TSTP Solution File: GEO217+3 by Metis---2.4
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : GEO217+3 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n029.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 05:25:31 EDT 2022
% Result : Theorem 0.19s 0.43s
% Output : CNFRefutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 27
% Number of leaves : 7
% Syntax : Number of formulae : 74 ( 21 unt; 0 def)
% Number of atoms : 155 ( 0 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 127 ( 46 ~; 64 |; 8 &)
% ( 3 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 3 ( 3 usr; 3 con; 0-0 aty)
% Number of variables : 104 ( 0 sgn 51 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(apart2,axiom,
! [X] : ~ distinct_lines(X,X) ).
fof(apart3,axiom,
! [X] : ~ convergent_lines(X,X) ).
fof(apart5,axiom,
! [X,Y,Z] :
( distinct_lines(X,Y)
=> ( distinct_lines(X,Z)
| distinct_lines(Y,Z) ) ) ).
fof(ceq3,axiom,
! [X,Y,Z] :
( convergent_lines(X,Y)
=> ( distinct_lines(Y,Z)
| convergent_lines(X,Z) ) ) ).
fof(p1,axiom,
! [X,Y] :
( distinct_lines(X,Y)
=> convergent_lines(X,Y) ) ).
fof(a3,axiom,
! [X,Y] :
( parallel_lines(X,Y)
<=> ~ convergent_lines(X,Y) ) ).
fof(con,conjecture,
! [L,M,N] :
( ( parallel_lines(L,M)
& parallel_lines(L,N) )
=> parallel_lines(M,N) ) ).
fof(subgoal_0,plain,
! [L,M,N] :
( ( parallel_lines(L,M)
& parallel_lines(L,N) )
=> parallel_lines(M,N) ),
inference(strip,[],[con]) ).
fof(negate_0_0,plain,
~ ! [L,M,N] :
( ( parallel_lines(L,M)
& parallel_lines(L,N) )
=> parallel_lines(M,N) ),
inference(negate,[],[subgoal_0]) ).
fof(normalize_0_0,plain,
? [L,M,N] :
( ~ parallel_lines(M,N)
& parallel_lines(L,M)
& parallel_lines(L,N) ),
inference(canonicalize,[],[negate_0_0]) ).
fof(normalize_0_1,plain,
( ~ parallel_lines(skolemFOFtoCNF_M,skolemFOFtoCNF_N)
& parallel_lines(skolemFOFtoCNF_L,skolemFOFtoCNF_M)
& parallel_lines(skolemFOFtoCNF_L,skolemFOFtoCNF_N) ),
inference(skolemize,[],[normalize_0_0]) ).
fof(normalize_0_2,plain,
parallel_lines(skolemFOFtoCNF_L,skolemFOFtoCNF_N),
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,
! [X] : ~ distinct_lines(X,X),
inference(canonicalize,[],[apart2]) ).
fof(normalize_0_10,plain,
! [X] : ~ distinct_lines(X,X),
inference(specialize,[],[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,
! [X,Y,Z] :
( ~ convergent_lines(X,Y)
| convergent_lines(X,Z)
| distinct_lines(Y,Z) ),
inference(canonicalize,[],[ceq3]) ).
fof(normalize_0_14,plain,
! [X,Y,Z] :
( ~ convergent_lines(X,Y)
| convergent_lines(X,Z)
| distinct_lines(Y,Z) ),
inference(specialize,[],[normalize_0_13]) ).
fof(normalize_0_15,plain,
~ parallel_lines(skolemFOFtoCNF_M,skolemFOFtoCNF_N),
inference(conjunct,[],[normalize_0_1]) ).
fof(normalize_0_16,plain,
! [X,Y] :
( convergent_lines(X,Y)
| parallel_lines(X,Y) ),
inference(conjunct,[],[normalize_0_5]) ).
fof(normalize_0_17,plain,
! [X] : ~ convergent_lines(X,X),
inference(canonicalize,[],[apart3]) ).
fof(normalize_0_18,plain,
! [X] : ~ convergent_lines(X,X),
inference(specialize,[],[normalize_0_17]) ).
fof(normalize_0_19,plain,
parallel_lines(skolemFOFtoCNF_L,skolemFOFtoCNF_M),
inference(conjunct,[],[normalize_0_1]) ).
