%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : GEO206+2 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n024.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 0.20s 0.43s
% Output : CNFRefutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 24
% Number of leaves : 7
% Syntax : Number of formulae : 61 ( 24 unt; 0 def)
% Number of atoms : 144 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 130 ( 47 ~; 70 |; 7 &)
% ( 0 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 3 con; 0-2 aty)
% Number of variables : 104 ( 3 sgn 51 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(apart2,axiom,
! [X] : ~ distinct_lines(X,X) ).
fof(apart5,axiom,
! [X,Y,Z] :
( distinct_lines(X,Y)
=> ( distinct_lines(X,Z)
| distinct_lines(Y,Z) ) ) ).
fof(apart6,axiom,
! [X,Y,Z] :
( convergent_lines(X,Y)
=> ( convergent_lines(X,Z)
| convergent_lines(Y,Z) ) ) ).
fof(cp1,axiom,
! [X,Y] : ~ convergent_lines(parallel_through_point(Y,X),Y) ).
fof(cp2,axiom,
! [X,Y] : ~ apart_point_and_line(X,parallel_through_point(Y,X)) ).
fof(cup1,axiom,
! [X,Y,Z] :
( distinct_lines(Y,Z)
=> ( apart_point_and_line(X,Y)
| apart_point_and_line(X,Z)
| convergent_lines(Y,Z) ) ) ).
fof(con,conjecture,
! [X,Y,Z] :
( ( ~ apart_point_and_line(X,Y)
& ~ convergent_lines(Y,Z) )
=> ~ distinct_lines(Y,parallel_through_point(Z,X)) ) ).
fof(subgoal_0,plain,
! [X,Y,Z] :
( ( ~ apart_point_and_line(X,Y)
& ~ convergent_lines(Y,Z) )
=> ~ distinct_lines(Y,parallel_through_point(Z,X)) ),
inference(strip,[],[con]) ).
fof(negate_0_0,plain,
~ ! [X,Y,Z] :
( ( ~ apart_point_and_line(X,Y)
& ~ convergent_lines(Y,Z) )
=> ~ distinct_lines(Y,parallel_through_point(Z,X)) ),
inference(negate,[],[subgoal_0]) ).
fof(normalize_0_0,plain,
! [X,Y] : ~ convergent_lines(parallel_through_point(Y,X),Y),
inference(canonicalize,[],[cp1]) ).
fof(normalize_0_1,plain,
! [X,Y] : ~ convergent_lines(parallel_through_point(Y,X),Y),
inference(specialize,[],[normalize_0_0]) ).
fof(normalize_0_2,plain,
! [X,Y,Z] :
( ~ convergent_lines(X,Y)
| convergent_lines(X,Z)
| convergent_lines(Y,Z) ),
inference(canonicalize,[],[apart6]) ).
fof(normalize_0_3,plain,
! [X,Y,Z] :
( ~ convergent_lines(X,Y)
| convergent_lines(X,Z)
| convergent_lines(Y,Z) ),
inference(specialize,[],[normalize_0_2]) ).
fof(normalize_0_4,plain,
! [X] : ~ distinct_lines(X,X),
inference(canonicalize,[],[apart2]) ).
fof(normalize_0_5,plain,
! [X] : ~ distinct_lines(X,X),
inference(specialize,[],[normalize_0_4]) ).
fof(normalize_0_6,plain,
! [X,Y] : ~ apart_point_and_line(X,parallel_through_point(Y,X)),
inference(canonicalize,[],[cp2]) ).
fof(normalize_0_7,plain,
! [X,Y] : ~ apart_point_and_line(X,parallel_through_point(Y,X)),
inference(specialize,[],[normalize_0_6]) ).
fof(normalize_0_8,plain,
! [X,Y,Z] :
( ~ distinct_lines(Y,Z)
| apart_point_and_line(X,Y)
| apart_point_and_line(X,Z)
| convergent_lines(Y,Z) ),
inference(canonicalize,[],[cup1]) ).
fof(normalize_0_9,plain,
! [X,Y,Z] :
( ~ distinct_lines(Y,Z)
| apart_point_and_line(X,Y)
| apart_point_and_line(X,Z)
| convergent_lines(Y,Z) ),
inference(specialize,[],[normalize_0_8]) ).
