%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : GRP623+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 : n017.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 12:34:50 PM UTC 2026
% Result : Theorem 3.35s 0.84s
% Output : CNFRefutation 3.35s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 26
% Syntax : Number of formulae : 115 ( 15 unt; 15 def)
% Number of atoms : 356 ( 0 equ)
% Maximal formula atoms : 8 ( 3 avg)
% Number of connectives : 386 ( 145 ~; 166 |; 43 &)
% ( 19 <=>; 13 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 29 ( 28 usr; 16 prp; 0-4 aty)
% Number of functors : 5 ( 5 usr; 1 con; 0-2 aty)
% Number of variables : 110 ( 107 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,conjecture,
! [A] :
( ( l1_group_1(A)
& v4_group_1(A)
& v3_group_1(A)
& v1_group_1(A)
& ~ v3_struct_0(A) )
=> r1_tarski(k4_autgroup(A),k1_autgroup(A)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f2,negated_conjecture,
~ ! [A] :
( ( l1_group_1(A)
& v4_group_1(A)
& v3_group_1(A)
& v1_group_1(A)
& ~ v3_struct_0(A) )
=> r1_tarski(k4_autgroup(A),k1_autgroup(A)) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
fof(f13,axiom,
! [A,B] :
( r1_tarski(A,B)
<=> ! [C] :
( r2_hidden(C,A)
=> r2_hidden(C,B) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f15,axiom,
! [A] :
( ( l1_group_1(A)
& v4_group_1(A)
& v3_group_1(A)
& v1_group_1(A)
& ~ v3_struct_0(A) )
=> m1_fraenkel(k1_autgroup(A),u1_struct_0(A),u1_struct_0(A)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f19,axiom,
! [A] :
( ( l1_group_1(A)
& v4_group_1(A)
& v3_group_1(A)
& v1_group_1(A)
& ~ v3_struct_0(A) )
=> m1_fraenkel(k4_autgroup(A),u1_struct_0(A),u1_struct_0(A)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f20,axiom,
! [A] :
( l1_group_1(A)
=> l1_struct_0(A) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f22,axiom,
! [A,B,C] :
( m1_fraenkel(C,A,B)
=> ( v1_fraenkel(C)
& ~ v1_xboole_0(C) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f37,axiom,
! [A] :
( ( l1_struct_0(A)
& ~ v3_struct_0(A) )
=> ~ v1_xboole_0(u1_struct_0(A)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f54,axiom,
! [A,B,C] :
( ( m1_fraenkel(C,A,B)
& ~ v1_xboole_0(B) )
=> ! [D] :
( m2_fraenkel(D,A,B,C)
<=> m1_subset_1(D,C) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f57,axiom,
! [A] :
( ( l1_group_1(A)
& v4_group_1(A)
& v3_group_1(A)
& v1_group_1(A)
& ~ v3_struct_0(A) )
=> ! [B] :
( m2_fraenkel(B,u1_struct_0(A),u1_struct_0(A),k4_autgroup(A))
=> m2_fraenkel(B,u1_struct_0(A),u1_struct_0(A),k1_autgroup(A)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f58,axiom,
! [A,B] :
( r2_hidden(A,B)
=> m1_subset_1(A,B) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f59,axiom,
! [A,B] :
( m1_subset_1(A,B)
=> ( r2_hidden(A,B)
| v1_xboole_0(B) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f66,plain,
? [A] :
( ~ r1_tarski(k4_autgroup(A),k1_autgroup(A))
& l1_group_1(A)
& v4_group_1(A)
& v3_group_1(A)
& v1_group_1(A)
& ~ v3_struct_0(A) ),
inference(pre_NNF_transformation,[status(thm)],[f2]) ).
fof(f67,plain,
( ~ r1_tarski(k4_autgroup(sK0_skl),k1_autgroup(sK0_skl))
& l1_group_1(sK0_skl)
& v4_group_1(sK0_skl)
& v3_group_1(sK0_skl)
& v1_group_1(sK0_skl)
& ~ v3_struct_0(sK0_skl) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl]),skolemize(A,sK0_skl)],[f66]) ).
fof(f68,plain,
~ v3_struct_0(sK0_skl),
inference(cnf_transformation,[status(thm)],[f67]) ).
