TSTP Solution File: GEO262+3 by Metis---2.4
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%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : GEO262+3 : TPTP v8.1.0. Released v4.0.0.
% 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 05:26:00 EDT 2022
% Result : Theorem 0.14s 0.39s
% Output : CNFRefutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 5
% Syntax : Number of formulae : 42 ( 11 unt; 0 def)
% Number of atoms : 117 ( 0 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 123 ( 48 ~; 32 |; 33 &)
% ( 6 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 7 ( 6 usr; 1 prp; 0-4 aty)
% Number of functors : 9 ( 9 usr; 6 con; 0-2 aty)
% Number of variables : 78 ( 4 sgn 56 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(a1_defns,axiom,
! [X,Y] :
( unequally_directed_opposite_lines(X,Y)
<=> unequally_directed_lines(X,reverse_line(Y)) ) ).
fof(a7_defns,axiom,
! [L,M] :
( convergent_lines(L,M)
<=> ( unequally_directed_lines(L,M)
& unequally_directed_opposite_lines(L,M) ) ) ).
fof(ax9_basics,axiom,
! [L,M] :
( ( unequally_directed_lines(L,M)
& unequally_directed_lines(L,reverse_line(M)) )
=> ( left_convergent_lines(L,M)
| left_convergent_lines(L,reverse_line(M)) ) ) ).
fof(ax11_basics,axiom,
! [L,M] :
~ ( left_convergent_lines(L,M)
| left_convergent_lines(L,reverse_line(M)) ) ).
fof(con,conjecture,
! [L,M,N,A,B,C] :
( ( between_on_line(L,A,B,C)
& convergent_lines(L,M)
& incident_point_and_line(B,M)
& convergent_lines(L,N)
& convergent_lines(M,N)
& incident_point_and_line(B,N) )
=> between_on_line(M,intersection_point(M,parallel_through_point(N,A)),B,intersection_point(M,parallel_through_point(N,C))) ) ).
fof(subgoal_0,plain,
! [L,M,N,A,B,C] :
( ( between_on_line(L,A,B,C)
& convergent_lines(L,M)
& incident_point_and_line(B,M)
& convergent_lines(L,N)
& convergent_lines(M,N)
& incident_point_and_line(B,N) )
=> between_on_line(M,intersection_point(M,parallel_through_point(N,A)),B,intersection_point(M,parallel_through_point(N,C))) ),
inference(strip,[],[con]) ).
fof(negate_0_0,plain,
~ ! [L,M,N,A,B,C] :
( ( between_on_line(L,A,B,C)
& convergent_lines(L,M)
& incident_point_and_line(B,M)
& convergent_lines(L,N)
& convergent_lines(M,N)
& incident_point_and_line(B,N) )
=> between_on_line(M,intersection_point(M,parallel_through_point(N,A)),B,intersection_point(M,parallel_through_point(N,C))) ),
inference(negate,[],[subgoal_0]) ).
fof(normalize_0_0,plain,
? [A,B,C,L,M,N] :
( ~ between_on_line(M,intersection_point(M,parallel_through_point(N,A)),B,intersection_point(M,parallel_through_point(N,C)))
& between_on_line(L,A,B,C)
& convergent_lines(L,M)
& convergent_lines(L,N)
& convergent_lines(M,N)
& incident_point_and_line(B,M)
& incident_point_and_line(B,N) ),
inference(canonicalize,[],[negate_0_0]) ).
fof(normalize_0_1,plain,
( ~ between_on_line(skolemFOFtoCNF_M,intersection_point(skolemFOFtoCNF_M,parallel_through_point(skolemFOFtoCNF_N,skolemFOFtoCNF_A)),skolemFOFtoCNF_B,intersection_point(skolemFOFtoCNF_M,parallel_through_point(skolemFOFtoCNF_N,skolemFOFtoCNF_C)))
& between_on_line(skolemFOFtoCNF_L,skolemFOFtoCNF_A,skolemFOFtoCNF_B,skolemFOFtoCNF_C)
& convergent_lines(skolemFOFtoCNF_L,skolemFOFtoCNF_M)
& convergent_lines(skolemFOFtoCNF_L,skolemFOFtoCNF_N)
& convergent_lines(skolemFOFtoCNF_M,skolemFOFtoCNF_N)
& incident_point_and_line(skolemFOFtoCNF_B,skolemFOFtoCNF_M)
& incident_point_and_line(skolemFOFtoCNF_B,skolemFOFtoCNF_N) ),
inference(skolemize,[],[normalize_0_0]) ).
fof(normalize_0_2,plain,
convergent_lines(skolemFOFtoCNF_L,skolemFOFtoCNF_M),
inference(conjunct,[],[normalize_0_1]) ).
