%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SEU420+2 : TPTP v9.3.1. Released v3.4.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n011.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 02:20:31 PM UTC 2026
% Result : Theorem 0.91s 1.66s
% Output : CNFRefutation 0.93s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 12
% Syntax : Number of formulae : 53 ( 14 unt; 6 def)
% Number of atoms : 117 ( 2 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 109 ( 45 ~; 41 |; 7 &)
% ( 6 <=>; 10 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 10 ( 8 usr; 7 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 54 ( 48 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f57,axiom,
! [A,B] : k3_xboole_0(A,B) = k3_xboole_0(B,A),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f86,axiom,
! [A,B] : r1_tarski(k3_xboole_0(A,B),A),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f88,axiom,
! [A,B,C] :
( ( r1_tarski(A,C)
& r1_tarski(A,B) )
=> r1_tarski(A,k3_xboole_0(B,C)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f563,axiom,
! [A,B] :
( v1_relat_1(B)
=> ( r1_tarski(A,B)
=> v1_relat_1(A) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f729,axiom,
! [A,B] :
( v1_relat_1(B)
=> ! [C] :
( v1_relat_1(C)
=> ( r1_tarski(B,C)
=> r1_tarski(k9_relat_1(B,A),k9_relat_1(C,A)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f4482,conjecture,
! [A,B] :
( v1_relat_1(B)
=> ! [C] :
( v1_relat_1(C)
=> r1_tarski(k9_relat_1(k3_xboole_0(B,C),k3_pua2mss1(A)),k3_xboole_0(k9_relat_1(B,k3_pua2mss1(A)),k9_relat_1(C,k3_pua2mss1(A)))) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f4483,negated_conjecture,
~ ! [A,B] :
( v1_relat_1(B)
=> ! [C] :
( v1_relat_1(C)
=> r1_tarski(k9_relat_1(k3_xboole_0(B,C),k3_pua2mss1(A)),k3_xboole_0(k9_relat_1(B,k3_pua2mss1(A)),k9_relat_1(C,k3_pua2mss1(A)))) ) ),
inference(negated_conjecture,[status(cth)],[f4482]) ).
fof(f4692,plain,
! [X0,X1] : k3_xboole_0(X0,X1) = k3_xboole_0(X1,X0),
inference(cnf_transformation,[status(thm)],[f57]) ).
fof(f4743,plain,
! [X0,X1] : r1_tarski(k3_xboole_0(X0,X1),X0),
inference(cnf_transformation,[status(thm)],[f86]) ).
fof(f4747,plain,
! [A,B,C] :
( r1_tarski(A,k3_xboole_0(B,C))
| ~ r1_tarski(A,C)
| ~ r1_tarski(A,B) ),
inference(pre_NNF_transformation,[status(thm)],[f88]) ).
fof(f4748,plain,
! [X0,X1,X2] :
( r1_tarski(X0,k3_xboole_0(X1,X2))
| ~ r1_tarski(X0,X2)
| ~ r1_tarski(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f4747]) ).
fof(f5876,plain,
! [A,B] :
( v1_relat_1(A)
| ~ r1_tarski(A,B)
| ~ v1_relat_1(B) ),
inference(pre_NNF_transformation,[status(thm)],[f563]) ).
fof(f5877,plain,
! [B] :
( ! [A] :
( v1_relat_1(A)
| ~ r1_tarski(A,B) )
| ~ v1_relat_1(B) ),
inference(miniscoping,[status(thm)],[f5876]) ).
fof(f5878,plain,
! [X0,X1] :
( v1_relat_1(X1)
| ~ r1_tarski(X1,X0)
| ~ v1_relat_1(X0) ),
inference(cnf_transformation,[status(thm)],[f5877]) ).
fof(f6333,plain,
! [A,B] :
( ! [C] :
( r1_tarski(k9_relat_1(B,A),k9_relat_1(C,A))
| ~ r1_tarski(B,C)
| ~ v1_relat_1(C) )
| ~ v1_relat_1(B) ),
inference(pre_NNF_transformation,[status(thm)],[f729]) ).
fof(f6334,plain,
! [B] :
( ! [C] :
( ! [A] : r1_tarski(k9_relat_1(B,A),k9_relat_1(C,A))
| ~ r1_tarski(B,C)
| ~ v1_relat_1(C) )
| ~ v1_relat_1(B) ),
inference(miniscoping,[status(thm)],[f6333]) ).
fof(f6335,plain,
! [X0,X1,X2] :
( r1_tarski(k9_relat_1(X0,X2),k9_relat_1(X1,X2))
| ~ r1_tarski(X0,X1)
| ~ v1_relat_1(X1)
| ~ v1_relat_1(X0) ),
inference(cnf_transformation,[status(thm)],[f6334]) ).
fof(f17518,plain,
? [A,B] :
( ? [C] :
( ~ r1_tarski(k9_relat_1(k3_xboole_0(B,C),k3_pua2mss1(A)),k3_xboole_0(k9_relat_1(B,k3_pua2mss1(A)),k9_relat_1(C,k3_pua2mss1(A))))
& v1_relat_1(C) )
& v1_relat_1(B) ),
inference(pre_NNF_transformation,[status(thm)],[f4483]) ).