fof(f69,plain,
v1_group_1(sK0_skl),
inference(cnf_transformation,[status(thm)],[f67]) ).
fof(f70,plain,
v3_group_1(sK0_skl),
inference(cnf_transformation,[status(thm)],[f67]) ).
fof(f71,plain,
v4_group_1(sK0_skl),
inference(cnf_transformation,[status(thm)],[f67]) ).
fof(f72,plain,
l1_group_1(sK0_skl),
inference(cnf_transformation,[status(thm)],[f67]) ).
fof(f73,plain,
~ r1_tarski(k4_autgroup(sK0_skl),k1_autgroup(sK0_skl)),
inference(cnf_transformation,[status(thm)],[f67]) ).
fof(f106,plain,
! [A,B] :
( r1_tarski(A,B)
<=> ! [C] :
( r2_hidden(C,B)
| ~ r2_hidden(C,A) ) ),
inference(pre_NNF_transformation,[status(thm)],[f13]) ).
fof(f107,plain,
! [A,B] :
( ( ? [C] :
( ~ r2_hidden(C,B)
& r2_hidden(C,A) )
| r1_tarski(A,B) )
& ( ! [C] :
( r2_hidden(C,B)
| ~ r2_hidden(C,A) )
| ~ r1_tarski(A,B) ) ),
inference(NNF_transformation,[status(thm)],[f106]) ).
fof(f108,plain,
( ! [A,B] :
( ? [C] :
( ~ r2_hidden(C,B)
& r2_hidden(C,A) )
| r1_tarski(A,B) )
& ! [A,B] :
( ! [C] :
( r2_hidden(C,B)
| ~ r2_hidden(C,A) )
| ~ r1_tarski(A,B) ) ),
inference(miniscoping,[status(thm)],[f107]) ).
fof(f109,plain,
( ! [A,B] :
( ( ~ r2_hidden(sK1_skl(B,A),B)
& r2_hidden(sK1_skl(B,A),A) )
| r1_tarski(A,B) )
& ! [A,B] :
( ! [C] :
( r2_hidden(C,B)
| ~ r2_hidden(C,A) )
| ~ r1_tarski(A,B) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1_skl]),skolemize(C,sK1_skl(B,A))],[f108]) ).
fof(f111,plain,
! [X0,X1] :
( r2_hidden(sK1_skl(X1,X0),X0)
| r1_tarski(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f109]) ).
fof(f112,plain,
! [X0,X1] :
( ~ r2_hidden(sK1_skl(X1,X0),X1)
| r1_tarski(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f109]) ).
fof(f116,plain,
! [A] :
( m1_fraenkel(k1_autgroup(A),u1_struct_0(A),u1_struct_0(A))
| ~ l1_group_1(A)
| ~ v4_group_1(A)
| ~ v3_group_1(A)
| ~ v1_group_1(A)
| v3_struct_0(A) ),
inference(pre_NNF_transformation,[status(thm)],[f15]) ).
fof(f117,plain,
! [X0] :
( m1_fraenkel(k1_autgroup(X0),u1_struct_0(X0),u1_struct_0(X0))
| ~ l1_group_1(X0)
| ~ v4_group_1(X0)
| ~ v3_group_1(X0)
| ~ v1_group_1(X0)
| v3_struct_0(X0) ),
inference(cnf_transformation,[status(thm)],[f116]) ).
fof(f118,plain,
! [A] :
( m1_fraenkel(k4_autgroup(A),u1_struct_0(A),u1_struct_0(A))
| ~ l1_group_1(A)
| ~ v4_group_1(A)
| ~ v3_group_1(A)
| ~ v1_group_1(A)
| v3_struct_0(A) ),
inference(pre_NNF_transformation,[status(thm)],[f19]) ).
fof(f119,plain,
! [X0] :
( m1_fraenkel(k4_autgroup(X0),u1_struct_0(X0),u1_struct_0(X0))
| ~ l1_group_1(X0)
| ~ v4_group_1(X0)
| ~ v3_group_1(X0)
| ~ v1_group_1(X0)
| v3_struct_0(X0) ),
inference(cnf_transformation,[status(thm)],[f118]) ).
