TSTP Solution File: GEO111+1 by Drodi---3.5.1
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- Process Solution
%------------------------------------------------------------------------------
% File : Drodi---3.5.1
% Problem : GEO111+1 : TPTP v8.1.2. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% Computer : n006.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 : Wed May 31 12:07:49 EDT 2023
% Result : Theorem 0.14s 0.42s
% Output : CNFRefutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 11
% Syntax : Number of formulae : 83 ( 15 unt; 0 def)
% Number of atoms : 297 ( 29 equ)
% Maximal formula atoms : 16 ( 3 avg)
% Number of connectives : 348 ( 134 ~; 130 |; 68 &)
% ( 12 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 5 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 13 ( 11 usr; 7 prp; 0-4 aty)
% Number of functors : 8 ( 8 usr; 4 con; 0-4 aty)
% Number of variables : 143 (; 130 !; 13 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [C,C1] :
( part_of(C1,C)
<=> ! [P] :
( incident_c(P,C1)
=> incident_c(P,C) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f3,axiom,
! [P,C] :
( end_point(P,C)
<=> ( incident_c(P,C)
& ! [C1,C2] :
( ( part_of(C1,C)
& part_of(C2,C)
& incident_c(P,C1)
& incident_c(P,C2) )
=> ( part_of(C1,C2)
| part_of(C2,C1) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f4,axiom,
! [P,C] :
( inner_point(P,C)
<=> ( incident_c(P,C)
& ~ end_point(P,C) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f17,axiom,
! [C,P,Q,R] :
( between_c(C,P,Q,R)
<=> ( P != R
& ? [Cpp] :
( part_of(Cpp,C)
& end_point(P,Cpp)
& end_point(R,Cpp)
& inner_point(Q,Cpp) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f18,conjecture,
! [C,P,Q,R] :
( between_c(C,P,Q,R)
=> ( incident_c(P,C)
& incident_c(Q,C)
& incident_c(R,C)
& P != Q
& Q != R
& P != R ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f19,negated_conjecture,
~ ! [C,P,Q,R] :
( between_c(C,P,Q,R)
=> ( incident_c(P,C)
& incident_c(Q,C)
& incident_c(R,C)
& P != Q
& Q != R
& P != R ) ),
inference(negated_conjecture,[status(cth)],[f18]) ).
fof(f20,plain,
! [C,C1] :
( part_of(C1,C)
<=> ! [P] :
( ~ incident_c(P,C1)
| incident_c(P,C) ) ),
inference(pre_NNF_transformation,[status(esa)],[f1]) ).
fof(f21,plain,
! [C,C1] :
( ( ~ part_of(C1,C)
| ! [P] :
( ~ incident_c(P,C1)
| incident_c(P,C) ) )
& ( part_of(C1,C)
| ? [P] :
( incident_c(P,C1)
& ~ incident_c(P,C) ) ) ),
inference(NNF_transformation,[status(esa)],[f20]) ).
fof(f22,plain,
( ! [C,C1] :
( ~ part_of(C1,C)
| ! [P] :
( ~ incident_c(P,C1)
| incident_c(P,C) ) )
& ! [C,C1] :
( part_of(C1,C)
| ? [P] :
( incident_c(P,C1)
& ~ incident_c(P,C) ) ) ),
inference(miniscoping,[status(esa)],[f21]) ).
fof(f23,plain,
( ! [C,C1] :
( ~ part_of(C1,C)
| ! [P] :
( ~ incident_c(P,C1)
| incident_c(P,C) ) )
& ! [C,C1] :
( part_of(C1,C)
| ( incident_c(sk0_0(C1,C),C1)
& ~ incident_c(sk0_0(C1,C),C) ) ) ),
inference(skolemization,[status(esa)],[f22]) ).
fof(f24,plain,
! [X0,X1,X2] :
( ~ part_of(X0,X1)
| ~ incident_c(X2,X0)
| incident_c(X2,X1) ),
inference(cnf_transformation,[status(esa)],[f23]) ).
fof(f36,plain,
! [P,C] :
( end_point(P,C)
<=> ( incident_c(P,C)
& ! [C1,C2] :
( ~ part_of(C1,C)
| ~ part_of(C2,C)
| ~ incident_c(P,C1)
| ~ incident_c(P,C2)
| part_of(C1,C2)
| part_of(C2,C1) ) ) ),
inference(pre_NNF_transformation,[status(esa)],[f3]) ).