fof(normalize_0_10,plain,
! [X,Y,Z] :
( ~ distinct_lines(X,Y)
| distinct_lines(X,Z)
| distinct_lines(Y,Z) ),
inference(canonicalize,[],[apart5]) ).
fof(normalize_0_11,plain,
! [X,Y,Z] :
( ~ distinct_lines(X,Y)
| distinct_lines(X,Z)
| distinct_lines(Y,Z) ),
inference(specialize,[],[normalize_0_10]) ).
fof(normalize_0_12,plain,
? [X,Y,Z] :
( ~ apart_point_and_line(X,Y)
& ~ convergent_lines(Y,Z)
& distinct_lines(Y,parallel_through_point(Z,X)) ),
inference(canonicalize,[],[negate_0_0]) ).
fof(normalize_0_13,plain,
( ~ apart_point_and_line(skolemFOFtoCNF_X,skolemFOFtoCNF_Y)
& ~ convergent_lines(skolemFOFtoCNF_Y,skolemFOFtoCNF_Z)
& distinct_lines(skolemFOFtoCNF_Y,parallel_through_point(skolemFOFtoCNF_Z,skolemFOFtoCNF_X)) ),
inference(skolemize,[],[normalize_0_12]) ).
fof(normalize_0_14,plain,
distinct_lines(skolemFOFtoCNF_Y,parallel_through_point(skolemFOFtoCNF_Z,skolemFOFtoCNF_X)),
inference(conjunct,[],[normalize_0_13]) ).
fof(normalize_0_15,plain,
~ apart_point_and_line(skolemFOFtoCNF_X,skolemFOFtoCNF_Y),
inference(conjunct,[],[normalize_0_13]) ).
fof(normalize_0_16,plain,
~ convergent_lines(skolemFOFtoCNF_Y,skolemFOFtoCNF_Z),
inference(conjunct,[],[normalize_0_13]) ).
cnf(refute_0_0,plain,
~ convergent_lines(parallel_through_point(Y,X),Y),
inference(canonicalize,[],[normalize_0_1]) ).
cnf(refute_0_1,plain,
~ convergent_lines(parallel_through_point(skolemFOFtoCNF_Z,skolemFOFtoCNF_X),skolemFOFtoCNF_Z),
inference(subst,[],[refute_0_0:[bind(X,$fot(skolemFOFtoCNF_X)),bind(Y,$fot(skolemFOFtoCNF_Z))]]) ).
cnf(refute_0_2,plain,
( ~ convergent_lines(X,Y)
| convergent_lines(X,Z)
| convergent_lines(Y,Z) ),
inference(canonicalize,[],[normalize_0_3]) ).
cnf(refute_0_3,plain,
( ~ convergent_lines(skolemFOFtoCNF_Y,parallel_through_point(skolemFOFtoCNF_Z,skolemFOFtoCNF_X))
| convergent_lines(parallel_through_point(skolemFOFtoCNF_Z,skolemFOFtoCNF_X),Z)
| convergent_lines(skolemFOFtoCNF_Y,Z) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(skolemFOFtoCNF_Y)),bind(Y,$fot(parallel_through_point(skolemFOFtoCNF_Z,skolemFOFtoCNF_X)))]]) ).
cnf(refute_0_4,plain,
~ distinct_lines(X,X),
inference(canonicalize,[],[normalize_0_5]) ).
cnf(refute_0_5,plain,
~ distinct_lines(parallel_through_point(skolemFOFtoCNF_Z,skolemFOFtoCNF_X),parallel_through_point(skolemFOFtoCNF_Z,skolemFOFtoCNF_X)),
inference(subst,[],[refute_0_4:[bind(X,$fot(parallel_through_point(skolemFOFtoCNF_Z,skolemFOFtoCNF_X)))]]) ).
cnf(refute_0_6,plain,
~ apart_point_and_line(X,parallel_through_point(Y,X)),
inference(canonicalize,[],[normalize_0_7]) ).
cnf(refute_0_7,plain,
~ apart_point_and_line(X_89,parallel_through_point(Y,X_89)),
inference(subst,[],[refute_0_6:[bind(X,$fot(X_89))]]) ).