fof(f120,plain,
! [A] :
( l1_struct_0(A)
| ~ l1_group_1(A) ),
inference(pre_NNF_transformation,[status(thm)],[f20]) ).
fof(f121,plain,
! [X0] :
( l1_struct_0(X0)
| ~ l1_group_1(X0) ),
inference(cnf_transformation,[status(thm)],[f120]) ).
fof(f122,plain,
! [A,B,C] :
( ( v1_fraenkel(C)
& ~ v1_xboole_0(C) )
| ~ m1_fraenkel(C,A,B) ),
inference(pre_NNF_transformation,[status(thm)],[f22]) ).
fof(f123,plain,
! [C] :
( ( v1_fraenkel(C)
& ~ v1_xboole_0(C) )
| ! [A,B] : ~ m1_fraenkel(C,A,B) ),
inference(miniscoping,[status(thm)],[f122]) ).
fof(f124,plain,
! [X0,X1,X2] :
( ~ v1_xboole_0(X0)
| ~ m1_fraenkel(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f123]) ).
fof(f154,plain,
! [A] :
( ~ v1_xboole_0(u1_struct_0(A))
| ~ l1_struct_0(A)
| v3_struct_0(A) ),
inference(pre_NNF_transformation,[status(thm)],[f37]) ).
fof(f155,plain,
! [X0] :
( ~ v1_xboole_0(u1_struct_0(X0))
| ~ l1_struct_0(X0)
| v3_struct_0(X0) ),
inference(cnf_transformation,[status(thm)],[f154]) ).
fof(f213,plain,
! [A,B,C] :
( ! [D] :
( m2_fraenkel(D,A,B,C)
<=> m1_subset_1(D,C) )
| ~ m1_fraenkel(C,A,B)
| v1_xboole_0(B) ),
inference(pre_NNF_transformation,[status(thm)],[f54]) ).
fof(f214,plain,
! [A,B,C] :
( ! [D] :
( ( ~ m1_subset_1(D,C)
| m2_fraenkel(D,A,B,C) )
& ( m1_subset_1(D,C)
| ~ m2_fraenkel(D,A,B,C) ) )
| ~ m1_fraenkel(C,A,B)
| v1_xboole_0(B) ),
inference(NNF_transformation,[status(thm)],[f213]) ).
fof(f215,plain,
! [A,B,C] :
( ( ! [D] :
( ~ m1_subset_1(D,C)
| m2_fraenkel(D,A,B,C) )
& ! [D] :
( m1_subset_1(D,C)
| ~ m2_fraenkel(D,A,B,C) ) )
| ~ m1_fraenkel(C,A,B)
| v1_xboole_0(B) ),
inference(miniscoping,[status(thm)],[f214]) ).
fof(f216,plain,
! [X0,X1,X2,X3] :
( m1_subset_1(X3,X1)
| ~ m2_fraenkel(X3,X2,X0,X1)
| ~ m1_fraenkel(X1,X2,X0)
| v1_xboole_0(X0) ),
inference(cnf_transformation,[status(thm)],[f215]) ).
fof(f217,plain,
! [X0,X1,X2,X3] :
( ~ m1_subset_1(X3,X1)
| m2_fraenkel(X3,X2,X0,X1)
| ~ m1_fraenkel(X1,X2,X0)
| v1_xboole_0(X0) ),
inference(cnf_transformation,[status(thm)],[f215]) ).
fof(f224,plain,
! [A] :
( ! [B] :
( m2_fraenkel(B,u1_struct_0(A),u1_struct_0(A),k1_autgroup(A))
| ~ m2_fraenkel(B,u1_struct_0(A),u1_struct_0(A),k4_autgroup(A)) )
| ~ l1_group_1(A)
| ~ v4_group_1(A)
| ~ v3_group_1(A)
| ~ v1_group_1(A)
| v3_struct_0(A) ),
inference(pre_NNF_transformation,[status(thm)],[f57]) ).
fof(f225,plain,
! [X0,X1] :
( m2_fraenkel(X1,u1_struct_0(X0),u1_struct_0(X0),k1_autgroup(X0))
| ~ m2_fraenkel(X1,u1_struct_0(X0),u1_struct_0(X0),k4_autgroup(X0))
| ~ l1_group_1(X0)
| ~ v4_group_1(X0)
| ~ v3_group_1(X0)
| ~ v1_group_1(X0)
| v3_struct_0(X0) ),
inference(cnf_transformation,[status(thm)],[f224]) ).