fof(f37,plain,
! [P,C] :
( ( ~ end_point(P,C)
| ( incident_c(P,C)
& ! [C1,C2] :
( ~ part_of(C1,C)
| ~ part_of(C2,C)
| ~ incident_c(P,C1)
| ~ incident_c(P,C2)
| part_of(C1,C2)
| part_of(C2,C1) ) ) )
& ( end_point(P,C)
| ~ incident_c(P,C)
| ? [C1,C2] :
( part_of(C1,C)
& part_of(C2,C)
& incident_c(P,C1)
& incident_c(P,C2)
& ~ part_of(C1,C2)
& ~ part_of(C2,C1) ) ) ),
inference(NNF_transformation,[status(esa)],[f36]) ).
fof(f38,plain,
( ! [P,C] :
( ~ end_point(P,C)
| ( incident_c(P,C)
& ! [C1,C2] :
( ~ part_of(C1,C)
| ~ part_of(C2,C)
| ~ incident_c(P,C1)
| ~ incident_c(P,C2)
| part_of(C1,C2)
| part_of(C2,C1) ) ) )
& ! [P,C] :
( end_point(P,C)
| ~ incident_c(P,C)
| ? [C1,C2] :
( part_of(C1,C)
& part_of(C2,C)
& incident_c(P,C1)
& incident_c(P,C2)
& ~ part_of(C1,C2)
& ~ part_of(C2,C1) ) ) ),
inference(miniscoping,[status(esa)],[f37]) ).
fof(f39,plain,
( ! [P,C] :
( ~ end_point(P,C)
| ( incident_c(P,C)
& ! [C1,C2] :
( ~ part_of(C1,C)
| ~ part_of(C2,C)
| ~ incident_c(P,C1)
| ~ incident_c(P,C2)
| part_of(C1,C2)
| part_of(C2,C1) ) ) )
& ! [P,C] :
( end_point(P,C)
| ~ incident_c(P,C)
| ( part_of(sk0_2(C,P),C)
& part_of(sk0_3(C,P),C)
& incident_c(P,sk0_2(C,P))
& incident_c(P,sk0_3(C,P))
& ~ part_of(sk0_2(C,P),sk0_3(C,P))
& ~ part_of(sk0_3(C,P),sk0_2(C,P)) ) ) ),
inference(skolemization,[status(esa)],[f38]) ).
fof(f40,plain,
! [X0,X1] :
( ~ end_point(X0,X1)
| incident_c(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f39]) ).
fof(f48,plain,
! [P,C] :
( ( ~ inner_point(P,C)
| ( incident_c(P,C)
& ~ end_point(P,C) ) )
& ( inner_point(P,C)
| ~ incident_c(P,C)
| end_point(P,C) ) ),
inference(NNF_transformation,[status(esa)],[f4]) ).
fof(f49,plain,
( ! [P,C] :
( ~ inner_point(P,C)
| ( incident_c(P,C)
& ~ end_point(P,C) ) )
& ! [P,C] :
( inner_point(P,C)
| ~ incident_c(P,C)
| end_point(P,C) ) ),
inference(miniscoping,[status(esa)],[f48]) ).
fof(f50,plain,
! [X0,X1] :
( ~ inner_point(X0,X1)
| incident_c(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f49]) ).
fof(f51,plain,
! [X0,X1] :
( ~ inner_point(X0,X1)
| ~ end_point(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f49]) ).
fof(f105,plain,
! [C,P,Q,R] :
( ( ~ between_c(C,P,Q,R)
| ( P != R
& ? [Cpp] :
( part_of(Cpp,C)
& end_point(P,Cpp)
& end_point(R,Cpp)
& inner_point(Q,Cpp) ) ) )
& ( between_c(C,P,Q,R)
| P = R
| ! [Cpp] :
( ~ part_of(Cpp,C)
| ~ end_point(P,Cpp)
| ~ end_point(R,Cpp)
| ~ inner_point(Q,Cpp) ) ) ),
inference(NNF_transformation,[status(esa)],[f17]) ).
fof(f106,plain,
( ! [C,P,Q,R] :
( ~ between_c(C,P,Q,R)
| ( P != R
& ? [Cpp] :
( part_of(Cpp,C)
& end_point(P,Cpp)
& end_point(R,Cpp)
& inner_point(Q,Cpp) ) ) )
& ! [C,P,Q,R] :
( between_c(C,P,Q,R)
| P = R
| ! [Cpp] :
( ~ part_of(Cpp,C)
| ~ end_point(P,Cpp)
| ~ end_point(R,Cpp)
| ~ inner_point(Q,Cpp) ) ) ),
inference(miniscoping,[status(esa)],[f105]) ).