cnf(refute_0_8,plain,
( ~ distinct_lines(Y,Z)
| apart_point_and_line(X,Y)
| apart_point_and_line(X,Z)
| convergent_lines(Y,Z) ),
inference(canonicalize,[],[normalize_0_9]) ).
cnf(refute_0_9,plain,
( ~ distinct_lines(skolemFOFtoCNF_Y,X_80)
| apart_point_and_line(X,X_80)
| apart_point_and_line(X,skolemFOFtoCNF_Y)
| convergent_lines(skolemFOFtoCNF_Y,X_80) ),
inference(subst,[],[refute_0_8:[bind(Y,$fot(skolemFOFtoCNF_Y)),bind(Z,$fot(X_80))]]) ).
cnf(refute_0_10,plain,
( ~ distinct_lines(X,Y)
| distinct_lines(X,Z)
| distinct_lines(Y,Z) ),
inference(canonicalize,[],[normalize_0_11]) ).
cnf(refute_0_11,plain,
( ~ distinct_lines(X_17,X_16)
| distinct_lines(X_16,Z)
| distinct_lines(X_17,Z) ),
inference(subst,[],[refute_0_10:[bind(X,$fot(X_17)),bind(Y,$fot(X_16))]]) ).
cnf(refute_0_12,plain,
( ~ distinct_lines(parallel_through_point(skolemFOFtoCNF_Z,skolemFOFtoCNF_X),X_15)
| distinct_lines(X_15,Z)
| distinct_lines(parallel_through_point(skolemFOFtoCNF_Z,skolemFOFtoCNF_X),Z) ),
inference(subst,[],[refute_0_10:[bind(X,$fot(parallel_through_point(skolemFOFtoCNF_Z,skolemFOFtoCNF_X))),bind(Y,$fot(X_15))]]) ).
cnf(refute_0_13,plain,
distinct_lines(skolemFOFtoCNF_Y,parallel_through_point(skolemFOFtoCNF_Z,skolemFOFtoCNF_X)),
inference(canonicalize,[],[normalize_0_14]) ).
cnf(refute_0_14,plain,
( ~ distinct_lines(skolemFOFtoCNF_Y,parallel_through_point(skolemFOFtoCNF_Z,skolemFOFtoCNF_X))
| distinct_lines(parallel_through_point(skolemFOFtoCNF_Z,skolemFOFtoCNF_X),X_14)
| distinct_lines(skolemFOFtoCNF_Y,X_14) ),
inference(subst,[],[refute_0_10:[bind(X,$fot(skolemFOFtoCNF_Y)),bind(Y,$fot(parallel_through_point(skolemFOFtoCNF_Z,skolemFOFtoCNF_X))),bind(Z,$fot(X_14))]]) ).
cnf(refute_0_15,plain,
( distinct_lines(parallel_through_point(skolemFOFtoCNF_Z,skolemFOFtoCNF_X),X_14)
| distinct_lines(skolemFOFtoCNF_Y,X_14) ),
inference(resolve,[$cnf( distinct_lines(skolemFOFtoCNF_Y,parallel_through_point(skolemFOFtoCNF_Z,skolemFOFtoCNF_X)) )],[refute_0_13,refute_0_14]) ).
cnf(refute_0_16,plain,
( distinct_lines(parallel_through_point(skolemFOFtoCNF_Z,skolemFOFtoCNF_X),X_15)
| distinct_lines(skolemFOFtoCNF_Y,X_15) ),
inference(subst,[],[refute_0_15:[bind(X_14,$fot(X_15))]]) ).
cnf(refute_0_17,plain,
( distinct_lines(X_15,Z)
| distinct_lines(parallel_through_point(skolemFOFtoCNF_Z,skolemFOFtoCNF_X),Z)
| distinct_lines(skolemFOFtoCNF_Y,X_15) ),
inference(resolve,[$cnf( distinct_lines(parallel_through_point(skolemFOFtoCNF_Z,skolemFOFtoCNF_X),X_15) )],[refute_0_16,refute_0_12]) ).