fof(f226,plain,
! [A,B] :
( m1_subset_1(A,B)
| ~ r2_hidden(A,B) ),
inference(pre_NNF_transformation,[status(thm)],[f58]) ).
fof(f227,plain,
! [X0,X1] :
( m1_subset_1(X0,X1)
| ~ r2_hidden(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f226]) ).
fof(f228,plain,
! [A,B] :
( r2_hidden(A,B)
| v1_xboole_0(B)
| ~ m1_subset_1(A,B) ),
inference(pre_NNF_transformation,[status(thm)],[f59]) ).
fof(f229,plain,
! [X0,X1] :
( r2_hidden(X0,X1)
| v1_xboole_0(X1)
| ~ m1_subset_1(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f228]) ).
fof(f250,plain,
( m1_fraenkel(k1_autgroup(sK0_skl),u1_struct_0(sK0_skl),u1_struct_0(sK0_skl))
| ~ l1_group_1(sK0_skl)
| ~ v4_group_1(sK0_skl)
| ~ v3_group_1(sK0_skl)
| v3_struct_0(sK0_skl) ),
inference(resolution,[status(thm)],[f117,f69]) ).
fof(f251,definition,
( sQ0_spl
<=> v3_struct_0(sK0_skl) ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f252,plain,
( ~ sQ0_spl
| v3_struct_0(sK0_skl) ),
inference(component_clause,[status(thm)],[f251]) ).
fof(f254,definition,
( sQ1_spl
<=> v3_group_1(sK0_skl) ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f256,plain,
( sQ1_spl
| ~ v3_group_1(sK0_skl) ),
inference(component_clause,[status(thm)],[f254]) ).
fof(f257,definition,
( sQ2_spl
<=> v4_group_1(sK0_skl) ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f259,plain,
( sQ2_spl
| ~ v4_group_1(sK0_skl) ),
inference(component_clause,[status(thm)],[f257]) ).
fof(f260,definition,
( sQ3_spl
<=> l1_group_1(sK0_skl) ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f262,plain,
( sQ3_spl
| ~ l1_group_1(sK0_skl) ),
inference(component_clause,[status(thm)],[f260]) ).
fof(f263,definition,
( sQ4_spl
<=> m1_fraenkel(k1_autgroup(sK0_skl),u1_struct_0(sK0_skl),u1_struct_0(sK0_skl)) ),
introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition]) ).
fof(f264,plain,
( ~ sQ4_spl
| m1_fraenkel(k1_autgroup(sK0_skl),u1_struct_0(sK0_skl),u1_struct_0(sK0_skl)) ),
inference(component_clause,[status(thm)],[f263]) ).
fof(f266,plain,
( sQ4_spl
| ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ1_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f250,f251,f254,f257,f260,f263]) ).
fof(f267,plain,
( m1_fraenkel(k4_autgroup(sK0_skl),u1_struct_0(sK0_skl),u1_struct_0(sK0_skl))
| ~ l1_group_1(sK0_skl)
| ~ v4_group_1(sK0_skl)
| ~ v3_group_1(sK0_skl)
| v3_struct_0(sK0_skl) ),
inference(resolution,[status(thm)],[f119,f69]) ).
fof(f268,definition,
( sQ5_spl
<=> m1_fraenkel(k4_autgroup(sK0_skl),u1_struct_0(sK0_skl),u1_struct_0(sK0_skl)) ),
introduced(definition,[new_symbols(definition,[sQ5_spl])],[split_symbol_definition]) ).
fof(f269,plain,
( ~ sQ5_spl
| m1_fraenkel(k4_autgroup(sK0_skl),u1_struct_0(sK0_skl),u1_struct_0(sK0_skl)) ),
inference(component_clause,[status(thm)],[f268]) ).
fof(f271,plain,
( sQ5_spl
| ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ1_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f267,f251,f254,f257,f260,f268]) ).
fof(f272,plain,
( sQ3_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f262,f72]) ).