cnf(refute_0_0,plain,
parallel_lines(skolemFOFtoCNF_L,skolemFOFtoCNF_N),
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_L,skolemFOFtoCNF_N)
| ~ parallel_lines(skolemFOFtoCNF_L,skolemFOFtoCNF_N) ),
inference(subst,[],[refute_0_1:[bind(X,$fot(skolemFOFtoCNF_L)),bind(Y,$fot(skolemFOFtoCNF_N))]]) ).
cnf(refute_0_3,plain,
~ convergent_lines(skolemFOFtoCNF_L,skolemFOFtoCNF_N),
inference(resolve,[$cnf( parallel_lines(skolemFOFtoCNF_L,skolemFOFtoCNF_N) )],[refute_0_0,refute_0_2]) ).
cnf(refute_0_4,plain,
( ~ distinct_lines(X,Y)
| convergent_lines(X,Y) ),
inference(canonicalize,[],[normalize_0_8]) ).
cnf(refute_0_5,plain,
( ~ distinct_lines(X_213,skolemFOFtoCNF_M)
| convergent_lines(X_213,skolemFOFtoCNF_M) ),
inference(subst,[],[refute_0_4:[bind(X,$fot(X_213)),bind(Y,$fot(skolemFOFtoCNF_M))]]) ).
cnf(refute_0_6,plain,
( ~ distinct_lines(X_212,skolemFOFtoCNF_N)
| convergent_lines(X_212,skolemFOFtoCNF_N) ),
inference(subst,[],[refute_0_4:[bind(X,$fot(X_212)),bind(Y,$fot(skolemFOFtoCNF_N))]]) ).
cnf(refute_0_7,plain,
~ distinct_lines(X,X),
inference(canonicalize,[],[normalize_0_10]) ).
cnf(refute_0_8,plain,
~ distinct_lines(skolemFOFtoCNF_N,skolemFOFtoCNF_N),
inference(subst,[],[refute_0_7:[bind(X,$fot(skolemFOFtoCNF_N))]]) ).
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_N,X_187)
| distinct_lines(X_187,Z)
| distinct_lines(skolemFOFtoCNF_N,Z) ),
inference(subst,[],[refute_0_9:[bind(X,$fot(skolemFOFtoCNF_N)),bind(Y,$fot(X_187))]]) ).
cnf(refute_0_11,plain,
( ~ convergent_lines(X,Y)
| convergent_lines(X,Z)
| distinct_lines(Y,Z) ),
inference(canonicalize,[],[normalize_0_14]) ).
cnf(refute_0_12,plain,
( ~ convergent_lines(X_186,X_185)
| convergent_lines(X_186,Z)
| distinct_lines(X_185,Z) ),
inference(subst,[],[refute_0_11:[bind(X,$fot(X_186)),bind(Y,$fot(X_185))]]) ).
cnf(refute_0_13,plain,
( ~ distinct_lines(X_144,X_143)
| convergent_lines(X_144,X_143) ),
inference(subst,[],[refute_0_4:[bind(X,$fot(X_144)),bind(Y,$fot(X_143))]]) ).
cnf(refute_0_14,plain,
( ~ distinct_lines(skolemFOFtoCNF_N,X_77)
| distinct_lines(X_77,Z)
| distinct_lines(skolemFOFtoCNF_N,Z) ),
inference(subst,[],[refute_0_9:[bind(X,$fot(skolemFOFtoCNF_N)),bind(Y,$fot(X_77))]]) ).
cnf(refute_0_15,plain,
~ parallel_lines(skolemFOFtoCNF_M,skolemFOFtoCNF_N),
inference(canonicalize,[],[normalize_0_15]) ).
cnf(refute_0_16,plain,
( convergent_lines(X,Y)
| parallel_lines(X,Y) ),
inference(canonicalize,[],[normalize_0_16]) ).
cnf(refute_0_17,plain,
( convergent_lines(skolemFOFtoCNF_M,skolemFOFtoCNF_N)
| parallel_lines(skolemFOFtoCNF_M,skolemFOFtoCNF_N) ),
inference(subst,[],[refute_0_16:[bind(X,$fot(skolemFOFtoCNF_M)),bind(Y,$fot(skolemFOFtoCNF_N))]]) ).
cnf(refute_0_18,plain,
convergent_lines(skolemFOFtoCNF_M,skolemFOFtoCNF_N),
inference(resolve,[$cnf( parallel_lines(skolemFOFtoCNF_M,skolemFOFtoCNF_N) )],[refute_0_17,refute_0_15]) ).