fof(f107,plain,
( ! [C,P,Q,R] :
( ~ between_c(C,P,Q,R)
| ( P != R
& part_of(sk0_13(R,Q,P,C),C)
& end_point(P,sk0_13(R,Q,P,C))
& end_point(R,sk0_13(R,Q,P,C))
& inner_point(Q,sk0_13(R,Q,P,C)) ) )
& ! [C,P,Q,R] :
( between_c(C,P,Q,R)
| P = R
| ! [Cpp] :
( ~ part_of(Cpp,C)
| ~ end_point(P,Cpp)
| ~ end_point(R,Cpp)
| ~ inner_point(Q,Cpp) ) ) ),
inference(skolemization,[status(esa)],[f106]) ).
fof(f108,plain,
! [X0,X1,X2,X3] :
( ~ between_c(X0,X1,X2,X3)
| X1 != X3 ),
inference(cnf_transformation,[status(esa)],[f107]) ).
fof(f109,plain,
! [X0,X1,X2,X3] :
( ~ between_c(X0,X1,X2,X3)
| part_of(sk0_13(X3,X2,X1,X0),X0) ),
inference(cnf_transformation,[status(esa)],[f107]) ).
fof(f110,plain,
! [X0,X1,X2,X3] :
( ~ between_c(X0,X1,X2,X3)
| end_point(X1,sk0_13(X3,X2,X1,X0)) ),
inference(cnf_transformation,[status(esa)],[f107]) ).
fof(f111,plain,
! [X0,X1,X2,X3] :
( ~ between_c(X0,X1,X2,X3)
| end_point(X3,sk0_13(X3,X2,X1,X0)) ),
inference(cnf_transformation,[status(esa)],[f107]) ).
fof(f112,plain,
! [X0,X1,X2,X3] :
( ~ between_c(X0,X1,X2,X3)
| inner_point(X2,sk0_13(X3,X2,X1,X0)) ),
inference(cnf_transformation,[status(esa)],[f107]) ).
fof(f114,plain,
? [C,P,Q,R] :
( between_c(C,P,Q,R)
& ( ~ incident_c(P,C)
| ~ incident_c(Q,C)
| ~ incident_c(R,C)
| P = Q
| Q = R
| P = R ) ),
inference(pre_NNF_transformation,[status(esa)],[f19]) ).
fof(f115,plain,
( between_c(sk0_14,sk0_15,sk0_16,sk0_17)
& ( ~ incident_c(sk0_15,sk0_14)
| ~ incident_c(sk0_16,sk0_14)
| ~ incident_c(sk0_17,sk0_14)
| sk0_15 = sk0_16
| sk0_16 = sk0_17
| sk0_15 = sk0_17 ) ),
inference(skolemization,[status(esa)],[f114]) ).
fof(f116,plain,
between_c(sk0_14,sk0_15,sk0_16,sk0_17),
inference(cnf_transformation,[status(esa)],[f115]) ).
fof(f117,plain,
( ~ incident_c(sk0_15,sk0_14)
| ~ incident_c(sk0_16,sk0_14)
| ~ incident_c(sk0_17,sk0_14)
| sk0_15 = sk0_16
| sk0_16 = sk0_17
| sk0_15 = sk0_17 ),
inference(cnf_transformation,[status(esa)],[f115]) ).
fof(f118,plain,
( spl0_0
<=> incident_c(sk0_15,sk0_14) ),
introduced(split_symbol_definition) ).
fof(f120,plain,
( ~ incident_c(sk0_15,sk0_14)
| spl0_0 ),
inference(component_clause,[status(thm)],[f118]) ).
fof(f121,plain,
( spl0_1
<=> incident_c(sk0_16,sk0_14) ),
introduced(split_symbol_definition) ).
fof(f123,plain,
( ~ incident_c(sk0_16,sk0_14)
| spl0_1 ),
inference(component_clause,[status(thm)],[f121]) ).
fof(f124,plain,
( spl0_2
<=> incident_c(sk0_17,sk0_14) ),
introduced(split_symbol_definition) ).
fof(f126,plain,
( ~ incident_c(sk0_17,sk0_14)
| spl0_2 ),
inference(component_clause,[status(thm)],[f124]) ).
fof(f127,plain,
( spl0_3
<=> sk0_15 = sk0_16 ),
introduced(split_symbol_definition) ).
fof(f128,plain,
( sk0_15 = sk0_16
| ~ spl0_3 ),
inference(component_clause,[status(thm)],[f127]) ).
fof(f130,plain,
( spl0_4
<=> sk0_16 = sk0_17 ),
introduced(split_symbol_definition) ).
