%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : GEO206+3 : TPTP v8.1.0. Bugfixed v4.0.1.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n013.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 05:25:21 EDT 2022
% Result : Theorem 0.14s 0.39s
% Output : CNFRefutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 6
% Syntax : Number of formulae : 48 ( 14 unt; 0 def)
% Number of atoms : 96 ( 0 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 84 ( 36 ~; 28 |; 9 &)
% ( 6 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 6 ( 5 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 3 con; 0-2 aty)
% Number of variables : 69 ( 1 sgn 50 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(apart5,axiom,
! [X,Y,Z] :
( distinct_lines(X,Y)
=> ( distinct_lines(X,Z)
| distinct_lines(Y,Z) ) ) ).
fof(p1,axiom,
! [X,Y] :
( distinct_lines(X,Y)
=> convergent_lines(X,Y) ) ).
fof(cp1,axiom,
! [X,Y] : ~ convergent_lines(parallel_through_point(Y,X),Y) ).
fof(ax2,axiom,
! [X,Y] :
( equal_lines(X,Y)
<=> ~ distinct_lines(X,Y) ) ).
fof(a3,axiom,
! [X,Y] :
( parallel_lines(X,Y)
<=> ~ convergent_lines(X,Y) ) ).
fof(con,conjecture,
! [X,Y,Z] :
( ( incident_point_and_line(X,Y)
& parallel_lines(Y,Z) )
=> equal_lines(Y,parallel_through_point(Z,X)) ) ).
fof(subgoal_0,plain,
! [X,Y,Z] :
( ( incident_point_and_line(X,Y)
& parallel_lines(Y,Z) )
=> equal_lines(Y,parallel_through_point(Z,X)) ),
inference(strip,[],[con]) ).
fof(negate_0_0,plain,
~ ! [X,Y,Z] :
( ( incident_point_and_line(X,Y)
& parallel_lines(Y,Z) )
=> equal_lines(Y,parallel_through_point(Z,X)) ),
inference(negate,[],[subgoal_0]) ).
fof(normalize_0_0,plain,
! [X,Y] :
( ~ distinct_lines(X,Y)
| convergent_lines(X,Y) ),
inference(canonicalize,[],[p1]) ).
fof(normalize_0_1,plain,
! [X,Y] :
( ~ distinct_lines(X,Y)
| convergent_lines(X,Y) ),
inference(specialize,[],[normalize_0_0]) ).
fof(normalize_0_2,plain,
! [X,Y] : ~ convergent_lines(parallel_through_point(Y,X),Y),
inference(canonicalize,[],[cp1]) ).
fof(normalize_0_3,plain,
! [X,Y] : ~ convergent_lines(parallel_through_point(Y,X),Y),
inference(specialize,[],[normalize_0_2]) ).
fof(normalize_0_4,plain,
? [X,Y,Z] :
( ~ equal_lines(Y,parallel_through_point(Z,X))
& incident_point_and_line(X,Y)
& parallel_lines(Y,Z) ),
inference(canonicalize,[],[negate_0_0]) ).
fof(normalize_0_5,plain,
( ~ equal_lines(skolemFOFtoCNF_Y,parallel_through_point(skolemFOFtoCNF_Z,skolemFOFtoCNF_X))
& incident_point_and_line(skolemFOFtoCNF_X,skolemFOFtoCNF_Y)
& parallel_lines(skolemFOFtoCNF_Y,skolemFOFtoCNF_Z) ),
inference(skolemize,[],[normalize_0_4]) ).
fof(normalize_0_6,plain,
~ equal_lines(skolemFOFtoCNF_Y,parallel_through_point(skolemFOFtoCNF_Z,skolemFOFtoCNF_X)),
inference(conjunct,[],[normalize_0_5]) ).
fof(normalize_0_7,plain,
! [X,Y] :
( ~ distinct_lines(X,Y)
<=> equal_lines(X,Y) ),
inference(canonicalize,[],[ax2]) ).
fof(normalize_0_8,plain,
! [X,Y] :
( ~ distinct_lines(X,Y)
<=> equal_lines(X,Y) ),
inference(specialize,[],[normalize_0_7]) ).
fof(normalize_0_9,plain,
! [X,Y] :
( ( ~ distinct_lines(X,Y)
| ~ equal_lines(X,Y) )
& ( distinct_lines(X,Y)
| equal_lines(X,Y) ) ),
inference(clausify,[],[normalize_0_8]) ).
fof(normalize_0_10,plain,
! [X,Y] :
( distinct_lines(X,Y)
| equal_lines(X,Y) ),
inference(conjunct,[],[normalize_0_9]) ).
fof(normalize_0_11,plain,
! [X,Y,Z] :
( ~ distinct_lines(X,Y)
| distinct_lines(X,Z)
| distinct_lines(Y,Z) ),
inference(canonicalize,[],[apart5]) ).