cnf(refute_0_18,plain,
( distinct_lines(X_17,X_16)
| distinct_lines(parallel_through_point(skolemFOFtoCNF_Z,skolemFOFtoCNF_X),X_16)
| distinct_lines(skolemFOFtoCNF_Y,X_17) ),
inference(subst,[],[refute_0_17:[bind(Z,$fot(X_16)),bind(X_15,$fot(X_17))]]) ).
cnf(refute_0_19,plain,
( distinct_lines(X_16,Z)
| distinct_lines(X_17,Z)
| distinct_lines(parallel_through_point(skolemFOFtoCNF_Z,skolemFOFtoCNF_X),X_16)
| distinct_lines(skolemFOFtoCNF_Y,X_17) ),
inference(resolve,[$cnf( distinct_lines(X_17,X_16) )],[refute_0_18,refute_0_11]) ).
cnf(refute_0_20,plain,
( distinct_lines(X_79,X_78)
| distinct_lines(X_80,X_78)
| distinct_lines(parallel_through_point(skolemFOFtoCNF_Z,skolemFOFtoCNF_X),X_79)
| distinct_lines(skolemFOFtoCNF_Y,X_80) ),
inference(subst,[],[refute_0_19:[bind(Z,$fot(X_78)),bind(X_16,$fot(X_79)),bind(X_17,$fot(X_80))]]) ).
cnf(refute_0_21,plain,
( apart_point_and_line(X,X_80)
| apart_point_and_line(X,skolemFOFtoCNF_Y)
| convergent_lines(skolemFOFtoCNF_Y,X_80)
| distinct_lines(X_79,X_78)
| distinct_lines(X_80,X_78)
| distinct_lines(parallel_through_point(skolemFOFtoCNF_Z,skolemFOFtoCNF_X),X_79) ),
inference(resolve,[$cnf( distinct_lines(skolemFOFtoCNF_Y,X_80) )],[refute_0_20,refute_0_9]) ).
cnf(refute_0_22,plain,
( apart_point_and_line(X,X_80)
| apart_point_and_line(X,skolemFOFtoCNF_Y)
| convergent_lines(skolemFOFtoCNF_Y,X_80)
| distinct_lines(X_80,parallel_through_point(skolemFOFtoCNF_Z,skolemFOFtoCNF_X))
| distinct_lines(parallel_through_point(skolemFOFtoCNF_Z,skolemFOFtoCNF_X),parallel_through_point(skolemFOFtoCNF_Z,skolemFOFtoCNF_X)) ),
inference(subst,[],[refute_0_21:[bind(X_78,$fot(parallel_through_point(skolemFOFtoCNF_Z,skolemFOFtoCNF_X))),bind(X_79,$fot(parallel_through_point(skolemFOFtoCNF_Z,skolemFOFtoCNF_X)))]]) ).
cnf(refute_0_23,plain,
( apart_point_and_line(X,X_80)
| apart_point_and_line(X,skolemFOFtoCNF_Y)
| convergent_lines(skolemFOFtoCNF_Y,X_80)
| distinct_lines(X_80,parallel_through_point(skolemFOFtoCNF_Z,skolemFOFtoCNF_X)) ),
inference(resolve,[$cnf( distinct_lines(parallel_through_point(skolemFOFtoCNF_Z,skolemFOFtoCNF_X),parallel_through_point(skolemFOFtoCNF_Z,skolemFOFtoCNF_X)) )],[refute_0_22,refute_0_5]) ).
cnf(refute_0_24,plain,
( apart_point_and_line(X_89,parallel_through_point(Y,X_89))
| apart_point_and_line(X_89,skolemFOFtoCNF_Y)
| convergent_lines(skolemFOFtoCNF_Y,parallel_through_point(Y,X_89))
| distinct_lines(parallel_through_point(Y,X_89),parallel_through_point(skolemFOFtoCNF_Z,skolemFOFtoCNF_X)) ),
inference(subst,[],[refute_0_23:[bind(X,$fot(X_89)),bind(X_80,$fot(parallel_through_point(Y,X_89)))]]) ).
cnf(refute_0_25,plain,
( apart_point_and_line(X_89,skolemFOFtoCNF_Y)
| convergent_lines(skolemFOFtoCNF_Y,parallel_through_point(Y,X_89))
| distinct_lines(parallel_through_point(Y,X_89),parallel_through_point(skolemFOFtoCNF_Z,skolemFOFtoCNF_X)) ),
inference(resolve,[$cnf( apart_point_and_line(X_89,parallel_through_point(Y,X_89)) )],[refute_0_24,refute_0_7]) ).