fof(f131,plain,
( sk0_16 = sk0_17
| ~ spl0_4 ),
inference(component_clause,[status(thm)],[f130]) ).
fof(f133,plain,
( spl0_5
<=> sk0_15 = sk0_17 ),
introduced(split_symbol_definition) ).
fof(f134,plain,
( sk0_15 = sk0_17
| ~ spl0_5 ),
inference(component_clause,[status(thm)],[f133]) ).
fof(f136,plain,
( ~ spl0_0
| ~ spl0_1
| ~ spl0_2
| spl0_3
| spl0_4
| spl0_5 ),
inference(split_clause,[status(thm)],[f117,f118,f121,f124,f127,f130,f133]) ).
fof(f137,plain,
! [X0,X1,X2] : ~ between_c(X0,X1,X2,X1),
inference(destructive_equality_resolution,[status(esa)],[f108]) ).
fof(f150,plain,
end_point(sk0_15,sk0_13(sk0_17,sk0_16,sk0_15,sk0_14)),
inference(resolution,[status(thm)],[f110,f116]) ).
fof(f152,plain,
incident_c(sk0_15,sk0_13(sk0_17,sk0_16,sk0_15,sk0_14)),
inference(resolution,[status(thm)],[f150,f40]) ).
fof(f175,plain,
end_point(sk0_17,sk0_13(sk0_17,sk0_16,sk0_15,sk0_14)),
inference(resolution,[status(thm)],[f111,f116]) ).
fof(f177,plain,
incident_c(sk0_17,sk0_13(sk0_17,sk0_16,sk0_15,sk0_14)),
inference(resolution,[status(thm)],[f175,f40]) ).
fof(f200,plain,
inner_point(sk0_16,sk0_13(sk0_17,sk0_16,sk0_15,sk0_14)),
inference(resolution,[status(thm)],[f112,f116]) ).
fof(f201,plain,
incident_c(sk0_16,sk0_13(sk0_17,sk0_16,sk0_15,sk0_14)),
inference(resolution,[status(thm)],[f200,f50]) ).
fof(f216,plain,
! [X0] :
( ~ part_of(X0,sk0_14)
| ~ incident_c(sk0_17,X0)
| spl0_2 ),
inference(resolution,[status(thm)],[f126,f24]) ).
fof(f217,plain,
! [X0,X1,X2] :
( ~ incident_c(sk0_17,sk0_13(X0,X1,X2,sk0_14))
| ~ between_c(sk0_14,X2,X1,X0)
| spl0_2 ),
inference(resolution,[status(thm)],[f216,f109]) ).
fof(f219,plain,
( ~ incident_c(sk0_17,sk0_13(sk0_17,sk0_16,sk0_15,sk0_14))
| spl0_2 ),
inference(resolution,[status(thm)],[f217,f116]) ).
fof(f220,plain,
( $false
| spl0_2 ),
inference(forward_subsumption_resolution,[status(thm)],[f219,f177]) ).
fof(f221,plain,
spl0_2,
inference(contradiction_clause,[status(thm)],[f220]) ).
fof(f226,plain,
! [X0] :
( ~ part_of(X0,sk0_14)
| ~ incident_c(sk0_16,X0)
| spl0_1 ),
inference(resolution,[status(thm)],[f123,f24]) ).
fof(f236,plain,
! [X0,X1,X2] :
( ~ incident_c(sk0_16,sk0_13(X0,X1,X2,sk0_14))
| ~ between_c(sk0_14,X2,X1,X0)
| spl0_1 ),
inference(resolution,[status(thm)],[f226,f109]) ).
fof(f238,plain,
( ~ incident_c(sk0_16,sk0_13(sk0_17,sk0_16,sk0_15,sk0_14))
| spl0_1 ),
inference(resolution,[status(thm)],[f236,f116]) ).
fof(f239,plain,
( $false
| spl0_1 ),
inference(forward_subsumption_resolution,[status(thm)],[f238,f201]) ).
fof(f240,plain,
spl0_1,
inference(contradiction_clause,[status(thm)],[f239]) ).
fof(f245,plain,
! [X0] :
( ~ part_of(X0,sk0_14)
| ~ incident_c(sk0_15,X0)
| spl0_0 ),
inference(resolution,[status(thm)],[f120,f24]) ).
fof(f248,plain,
! [X0,X1,X2] :
( ~ incident_c(sk0_15,sk0_13(X0,X1,X2,sk0_14))
| ~ between_c(sk0_14,X2,X1,X0)
| spl0_0 ),
inference(resolution,[status(thm)],[f245,f109]) ).