fof(normalize_0_12,plain,
! [X,Y,Z] :
( ~ distinct_lines(X,Y)
| distinct_lines(X,Z)
| distinct_lines(Y,Z) ),
inference(specialize,[],[normalize_0_11]) ).
fof(normalize_0_13,plain,
parallel_lines(skolemFOFtoCNF_Y,skolemFOFtoCNF_Z),
inference(conjunct,[],[normalize_0_5]) ).
fof(normalize_0_14,plain,
! [X,Y] :
( ~ convergent_lines(X,Y)
<=> parallel_lines(X,Y) ),
inference(canonicalize,[],[a3]) ).
fof(normalize_0_15,plain,
! [X,Y] :
( ~ convergent_lines(X,Y)
<=> parallel_lines(X,Y) ),
inference(specialize,[],[normalize_0_14]) ).
fof(normalize_0_16,plain,
! [X,Y] :
( ( ~ convergent_lines(X,Y)
| ~ parallel_lines(X,Y) )
& ( convergent_lines(X,Y)
| parallel_lines(X,Y) ) ),
inference(clausify,[],[normalize_0_15]) ).
fof(normalize_0_17,plain,
! [X,Y] :
( ~ convergent_lines(X,Y)
| ~ parallel_lines(X,Y) ),
inference(conjunct,[],[normalize_0_16]) ).
cnf(refute_0_0,plain,
( ~ distinct_lines(X,Y)
| convergent_lines(X,Y) ),
inference(canonicalize,[],[normalize_0_1]) ).
cnf(refute_0_1,plain,
( ~ distinct_lines(skolemFOFtoCNF_Y,skolemFOFtoCNF_Z)
| convergent_lines(skolemFOFtoCNF_Y,skolemFOFtoCNF_Z) ),
inference(subst,[],[refute_0_0:[bind(X,$fot(skolemFOFtoCNF_Y)),bind(Y,$fot(skolemFOFtoCNF_Z))]]) ).
cnf(refute_0_2,plain,
~ convergent_lines(parallel_through_point(Y,X),Y),
inference(canonicalize,[],[normalize_0_3]) ).
cnf(refute_0_3,plain,
~ convergent_lines(parallel_through_point(skolemFOFtoCNF_Z,skolemFOFtoCNF_X),skolemFOFtoCNF_Z),
inference(subst,[],[refute_0_2:[bind(X,$fot(skolemFOFtoCNF_X)),bind(Y,$fot(skolemFOFtoCNF_Z))]]) ).
cnf(refute_0_4,plain,
( ~ distinct_lines(parallel_through_point(skolemFOFtoCNF_Z,skolemFOFtoCNF_X),X_56)
| convergent_lines(parallel_through_point(skolemFOFtoCNF_Z,skolemFOFtoCNF_X),X_56) ),
inference(subst,[],[refute_0_0:[bind(X,$fot(parallel_through_point(skolemFOFtoCNF_Z,skolemFOFtoCNF_X))),bind(Y,$fot(X_56))]]) ).
cnf(refute_0_5,plain,
~ equal_lines(skolemFOFtoCNF_Y,parallel_through_point(skolemFOFtoCNF_Z,skolemFOFtoCNF_X)),
inference(canonicalize,[],[normalize_0_6]) ).
cnf(refute_0_6,plain,
( distinct_lines(X,Y)
| equal_lines(X,Y) ),
inference(canonicalize,[],[normalize_0_10]) ).
cnf(refute_0_7,plain,
( distinct_lines(skolemFOFtoCNF_Y,parallel_through_point(skolemFOFtoCNF_Z,skolemFOFtoCNF_X))
| equal_lines(skolemFOFtoCNF_Y,parallel_through_point(skolemFOFtoCNF_Z,skolemFOFtoCNF_X)) ),
inference(subst,[],[refute_0_6:[bind(X,$fot(skolemFOFtoCNF_Y)),bind(Y,$fot(parallel_through_point(skolemFOFtoCNF_Z,skolemFOFtoCNF_X)))]]) ).
cnf(refute_0_8,plain,
distinct_lines(skolemFOFtoCNF_Y,parallel_through_point(skolemFOFtoCNF_Z,skolemFOFtoCNF_X)),
inference(resolve,[$cnf( equal_lines(skolemFOFtoCNF_Y,parallel_through_point(skolemFOFtoCNF_Z,skolemFOFtoCNF_X)) )],[refute_0_7,refute_0_5]) ).
cnf(refute_0_9,plain,
( ~ distinct_lines(X,Y)
| distinct_lines(X,Z)
| distinct_lines(Y,Z) ),
inference(canonicalize,[],[normalize_0_12]) ).
