%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : TOP026+1 : TPTP v9.3.1. Released v3.4.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/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 03:53:25 PM UTC 2026
% Result : Theorem 0.15s 0.42s
% Output : CNFRefutation 0.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 12
% Syntax : Number of formulae : 54 ( 14 unt; 8 def)
% Number of atoms : 155 ( 8 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 162 ( 61 ~; 57 |; 21 &)
% ( 8 <=>; 15 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 4 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 16 ( 14 usr; 9 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 3 con; 0-3 aty)
% Number of variables : 30 ( 27 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,conjecture,
! [A] :
( ( l1_pre_topc(A)
& v2_pre_topc(A)
& ~ v3_struct_0(A) )
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
=> ( v1_tsp_2(B,A)
=> ! [C] :
( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
=> k6_pre_topc(A,C) = k3_tex_4(A,k5_subset_1(u1_struct_0(A),B,k6_pre_topc(A,C))) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f2,negated_conjecture,
~ ! [A] :
( ( l1_pre_topc(A)
& v2_pre_topc(A)
& ~ v3_struct_0(A) )
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
=> ( v1_tsp_2(B,A)
=> ! [C] :
( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
=> k6_pre_topc(A,C) = k3_tex_4(A,k5_subset_1(u1_struct_0(A),B,k6_pre_topc(A,C))) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
fof(f71,axiom,
! [A,B] :
( ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
& l1_pre_topc(A) )
=> m1_subset_1(k6_pre_topc(A,B),k1_zfmisc_1(u1_struct_0(A))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f76,axiom,
! [A,B] :
( ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
& l1_pre_topc(A)
& v2_pre_topc(A) )
=> v4_pre_topc(k6_pre_topc(A,B),A) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f79,axiom,
! [A] :
( ( l1_pre_topc(A)
& v2_pre_topc(A)
& ~ v3_struct_0(A) )
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
=> ( v1_tsp_2(B,A)
=> ! [C] :
( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
=> ( v4_pre_topc(C,A)
=> C = k3_tex_4(A,k5_subset_1(u1_struct_0(A),B,C)) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f80,plain,
? [A] :
( ? [B] :
( ? [C] :
( k6_pre_topc(A,C) != k3_tex_4(A,k5_subset_1(u1_struct_0(A),B,k6_pre_topc(A,C)))
& m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) )
& v1_tsp_2(B,A)
& m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
& l1_pre_topc(A)
& v2_pre_topc(A)
& ~ v3_struct_0(A) ),
inference(pre_NNF_transformation,[status(thm)],[f2]) ).
fof(f81,plain,
( k6_pre_topc(sK0_skl,sK2_skl) != k3_tex_4(sK0_skl,k5_subset_1(u1_struct_0(sK0_skl),sK1_skl,k6_pre_topc(sK0_skl,sK2_skl)))
& m1_subset_1(sK2_skl,k1_zfmisc_1(u1_struct_0(sK0_skl)))
& v1_tsp_2(sK1_skl,sK0_skl)
& m1_subset_1(sK1_skl,k1_zfmisc_1(u1_struct_0(sK0_skl)))
& l1_pre_topc(sK0_skl)
& v2_pre_topc(sK0_skl)
& ~ v3_struct_0(sK0_skl) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl,sK1_skl,sK2_skl]),skolemize(A,sK0_skl),skolemize(B,sK1_skl),skolemize(C,sK2_skl)],[f80]) ).
fof(f82,plain,
~ v3_struct_0(sK0_skl),
inference(cnf_transformation,[status(thm)],[f81]) ).
fof(f83,plain,
v2_pre_topc(sK0_skl),
inference(cnf_transformation,[status(thm)],[f81]) ).
fof(f84,plain,
l1_pre_topc(sK0_skl),
inference(cnf_transformation,[status(thm)],[f81]) ).
fof(f85,plain,
m1_subset_1(sK1_skl,k1_zfmisc_1(u1_struct_0(sK0_skl))),
inference(cnf_transformation,[status(thm)],[f81]) ).
fof(f86,plain,
v1_tsp_2(sK1_skl,sK0_skl),
inference(cnf_transformation,[status(thm)],[f81]) ).
fof(f87,plain,
m1_subset_1(sK2_skl,k1_zfmisc_1(u1_struct_0(sK0_skl))),
inference(cnf_transformation,[status(thm)],[f81]) ).
fof(f88,plain,
k6_pre_topc(sK0_skl,sK2_skl) != k3_tex_4(sK0_skl,k5_subset_1(u1_struct_0(sK0_skl),sK1_skl,k6_pre_topc(sK0_skl,sK2_skl))),
inference(cnf_transformation,[status(thm)],[f81]) ).