fof(f250,plain,
( ~ incident_c(sk0_15,sk0_13(sk0_17,sk0_16,sk0_15,sk0_14))
| spl0_0 ),
inference(resolution,[status(thm)],[f248,f116]) ).
fof(f251,plain,
( $false
| spl0_0 ),
inference(forward_subsumption_resolution,[status(thm)],[f250,f152]) ).
fof(f252,plain,
spl0_0,
inference(contradiction_clause,[status(thm)],[f251]) ).
fof(f267,plain,
( between_c(sk0_14,sk0_15,sk0_16,sk0_15)
| ~ spl0_5 ),
inference(backward_demodulation,[status(thm)],[f134,f116]) ).
fof(f268,plain,
( $false
| ~ spl0_5 ),
inference(forward_subsumption_resolution,[status(thm)],[f267,f137]) ).
fof(f269,plain,
~ spl0_5,
inference(contradiction_clause,[status(thm)],[f268]) ).
fof(f295,plain,
( inner_point(sk0_15,sk0_13(sk0_17,sk0_16,sk0_15,sk0_14))
| ~ spl0_3 ),
inference(forward_demodulation,[status(thm)],[f128,f200]) ).
fof(f296,plain,
( inner_point(sk0_15,sk0_13(sk0_17,sk0_15,sk0_15,sk0_14))
| ~ spl0_3 ),
inference(forward_demodulation,[status(thm)],[f128,f295]) ).
fof(f322,plain,
( end_point(sk0_15,sk0_13(sk0_17,sk0_15,sk0_15,sk0_14))
| ~ spl0_3 ),
inference(forward_demodulation,[status(thm)],[f128,f150]) ).
fof(f323,plain,
( ~ inner_point(sk0_15,sk0_13(sk0_17,sk0_15,sk0_15,sk0_14))
| ~ spl0_3 ),
inference(resolution,[status(thm)],[f322,f51]) ).
fof(f324,plain,
( $false
| ~ spl0_3 ),
inference(forward_subsumption_resolution,[status(thm)],[f323,f296]) ).
fof(f325,plain,
~ spl0_3,
inference(contradiction_clause,[status(thm)],[f324]) ).
fof(f410,plain,
( inner_point(sk0_16,sk0_13(sk0_16,sk0_16,sk0_15,sk0_14))
| ~ spl0_4 ),
inference(backward_demodulation,[status(thm)],[f131,f200]) ).
fof(f413,plain,
( end_point(sk0_17,sk0_13(sk0_16,sk0_16,sk0_15,sk0_14))
| ~ spl0_4 ),
inference(backward_demodulation,[status(thm)],[f131,f175]) ).
fof(f414,plain,
( end_point(sk0_16,sk0_13(sk0_16,sk0_16,sk0_15,sk0_14))
| ~ spl0_4 ),
inference(forward_demodulation,[status(thm)],[f131,f413]) ).
fof(f446,plain,
( ~ inner_point(sk0_16,sk0_13(sk0_16,sk0_16,sk0_15,sk0_14))
| ~ spl0_4 ),
inference(resolution,[status(thm)],[f414,f51]) ).
fof(f447,plain,
( $false
| ~ spl0_4 ),
inference(forward_subsumption_resolution,[status(thm)],[f446,f410]) ).
fof(f448,plain,
~ spl0_4,
inference(contradiction_clause,[status(thm)],[f447]) ).
fof(f449,plain,
$false,
inference(sat_refutation,[status(thm)],[f136,f221,f240,f252,f269,f325,f448]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.10 % Problem : GEO111+1 : TPTP v8.1.2. Released v2.4.0.
% 0.04/0.11 % Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.09/0.30 % Computer : n006.cluster.edu
% 0.09/0.30 % Model : x86_64 x86_64
% 0.09/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.30 % Memory : 8042.1875MB
% 0.09/0.30 % OS : Linux 3.10.0-693.el7.x86_64
% 0.09/0.30 % CPULimit : 300
% 0.09/0.30 % WCLimit : 300
% 0.09/0.30 % DateTime : Tue May 30 12:00:47 EDT 2023
% 0.09/0.30 % CPUTime :
% 0.14/0.31 % Drodi V3.5.1
% 0.14/0.42 % Refutation found
% 0.14/0.42 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.14/0.42 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.14/0.44 % Elapsed time: 0.129498 seconds
% 0.14/0.44 % CPU time: 0.530398 seconds
% 0.14/0.44 % Memory used: 50.828 MB
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