fof(normalize_0_3,plain,
! [L,M] :
( ~ convergent_lines(L,M)
<=> ( ~ unequally_directed_lines(L,M)
| ~ unequally_directed_opposite_lines(L,M) ) ),
inference(canonicalize,[],[a7_defns]) ).
fof(normalize_0_4,plain,
! [L,M] :
( ~ convergent_lines(L,M)
<=> ( ~ unequally_directed_lines(L,M)
| ~ unequally_directed_opposite_lines(L,M) ) ),
inference(specialize,[],[normalize_0_3]) ).
fof(normalize_0_5,plain,
! [L,M] :
( ( ~ convergent_lines(L,M)
| unequally_directed_lines(L,M) )
& ( ~ convergent_lines(L,M)
| unequally_directed_opposite_lines(L,M) )
& ( ~ unequally_directed_lines(L,M)
| ~ unequally_directed_opposite_lines(L,M)
| convergent_lines(L,M) ) ),
inference(clausify,[],[normalize_0_4]) ).
fof(normalize_0_6,plain,
! [L,M] :
( ~ convergent_lines(L,M)
| unequally_directed_opposite_lines(L,M) ),
inference(conjunct,[],[normalize_0_5]) ).
fof(normalize_0_7,plain,
! [X,Y] :
( ~ unequally_directed_lines(X,reverse_line(Y))
<=> ~ unequally_directed_opposite_lines(X,Y) ),
inference(canonicalize,[],[a1_defns]) ).
fof(normalize_0_8,plain,
! [X,Y] :
( ~ unequally_directed_lines(X,reverse_line(Y))
<=> ~ unequally_directed_opposite_lines(X,Y) ),
inference(specialize,[],[normalize_0_7]) ).
fof(normalize_0_9,plain,
! [X,Y] :
( ( ~ unequally_directed_lines(X,reverse_line(Y))
| unequally_directed_opposite_lines(X,Y) )
& ( ~ unequally_directed_opposite_lines(X,Y)
| unequally_directed_lines(X,reverse_line(Y)) ) ),
inference(clausify,[],[normalize_0_8]) ).
fof(normalize_0_10,plain,
! [X,Y] :
( ~ unequally_directed_opposite_lines(X,Y)
| unequally_directed_lines(X,reverse_line(Y)) ),
inference(conjunct,[],[normalize_0_9]) ).
fof(normalize_0_11,plain,
! [L,M] :
( ~ unequally_directed_lines(L,M)
| ~ unequally_directed_lines(L,reverse_line(M))
| left_convergent_lines(L,M)
| left_convergent_lines(L,reverse_line(M)) ),
inference(canonicalize,[],[ax9_basics]) ).
fof(normalize_0_12,plain,
! [L,M] :
( ~ unequally_directed_lines(L,M)
| ~ unequally_directed_lines(L,reverse_line(M))
| left_convergent_lines(L,M)
| left_convergent_lines(L,reverse_line(M)) ),
inference(specialize,[],[normalize_0_11]) ).
fof(normalize_0_13,plain,
( ! [L,M] : ~ left_convergent_lines(L,M)
& ! [L,M] : ~ left_convergent_lines(L,reverse_line(M)) ),
inference(canonicalize,[],[ax11_basics]) ).
fof(normalize_0_14,plain,
! [L,M] : ~ left_convergent_lines(L,M),
inference(conjunct,[],[normalize_0_13]) ).
fof(normalize_0_15,plain,
! [L,M] : ~ left_convergent_lines(L,M),
inference(specialize,[],[normalize_0_14]) ).
fof(normalize_0_16,plain,
! [L,M] :
( ~ convergent_lines(L,M)
| unequally_directed_lines(L,M) ),
inference(conjunct,[],[normalize_0_5]) ).
cnf(refute_0_0,plain,
convergent_lines(skolemFOFtoCNF_L,skolemFOFtoCNF_M),
inference(canonicalize,[],[normalize_0_2]) ).
cnf(refute_0_1,plain,
( ~ convergent_lines(L,M)
| unequally_directed_opposite_lines(L,M) ),
inference(canonicalize,[],[normalize_0_6]) ).
cnf(refute_0_2,plain,
( ~ convergent_lines(skolemFOFtoCNF_L,skolemFOFtoCNF_M)
| unequally_directed_opposite_lines(skolemFOFtoCNF_L,skolemFOFtoCNF_M) ),
inference(subst,[],[refute_0_1:[bind(L,$fot(skolemFOFtoCNF_L)),bind(M,$fot(skolemFOFtoCNF_M))]]) ).
cnf(refute_0_3,plain,
unequally_directed_opposite_lines(skolemFOFtoCNF_L,skolemFOFtoCNF_M),
inference(resolve,[$cnf( convergent_lines(skolemFOFtoCNF_L,skolemFOFtoCNF_M) )],[refute_0_0,refute_0_2]) ).
