A,B)
| before_on_line(L,C,B) ),
inference(canonicalize,[],[normalize_0_8]) ).
cnf(refute_0_9,plain,
( ~ between_on_line(skolemFOFtoCNF_L,skolemFOFtoCNF_A,skolemFOFtoCNF_B,skolemFOFtoCNF_C)
| before_on_line(skolemFOFtoCNF_L,skolemFOFtoCNF_A,skolemFOFtoCNF_B)
| before_on_line(skolemFOFtoCNF_L,skolemFOFtoCNF_C,skolemFOFtoCNF_B) ),
inference(subst,[],[refute_0_8:[bind(A,$fot(skolemFOFtoCNF_A)),bind(B,$fot(skolemFOFtoCNF_B)),bind(C,$fot(skolemFOFtoCNF_C)),bind(L,$fot(skolemFOFtoCNF_L))]]) ).
cnf(refute_0_10,plain,
( before_on_line(skolemFOFtoCNF_L,skolemFOFtoCNF_A,skolemFOFtoCNF_B)
| before_on_line(skolemFOFtoCNF_L,skolemFOFtoCNF_C,skolemFOFtoCNF_B) ),
inference(resolve,[$cnf( between_on_line(skolemFOFtoCNF_L,skolemFOFtoCNF_A,skolemFOFtoCNF_B,skolemFOFtoCNF_C) )],[refute_0_2,refute_0_9]) ).
cnf(refute_0_11,plain,
( before_on_line(skolemFOFtoCNF_L,skolemFOFtoCNF_A,skolemFOFtoCNF_B)
| between_on_line(skolemFOFtoCNF_L,skolemFOFtoCNF_C,skolemFOFtoCNF_B,skolemFOFtoCNF_A) ),
inference(resolve,[$cnf( before_on_line(skolemFOFtoCNF_L,skolemFOFtoCNF_C,skolemFOFtoCNF_B) )],[refute_0_10,refute_0_7]) ).
cnf(refute_0_12,plain,
~ between_on_line(skolemFOFtoCNF_L,skolemFOFtoCNF_C,skolemFOFtoCNF_B,skolemFOFtoCNF_A),
inference(canonicalize,[],[normalize_0_9]) ).
cnf(refute_0_13,plain,
before_on_line(skolemFOFtoCNF_L,skolemFOFtoCNF_A,skolemFOFtoCNF_B),
inference(resolve,[$cnf( between_on_line(skolemFOFtoCNF_L,skolemFOFtoCNF_C,skolemFOFtoCNF_B,skolemFOFtoCNF_A) )],[refute_0_11,refute_0_12]) ).
cnf(refute_0_14,plain,
( ~ before_on_line(L,B,A)
| ~ before_on_line(L,C,B)
| between_on_line(L,A,B,C) ),
inference(canonicalize,[],[normalize_0_10]) ).
cnf(refute_0_15,plain,
( ~ before_on_line(skolemFOFtoCNF_L,C,skolemFOFtoCNF_B)
| ~ before_on_line(skolemFOFtoCNF_L,skolemFOFtoCNF_B,skolemFOFtoCNF_C)
| between_on_line(skolemFOFtoCNF_L,skolemFOFtoCNF_C,skolemFOFtoCNF_B,C) ),
inference(subst,[],[refute_0_14:[bind(A,$fot(skolemFOFtoCNF_C)),bind(B,$fot(skolemFOFtoCNF_B)),bind(L,$fot(skolemFOFtoCNF_L))]]) ).
cnf(refute_0_16,plain,
( ~ between_on_line(L,A,B,C)
| before_on_line(L,B,A)
| before_on_line(L,B,C) ),
inference(canonicalize,[],[normalize_0_11]) ).
cnf(refute_0_17,plain,
( ~ between_on_line(skolemFOFtoCNF_L,skolemFOFtoCNF_A,skolemFOFtoCNF_B,skolemFOFtoCNF_C)
| before_on_line(skolemFOFtoCNF_L,skolemFOFtoCNF_B,skolemFOFtoCNF_A)
| before_on_line(skolemFOFtoCNF_L,skolemFOFtoCNF_B,skolemFOFtoCNF_C) ),
inference(subst,[],[refute_0_16:[bind(A,$fot(skolemFOFtoCNF_A)),bind(B,$fot(skolemFOFtoCNF_B)),bind(C,$fot(skolemFOFtoCNF_C)),bind(L,$fot(skolemFOFtoCNF_L))]]) ).
