TSTP Solution File: GEO254+1 by Drodi---3.6.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Drodi---3.6.0
% Problem : GEO254+1 : TPTP v8.1.2. Bugfixed v6.4.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% Computer : n032.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 : 300s
% DateTime : Tue Apr 30 20:17:46 EDT 2024
% Result : Theorem 0.13s 0.39s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 12
% Syntax : Number of formulae : 64 ( 14 unt; 0 def)
% Number of atoms : 190 ( 0 equ)
% Maximal formula atoms : 14 ( 2 avg)
% Number of connectives : 218 ( 92 ~; 80 |; 37 &)
% ( 4 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 9 ( 8 usr; 3 prp; 0-3 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 124 ( 121 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f4,axiom,
! [L,A,B] :
( before_on_line(L,A,B)
<=> ( distinct_points(A,B)
& ~ ( left_apart_point(A,L)
| left_apart_point(A,reverse_line(L)) )
& ~ ( left_apart_point(B,L)
| left_apart_point(B,reverse_line(L)) )
& ~ unequally_directed_lines(L,line_connecting(A,B)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f6,axiom,
! [A] : ~ distinct_points(A,A),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f7,axiom,
! [A,B,C] :
( distinct_points(A,B)
=> ( distinct_points(A,C)
| distinct_points(B,C) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f10,axiom,
! [L] : ~ unequally_directed_lines(L,L),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f11,axiom,
! [L,M,N] :
( unequally_directed_lines(L,M)
=> ( unequally_directed_lines(L,N)
| unequally_directed_lines(M,N) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f14,axiom,
! [L,M] :
( ( unequally_directed_lines(L,M)
& unequally_directed_lines(L,reverse_line(M)) )
=> ( left_convergent_lines(L,M)
| left_convergent_lines(L,reverse_line(M)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f15,axiom,
! [A,L] :
~ ( left_apart_point(A,L)
| left_apart_point(A,reverse_line(L)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f16,axiom,
! [L,M] :
~ ( left_convergent_lines(L,M)
| left_convergent_lines(L,reverse_line(M)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f25,axiom,
! [A,B] : ~ unequally_directed_lines(line_connecting(A,B),reverse_line(line_connecting(B,A))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f32,conjecture,
! [A,B,L] :
( ( distinct_points(A,B)
& ~ apart_point_and_line(A,L)
& ~ apart_point_and_line(B,L) )
=> ( before_on_line(L,A,B)
& before_on_line(L,B,A) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f33,negated_conjecture,
~ ! [A,B,L] :
( ( distinct_points(A,B)
& ~ apart_point_and_line(A,L)
& ~ apart_point_and_line(B,L) )
=> ( before_on_line(L,A,B)
& before_on_line(L,B,A) ) ),
inference(negated_conjecture,[status(cth)],[f32]) ).
fof(f52,plain,
! [L,A,B] :
( before_on_line(L,A,B)
<=> ( distinct_points(A,B)
& ~ left_apart_point(A,L)
& ~ left_apart_point(A,reverse_line(L))
& ~ left_apart_point(B,L)
& ~ left_apart_point(B,reverse_line(L))
& ~ unequally_directed_lines(L,line_connecting(A,B)) ) ),
inference(pre_NNF_transformation,[status(esa)],[f4]) ).
fof(f53,plain,
! [L,A,B] :
( ( ~ before_on_line(L,A,B)
| ( distinct_points(A,B)
& ~ left_apart_point(A,L)
& ~ left_apart_point(A,reverse_line(L))
& ~ left_apart_point(B,L)
& ~ left_apart_point(B,reverse_line(L))
& ~ unequally_directed_lines(L,line_connecting(A,B)) ) )
& ( before_on_line(L,A,B)
| ~ distinct_points(A,B)
| left_apart_point(A,L)
| left_apart_point(A,reverse_line(L))
| left_apart_point(B,L)
| left_apart_point(B,reverse_line(L))
| unequally_directed_lines(L,line_connecting(A,B)) ) ),
inference(NNF_transformation,[status(esa)],[f52]) ).