fof(f17519,plain,
? [B] :
( ? [C] :
( ? [A] : ~ r1_tarski(k9_relat_1(k3_xboole_0(B,C),k3_pua2mss1(A)),k3_xboole_0(k9_relat_1(B,k3_pua2mss1(A)),k9_relat_1(C,k3_pua2mss1(A))))
& v1_relat_1(C) )
& v1_relat_1(B) ),
inference(miniscoping,[status(thm)],[f17518]) ).
fof(f17520,plain,
( ~ r1_tarski(k9_relat_1(k3_xboole_0(sK1204_skl,sK1205_skl),k3_pua2mss1(sK1206_skl)),k3_xboole_0(k9_relat_1(sK1204_skl,k3_pua2mss1(sK1206_skl)),k9_relat_1(sK1205_skl,k3_pua2mss1(sK1206_skl))))
& v1_relat_1(sK1205_skl)
& v1_relat_1(sK1204_skl) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1204_skl,sK1205_skl,sK1206_skl]),skolemize(B,sK1204_skl),skolemize(C,sK1205_skl),skolemize(A,sK1206_skl)],[f17519]) ).
fof(f17521,plain,
v1_relat_1(sK1204_skl),
inference(cnf_transformation,[status(thm)],[f17520]) ).
fof(f17522,plain,
v1_relat_1(sK1205_skl),
inference(cnf_transformation,[status(thm)],[f17520]) ).
fof(f17523,plain,
~ r1_tarski(k9_relat_1(k3_xboole_0(sK1204_skl,sK1205_skl),k3_pua2mss1(sK1206_skl)),k3_xboole_0(k9_relat_1(sK1204_skl,k3_pua2mss1(sK1206_skl)),k9_relat_1(sK1205_skl,k3_pua2mss1(sK1206_skl)))),
inference(cnf_transformation,[status(thm)],[f17520]) ).
fof(f22018,plain,
~ r1_tarski(k9_relat_1(k3_xboole_0(sK1204_skl,sK1205_skl),k3_pua2mss1(sK1206_skl)),k3_xboole_0(k9_relat_1(sK1205_skl,k3_pua2mss1(sK1206_skl)),k9_relat_1(sK1204_skl,k3_pua2mss1(sK1206_skl)))),
inference(paramodulation,[status(thm)],[f4692,f17523]) ).
fof(f22021,plain,
! [X0,X1] : r1_tarski(k3_xboole_0(X0,X1),X1),
inference(paramodulation,[status(thm)],[f4692,f4743]) ).
fof(f22271,plain,
( ~ r1_tarski(k9_relat_1(k3_xboole_0(sK1204_skl,sK1205_skl),k3_pua2mss1(sK1206_skl)),k9_relat_1(sK1204_skl,k3_pua2mss1(sK1206_skl)))
| ~ r1_tarski(k9_relat_1(k3_xboole_0(sK1204_skl,sK1205_skl),k3_pua2mss1(sK1206_skl)),k9_relat_1(sK1205_skl,k3_pua2mss1(sK1206_skl))) ),
inference(resolution,[status(thm)],[f4748,f22018]) ).
fof(f22291,definition,
( sQ584_spl
<=> r1_tarski(k9_relat_1(k3_xboole_0(sK1204_skl,sK1205_skl),k3_pua2mss1(sK1206_skl)),k9_relat_1(sK1205_skl,k3_pua2mss1(sK1206_skl))) ),
introduced(definition,[new_symbols(definition,[sQ584_spl])],[split_symbol_definition]) ).
fof(f22293,plain,
( sQ584_spl
| ~ r1_tarski(k9_relat_1(k3_xboole_0(sK1204_skl,sK1205_skl),k3_pua2mss1(sK1206_skl)),k9_relat_1(sK1205_skl,k3_pua2mss1(sK1206_skl))) ),
inference(component_clause,[status(thm)],[f22291]) ).
fof(f22294,definition,
( sQ585_spl
<=> r1_tarski(k9_relat_1(k3_xboole_0(sK1204_skl,sK1205_skl),k3_pua2mss1(sK1206_skl)),k9_relat_1(sK1204_skl,k3_pua2mss1(sK1206_skl))) ),
introduced(definition,[new_symbols(definition,[sQ585_spl])],[split_symbol_definition]) ).
fof(f22296,plain,
( sQ585_spl
| ~ r1_tarski(k9_relat_1(k3_xboole_0(sK1204_skl,sK1205_skl),k3_pua2mss1(sK1206_skl)),k9_relat_1(sK1204_skl,k3_pua2mss1(sK1206_skl))) ),
inference(component_clause,[status(thm)],[f22294]) ).
fof(f22297,plain,
( ~ sQ585_spl
| ~ sQ584_spl ),
inference(split_clause,[status(thm)],[f22271,f22291,f22294]) ).
