TSTP Solution File: GEO209+3 by Metis---2.4
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%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : GEO209+3 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n018.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 0.13s 0.36s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 5
% Syntax : Number of formulae : 48 ( 11 unt; 0 def)
% Number of atoms : 114 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 100 ( 34 ~; 31 |; 24 &)
% ( 6 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 7 ( 6 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 4 con; 0-0 aty)
% Number of variables : 68 ( 0 sgn 47 !; 4 ?)
% 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(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,
! [A,L,M,N] :
( ( apart_point_and_line(A,L)
& incident_point_and_line(A,M)
& incident_point_and_line(A,N)
& parallel_lines(M,L)
& parallel_lines(N,L) )
=> equal_lines(M,N) ) ).
fof(subgoal_0,plain,
! [A,L,M,N] :
( ( apart_point_and_line(A,L)
& incident_point_and_line(A,M)
& incident_point_and_line(A,N)
& parallel_lines(M,L)
& parallel_lines(N,L) )
=> equal_lines(M,N) ),
inference(strip,[],[con]) ).
fof(negate_0_0,plain,
~ ! [A,L,M,N] :
( ( apart_point_and_line(A,L)
& incident_point_and_line(A,M)
& incident_point_and_line(A,N)
& parallel_lines(M,L)
& parallel_lines(N,L) )
=> equal_lines(M,N) ),
inference(negate,[],[subgoal_0]) ).
fof(normalize_0_0,plain,
? [A,L,M,N] :
( ~ equal_lines(M,N)
& apart_point_and_line(A,L)
& incident_point_and_line(A,M)
& incident_point_and_line(A,N)
& parallel_lines(M,L)
& parallel_lines(N,L) ),
inference(canonicalize,[],[negate_0_0]) ).
fof(normalize_0_1,plain,
( ~ equal_lines(skolemFOFtoCNF_M,skolemFOFtoCNF_N)
& apart_point_and_line(skolemFOFtoCNF_A,skolemFOFtoCNF_L)
& incident_point_and_line(skolemFOFtoCNF_A,skolemFOFtoCNF_M)
& incident_point_and_line(skolemFOFtoCNF_A,skolemFOFtoCNF_N)
& parallel_lines(skolemFOFtoCNF_M,skolemFOFtoCNF_L)
& parallel_lines(skolemFOFtoCNF_N,skolemFOFtoCNF_L) ),
inference(skolemize,[],[normalize_0_0]) ).
fof(normalize_0_2,plain,
parallel_lines(skolemFOFtoCNF_N,skolemFOFtoCNF_L),
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_M,skolemFOFtoCNF_N),
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]) ).
fof(normalize_0_14,plain,
! [X,Y,Z] :
( ~ distinct_lines(X,Y)
| distinct_lines(X,Z)
| distinct_lines(Y,Z) ),
inference(canonicalize,[],[apart5]) ).
fof(normalize_0_15,plain,
! [X,Y,Z] :
( ~ distinct_lines(X,Y)
| distinct_lines(X,Z)
| distinct_lines(Y,Z) ),
inference(specialize,[],[normalize_0_14]) ).
fof(normalize_0_16,plain,
parallel_lines(skolemFOFtoCNF_M,skolemFOFtoCNF_L),
inference(conjunct,[],[normalize_0_1]) ).
cnf(refute_0_0,plain,
parallel_lines(skolemFOFtoCNF_N,skolemFOFtoCNF_L),
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_N,skolemFOFtoCNF_L)
| ~ parallel_lines(skolemFOFtoCNF_N,skolemFOFtoCNF_L) ),
inference(subst,[],[refute_0_1:[bind(X,$fot(skolemFOFtoCNF_N)),bind(Y,$fot(skolemFOFtoCNF_L))]]) ).
cnf(refute_0_3,plain,
~ convergent_lines(skolemFOFtoCNF_N,skolemFOFtoCNF_L),
inference(resolve,[$cnf( parallel_lines(skolemFOFtoCNF_N,skolemFOFtoCNF_L) )],[refute_0_0,refute_0_2]) ).
cnf(refute_0_4,plain,
( ~ distinct_lines(X,Y)
| convergent_lines(X,Y) ),
inference(canonicalize,[],[normalize_0_8]) ).
cnf(refute_0_5,plain,
( ~ distinct_lines(skolemFOFtoCNF_M,X_60)
| convergent_lines(skolemFOFtoCNF_M,X_60) ),
inference(subst,[],[refute_0_4:[bind(X,$fot(skolemFOFtoCNF_M)),bind(Y,$fot(X_60))]]) ).
cnf(refute_0_6,plain,
( ~ distinct_lines(skolemFOFtoCNF_N,X_59)
| convergent_lines(skolemFOFtoCNF_N,X_59) ),
inference(subst,[],[refute_0_4:[bind(X,$fot(skolemFOFtoCNF_N)),bind(Y,$fot(X_59))]]) ).
cnf(refute_0_7,plain,
~ equal_lines(skolemFOFtoCNF_M,skolemFOFtoCNF_N),
inference(canonicalize,[],[normalize_0_9]) ).
cnf(refute_0_8,plain,
( distinct_lines(X,Y)
| equal_lines(X,Y) ),
inference(canonicalize,[],[normalize_0_13]) ).
