TSTP Solution File: GEO208+3 by Metis---2.4
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%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : GEO208+3 : TPTP v8.1.0. Released v4.0.0.
% 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 05:25:23 EDT 2022
% Result : Theorem 0.19s 0.36s
% Output : CNFRefutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 4
% Syntax : Number of formulae : 32 ( 8 unt; 0 def)
% Number of atoms : 70 ( 0 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 64 ( 26 ~; 14 |; 14 &)
% ( 6 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 6 ( 5 usr; 1 prp; 0-2 aty)
% Number of functors : 3 ( 3 usr; 3 con; 0-0 aty)
% Number of variables : 44 ( 0 sgn 35 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(p1,axiom,
! [X,Y] :
( distinct_lines(X,Y)
=> convergent_lines(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)
& incident_point_and_line(X,Z)
& parallel_lines(Y,Z) )
=> equal_lines(Y,Z) ) ).
fof(subgoal_0,plain,
! [X,Y,Z] :
( ( incident_point_and_line(X,Y)
& incident_point_and_line(X,Z)
& parallel_lines(Y,Z) )
=> equal_lines(Y,Z) ),
inference(strip,[],[con]) ).
fof(negate_0_0,plain,
~ ! [X,Y,Z] :
( ( incident_point_and_line(X,Y)
& incident_point_and_line(X,Z)
& parallel_lines(Y,Z) )
=> equal_lines(Y,Z) ),
inference(negate,[],[subgoal_0]) ).
fof(normalize_0_0,plain,
? [X,Y,Z] :
( ~ equal_lines(Y,Z)
& incident_point_and_line(X,Y)
& incident_point_and_line(X,Z)
& parallel_lines(Y,Z) ),
inference(canonicalize,[],[negate_0_0]) ).
fof(normalize_0_1,plain,
( ~ equal_lines(skolemFOFtoCNF_Y,skolemFOFtoCNF_Z)
& incident_point_and_line(skolemFOFtoCNF_X,skolemFOFtoCNF_Y)
& incident_point_and_line(skolemFOFtoCNF_X,skolemFOFtoCNF_Z)
& parallel_lines(skolemFOFtoCNF_Y,skolemFOFtoCNF_Z) ),
inference(skolemize,[],[normalize_0_0]) ).
fof(normalize_0_2,plain,
parallel_lines(skolemFOFtoCNF_Y,skolemFOFtoCNF_Z),
inference(conjunct,[],[normalize_0_1]) ).
fof(normalize_0_3,plain,
! [X,Y] :
( ~ convergent_lines(X,Y)
<=> parallel_lines(X,Y) ),
inference(canonicalize,[],[a3]) ).
fof(normalize_0_4,plain,
! [X,Y] :
( ~ convergent_lines(X,Y)
<=> parallel_lines(X,Y) ),
inference(specialize,[],[normalize_0_3]) ).
fof(normalize_0_5,plain,
! [X,Y] :
( ( ~ convergent_lines(X,Y)
| ~ parallel_lines(X,Y) )
& ( convergent_lines(X,Y)
| parallel_lines(X,Y) ) ),
inference(clausify,[],[normalize_0_4]) ).
fof(normalize_0_6,plain,
! [X,Y] :
( ~ convergent_lines(X,Y)
| ~ parallel_lines(X,Y) ),
inference(conjunct,[],[normalize_0_5]) ).
fof(normalize_0_7,plain,
! [X,Y] :
( ~ distinct_lines(X,Y)
| convergent_lines(X,Y) ),
inference(canonicalize,[],[p1]) ).
fof(normalize_0_8,plain,
! [X,Y] :
( ~ distinct_lines(X,Y)
| convergent_lines(X,Y) ),
inference(specialize,[],[normalize_0_7]) ).
fof(normalize_0_9,plain,
~ equal_lines(skolemFOFtoCNF_Y,skolemFOFtoCNF_Z),
inference(conjunct,[],[normalize_0_1]) ).
fof(normalize_0_10,plain,
! [X,Y] :
( ~ distinct_lines(X,Y)
<=> equal_lines(X,Y) ),
inference(canonicalize,[],[ax2]) ).
fof(normalize_0_11,plain,
! [X,Y] :
( ~ distinct_lines(X,Y)
<=> equal_lines(X,Y) ),
inference(specialize,[],[normalize_0_10]) ).