fof(f25264,plain,
! [X0,X1,X2] :
( r1_tarski(k9_relat_1(X1,X2),k9_relat_1(X0,X2))
| ~ r1_tarski(X1,X0)
| ~ v1_relat_1(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f6335,f5878]) ).
fof(f25267,plain,
( sQ585_spl
| ~ r1_tarski(k3_xboole_0(sK1204_skl,sK1205_skl),sK1204_skl)
| ~ v1_relat_1(sK1204_skl) ),
inference(resolution,[status(thm)],[f25264,f22296]) ).
fof(f25268,plain,
( sQ584_spl
| ~ r1_tarski(k3_xboole_0(sK1204_skl,sK1205_skl),sK1205_skl)
| ~ v1_relat_1(sK1205_skl) ),
inference(resolution,[status(thm)],[f25264,f22293]) ).
fof(f25274,definition,
( sQ646_spl
<=> v1_relat_1(sK1204_skl) ),
introduced(definition,[new_symbols(definition,[sQ646_spl])],[split_symbol_definition]) ).
fof(f25276,plain,
( sQ646_spl
| ~ v1_relat_1(sK1204_skl) ),
inference(component_clause,[status(thm)],[f25274]) ).
fof(f25281,definition,
( sQ648_spl
<=> v1_relat_1(sK1205_skl) ),
introduced(definition,[new_symbols(definition,[sQ648_spl])],[split_symbol_definition]) ).
fof(f25283,plain,
( sQ648_spl
| ~ v1_relat_1(sK1205_skl) ),
inference(component_clause,[status(thm)],[f25281]) ).
fof(f25288,definition,
( sQ650_spl
<=> r1_tarski(k3_xboole_0(sK1204_skl,sK1205_skl),sK1204_skl) ),
introduced(definition,[new_symbols(definition,[sQ650_spl])],[split_symbol_definition]) ).
fof(f25290,plain,
( sQ650_spl
| ~ r1_tarski(k3_xboole_0(sK1204_skl,sK1205_skl),sK1204_skl) ),
inference(component_clause,[status(thm)],[f25288]) ).
fof(f25291,plain,
( sQ585_spl
| ~ sQ650_spl
| ~ sQ646_spl ),
inference(split_clause,[status(thm)],[f25267,f25274,f25288,f22294]) ).
fof(f25292,definition,
( sQ651_spl
<=> r1_tarski(k3_xboole_0(sK1204_skl,sK1205_skl),sK1205_skl) ),
introduced(definition,[new_symbols(definition,[sQ651_spl])],[split_symbol_definition]) ).
fof(f25294,plain,
( sQ651_spl
| ~ r1_tarski(k3_xboole_0(sK1204_skl,sK1205_skl),sK1205_skl) ),
inference(component_clause,[status(thm)],[f25292]) ).
fof(f25295,plain,
( sQ584_spl
| ~ sQ651_spl
| ~ sQ648_spl ),
inference(split_clause,[status(thm)],[f25268,f25281,f25292,f22291]) ).
fof(f25300,plain,
( sQ648_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f25283,f17522]) ).
fof(f25301,plain,
sQ648_spl,
inference(contradiction_clause,[status(thm)],[f25300]) ).
fof(f25302,plain,
( sQ646_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f25276,f17521]) ).
fof(f25303,plain,
sQ646_spl,
inference(contradiction_clause,[status(thm)],[f25302]) ).
fof(f25304,plain,
( sQ651_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f25294,f22021]) ).
fof(f25305,plain,
sQ651_spl,
inference(contradiction_clause,[status(thm)],[f25304]) ).
fof(f25306,plain,
( sQ650_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f25290,f4743]) ).
fof(f25307,plain,
sQ650_spl,
inference(contradiction_clause,[status(thm)],[f25306]) ).
fof(f25308,plain,
$false,
inference(sat_refutation,[status(thm)],[f22297,f25291,f25295,f25301,f25303,f25305,f25307]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SEU420+2 : TPTP v9.3.1. Released v3.4.0.
% 0.00/0.07 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.17/0.44 % Computer : n011.cluster.edu
% 0.17/0.44 % Model : x86_64 x86_64
% 0.17/0.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.44 % Memory : 8046.5625MB
% 0.17/0.44 % OS : Linux 6.8.0-71-generic
% 0.17/0.44 % CPULimit : 300
% 0.17/0.44 % WCLimit : 300
% 0.17/0.44 % DateTime : Mon Sep 21 06:25:25 UTC 2026
% 0.17/0.45 % CPUTime :
% 0.72/1.12 % Drodi V4.1.1
% 0.91/1.66 % Refutation found
% 0.91/1.66 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.91/1.66 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.93/1.81 % Elapsed time: 1.346277 seconds
% 0.93/1.81 % CPU time: 5.033764 seconds
% 0.93/1.81 % Total memory used: 752.067 MB
% 0.93/1.81 % Net memory used: 743.410 MB
%------------------------------------------------------------------------------