cnf(refute_0_9,plain,
( distinct_lines(skolemFOFtoCNF_M,skolemFOFtoCNF_N)
| equal_lines(skolemFOFtoCNF_M,skolemFOFtoCNF_N) ),
inference(subst,[],[refute_0_8:[bind(X,$fot(skolemFOFtoCNF_M)),bind(Y,$fot(skolemFOFtoCNF_N))]]) ).
cnf(refute_0_10,plain,
distinct_lines(skolemFOFtoCNF_M,skolemFOFtoCNF_N),
inference(resolve,[$cnf( equal_lines(skolemFOFtoCNF_M,skolemFOFtoCNF_N) )],[refute_0_9,refute_0_7]) ).
cnf(refute_0_11,plain,
( ~ distinct_lines(X,Y)
| distinct_lines(X,Z)
| distinct_lines(Y,Z) ),
inference(canonicalize,[],[normalize_0_15]) ).
cnf(refute_0_12,plain,
( ~ distinct_lines(skolemFOFtoCNF_M,skolemFOFtoCNF_N)
| distinct_lines(skolemFOFtoCNF_M,X_58)
| distinct_lines(skolemFOFtoCNF_N,X_58) ),
inference(subst,[],[refute_0_11:[bind(X,$fot(skolemFOFtoCNF_M)),bind(Y,$fot(skolemFOFtoCNF_N)),bind(Z,$fot(X_58))]]) ).
cnf(refute_0_13,plain,
( distinct_lines(skolemFOFtoCNF_M,X_58)
| distinct_lines(skolemFOFtoCNF_N,X_58) ),
inference(resolve,[$cnf( distinct_lines(skolemFOFtoCNF_M,skolemFOFtoCNF_N) )],[refute_0_10,refute_0_12]) ).
cnf(refute_0_14,plain,
( distinct_lines(skolemFOFtoCNF_M,X_59)
| distinct_lines(skolemFOFtoCNF_N,X_59) ),
inference(subst,[],[refute_0_13:[bind(X_58,$fot(X_59))]]) ).
cnf(refute_0_15,plain,
( convergent_lines(skolemFOFtoCNF_N,X_59)
| distinct_lines(skolemFOFtoCNF_M,X_59) ),
inference(resolve,[$cnf( distinct_lines(skolemFOFtoCNF_N,X_59) )],[refute_0_14,refute_0_6]) ).
cnf(refute_0_16,plain,
( convergent_lines(skolemFOFtoCNF_N,X_60)
| distinct_lines(skolemFOFtoCNF_M,X_60) ),
inference(subst,[],[refute_0_15:[bind(X_59,$fot(X_60))]]) ).
cnf(refute_0_17,plain,
( convergent_lines(skolemFOFtoCNF_M,X_60)
| convergent_lines(skolemFOFtoCNF_N,X_60) ),
inference(resolve,[$cnf( distinct_lines(skolemFOFtoCNF_M,X_60) )],[refute_0_16,refute_0_5]) ).
cnf(refute_0_18,plain,
( convergent_lines(skolemFOFtoCNF_M,skolemFOFtoCNF_L)
| convergent_lines(skolemFOFtoCNF_N,skolemFOFtoCNF_L) ),
inference(subst,[],[refute_0_17:[bind(X_60,$fot(skolemFOFtoCNF_L))]]) ).
cnf(refute_0_19,plain,
convergent_lines(skolemFOFtoCNF_M,skolemFOFtoCNF_L),
inference(resolve,[$cnf( convergent_lines(skolemFOFtoCNF_N,skolemFOFtoCNF_L) )],[refute_0_18,refute_0_3]) ).
cnf(refute_0_20,plain,
parallel_lines(skolemFOFtoCNF_M,skolemFOFtoCNF_L),
inference(canonicalize,[],[normalize_0_16]) ).
cnf(refute_0_21,plain,
( ~ convergent_lines(skolemFOFtoCNF_M,skolemFOFtoCNF_L)
| ~ parallel_lines(skolemFOFtoCNF_M,skolemFOFtoCNF_L) ),
inference(subst,[],[refute_0_1:[bind(X,$fot(skolemFOFtoCNF_M)),bind(Y,$fot(skolemFOFtoCNF_L))]]) ).
cnf(refute_0_22,plain,
~ convergent_lines(skolemFOFtoCNF_M,skolemFOFtoCNF_L),
inference(resolve,[$cnf( parallel_lines(skolemFOFtoCNF_M,skolemFOFtoCNF_L) )],[refute_0_20,refute_0_21]) ).
cnf(refute_0_23,plain,
$false,
inference(resolve,[$cnf( convergent_lines(skolemFOFtoCNF_M,skolemFOFtoCNF_L) )],[refute_0_19,refute_0_22]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : GEO209+3 : TPTP v8.1.0. Released v4.0.0.
% 0.06/0.13 % Command : metis --show proof --show saturation %s
% 0.13/0.34 % Computer : n018.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 : Sat Jun 18 15:39:03 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.13/0.34 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.13/0.36 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.13/0.36
% 0.13/0.36 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 0.13/0.37
%------------------------------------------------------------------------------