TSTP Solution File: NUM394+1 by Drodi---3.5.1
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Drodi---3.5.1
% Problem : NUM394+1 : TPTP v8.1.2. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% Computer : n003.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 12:29:01 EDT 2023
% Result : Theorem 0.12s 0.36s
% Output : CNFRefutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 12
% Syntax : Number of formulae : 58 ( 9 unt; 0 def)
% Number of atoms : 170 ( 7 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 182 ( 70 ~; 73 |; 19 &)
% ( 10 <=>; 10 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 14 ( 12 usr; 7 prp; 0-2 aty)
% Number of functors : 3 ( 3 usr; 2 con; 0-1 aty)
% Number of variables : 51 (; 47 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f3,axiom,
! [A] :
( ordinal(A)
=> ( epsilon_transitive(A)
& epsilon_connected(A) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f7,axiom,
! [A,B] :
( ( ordinal(A)
& ordinal(B) )
=> ( ordinal_subset(A,B)
| ordinal_subset(B,A) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f8,axiom,
! [A] :
( epsilon_transitive(A)
<=> ! [B] :
( in(B,A)
=> subset(B,A) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f24,axiom,
! [A,B] :
( ( ordinal(A)
& ordinal(B) )
=> ( ordinal_subset(A,B)
<=> subset(A,B) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f28,axiom,
! [A] :
( ordinal(A)
=> ! [B] :
( ordinal(B)
=> ~ ( ~ in(A,B)
& A != B
& ~ in(B,A) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f29,conjecture,
! [A] :
( ordinal(A)
=> ! [B] :
( ordinal(B)
=> ( ordinal_subset(A,B)
| in(B,A) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f30,negated_conjecture,
~ ! [A] :
( ordinal(A)
=> ! [B] :
( ordinal(B)
=> ( ordinal_subset(A,B)
| in(B,A) ) ) ),
inference(negated_conjecture,[status(cth)],[f29]) ).
fof(f42,plain,
! [A] :
( ~ ordinal(A)
| ( epsilon_transitive(A)
& epsilon_connected(A) ) ),
inference(pre_NNF_transformation,[status(esa)],[f3]) ).
fof(f43,plain,
! [X0] :
( ~ ordinal(X0)
| epsilon_transitive(X0) ),
inference(cnf_transformation,[status(esa)],[f42]) ).
fof(f53,plain,
! [A,B] :
( ~ ordinal(A)
| ~ ordinal(B)
| ordinal_subset(A,B)
| ordinal_subset(B,A) ),
inference(pre_NNF_transformation,[status(esa)],[f7]) ).
fof(f54,plain,
! [X0,X1] :
( ~ ordinal(X0)
| ~ ordinal(X1)
| ordinal_subset(X0,X1)
| ordinal_subset(X1,X0) ),
inference(cnf_transformation,[status(esa)],[f53]) ).
fof(f55,plain,
! [A] :
( epsilon_transitive(A)
<=> ! [B] :
( ~ in(B,A)
| subset(B,A) ) ),
inference(pre_NNF_transformation,[status(esa)],[f8]) ).
fof(f56,plain,
! [A] :
( ( ~ epsilon_transitive(A)
| ! [B] :
( ~ in(B,A)
| subset(B,A) ) )
& ( epsilon_transitive(A)
| ? [B] :
( in(B,A)
& ~ subset(B,A) ) ) ),
inference(NNF_transformation,[status(esa)],[f55]) ).
fof(f57,plain,
( ! [A] :
( ~ epsilon_transitive(A)
| ! [B] :
( ~ in(B,A)
| subset(B,A) ) )
& ! [A] :
( epsilon_transitive(A)
| ? [B] :
( in(B,A)
& ~ subset(B,A) ) ) ),
inference(miniscoping,[status(esa)],[f56]) ).
fof(f58,plain,
( ! [A] :
( ~ epsilon_transitive(A)
| ! [B] :
( ~ in(B,A)
| subset(B,A) ) )
& ! [A] :
( epsilon_transitive(A)
| ( in(sk0_0(A),A)
& ~ subset(sk0_0(A),A) ) ) ),
inference(skolemization,[status(esa)],[f57]) ).