fof(f54,plain,
( ! [L,A,B] :
( ~ before_on_line(L,A,B)
| ( distinct_points(A,B)
& ~ left_apart_point(A,L)
& ~ left_apart_point(A,reverse_line(L))
& ~ left_apart_point(B,L)
& ~ left_apart_point(B,reverse_line(L))
& ~ unequally_directed_lines(L,line_connecting(A,B)) ) )
& ! [L,A,B] :
( before_on_line(L,A,B)
| ~ distinct_points(A,B)
| left_apart_point(A,L)
| left_apart_point(A,reverse_line(L))
| left_apart_point(B,L)
| left_apart_point(B,reverse_line(L))
| unequally_directed_lines(L,line_connecting(A,B)) ) ),
inference(miniscoping,[status(esa)],[f53]) ).
fof(f61,plain,
! [X0,X1,X2] :
( before_on_line(X0,X1,X2)
| ~ distinct_points(X1,X2)
| left_apart_point(X1,X0)
| left_apart_point(X1,reverse_line(X0))
| left_apart_point(X2,X0)
| left_apart_point(X2,reverse_line(X0))
| unequally_directed_lines(X0,line_connecting(X1,X2)) ),
inference(cnf_transformation,[status(esa)],[f54]) ).
fof(f70,plain,
! [X0] : ~ distinct_points(X0,X0),
inference(cnf_transformation,[status(esa)],[f6]) ).
fof(f71,plain,
! [A,B,C] :
( ~ distinct_points(A,B)
| distinct_points(A,C)
| distinct_points(B,C) ),
inference(pre_NNF_transformation,[status(esa)],[f7]) ).
fof(f72,plain,
! [A,B] :
( ~ distinct_points(A,B)
| ! [C] :
( distinct_points(A,C)
| distinct_points(B,C) ) ),
inference(miniscoping,[status(esa)],[f71]) ).
fof(f73,plain,
! [X0,X1,X2] :
( ~ distinct_points(X0,X1)
| distinct_points(X0,X2)
| distinct_points(X1,X2) ),
inference(cnf_transformation,[status(esa)],[f72]) ).
fof(f78,plain,
! [X0] : ~ unequally_directed_lines(X0,X0),
inference(cnf_transformation,[status(esa)],[f10]) ).
fof(f79,plain,
! [L,M,N] :
( ~ unequally_directed_lines(L,M)
| unequally_directed_lines(L,N)
| unequally_directed_lines(M,N) ),
inference(pre_NNF_transformation,[status(esa)],[f11]) ).
fof(f80,plain,
! [L,M] :
( ~ unequally_directed_lines(L,M)
| ! [N] :
( unequally_directed_lines(L,N)
| unequally_directed_lines(M,N) ) ),
inference(miniscoping,[status(esa)],[f79]) ).
fof(f81,plain,
! [X0,X1,X2] :
( ~ unequally_directed_lines(X0,X1)
| unequally_directed_lines(X0,X2)
| unequally_directed_lines(X1,X2) ),
inference(cnf_transformation,[status(esa)],[f80]) ).
fof(f90,plain,
! [L,M] :
( ~ unequally_directed_lines(L,M)
| ~ unequally_directed_lines(L,reverse_line(M))
| left_convergent_lines(L,M)
| left_convergent_lines(L,reverse_line(M)) ),
inference(pre_NNF_transformation,[status(esa)],[f14]) ).
fof(f91,plain,
! [X0,X1] :
( ~ unequally_directed_lines(X0,X1)
| ~ unequally_directed_lines(X0,reverse_line(X1))
| left_convergent_lines(X0,X1)
| left_convergent_lines(X0,reverse_line(X1)) ),
inference(cnf_transformation,[status(esa)],[f90]) ).
fof(f92,plain,
! [A,L] :
( ~ left_apart_point(A,L)
& ~ left_apart_point(A,reverse_line(L)) ),
inference(pre_NNF_transformation,[status(esa)],[f15]) ).
fof(f93,plain,
( ! [A,L] : ~ left_apart_point(A,L)
& ! [A,L] : ~ left_apart_point(A,reverse_line(L)) ),
inference(miniscoping,[status(esa)],[f92]) ).
fof(f94,plain,
! [X0,X1] : ~ left_apart_point(X0,X1),
inference(cnf_transformation,[status(esa)],[f93]) ).
fof(f96,plain,
! [L,M] :
( ~ left_convergent_lines(L,M)
& ~ left_convergent_lines(L,reverse_line(M)) ),
inference(pre_NNF_transformation,[status(esa)],[f16]) ).
fof(f97,plain,
( ! [L,M] : ~ left_convergent_lines(L,M)
& ! [L,M] : ~ left_convergent_lines(L,reverse_line(M)) ),
inference(miniscoping,[status(esa)],[f96]) ).