cnf(refute_0_10,plain,
( ~ distinct_lines(skolemFOFtoCNF_Y,parallel_through_point(skolemFOFtoCNF_Z,skolemFOFtoCNF_X))
| distinct_lines(parallel_through_point(skolemFOFtoCNF_Z,skolemFOFtoCNF_X),X_55)
| distinct_lines(skolemFOFtoCNF_Y,X_55) ),
inference(subst,[],[refute_0_9:[bind(X,$fot(skolemFOFtoCNF_Y)),bind(Y,$fot(parallel_through_point(skolemFOFtoCNF_Z,skolemFOFtoCNF_X))),bind(Z,$fot(X_55))]]) ).
cnf(refute_0_11,plain,
( distinct_lines(parallel_through_point(skolemFOFtoCNF_Z,skolemFOFtoCNF_X),X_55)
| distinct_lines(skolemFOFtoCNF_Y,X_55) ),
inference(resolve,[$cnf( distinct_lines(skolemFOFtoCNF_Y,parallel_through_point(skolemFOFtoCNF_Z,skolemFOFtoCNF_X)) )],[refute_0_8,refute_0_10]) ).
cnf(refute_0_12,plain,
( distinct_lines(parallel_through_point(skolemFOFtoCNF_Z,skolemFOFtoCNF_X),X_56)
| distinct_lines(skolemFOFtoCNF_Y,X_56) ),
inference(subst,[],[refute_0_11:[bind(X_55,$fot(X_56))]]) ).
cnf(refute_0_13,plain,
( convergent_lines(parallel_through_point(skolemFOFtoCNF_Z,skolemFOFtoCNF_X),X_56)
| distinct_lines(skolemFOFtoCNF_Y,X_56) ),
inference(resolve,[$cnf( distinct_lines(parallel_through_point(skolemFOFtoCNF_Z,skolemFOFtoCNF_X),X_56) )],[refute_0_12,refute_0_4]) ).
cnf(refute_0_14,plain,
( convergent_lines(parallel_through_point(skolemFOFtoCNF_Z,skolemFOFtoCNF_X),skolemFOFtoCNF_Z)
| distinct_lines(skolemFOFtoCNF_Y,skolemFOFtoCNF_Z) ),
inference(subst,[],[refute_0_13:[bind(X_56,$fot(skolemFOFtoCNF_Z))]]) ).
cnf(refute_0_15,plain,
distinct_lines(skolemFOFtoCNF_Y,skolemFOFtoCNF_Z),
inference(resolve,[$cnf( convergent_lines(parallel_through_point(skolemFOFtoCNF_Z,skolemFOFtoCNF_X),skolemFOFtoCNF_Z) )],[refute_0_14,refute_0_3]) ).
cnf(refute_0_16,plain,
convergent_lines(skolemFOFtoCNF_Y,skolemFOFtoCNF_Z),
inference(resolve,[$cnf( distinct_lines(skolemFOFtoCNF_Y,skolemFOFtoCNF_Z) )],[refute_0_15,refute_0_1]) ).
cnf(refute_0_17,plain,
parallel_lines(skolemFOFtoCNF_Y,skolemFOFtoCNF_Z),
inference(canonicalize,[],[normalize_0_13]) ).
cnf(refute_0_18,plain,
( ~ convergent_lines(X,Y)
| ~ parallel_lines(X,Y) ),
inference(canonicalize,[],[normalize_0_17]) ).
cnf(refute_0_19,plain,
( ~ convergent_lines(skolemFOFtoCNF_Y,skolemFOFtoCNF_Z)
| ~ parallel_lines(skolemFOFtoCNF_Y,skolemFOFtoCNF_Z) ),
inference(subst,[],[refute_0_18:[bind(X,$fot(skolemFOFtoCNF_Y)),bind(Y,$fot(skolemFOFtoCNF_Z))]]) ).
cnf(refute_0_20,plain,
~ convergent_lines(skolemFOFtoCNF_Y,skolemFOFtoCNF_Z),
inference(resolve,[$cnf( parallel_lines(skolemFOFtoCNF_Y,skolemFOFtoCNF_Z) )],[refute_0_17,refute_0_19]) ).
cnf(refute_0_21,plain,
$false,
inference(resolve,[$cnf( convergent_lines(skolemFOFtoCNF_Y,skolemFOFtoCNF_Z) )],[refute_0_16,refute_0_20]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.14 % Problem : GEO206+3 : TPTP v8.1.0. Bugfixed v4.0.1.
% 0.08/0.15 % Command : metis --show proof --show saturation %s
% 0.14/0.37 % Computer : n013.cluster.edu
% 0.14/0.37 % Model : x86_64 x86_64
% 0.14/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.37 % Memory : 8042.1875MB
% 0.14/0.37 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.37 % CPULimit : 300
% 0.14/0.37 % WCLimit : 600
% 0.14/0.37 % DateTime : Sat Jun 18 15:27:59 EDT 2022
% 0.14/0.37 % CPUTime :
% 0.14/0.37 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.14/0.39 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.14/0.39
% 0.14/0.39 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 0.14/0.40
%------------------------------------------------------------------------------