fof(f273,plain,
sQ3_spl,
inference(contradiction_clause,[status(thm)],[f272]) ).
fof(f274,plain,
( sQ2_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f259,f71]) ).
fof(f275,plain,
sQ2_spl,
inference(contradiction_clause,[status(thm)],[f274]) ).
fof(f276,plain,
( sQ1_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f256,f70]) ).
fof(f277,plain,
sQ1_spl,
inference(contradiction_clause,[status(thm)],[f276]) ).
fof(f278,plain,
( ~ sQ0_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f252,f68]) ).
fof(f279,plain,
~ sQ0_spl,
inference(contradiction_clause,[status(thm)],[f278]) ).
fof(f350,plain,
l1_struct_0(sK0_skl),
inference(resolution,[status(thm)],[f121,f72]) ).
fof(f352,plain,
( ~ sQ4_spl
| ~ v1_xboole_0(k1_autgroup(sK0_skl)) ),
inference(resolution,[status(thm)],[f124,f264]) ).
fof(f390,definition,
( sQ21_spl
<=> v1_xboole_0(u1_struct_0(sK0_skl)) ),
introduced(definition,[new_symbols(definition,[sQ21_spl])],[split_symbol_definition]) ).
fof(f391,plain,
( ~ sQ21_spl
| v1_xboole_0(u1_struct_0(sK0_skl)) ),
inference(component_clause,[status(thm)],[f390]) ).
fof(f437,plain,
( ~ sQ21_spl
| ~ l1_struct_0(sK0_skl)
| v3_struct_0(sK0_skl) ),
inference(resolution,[status(thm)],[f155,f391]) ).
fof(f438,definition,
( sQ29_spl
<=> l1_struct_0(sK0_skl) ),
introduced(definition,[new_symbols(definition,[sQ29_spl])],[split_symbol_definition]) ).
fof(f440,plain,
( sQ29_spl
| ~ l1_struct_0(sK0_skl) ),
inference(component_clause,[status(thm)],[f438]) ).
fof(f441,plain,
( ~ sQ21_spl
| ~ sQ29_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f437,f251,f438,f390]) ).
fof(f442,plain,
( sQ29_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f440,f350]) ).
fof(f443,plain,
sQ29_spl,
inference(contradiction_clause,[status(thm)],[f442]) ).
fof(f471,definition,
( sQ34_spl
<=> v1_group_1(sK0_skl) ),
introduced(definition,[new_symbols(definition,[sQ34_spl])],[split_symbol_definition]) ).
fof(f473,plain,
( sQ34_spl
| ~ v1_group_1(sK0_skl) ),
inference(component_clause,[status(thm)],[f471]) ).
fof(f490,plain,
( sQ34_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f473,f69]) ).
fof(f491,plain,
sQ34_spl,
inference(contradiction_clause,[status(thm)],[f490]) ).
fof(f731,plain,
! [X0] :
( ~ sQ5_spl
| ~ m1_subset_1(X0,k4_autgroup(sK0_skl))
| m2_fraenkel(X0,u1_struct_0(sK0_skl),u1_struct_0(sK0_skl),k4_autgroup(sK0_skl))
| v1_xboole_0(u1_struct_0(sK0_skl)) ),
inference(resolution,[status(thm)],[f217,f269]) ).
fof(f738,definition,
! [X0] :
( sQ78_spl
<=> ( ~ m1_subset_1(X0,k4_autgroup(sK0_skl))
| m2_fraenkel(X0,u1_struct_0(sK0_skl),u1_struct_0(sK0_skl),k4_autgroup(sK0_skl)) ) ),
introduced(definition,[new_symbols(definition,[sQ78_spl])],[split_symbol_definition]) ).
fof(f739,plain,
! [X0] :
( ~ sQ78_spl
| ~ m1_subset_1(X0,k4_autgroup(sK0_skl))
| m2_fraenkel(X0,u1_struct_0(sK0_skl),u1_struct_0(sK0_skl),k4_autgroup(sK0_skl)) ),
inference(component_clause,[status(thm)],[f738]) ).
fof(f741,plain,
( ~ sQ5_spl
| sQ78_spl
| sQ21_spl ),
inference(split_clause,[status(thm)],[f731,f390,f738,f268]) ).