fof(f331,plain,
! [A,B] :
( m1_subset_1(k6_pre_topc(A,B),k1_zfmisc_1(u1_struct_0(A)))
| ~ m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
| ~ l1_pre_topc(A) ),
inference(pre_NNF_transformation,[status(thm)],[f71]) ).
fof(f332,plain,
! [X0,X1] :
( m1_subset_1(k6_pre_topc(X0,X1),k1_zfmisc_1(u1_struct_0(X0)))
| ~ m1_subset_1(X1,k1_zfmisc_1(u1_struct_0(X0)))
| ~ l1_pre_topc(X0) ),
inference(cnf_transformation,[status(thm)],[f331]) ).
fof(f336,plain,
! [A,B] :
( v4_pre_topc(k6_pre_topc(A,B),A)
| ~ m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
| ~ l1_pre_topc(A)
| ~ v2_pre_topc(A) ),
inference(pre_NNF_transformation,[status(thm)],[f76]) ).
fof(f337,plain,
! [X0,X1] :
( v4_pre_topc(k6_pre_topc(X0,X1),X0)
| ~ m1_subset_1(X1,k1_zfmisc_1(u1_struct_0(X0)))
| ~ l1_pre_topc(X0)
| ~ v2_pre_topc(X0) ),
inference(cnf_transformation,[status(thm)],[f336]) ).
fof(f346,plain,
! [A] :
( ! [B] :
( ! [C] :
( C = k3_tex_4(A,k5_subset_1(u1_struct_0(A),B,C))
| ~ v4_pre_topc(C,A)
| ~ m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) )
| ~ v1_tsp_2(B,A)
| ~ m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
| ~ l1_pre_topc(A)
| ~ v2_pre_topc(A)
| v3_struct_0(A) ),
inference(pre_NNF_transformation,[status(thm)],[f79]) ).
fof(f347,plain,
! [X0,X1,X2] :
( X2 = k3_tex_4(X0,k5_subset_1(u1_struct_0(X0),X1,X2))
| ~ v4_pre_topc(X2,X0)
| ~ m1_subset_1(X2,k1_zfmisc_1(u1_struct_0(X0)))
| ~ v1_tsp_2(X1,X0)
| ~ m1_subset_1(X1,k1_zfmisc_1(u1_struct_0(X0)))
| ~ l1_pre_topc(X0)
| ~ v2_pre_topc(X0)
| v3_struct_0(X0) ),
inference(cnf_transformation,[status(thm)],[f346]) ).
fof(f348,plain,
( v4_pre_topc(k6_pre_topc(sK0_skl,sK2_skl),sK0_skl)
| ~ l1_pre_topc(sK0_skl)
| ~ v2_pre_topc(sK0_skl) ),
inference(resolution,[status(thm)],[f337,f87]) ).
fof(f350,definition,
( sQ0_spl
<=> v2_pre_topc(sK0_skl) ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f352,plain,
( sQ0_spl
| ~ v2_pre_topc(sK0_skl) ),
inference(component_clause,[status(thm)],[f350]) ).
fof(f353,definition,
( sQ1_spl
<=> l1_pre_topc(sK0_skl) ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f355,plain,
( sQ1_spl
| ~ l1_pre_topc(sK0_skl) ),
inference(component_clause,[status(thm)],[f353]) ).
fof(f356,definition,
( sQ2_spl
<=> v4_pre_topc(k6_pre_topc(sK0_skl,sK2_skl),sK0_skl) ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f359,plain,
( sQ2_spl
| ~ sQ1_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f348,f350,f353,f356]) ).
fof(f364,plain,
( sQ1_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f355,f84]) ).
fof(f365,plain,
sQ1_spl,
inference(contradiction_clause,[status(thm)],[f364]) ).
fof(f366,plain,
( sQ0_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f352,f83]) ).
fof(f367,plain,
sQ0_spl,
inference(contradiction_clause,[status(thm)],[f366]) ).
fof(f373,plain,
( ~ v4_pre_topc(k6_pre_topc(sK0_skl,sK2_skl),sK0_skl)
| ~ m1_subset_1(k6_pre_topc(sK0_skl,sK2_skl),k1_zfmisc_1(u1_struct_0(sK0_skl)))
| ~ v1_tsp_2(sK1_skl,sK0_skl)
| ~ m1_subset_1(sK1_skl,k1_zfmisc_1(u1_struct_0(sK0_skl)))
| ~ l1_pre_topc(sK0_skl)
| ~ v2_pre_topc(sK0_skl)
| v3_struct_0(sK0_skl) ),
inference(resolution,[status(thm)],[f347,f88]) ).