fof(normalize_0_12,plain,
! [X,Y] :
( ( ~ distinct_lines(X,Y)
| ~ equal_lines(X,Y) )
& ( distinct_lines(X,Y)
| equal_lines(X,Y) ) ),
inference(clausify,[],[normalize_0_11]) ).
fof(normalize_0_13,plain,
! [X,Y] :
( distinct_lines(X,Y)
| equal_lines(X,Y) ),
inference(conjunct,[],[normalize_0_12]) ).
cnf(refute_0_0,plain,
parallel_lines(skolemFOFtoCNF_Y,skolemFOFtoCNF_Z),
inference(canonicalize,[],[normalize_0_2]) ).
cnf(refute_0_1,plain,
( ~ convergent_lines(X,Y)
| ~ parallel_lines(X,Y) ),
inference(canonicalize,[],[normalize_0_6]) ).
cnf(refute_0_2,plain,
( ~ convergent_lines(skolemFOFtoCNF_Y,skolemFOFtoCNF_Z)
| ~ parallel_lines(skolemFOFtoCNF_Y,skolemFOFtoCNF_Z) ),
inference(subst,[],[refute_0_1:[bind(X,$fot(skolemFOFtoCNF_Y)),bind(Y,$fot(skolemFOFtoCNF_Z))]]) ).
cnf(refute_0_3,plain,
~ convergent_lines(skolemFOFtoCNF_Y,skolemFOFtoCNF_Z),
inference(resolve,[$cnf( parallel_lines(skolemFOFtoCNF_Y,skolemFOFtoCNF_Z) )],[refute_0_0,refute_0_2]) ).
cnf(refute_0_4,plain,
( ~ distinct_lines(X,Y)
| convergent_lines(X,Y) ),
inference(canonicalize,[],[normalize_0_8]) ).
cnf(refute_0_5,plain,
( ~ distinct_lines(skolemFOFtoCNF_Y,skolemFOFtoCNF_Z)
| convergent_lines(skolemFOFtoCNF_Y,skolemFOFtoCNF_Z) ),
inference(subst,[],[refute_0_4:[bind(X,$fot(skolemFOFtoCNF_Y)),bind(Y,$fot(skolemFOFtoCNF_Z))]]) ).
cnf(refute_0_6,plain,
~ equal_lines(skolemFOFtoCNF_Y,skolemFOFtoCNF_Z),
inference(canonicalize,[],[normalize_0_9]) ).
cnf(refute_0_7,plain,
( distinct_lines(X,Y)
| equal_lines(X,Y) ),
inference(canonicalize,[],[normalize_0_13]) ).
cnf(refute_0_8,plain,
( distinct_lines(skolemFOFtoCNF_Y,skolemFOFtoCNF_Z)
| equal_lines(skolemFOFtoCNF_Y,skolemFOFtoCNF_Z) ),
inference(subst,[],[refute_0_7:[bind(X,$fot(skolemFOFtoCNF_Y)),bind(Y,$fot(skolemFOFtoCNF_Z))]]) ).
cnf(refute_0_9,plain,
distinct_lines(skolemFOFtoCNF_Y,skolemFOFtoCNF_Z),
inference(resolve,[$cnf( equal_lines(skolemFOFtoCNF_Y,skolemFOFtoCNF_Z) )],[refute_0_8,refute_0_6]) ).
cnf(refute_0_10,plain,
convergent_lines(skolemFOFtoCNF_Y,skolemFOFtoCNF_Z),
inference(resolve,[$cnf( distinct_lines(skolemFOFtoCNF_Y,skolemFOFtoCNF_Z) )],[refute_0_9,refute_0_5]) ).
cnf(refute_0_11,plain,
$false,
inference(resolve,[$cnf( convergent_lines(skolemFOFtoCNF_Y,skolemFOFtoCNF_Z) )],[refute_0_10,refute_0_3]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : GEO208+3 : TPTP v8.1.0. Released v4.0.0.
% 0.03/0.13 % Command : metis --show proof --show saturation %s
% 0.12/0.34 % Computer : n012.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 600
% 0.12/0.34 % DateTime : Fri Jun 17 22:22:53 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.12/0.34 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.19/0.36 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.19/0.36
% 0.19/0.36 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 0.19/0.37
%------------------------------------------------------------------------------