cnf(refute_0_19,plain,
( ~ convergent_lines(skolemFOFtoCNF_M,skolemFOFtoCNF_N)
| convergent_lines(skolemFOFtoCNF_M,X_76)
| distinct_lines(skolemFOFtoCNF_N,X_76) ),
inference(subst,[],[refute_0_11:[bind(X,$fot(skolemFOFtoCNF_M)),bind(Y,$fot(skolemFOFtoCNF_N)),bind(Z,$fot(X_76))]]) ).
cnf(refute_0_20,plain,
( convergent_lines(skolemFOFtoCNF_M,X_76)
| distinct_lines(skolemFOFtoCNF_N,X_76) ),
inference(resolve,[$cnf( convergent_lines(skolemFOFtoCNF_M,skolemFOFtoCNF_N) )],[refute_0_18,refute_0_19]) ).
cnf(refute_0_21,plain,
( convergent_lines(skolemFOFtoCNF_M,X_77)
| distinct_lines(skolemFOFtoCNF_N,X_77) ),
inference(subst,[],[refute_0_20:[bind(X_76,$fot(X_77))]]) ).
cnf(refute_0_22,plain,
( convergent_lines(skolemFOFtoCNF_M,X_77)
| distinct_lines(X_77,Z)
| distinct_lines(skolemFOFtoCNF_N,Z) ),
inference(resolve,[$cnf( distinct_lines(skolemFOFtoCNF_N,X_77) )],[refute_0_21,refute_0_14]) ).
cnf(refute_0_23,plain,
( convergent_lines(skolemFOFtoCNF_M,X_144)
| distinct_lines(X_144,X_143)
| distinct_lines(skolemFOFtoCNF_N,X_143) ),
inference(subst,[],[refute_0_22:[bind(Z,$fot(X_143)),bind(X_77,$fot(X_144))]]) ).
cnf(refute_0_24,plain,
( convergent_lines(X_144,X_143)
| convergent_lines(skolemFOFtoCNF_M,X_144)
| distinct_lines(skolemFOFtoCNF_N,X_143) ),
inference(resolve,[$cnf( distinct_lines(X_144,X_143) )],[refute_0_23,refute_0_13]) ).
cnf(refute_0_25,plain,
( convergent_lines(X_186,X_185)
| convergent_lines(skolemFOFtoCNF_M,X_186)
| distinct_lines(skolemFOFtoCNF_N,X_185) ),
inference(subst,[],[refute_0_24:[bind(X_143,$fot(X_185)),bind(X_144,$fot(X_186))]]) ).
cnf(refute_0_26,plain,
( convergent_lines(X_186,Z)
| convergent_lines(skolemFOFtoCNF_M,X_186)
| distinct_lines(X_185,Z)
| distinct_lines(skolemFOFtoCNF_N,X_185) ),
inference(resolve,[$cnf( convergent_lines(X_186,X_185) )],[refute_0_25,refute_0_12]) ).
cnf(refute_0_27,plain,
( convergent_lines(skolemFOFtoCNF_M,skolemFOFtoCNF_M)
| distinct_lines(X_185,skolemFOFtoCNF_M)
| distinct_lines(skolemFOFtoCNF_N,X_185) ),
inference(subst,[],[refute_0_26:[bind(Z,$fot(skolemFOFtoCNF_M)),bind(X_186,$fot(skolemFOFtoCNF_M))]]) ).
cnf(refute_0_28,plain,
~ convergent_lines(X,X),
inference(canonicalize,[],[normalize_0_18]) ).
cnf(refute_0_29,plain,
~ convergent_lines(skolemFOFtoCNF_M,skolemFOFtoCNF_M),
inference(subst,[],[refute_0_28:[bind(X,$fot(skolemFOFtoCNF_M))]]) ).
cnf(refute_0_30,plain,
( distinct_lines(X_185,skolemFOFtoCNF_M)
| distinct_lines(skolemFOFtoCNF_N,X_185) ),
inference(resolve,[$cnf( convergent_lines(skolemFOFtoCNF_M,skolemFOFtoCNF_M) )],[refute_0_27,refute_0_29]) ).
cnf(refute_0_31,plain,
( distinct_lines(X_187,skolemFOFtoCNF_M)
| distinct_lines(skolemFOFtoCNF_N,X_187) ),
inference(subst,[],[refute_0_30:[bind(X_185,$fot(X_187))]]) ).