cnf(refute_0_26,plain,
( apart_point_and_line(skolemFOFtoCNF_X,skolemFOFtoCNF_Y)
| convergent_lines(skolemFOFtoCNF_Y,parallel_through_point(skolemFOFtoCNF_Z,skolemFOFtoCNF_X))
| distinct_lines(parallel_through_point(skolemFOFtoCNF_Z,skolemFOFtoCNF_X),parallel_through_point(skolemFOFtoCNF_Z,skolemFOFtoCNF_X)) ),
inference(subst,[],[refute_0_25:[bind(Y,$fot(skolemFOFtoCNF_Z)),bind(X_89,$fot(skolemFOFtoCNF_X))]]) ).
cnf(refute_0_27,plain,
( apart_point_and_line(skolemFOFtoCNF_X,skolemFOFtoCNF_Y)
| convergent_lines(skolemFOFtoCNF_Y,parallel_through_point(skolemFOFtoCNF_Z,skolemFOFtoCNF_X)) ),
inference(resolve,[$cnf( distinct_lines(parallel_through_point(skolemFOFtoCNF_Z,skolemFOFtoCNF_X),parallel_through_point(skolemFOFtoCNF_Z,skolemFOFtoCNF_X)) )],[refute_0_26,refute_0_5]) ).
cnf(refute_0_28,plain,
~ apart_point_and_line(skolemFOFtoCNF_X,skolemFOFtoCNF_Y),
inference(canonicalize,[],[normalize_0_15]) ).
cnf(refute_0_29,plain,
convergent_lines(skolemFOFtoCNF_Y,parallel_through_point(skolemFOFtoCNF_Z,skolemFOFtoCNF_X)),
inference(resolve,[$cnf( apart_point_and_line(skolemFOFtoCNF_X,skolemFOFtoCNF_Y) )],[refute_0_27,refute_0_28]) ).
cnf(refute_0_30,plain,
( convergent_lines(parallel_through_point(skolemFOFtoCNF_Z,skolemFOFtoCNF_X),Z)
| convergent_lines(skolemFOFtoCNF_Y,Z) ),
inference(resolve,[$cnf( convergent_lines(skolemFOFtoCNF_Y,parallel_through_point(skolemFOFtoCNF_Z,skolemFOFtoCNF_X)) )],[refute_0_29,refute_0_3]) ).
cnf(refute_0_31,plain,
( convergent_lines(parallel_through_point(skolemFOFtoCNF_Z,skolemFOFtoCNF_X),skolemFOFtoCNF_Z)
| convergent_lines(skolemFOFtoCNF_Y,skolemFOFtoCNF_Z) ),
inference(subst,[],[refute_0_30:[bind(Z,$fot(skolemFOFtoCNF_Z))]]) ).
cnf(refute_0_32,plain,
convergent_lines(skolemFOFtoCNF_Y,skolemFOFtoCNF_Z),
inference(resolve,[$cnf( convergent_lines(parallel_through_point(skolemFOFtoCNF_Z,skolemFOFtoCNF_X),skolemFOFtoCNF_Z) )],[refute_0_31,refute_0_1]) ).
cnf(refute_0_33,plain,
~ convergent_lines(skolemFOFtoCNF_Y,skolemFOFtoCNF_Z),
inference(canonicalize,[],[normalize_0_16]) ).
cnf(refute_0_34,plain,
$false,
inference(resolve,[$cnf( convergent_lines(skolemFOFtoCNF_Y,skolemFOFtoCNF_Z) )],[refute_0_32,refute_0_33]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : GEO206+2 : TPTP v8.1.0. Released v3.3.0.
% 0.07/0.13 % Command : metis --show proof --show saturation %s
% 0.13/0.34 % Computer : n024.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 600
% 0.13/0.34 % DateTime : Fri Jun 17 15:48:48 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.13/0.35 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.20/0.43 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.20/0.43
% 0.20/0.43 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 0.20/0.44
%------------------------------------------------------------------------------