fof(f59,plain,
! [X0,X1] :
( ~ epsilon_transitive(X0)
| ~ in(X1,X0)
| subset(X1,X0) ),
inference(cnf_transformation,[status(esa)],[f58]) ).
fof(f106,plain,
! [A,B] :
( ~ ordinal(A)
| ~ ordinal(B)
| ( ordinal_subset(A,B)
<=> subset(A,B) ) ),
inference(pre_NNF_transformation,[status(esa)],[f24]) ).
fof(f107,plain,
! [A,B] :
( ~ ordinal(A)
| ~ ordinal(B)
| ( ( ~ ordinal_subset(A,B)
| subset(A,B) )
& ( ordinal_subset(A,B)
| ~ subset(A,B) ) ) ),
inference(NNF_transformation,[status(esa)],[f106]) ).
fof(f109,plain,
! [X0,X1] :
( ~ ordinal(X0)
| ~ ordinal(X1)
| ordinal_subset(X0,X1)
| ~ subset(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f107]) ).
fof(f117,plain,
! [A] :
( ~ ordinal(A)
| ! [B] :
( ~ ordinal(B)
| in(A,B)
| A = B
| in(B,A) ) ),
inference(pre_NNF_transformation,[status(esa)],[f28]) ).
fof(f118,plain,
! [X0,X1] :
( ~ ordinal(X0)
| ~ ordinal(X1)
| in(X0,X1)
| X0 = X1
| in(X1,X0) ),
inference(cnf_transformation,[status(esa)],[f117]) ).
fof(f119,plain,
? [A] :
( ordinal(A)
& ? [B] :
( ordinal(B)
& ~ ordinal_subset(A,B)
& ~ in(B,A) ) ),
inference(pre_NNF_transformation,[status(esa)],[f30]) ).
fof(f120,plain,
( ordinal(sk0_13)
& ordinal(sk0_14)
& ~ ordinal_subset(sk0_13,sk0_14)
& ~ in(sk0_14,sk0_13) ),
inference(skolemization,[status(esa)],[f119]) ).
fof(f121,plain,
ordinal(sk0_13),
inference(cnf_transformation,[status(esa)],[f120]) ).
fof(f122,plain,
ordinal(sk0_14),
inference(cnf_transformation,[status(esa)],[f120]) ).
fof(f123,plain,
~ ordinal_subset(sk0_13,sk0_14),
inference(cnf_transformation,[status(esa)],[f120]) ).
fof(f124,plain,
~ in(sk0_14,sk0_13),
inference(cnf_transformation,[status(esa)],[f120]) ).
fof(f153,plain,
! [X0] :
( ~ ordinal(X0)
| ordinal_subset(X0,sk0_13)
| ordinal_subset(sk0_13,X0) ),
inference(resolution,[status(thm)],[f54,f121]) ).
fof(f171,plain,
( spl0_5
<=> ordinal_subset(sk0_13,sk0_13) ),
introduced(split_symbol_definition) ).
fof(f172,plain,
( ordinal_subset(sk0_13,sk0_13)
| ~ spl0_5 ),
inference(component_clause,[status(thm)],[f171]) ).
fof(f174,plain,
( ordinal_subset(sk0_13,sk0_13)
| ordinal_subset(sk0_13,sk0_13) ),
inference(resolution,[status(thm)],[f153,f121]) ).
fof(f175,plain,
spl0_5,
inference(split_clause,[status(thm)],[f174,f171]) ).
fof(f176,plain,
! [X0] :
( ~ ordinal(X0)
| in(X0,sk0_14)
| X0 = sk0_14
| in(sk0_14,X0) ),
inference(resolution,[status(thm)],[f118,f122]) ).
fof(f186,plain,
( spl0_8
<=> in(sk0_13,sk0_14) ),
introduced(split_symbol_definition) ).
fof(f189,plain,
( spl0_9
<=> sk0_13 = sk0_14 ),
introduced(split_symbol_definition) ).
fof(f190,plain,
( sk0_13 = sk0_14
| ~ spl0_9 ),
inference(component_clause,[status(thm)],[f189]) ).
fof(f192,plain,
( spl0_10
<=> in(sk0_14,sk0_13) ),
introduced(split_symbol_definition) ).