cnf(refute_0_18,plain,
( before_on_line(skolemFOFtoCNF_L,skolemFOFtoCNF_B,skolemFOFtoCNF_A)
| before_on_line(skolemFOFtoCNF_L,skolemFOFtoCNF_B,skolemFOFtoCNF_C) ),
inference(resolve,[$cnf( between_on_line(skolemFOFtoCNF_L,skolemFOFtoCNF_A,skolemFOFtoCNF_B,skolemFOFtoCNF_C) )],[refute_0_2,refute_0_17]) ).
cnf(refute_0_19,plain,
( ~ before_on_line(skolemFOFtoCNF_L,C,skolemFOFtoCNF_B)
| before_on_line(skolemFOFtoCNF_L,skolemFOFtoCNF_B,skolemFOFtoCNF_A)
| between_on_line(skolemFOFtoCNF_L,skolemFOFtoCNF_C,skolemFOFtoCNF_B,C) ),
inference(resolve,[$cnf( before_on_line(skolemFOFtoCNF_L,skolemFOFtoCNF_B,skolemFOFtoCNF_C) )],[refute_0_18,refute_0_15]) ).
cnf(refute_0_20,plain,
( ~ before_on_line(skolemFOFtoCNF_L,skolemFOFtoCNF_A,skolemFOFtoCNF_B)
| before_on_line(skolemFOFtoCNF_L,skolemFOFtoCNF_B,skolemFOFtoCNF_A)
| between_on_line(skolemFOFtoCNF_L,skolemFOFtoCNF_C,skolemFOFtoCNF_B,skolemFOFtoCNF_A) ),
inference(subst,[],[refute_0_19:[bind(C,$fot(skolemFOFtoCNF_A))]]) ).
cnf(refute_0_21,plain,
( before_on_line(skolemFOFtoCNF_L,skolemFOFtoCNF_B,skolemFOFtoCNF_A)
| between_on_line(skolemFOFtoCNF_L,skolemFOFtoCNF_C,skolemFOFtoCNF_B,skolemFOFtoCNF_A) ),
inference(resolve,[$cnf( before_on_line(skolemFOFtoCNF_L,skolemFOFtoCNF_A,skolemFOFtoCNF_B) )],[refute_0_13,refute_0_20]) ).
cnf(refute_0_22,plain,
before_on_line(skolemFOFtoCNF_L,skolemFOFtoCNF_B,skolemFOFtoCNF_A),
inference(resolve,[$cnf( between_on_line(skolemFOFtoCNF_L,skolemFOFtoCNF_C,skolemFOFtoCNF_B,skolemFOFtoCNF_A) )],[refute_0_21,refute_0_12]) ).
cnf(refute_0_23,plain,
( ~ before_on_line(skolemFOFtoCNF_L,A,skolemFOFtoCNF_B)
| between_on_line(skolemFOFtoCNF_L,A,skolemFOFtoCNF_B,skolemFOFtoCNF_A) ),
inference(resolve,[$cnf( before_on_line(skolemFOFtoCNF_L,skolemFOFtoCNF_B,skolemFOFtoCNF_A) )],[refute_0_22,refute_0_1]) ).
cnf(refute_0_24,plain,
( ~ before_on_line(skolemFOFtoCNF_L,skolemFOFtoCNF_C,skolemFOFtoCNF_B)
| between_on_line(skolemFOFtoCNF_L,skolemFOFtoCNF_C,skolemFOFtoCNF_B,skolemFOFtoCNF_A) ),
inference(subst,[],[refute_0_23:[bind(A,$fot(skolemFOFtoCNF_C))]]) ).
cnf(refute_0_25,plain,
( ~ between_on_line(L,A,B,C)
| before_on_line(L,B,C)
| before_on_line(L,C,B) ),
inference(canonicalize,[],[normalize_0_12]) ).