fof(f374,definition,
( sQ4_spl
<=> v3_struct_0(sK0_skl) ),
introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition]) ).
fof(f375,plain,
( ~ sQ4_spl
| v3_struct_0(sK0_skl) ),
inference(component_clause,[status(thm)],[f374]) ).
fof(f377,definition,
( sQ5_spl
<=> m1_subset_1(sK1_skl,k1_zfmisc_1(u1_struct_0(sK0_skl))) ),
introduced(definition,[new_symbols(definition,[sQ5_spl])],[split_symbol_definition]) ).
fof(f379,plain,
( sQ5_spl
| ~ m1_subset_1(sK1_skl,k1_zfmisc_1(u1_struct_0(sK0_skl))) ),
inference(component_clause,[status(thm)],[f377]) ).
fof(f380,definition,
( sQ6_spl
<=> v1_tsp_2(sK1_skl,sK0_skl) ),
introduced(definition,[new_symbols(definition,[sQ6_spl])],[split_symbol_definition]) ).
fof(f382,plain,
( sQ6_spl
| ~ v1_tsp_2(sK1_skl,sK0_skl) ),
inference(component_clause,[status(thm)],[f380]) ).
fof(f383,definition,
( sQ7_spl
<=> m1_subset_1(k6_pre_topc(sK0_skl,sK2_skl),k1_zfmisc_1(u1_struct_0(sK0_skl))) ),
introduced(definition,[new_symbols(definition,[sQ7_spl])],[split_symbol_definition]) ).
fof(f385,plain,
( sQ7_spl
| ~ m1_subset_1(k6_pre_topc(sK0_skl,sK2_skl),k1_zfmisc_1(u1_struct_0(sK0_skl))) ),
inference(component_clause,[status(thm)],[f383]) ).
fof(f386,plain,
( ~ sQ2_spl
| ~ sQ7_spl
| ~ sQ6_spl
| ~ sQ5_spl
| ~ sQ1_spl
| ~ sQ0_spl
| sQ4_spl ),
inference(split_clause,[status(thm)],[f373,f374,f350,f353,f377,f380,f383,f356]) ).
fof(f413,plain,
( sQ7_spl
| ~ m1_subset_1(sK2_skl,k1_zfmisc_1(u1_struct_0(sK0_skl)))
| ~ l1_pre_topc(sK0_skl) ),
inference(resolution,[status(thm)],[f385,f332]) ).
fof(f414,definition,
( sQ12_spl
<=> m1_subset_1(sK2_skl,k1_zfmisc_1(u1_struct_0(sK0_skl))) ),
introduced(definition,[new_symbols(definition,[sQ12_spl])],[split_symbol_definition]) ).
fof(f416,plain,
( sQ12_spl
| ~ m1_subset_1(sK2_skl,k1_zfmisc_1(u1_struct_0(sK0_skl))) ),
inference(component_clause,[status(thm)],[f414]) ).
fof(f417,plain,
( sQ7_spl
| ~ sQ12_spl
| ~ sQ1_spl ),
inference(split_clause,[status(thm)],[f413,f353,f414,f383]) ).
fof(f418,plain,
( sQ12_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f416,f87]) ).
fof(f419,plain,
sQ12_spl,
inference(contradiction_clause,[status(thm)],[f418]) ).
fof(f420,plain,
( sQ6_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f382,f86]) ).
fof(f421,plain,
sQ6_spl,
inference(contradiction_clause,[status(thm)],[f420]) ).
fof(f422,plain,
( ~ sQ4_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f375,f82]) ).
fof(f423,plain,
~ sQ4_spl,
inference(contradiction_clause,[status(thm)],[f422]) ).
fof(f424,plain,
( sQ5_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f379,f85]) ).
fof(f425,plain,
sQ5_spl,
inference(contradiction_clause,[status(thm)],[f424]) ).
fof(f426,plain,
$false,
inference(sat_refutation,[status(thm)],[f359,f365,f367,f386,f417,f419,f421,f423,f425]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : TOP026+1 : TPTP v9.3.1. Released v3.4.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.37 % Computer : n002.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Mon Sep 21 12:42:46 UTC 2026
% 0.15/0.37 % CPUTime :
% 0.15/0.38 % Drodi V4.1.1
% 0.15/0.42 % Refutation found
% 0.15/0.42 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.15/0.42 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.15/0.44 % Elapsed time: 0.064721 seconds
% 0.15/0.44 % CPU time: 0.164727 seconds
% 0.15/0.44 % Total memory used: 108.317 MB
% 0.15/0.44 % Net memory used: 108.206 MB
%------------------------------------------------------------------------------