fof(f193,plain,
( in(sk0_14,sk0_13)
| ~ spl0_10 ),
inference(component_clause,[status(thm)],[f192]) ).
fof(f195,plain,
( in(sk0_13,sk0_14)
| sk0_13 = sk0_14
| in(sk0_14,sk0_13) ),
inference(resolution,[status(thm)],[f176,f121]) ).
fof(f196,plain,
( spl0_8
| spl0_9
| spl0_10 ),
inference(split_clause,[status(thm)],[f195,f186,f189,f192]) ).
fof(f197,plain,
( $false
| ~ spl0_10 ),
inference(forward_subsumption_resolution,[status(thm)],[f193,f124]) ).
fof(f198,plain,
~ spl0_10,
inference(contradiction_clause,[status(thm)],[f197]) ).
fof(f331,plain,
! [X0,X1] :
( ~ epsilon_transitive(X0)
| ~ in(X1,X0)
| ~ ordinal(X1)
| ~ ordinal(X0)
| ordinal_subset(X1,X0) ),
inference(resolution,[status(thm)],[f59,f109]) ).
fof(f332,plain,
! [X0,X1] :
( ~ in(X0,X1)
| ~ ordinal(X0)
| ~ ordinal(X1)
| ordinal_subset(X0,X1) ),
inference(forward_subsumption_resolution,[status(thm)],[f331,f43]) ).
fof(f333,plain,
( spl0_28
<=> ordinal(sk0_13) ),
introduced(split_symbol_definition) ).
fof(f335,plain,
( ~ ordinal(sk0_13)
| spl0_28 ),
inference(component_clause,[status(thm)],[f333]) ).
fof(f336,plain,
( spl0_29
<=> ordinal(sk0_14) ),
introduced(split_symbol_definition) ).
fof(f338,plain,
( ~ ordinal(sk0_14)
| spl0_29 ),
inference(component_clause,[status(thm)],[f336]) ).
fof(f339,plain,
( ~ in(sk0_13,sk0_14)
| ~ ordinal(sk0_13)
| ~ ordinal(sk0_14) ),
inference(resolution,[status(thm)],[f332,f123]) ).
fof(f340,plain,
( ~ spl0_8
| ~ spl0_28
| ~ spl0_29 ),
inference(split_clause,[status(thm)],[f339,f186,f333,f336]) ).
fof(f341,plain,
( $false
| spl0_29 ),
inference(forward_subsumption_resolution,[status(thm)],[f338,f122]) ).
fof(f342,plain,
spl0_29,
inference(contradiction_clause,[status(thm)],[f341]) ).
fof(f343,plain,
( $false
| spl0_28 ),
inference(forward_subsumption_resolution,[status(thm)],[f335,f121]) ).
fof(f344,plain,
spl0_28,
inference(contradiction_clause,[status(thm)],[f343]) ).
fof(f371,plain,
( ~ ordinal_subset(sk0_13,sk0_13)
| ~ spl0_9 ),
inference(backward_demodulation,[status(thm)],[f190,f123]) ).
fof(f372,plain,
( $false
| ~ spl0_5
| ~ spl0_9 ),
inference(forward_subsumption_resolution,[status(thm)],[f371,f172]) ).
fof(f373,plain,
( ~ spl0_5
| ~ spl0_9 ),
inference(contradiction_clause,[status(thm)],[f372]) ).
fof(f374,plain,
$false,
inference(sat_refutation,[status(thm)],[f175,f196,f198,f340,f342,f344,f373]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : NUM394+1 : TPTP v8.1.2. Released v3.2.0.
% 0.07/0.13 % Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.12/0.34 % Computer : n003.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 : 300
% 0.12/0.34 % DateTime : Tue May 30 10:02:08 EDT 2023
% 0.12/0.34 % CPUTime :
% 0.12/0.35 % Drodi V3.5.1
% 0.12/0.36 % Refutation found
% 0.12/0.36 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.12/0.36 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.19/0.58 % Elapsed time: 0.021574 seconds
% 0.19/0.58 % CPU time: 0.026168 seconds
% 0.19/0.58 % Memory used: 3.021 MB
%------------------------------------------------------------------------------