%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : NUM414+1 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n002.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Sep 24 01:40:27 PM UTC 2026
% Result : Theorem 0.20s 0.50s
% Output : CNFRefutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 8
% Syntax : Number of formulae : 44 ( 10 unt; 4 def)
% Number of atoms : 140 ( 20 equ)
% Maximal formula atoms : 8 ( 3 avg)
% Number of connectives : 162 ( 66 ~; 63 |; 20 &)
% ( 7 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 10 ( 8 usr; 5 prp; 0-2 aty)
% Number of functors : 2 ( 2 usr; 2 con; 0-0 aty)
% Number of variables : 40 ( 38 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f9,axiom,
! [A,B] :
( ( ordinal(B)
& ordinal(A) )
=> ( ordinal_subset(B,A)
| ordinal_subset(A,B) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f10,axiom,
! [A,B] :
( proper_subset(A,B)
<=> ( A != B
& subset(A,B) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f31,axiom,
! [A,B] :
( ( ordinal(B)
& ordinal(A) )
=> ( ordinal_subset(A,B)
<=> subset(A,B) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f38,conjecture,
! [A] :
( ordinal(A)
=> ! [B] :
( ordinal(B)
=> ~ ( ~ proper_subset(B,A)
& A != B
& ~ proper_subset(A,B) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f39,negated_conjecture,
~ ! [A] :
( ordinal(A)
=> ! [B] :
( ordinal(B)
=> ~ ( ~ proper_subset(B,A)
& A != B
& ~ proper_subset(A,B) ) ) ),
inference(negated_conjecture,[status(cth)],[f38]) ).
fof(f65,plain,
! [A,B] :
( ordinal_subset(B,A)
| ordinal_subset(A,B)
| ~ ordinal(B)
| ~ ordinal(A) ),
inference(pre_NNF_transformation,[status(thm)],[f9]) ).
fof(f66,plain,
! [X0,X1] :
( ordinal_subset(X1,X0)
| ordinal_subset(X0,X1)
| ~ ordinal(X1)
| ~ ordinal(X0) ),
inference(cnf_transformation,[status(thm)],[f65]) ).
fof(f67,plain,
! [A,B] :
( ( A = B
| ~ subset(A,B)
| proper_subset(A,B) )
& ( ( A != B
& subset(A,B) )
| ~ proper_subset(A,B) ) ),
inference(NNF_transformation,[status(thm)],[f10]) ).
fof(f68,plain,
( ! [A,B] :
( A = B
| ~ subset(A,B)
| proper_subset(A,B) )
& ! [A,B] :
( ( A != B
& subset(A,B) )
| ~ proper_subset(A,B) ) ),
inference(miniscoping,[status(thm)],[f67]) ).
fof(f71,plain,
! [X0,X1] :
( X0 = X1
| ~ subset(X0,X1)
| proper_subset(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f68]) ).
fof(f143,plain,
! [A,B] :
( ( ordinal_subset(A,B)
<=> subset(A,B) )
| ~ ordinal(B)
| ~ ordinal(A) ),
inference(pre_NNF_transformation,[status(thm)],[f31]) ).
fof(f144,plain,
! [A,B] :
( ( ( ~ subset(A,B)
| ordinal_subset(A,B) )
& ( subset(A,B)
| ~ ordinal_subset(A,B) ) )
| ~ ordinal(B)
| ~ ordinal(A) ),
inference(NNF_transformation,[status(thm)],[f143]) ).
fof(f145,plain,
! [X0,X1] :
( subset(X0,X1)
| ~ ordinal_subset(X0,X1)
| ~ ordinal(X1)
| ~ ordinal(X0) ),
inference(cnf_transformation,[status(thm)],[f144]) ).
fof(f163,plain,
? [A] :
( ? [B] :
( ~ proper_subset(B,A)
& A != B
& ~ proper_subset(A,B)
& ordinal(B) )
& ordinal(A) ),
inference(pre_NNF_transformation,[status(thm)],[f39]) ).
fof(f164,plain,
( ~ proper_subset(sK16_skl,sK15_skl)
& sK15_skl != sK16_skl
& ~ proper_subset(sK15_skl,sK16_skl)
& ordinal(sK16_skl)
& ordinal(sK15_skl) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK15_skl,sK16_skl]),skolemize(A,sK15_skl),skolemize(B,sK16_skl)],[f163]) ).
fof(f165,plain,
ordinal(sK15_skl),
inference(cnf_transformation,[status(thm)],[f164]) ).
fof(f166,plain,
ordinal(sK16_skl),
inference(cnf_transformation,[status(thm)],[f164]) ).
fof(f167,plain,
~ proper_subset(sK15_skl,sK16_skl),
inference(cnf_transformation,[status(thm)],[f164]) ).
fof(f168,plain,
sK15_skl != sK16_skl,
inference(cnf_transformation,[status(thm)],[f164]) ).
fof(f169,plain,
~ proper_subset(sK16_skl,sK15_skl),
inference(cnf_transformation,[status(thm)],[f164]) ).