cnf(refute_0_32,plain,
( distinct_lines(X_187,Z)
| distinct_lines(X_187,skolemFOFtoCNF_M)
| distinct_lines(skolemFOFtoCNF_N,Z) ),
inference(resolve,[$cnf( distinct_lines(skolemFOFtoCNF_N,X_187) )],[refute_0_31,refute_0_10]) ).
cnf(refute_0_33,plain,
( distinct_lines(X_211,skolemFOFtoCNF_M)
| distinct_lines(X_211,skolemFOFtoCNF_N)
| distinct_lines(skolemFOFtoCNF_N,skolemFOFtoCNF_N) ),
inference(subst,[],[refute_0_32:[bind(Z,$fot(skolemFOFtoCNF_N)),bind(X_187,$fot(X_211))]]) ).
cnf(refute_0_34,plain,
( distinct_lines(X_211,skolemFOFtoCNF_M)
| distinct_lines(X_211,skolemFOFtoCNF_N) ),
inference(resolve,[$cnf( distinct_lines(skolemFOFtoCNF_N,skolemFOFtoCNF_N) )],[refute_0_33,refute_0_8]) ).
cnf(refute_0_35,plain,
( distinct_lines(X_212,skolemFOFtoCNF_M)
| distinct_lines(X_212,skolemFOFtoCNF_N) ),
inference(subst,[],[refute_0_34:[bind(X_211,$fot(X_212))]]) ).
cnf(refute_0_36,plain,
( convergent_lines(X_212,skolemFOFtoCNF_N)
| distinct_lines(X_212,skolemFOFtoCNF_M) ),
inference(resolve,[$cnf( distinct_lines(X_212,skolemFOFtoCNF_N) )],[refute_0_35,refute_0_6]) ).
cnf(refute_0_37,plain,
( convergent_lines(X_213,skolemFOFtoCNF_N)
| distinct_lines(X_213,skolemFOFtoCNF_M) ),
inference(subst,[],[refute_0_36:[bind(X_212,$fot(X_213))]]) ).
cnf(refute_0_38,plain,
( convergent_lines(X_213,skolemFOFtoCNF_M)
| convergent_lines(X_213,skolemFOFtoCNF_N) ),
inference(resolve,[$cnf( distinct_lines(X_213,skolemFOFtoCNF_M) )],[refute_0_37,refute_0_5]) ).
cnf(refute_0_39,plain,
( convergent_lines(skolemFOFtoCNF_L,skolemFOFtoCNF_M)
| convergent_lines(skolemFOFtoCNF_L,skolemFOFtoCNF_N) ),
inference(subst,[],[refute_0_38:[bind(X_213,$fot(skolemFOFtoCNF_L))]]) ).
cnf(refute_0_40,plain,
convergent_lines(skolemFOFtoCNF_L,skolemFOFtoCNF_M),
inference(resolve,[$cnf( convergent_lines(skolemFOFtoCNF_L,skolemFOFtoCNF_N) )],[refute_0_39,refute_0_3]) ).
cnf(refute_0_41,plain,
parallel_lines(skolemFOFtoCNF_L,skolemFOFtoCNF_M),
inference(canonicalize,[],[normalize_0_19]) ).
cnf(refute_0_42,plain,
( ~ convergent_lines(skolemFOFtoCNF_L,skolemFOFtoCNF_M)
| ~ parallel_lines(skolemFOFtoCNF_L,skolemFOFtoCNF_M) ),
inference(subst,[],[refute_0_1:[bind(X,$fot(skolemFOFtoCNF_L)),bind(Y,$fot(skolemFOFtoCNF_M))]]) ).
cnf(refute_0_43,plain,
~ convergent_lines(skolemFOFtoCNF_L,skolemFOFtoCNF_M),
inference(resolve,[$cnf( parallel_lines(skolemFOFtoCNF_L,skolemFOFtoCNF_M) )],[refute_0_41,refute_0_42]) ).
cnf(refute_0_44,plain,
$false,
inference(resolve,[$cnf( convergent_lines(skolemFOFtoCNF_L,skolemFOFtoCNF_M) )],[refute_0_40,refute_0_43]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : GEO217+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 : n029.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 : Sat Jun 18 08:50:14 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.12/0.34 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.19/0.43 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.19/0.43
% 0.19/0.43 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 0.19/0.43
%------------------------------------------------------------------------------