fof(f831,plain,
! [X0,X1] :
( r1_tarski(X1,X0)
| m1_subset_1(sK1_skl(X0,X1),X1) ),
inference(resolution,[status(thm)],[f227,f111]) ).
fof(f1044,definition,
( sQ127_spl
<=> v1_xboole_0(k1_autgroup(sK0_skl)) ),
introduced(definition,[new_symbols(definition,[sQ127_spl])],[split_symbol_definition]) ).
fof(f1045,plain,
( ~ sQ127_spl
| v1_xboole_0(k1_autgroup(sK0_skl)) ),
inference(component_clause,[status(thm)],[f1044]) ).
fof(f1058,plain,
( ~ sQ127_spl
| ~ sQ4_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1045,f352]) ).
fof(f1059,plain,
( ~ sQ127_spl
| ~ sQ4_spl ),
inference(contradiction_clause,[status(thm)],[f1058]) ).
fof(f2098,plain,
! [X0] :
( ~ sQ78_spl
| r1_tarski(k4_autgroup(sK0_skl),X0)
| m2_fraenkel(sK1_skl(X0,k4_autgroup(sK0_skl)),u1_struct_0(sK0_skl),u1_struct_0(sK0_skl),k4_autgroup(sK0_skl)) ),
inference(resolution,[status(thm)],[f739,f831]) ).
fof(f2172,plain,
! [X0] :
( ~ sQ78_spl
| m2_fraenkel(sK1_skl(X0,k4_autgroup(sK0_skl)),u1_struct_0(sK0_skl),u1_struct_0(sK0_skl),k1_autgroup(sK0_skl))
| ~ l1_group_1(sK0_skl)
| ~ v4_group_1(sK0_skl)
| ~ v3_group_1(sK0_skl)
| ~ v1_group_1(sK0_skl)
| v3_struct_0(sK0_skl)
| r1_tarski(k4_autgroup(sK0_skl),X0) ),
inference(resolution,[status(thm)],[f2098,f225]) ).
fof(f2177,definition,
! [X0] :
( sQ225_spl
<=> ( m2_fraenkel(sK1_skl(X0,k4_autgroup(sK0_skl)),u1_struct_0(sK0_skl),u1_struct_0(sK0_skl),k1_autgroup(sK0_skl))
| r1_tarski(k4_autgroup(sK0_skl),X0) ) ),
introduced(definition,[new_symbols(definition,[sQ225_spl])],[split_symbol_definition]) ).
fof(f2178,plain,
! [X0] :
( ~ sQ225_spl
| m2_fraenkel(sK1_skl(X0,k4_autgroup(sK0_skl)),u1_struct_0(sK0_skl),u1_struct_0(sK0_skl),k1_autgroup(sK0_skl))
| r1_tarski(k4_autgroup(sK0_skl),X0) ),
inference(component_clause,[status(thm)],[f2177]) ).
fof(f2180,plain,
( ~ sQ78_spl
| ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ1_spl
| ~ sQ34_spl
| sQ0_spl
| sQ225_spl ),
inference(split_clause,[status(thm)],[f2172,f2177,f251,f471,f254,f257,f260,f738]) ).
fof(f2326,plain,
! [X0] :
( ~ sQ225_spl
| m1_subset_1(sK1_skl(X0,k4_autgroup(sK0_skl)),k1_autgroup(sK0_skl))
| ~ m1_fraenkel(k1_autgroup(sK0_skl),u1_struct_0(sK0_skl),u1_struct_0(sK0_skl))
| v1_xboole_0(u1_struct_0(sK0_skl))
| r1_tarski(k4_autgroup(sK0_skl),X0) ),
inference(resolution,[status(thm)],[f2178,f216]) ).
fof(f2330,definition,
! [X0] :
( sQ248_spl
<=> ( m1_subset_1(sK1_skl(X0,k4_autgroup(sK0_skl)),k1_autgroup(sK0_skl))
| r1_tarski(k4_autgroup(sK0_skl),X0) ) ),
introduced(definition,[new_symbols(definition,[sQ248_spl])],[split_symbol_definition]) ).