fof(f98,plain,
! [X0,X1] : ~ left_convergent_lines(X0,X1),
inference(cnf_transformation,[status(esa)],[f97]) ).
fof(f116,plain,
! [X0,X1] : ~ unequally_directed_lines(line_connecting(X0,X1),reverse_line(line_connecting(X1,X0))),
inference(cnf_transformation,[status(esa)],[f25]) ).
fof(f130,plain,
? [A,B,L] :
( distinct_points(A,B)
& ~ apart_point_and_line(A,L)
& ~ apart_point_and_line(B,L)
& ( ~ before_on_line(L,A,B)
| ~ before_on_line(L,B,A) ) ),
inference(pre_NNF_transformation,[status(esa)],[f33]) ).
fof(f131,plain,
( distinct_points(sk0_0,sk0_1)
& ~ apart_point_and_line(sk0_0,sk0_2)
& ~ apart_point_and_line(sk0_1,sk0_2)
& ( ~ before_on_line(sk0_2,sk0_0,sk0_1)
| ~ before_on_line(sk0_2,sk0_1,sk0_0) ) ),
inference(skolemization,[status(esa)],[f130]) ).
fof(f132,plain,
distinct_points(sk0_0,sk0_1),
inference(cnf_transformation,[status(esa)],[f131]) ).
fof(f135,plain,
( ~ before_on_line(sk0_2,sk0_0,sk0_1)
| ~ before_on_line(sk0_2,sk0_1,sk0_0) ),
inference(cnf_transformation,[status(esa)],[f131]) ).
fof(f139,plain,
( spl0_0
<=> before_on_line(sk0_2,sk0_0,sk0_1) ),
introduced(split_symbol_definition) ).
fof(f141,plain,
( ~ before_on_line(sk0_2,sk0_0,sk0_1)
| spl0_0 ),
inference(component_clause,[status(thm)],[f139]) ).
fof(f142,plain,
( spl0_1
<=> before_on_line(sk0_2,sk0_1,sk0_0) ),
introduced(split_symbol_definition) ).
fof(f144,plain,
( ~ before_on_line(sk0_2,sk0_1,sk0_0)
| spl0_1 ),
inference(component_clause,[status(thm)],[f142]) ).
fof(f145,plain,
( ~ spl0_0
| ~ spl0_1 ),
inference(split_clause,[status(thm)],[f135,f139,f142]) ).
fof(f147,plain,
! [X0,X1,X2] :
( before_on_line(X0,X1,X2)
| ~ distinct_points(X1,X2)
| left_apart_point(X1,reverse_line(X0))
| left_apart_point(X2,X0)
| left_apart_point(X2,reverse_line(X0))
| unequally_directed_lines(X0,line_connecting(X1,X2)) ),
inference(backward_subsumption_resolution,[status(thm)],[f61,f94]) ).
fof(f148,plain,
! [X0,X1,X2] :
( before_on_line(X0,X1,X2)
| ~ distinct_points(X1,X2)
| left_apart_point(X2,X0)
| left_apart_point(X2,reverse_line(X0))
| unequally_directed_lines(X0,line_connecting(X1,X2)) ),
inference(forward_subsumption_resolution,[status(thm)],[f147,f94]) ).
fof(f156,plain,
! [X0,X1] :
( ~ unequally_directed_lines(X0,X1)
| ~ unequally_directed_lines(X0,reverse_line(X1))
| left_convergent_lines(X0,reverse_line(X1)) ),
inference(backward_subsumption_resolution,[status(thm)],[f91,f98]) ).
fof(f157,plain,
! [X0,X1] :
( ~ unequally_directed_lines(X0,X1)
| ~ unequally_directed_lines(X0,reverse_line(X1)) ),
inference(forward_subsumption_resolution,[status(thm)],[f156,f98]) ).
fof(f159,plain,
! [X0,X1] :
( ~ distinct_points(X0,X1)
| distinct_points(X1,X0) ),
inference(resolution,[status(thm)],[f73,f70]) ).
fof(f192,plain,
! [X0,X1] :
( ~ unequally_directed_lines(X0,X1)
| unequally_directed_lines(X1,X0) ),
inference(resolution,[status(thm)],[f81,f78]) ).
fof(f267,plain,
! [X0,X1,X2] :
( ~ unequally_directed_lines(line_connecting(X0,X1),X2)
| unequally_directed_lines(X2,reverse_line(line_connecting(X1,X0))) ),
inference(resolution,[status(thm)],[f116,f81]) ).