fof(f193,plain,
! [X0,X1] :
( X0 = X1
| proper_subset(X0,X1)
| ~ ordinal_subset(X0,X1)
| ~ ordinal(X1)
| ~ ordinal(X0) ),
inference(resolution,[status(thm)],[f145,f71]) ).
fof(f194,plain,
! [X0,X1] :
( ordinal_subset(X1,X0)
| ~ ordinal(X0)
| ~ ordinal(X1)
| X0 = X1
| proper_subset(X0,X1)
| ~ ordinal(X1)
| ~ ordinal(X0) ),
inference(resolution,[status(thm)],[f193,f66]) ).
fof(f195,plain,
! [X0,X1] :
( ordinal_subset(X1,X0)
| X0 = X1
| proper_subset(X0,X1)
| ~ ordinal(X1)
| ~ ordinal(X0) ),
inference(duplicate_literals_removal,[status(thm)],[f194]) ).
fof(f196,plain,
! [X0,X1] :
( X1 = X0
| proper_subset(X1,X0)
| ~ ordinal(X0)
| ~ ordinal(X1)
| X0 = X1
| proper_subset(X0,X1)
| ~ ordinal(X1)
| ~ ordinal(X0) ),
inference(resolution,[status(thm)],[f195,f193]) ).
fof(f197,plain,
! [X0,X1] :
( proper_subset(X1,X0)
| X0 = X1
| proper_subset(X0,X1)
| ~ ordinal(X1)
| ~ ordinal(X0) ),
inference(duplicate_literals_removal,[status(thm)],[f196]) ).
fof(f198,plain,
( sK15_skl = sK16_skl
| proper_subset(sK15_skl,sK16_skl)
| ~ ordinal(sK16_skl)
| ~ ordinal(sK15_skl) ),
inference(resolution,[status(thm)],[f197,f169]) ).
fof(f203,definition,
( sQ2_spl
<=> ordinal(sK15_skl) ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f205,plain,
( sQ2_spl
| ~ ordinal(sK15_skl) ),
inference(component_clause,[status(thm)],[f203]) ).
fof(f206,definition,
( sQ3_spl
<=> ordinal(sK16_skl) ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f208,plain,
( sQ3_spl
| ~ ordinal(sK16_skl) ),
inference(component_clause,[status(thm)],[f206]) ).
fof(f209,definition,
( sQ4_spl
<=> proper_subset(sK15_skl,sK16_skl) ),
introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition]) ).
fof(f210,plain,
( ~ sQ4_spl
| proper_subset(sK15_skl,sK16_skl) ),
inference(component_clause,[status(thm)],[f209]) ).
fof(f212,definition,
( sQ5_spl
<=> sK15_skl = sK16_skl ),
introduced(definition,[new_symbols(definition,[sQ5_spl])],[split_symbol_definition]) ).
fof(f213,plain,
( ~ sQ5_spl
| sK15_skl = sK16_skl ),
inference(component_clause,[status(thm)],[f212]) ).
fof(f215,plain,
( sQ5_spl
| sQ4_spl
| ~ sQ3_spl
| ~ sQ2_spl ),
inference(split_clause,[status(thm)],[f198,f203,f206,f209,f212]) ).
fof(f220,plain,
( ~ sQ5_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f213,f168]) ).
fof(f221,plain,
~ sQ5_spl,
inference(contradiction_clause,[status(thm)],[f220]) ).
fof(f222,plain,
( sQ2_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f205,f165]) ).
fof(f223,plain,
sQ2_spl,
inference(contradiction_clause,[status(thm)],[f222]) ).
fof(f224,plain,
( sQ3_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f208,f166]) ).
fof(f225,plain,
sQ3_spl,
inference(contradiction_clause,[status(thm)],[f224]) ).
fof(f226,plain,
( ~ sQ4_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f210,f167]) ).
fof(f227,plain,
~ sQ4_spl,
inference(contradiction_clause,[status(thm)],[f226]) ).
fof(f228,plain,
$false,
inference(sat_refutation,[status(thm)],[f215,f221,f223,f225,f227]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : NUM414+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.06 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.20/0.45 % Computer : n002.cluster.edu
% 0.20/0.45 % Model : x86_64 x86_64
% 0.20/0.45 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.20/0.45 % Memory : 8046.5625MB
% 0.20/0.45 % OS : Linux 6.8.0-71-generic
% 0.20/0.45 % CPULimit : 300
% 0.20/0.45 % WCLimit : 300
% 0.20/0.45 % DateTime : Mon Sep 21 02:30:31 UTC 2026
% 0.20/0.45 % CPUTime :
% 0.20/0.48 % Drodi V4.1.1
% 0.20/0.50 % Refutation found
% 0.20/0.50 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.20/0.50 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.26/0.59 % Elapsed time: 0.115548 seconds
% 0.26/0.59 % CPU time: 0.129856 seconds
% 0.26/0.59 % Total memory used: 15.636 MB
% 0.26/0.59 % Net memory used: 15.626 MB
%------------------------------------------------------------------------------