fof(f2331,plain,
! [X0] :
( ~ sQ248_spl
| m1_subset_1(sK1_skl(X0,k4_autgroup(sK0_skl)),k1_autgroup(sK0_skl))
| r1_tarski(k4_autgroup(sK0_skl),X0) ),
inference(component_clause,[status(thm)],[f2330]) ).
fof(f2333,plain,
( ~ sQ225_spl
| ~ sQ4_spl
| sQ21_spl
| sQ248_spl ),
inference(split_clause,[status(thm)],[f2326,f2330,f390,f263,f2177]) ).
fof(f2339,plain,
! [X0] :
( ~ sQ248_spl
| r2_hidden(sK1_skl(X0,k4_autgroup(sK0_skl)),k1_autgroup(sK0_skl))
| v1_xboole_0(k1_autgroup(sK0_skl))
| r1_tarski(k4_autgroup(sK0_skl),X0) ),
inference(resolution,[status(thm)],[f2331,f229]) ).
fof(f2342,definition,
! [X0] :
( sQ249_spl
<=> ( r2_hidden(sK1_skl(X0,k4_autgroup(sK0_skl)),k1_autgroup(sK0_skl))
| r1_tarski(k4_autgroup(sK0_skl),X0) ) ),
introduced(definition,[new_symbols(definition,[sQ249_spl])],[split_symbol_definition]) ).
fof(f2343,plain,
! [X0] :
( ~ sQ249_spl
| r2_hidden(sK1_skl(X0,k4_autgroup(sK0_skl)),k1_autgroup(sK0_skl))
| r1_tarski(k4_autgroup(sK0_skl),X0) ),
inference(component_clause,[status(thm)],[f2342]) ).
fof(f2345,plain,
( ~ sQ248_spl
| sQ127_spl
| sQ249_spl ),
inference(split_clause,[status(thm)],[f2339,f2342,f1044,f2330]) ).
fof(f2883,plain,
( ~ sQ249_spl
| r1_tarski(k4_autgroup(sK0_skl),k1_autgroup(sK0_skl))
| r1_tarski(k4_autgroup(sK0_skl),k1_autgroup(sK0_skl)) ),
inference(resolution,[status(thm)],[f2343,f112]) ).
fof(f2888,definition,
( sQ294_spl
<=> r1_tarski(k4_autgroup(sK0_skl),k1_autgroup(sK0_skl)) ),
introduced(definition,[new_symbols(definition,[sQ294_spl])],[split_symbol_definition]) ).
fof(f2889,plain,
( ~ sQ294_spl
| r1_tarski(k4_autgroup(sK0_skl),k1_autgroup(sK0_skl)) ),
inference(component_clause,[status(thm)],[f2888]) ).
fof(f2891,plain,
( ~ sQ249_spl
| sQ294_spl ),
inference(split_clause,[status(thm)],[f2883,f2888,f2342]) ).
fof(f2902,plain,
( ~ sQ294_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f2889,f73]) ).
fof(f2903,plain,
~ sQ294_spl,
inference(contradiction_clause,[status(thm)],[f2902]) ).
fof(f2904,plain,
$false,
inference(sat_refutation,[status(thm)],[f266,f271,f273,f275,f277,f279,f441,f443,f491,f741,f1059,f2180,f2333,f2345,f2891,f2903]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP623+1 : TPTP v9.3.1. Released v3.4.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.11/0.36 % Computer : n017.cluster.edu
% 0.11/0.36 % Model : x86_64 x86_64
% 0.11/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.36 % Memory : 8046.5625MB
% 0.11/0.36 % OS : Linux 6.8.0-71-generic
% 0.11/0.36 % CPULimit : 300
% 0.11/0.36 % WCLimit : 300
% 0.11/0.36 % DateTime : Sun Sep 20 20:14:42 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.38 % Drodi V4.1.1
% 3.35/0.84 % Refutation found
% 3.35/0.84 % SZS status Theorem for theBenchmark: Theorem is valid
% 3.35/0.84 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 3.35/0.87 % Elapsed time: 0.492233 seconds
% 3.35/0.87 % CPU time: 3.643333 seconds
% 3.35/0.87 % Total memory used: 120.745 MB
% 3.35/0.87 % Net memory used: 117.970 MB
%------------------------------------------------------------------------------