fof(f790,plain,
! [X0,X1,X2] :
( ~ unequally_directed_lines(line_connecting(X0,X1),X2)
| ~ unequally_directed_lines(X2,line_connecting(X1,X0)) ),
inference(resolution,[status(thm)],[f267,f157]) ).
fof(f808,plain,
! [X0,X1,X2] :
( ~ unequally_directed_lines(X0,line_connecting(X1,X2))
| ~ unequally_directed_lines(X0,line_connecting(X2,X1)) ),
inference(resolution,[status(thm)],[f790,f192]) ).
fof(f833,plain,
! [X0,X1,X2] :
( ~ unequally_directed_lines(X0,X1)
| unequally_directed_lines(X1,line_connecting(X2,X2)) ),
inference(resolution,[status(thm)],[f808,f81]) ).
fof(f842,plain,
! [X0,X1] : ~ unequally_directed_lines(X0,line_connecting(X1,X1)),
inference(factoring,[status(esa)],[f808]) ).
fof(f843,plain,
! [X0,X1] : ~ unequally_directed_lines(X0,X1),
inference(backward_subsumption_resolution,[status(thm)],[f833,f842]) ).
fof(f847,plain,
! [X0,X1,X2] :
( before_on_line(X0,X1,X2)
| ~ distinct_points(X1,X2)
| left_apart_point(X2,X0)
| left_apart_point(X2,reverse_line(X0)) ),
inference(backward_subsumption_resolution,[status(thm)],[f148,f843]) ).
fof(f848,plain,
! [X0,X1,X2] :
( before_on_line(X0,X1,X2)
| ~ distinct_points(X1,X2)
| left_apart_point(X2,reverse_line(X0)) ),
inference(forward_subsumption_resolution,[status(thm)],[f847,f94]) ).
fof(f1152,plain,
! [X0,X1,X2] :
( before_on_line(X0,X1,X2)
| ~ distinct_points(X1,X2) ),
inference(forward_subsumption_resolution,[status(thm)],[f848,f94]) ).
fof(f1201,plain,
( ~ distinct_points(sk0_0,sk0_1)
| spl0_0 ),
inference(resolution,[status(thm)],[f141,f1152]) ).
fof(f1202,plain,
( $false
| spl0_0 ),
inference(forward_subsumption_resolution,[status(thm)],[f1201,f132]) ).
fof(f1203,plain,
spl0_0,
inference(contradiction_clause,[status(thm)],[f1202]) ).
fof(f1209,plain,
( ~ distinct_points(sk0_1,sk0_0)
| spl0_1 ),
inference(resolution,[status(thm)],[f144,f1152]) ).
fof(f1218,plain,
( ~ distinct_points(sk0_0,sk0_1)
| spl0_1 ),
inference(resolution,[status(thm)],[f1209,f159]) ).
fof(f1219,plain,
( $false
| spl0_1 ),
inference(forward_subsumption_resolution,[status(thm)],[f1218,f132]) ).
fof(f1220,plain,
spl0_1,
inference(contradiction_clause,[status(thm)],[f1219]) ).
fof(f1221,plain,
$false,
inference(sat_refutation,[status(thm)],[f145,f1203,f1220]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.02/0.08 % Problem : GEO254+1 : TPTP v8.1.2. Bugfixed v6.4.0.
% 0.02/0.08 % Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.09/0.27 % Computer : n032.cluster.edu
% 0.09/0.27 % Model : x86_64 x86_64
% 0.09/0.27 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.27 % Memory : 8042.1875MB
% 0.09/0.27 % OS : Linux 3.10.0-693.el7.x86_64
% 0.09/0.27 % CPULimit : 300
% 0.09/0.27 % WCLimit : 300
% 0.09/0.27 % DateTime : Tue Apr 30 01:47:36 EDT 2024
% 0.09/0.27 % CPUTime :
% 0.09/0.28 % Drodi V3.6.0
% 0.13/0.39 % Refutation found
% 0.13/0.39 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.13/0.39 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.13/0.40 % Elapsed time: 0.120823 seconds
% 0.13/0.40 % CPU time: 0.887274 seconds
% 0.13/0.40 % Total memory used: 21.150 MB
% 0.13/0.40 % Net memory used: 19.836 MB
%------------------------------------------------------------------------------