cnf(refute_0_4,plain,
( ~ unequally_directed_opposite_lines(X,Y)
| unequally_directed_lines(X,reverse_line(Y)) ),
inference(canonicalize,[],[normalize_0_10]) ).
cnf(refute_0_5,plain,
( ~ unequally_directed_opposite_lines(skolemFOFtoCNF_L,skolemFOFtoCNF_M)
| unequally_directed_lines(skolemFOFtoCNF_L,reverse_line(skolemFOFtoCNF_M)) ),
inference(subst,[],[refute_0_4:[bind(X,$fot(skolemFOFtoCNF_L)),bind(Y,$fot(skolemFOFtoCNF_M))]]) ).
cnf(refute_0_6,plain,
unequally_directed_lines(skolemFOFtoCNF_L,reverse_line(skolemFOFtoCNF_M)),
inference(resolve,[$cnf( unequally_directed_opposite_lines(skolemFOFtoCNF_L,skolemFOFtoCNF_M) )],[refute_0_3,refute_0_5]) ).
cnf(refute_0_7,plain,
( ~ unequally_directed_lines(L,M)
| ~ unequally_directed_lines(L,reverse_line(M))
| left_convergent_lines(L,M)
| left_convergent_lines(L,reverse_line(M)) ),
inference(canonicalize,[],[normalize_0_12]) ).
cnf(refute_0_8,plain,
~ left_convergent_lines(L,M),
inference(canonicalize,[],[normalize_0_15]) ).
cnf(refute_0_9,plain,
( ~ unequally_directed_lines(L,M)
| ~ unequally_directed_lines(L,reverse_line(M))
| left_convergent_lines(L,reverse_line(M)) ),
inference(resolve,[$cnf( left_convergent_lines(L,M) )],[refute_0_7,refute_0_8]) ).
cnf(refute_0_10,plain,
~ left_convergent_lines(L,reverse_line(M)),
inference(subst,[],[refute_0_8:[bind(M,$fot(reverse_line(M)))]]) ).
cnf(refute_0_11,plain,
( ~ unequally_directed_lines(L,M)
| ~ unequally_directed_lines(L,reverse_line(M)) ),
inference(resolve,[$cnf( left_convergent_lines(L,reverse_line(M)) )],[refute_0_9,refute_0_10]) ).
cnf(refute_0_12,plain,
( ~ unequally_directed_lines(skolemFOFtoCNF_L,reverse_line(skolemFOFtoCNF_M))
| ~ unequally_directed_lines(skolemFOFtoCNF_L,skolemFOFtoCNF_M) ),
inference(subst,[],[refute_0_11:[bind(L,$fot(skolemFOFtoCNF_L)),bind(M,$fot(skolemFOFtoCNF_M))]]) ).
cnf(refute_0_13,plain,
~ unequally_directed_lines(skolemFOFtoCNF_L,skolemFOFtoCNF_M),
inference(resolve,[$cnf( unequally_directed_lines(skolemFOFtoCNF_L,reverse_line(skolemFOFtoCNF_M)) )],[refute_0_6,refute_0_12]) ).
cnf(refute_0_14,plain,
( ~ convergent_lines(L,M)
| unequally_directed_lines(L,M) ),
inference(canonicalize,[],[normalize_0_16]) ).
cnf(refute_0_15,plain,
( ~ convergent_lines(skolemFOFtoCNF_L,skolemFOFtoCNF_M)
| unequally_directed_lines(skolemFOFtoCNF_L,skolemFOFtoCNF_M) ),
inference(subst,[],[refute_0_14:[bind(L,$fot(skolemFOFtoCNF_L)),bind(M,$fot(skolemFOFtoCNF_M))]]) ).
cnf(refute_0_16,plain,
unequally_directed_lines(skolemFOFtoCNF_L,skolemFOFtoCNF_M),
inference(resolve,[$cnf( convergent_lines(skolemFOFtoCNF_L,skolemFOFtoCNF_M) )],[refute_0_0,refute_0_15]) ).
cnf(refute_0_17,plain,
$false,
inference(resolve,[$cnf( unequally_directed_lines(skolemFOFtoCNF_L,skolemFOFtoCNF_M) )],[refute_0_16,refute_0_13]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.13 % Problem : GEO262+3 : TPTP v8.1.0. Released v4.0.0.
% 0.12/0.14 % Command : metis --show proof --show saturation %s
% 0.14/0.36 % Computer : n015.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 04:36:13 EDT 2022
% 0.14/0.36 % CPUTime :
% 0.14/0.36 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.14/0.39 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.14/0.39
% 0.14/0.39 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 0.14/0.39
%------------------------------------------------------------------------------