cnf(refute_0_26,plain,
( ~ between_on_line(skolemFOFtoCNF_L,skolemFOFtoCNF_A,skolemFOFtoCNF_B,skolemFOFtoCNF_C)
| before_on_line(skolemFOFtoCNF_L,skolemFOFtoCNF_B,skolemFOFtoCNF_C)
| before_on_line(skolemFOFtoCNF_L,skolemFOFtoCNF_C,skolemFOFtoCNF_B) ),
inference(subst,[],[refute_0_25:[bind(A,$fot(skolemFOFtoCNF_A)),bind(B,$fot(skolemFOFtoCNF_B)),bind(C,$fot(skolemFOFtoCNF_C)),bind(L,$fot(skolemFOFtoCNF_L))]]) ).
cnf(refute_0_27,plain,
( before_on_line(skolemFOFtoCNF_L,skolemFOFtoCNF_B,skolemFOFtoCNF_C)
| before_on_line(skolemFOFtoCNF_L,skolemFOFtoCNF_C,skolemFOFtoCNF_B) ),
inference(resolve,[$cnf( between_on_line(skolemFOFtoCNF_L,skolemFOFtoCNF_A,skolemFOFtoCNF_B,skolemFOFtoCNF_C) )],[refute_0_2,refute_0_26]) ).
cnf(refute_0_28,plain,
( before_on_line(skolemFOFtoCNF_L,skolemFOFtoCNF_B,skolemFOFtoCNF_C)
| between_on_line(skolemFOFtoCNF_L,skolemFOFtoCNF_C,skolemFOFtoCNF_B,skolemFOFtoCNF_A) ),
inference(resolve,[$cnf( before_on_line(skolemFOFtoCNF_L,skolemFOFtoCNF_C,skolemFOFtoCNF_B) )],[refute_0_27,refute_0_24]) ).
cnf(refute_0_29,plain,
before_on_line(skolemFOFtoCNF_L,skolemFOFtoCNF_B,skolemFOFtoCNF_C),
inference(resolve,[$cnf( between_on_line(skolemFOFtoCNF_L,skolemFOFtoCNF_C,skolemFOFtoCNF_B,skolemFOFtoCNF_A) )],[refute_0_28,refute_0_12]) ).
cnf(refute_0_30,plain,
( ~ before_on_line(skolemFOFtoCNF_L,C,skolemFOFtoCNF_B)
| between_on_line(skolemFOFtoCNF_L,skolemFOFtoCNF_C,skolemFOFtoCNF_B,C) ),
inference(resolve,[$cnf( before_on_line(skolemFOFtoCNF_L,skolemFOFtoCNF_B,skolemFOFtoCNF_C) )],[refute_0_29,refute_0_15]) ).
cnf(refute_0_31,plain,
( ~ before_on_line(skolemFOFtoCNF_L,skolemFOFtoCNF_A,skolemFOFtoCNF_B)
| between_on_line(skolemFOFtoCNF_L,skolemFOFtoCNF_C,skolemFOFtoCNF_B,skolemFOFtoCNF_A) ),
inference(subst,[],[refute_0_30:[bind(C,$fot(skolemFOFtoCNF_A))]]) ).
cnf(refute_0_32,plain,
between_on_line(skolemFOFtoCNF_L,skolemFOFtoCNF_C,skolemFOFtoCNF_B,skolemFOFtoCNF_A),
inference(resolve,[$cnf( before_on_line(skolemFOFtoCNF_L,skolemFOFtoCNF_A,skolemFOFtoCNF_B) )],[refute_0_13,refute_0_31]) ).
cnf(refute_0_33,plain,
$false,
inference(resolve,[$cnf( between_on_line(skolemFOFtoCNF_L,skolemFOFtoCNF_C,skolemFOFtoCNF_B,skolemFOFtoCNF_A) )],[refute_0_32,refute_0_12]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : GEO258+1 : TPTP v8.1.0. Bugfixed v6.4.0.
% 0.07/0.14 % Command : metis --show proof --show saturation %s
% 0.14/0.35 % Computer : n012.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.36 % WCLimit : 600
% 0.14/0.36 % DateTime : Sat Jun 18 06:55:53 EDT 2022
% 0.14/0.36 % CPUTime :
% 0.14/0.36 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.21/0.39 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.21/0.39
% 0.21/0.39 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 0.21/0.40
%------------------------------------------------------------------------------