%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SEU418+4 : TPTP v9.3.1. Released v3.4.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n012.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 02:20:30 PM UTC 2026
% Result : Theorem 70.32s 21.60s
% Output : CNFRefutation 73.54s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 16
% Syntax : Number of formulae : 67 ( 18 unt; 10 def)
% Number of atoms : 148 ( 2 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 133 ( 52 ~; 52 |; 7 &)
% ( 10 <=>; 12 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 14 ( 12 usr; 11 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 45 ( 42 !; 3 ?)
% 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(f708,axiom,
! [A,B] :
( v1_relat_1(B)
=> v1_relat_1(k3_xboole_0(A,B)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f753,axiom,
! [A] :
( v1_relat_1(A)
=> ! [B] :
( v1_relat_1(B)
=> ! [C] :
( v1_relat_1(C)
=> ( r1_tarski(A,B)
=> r1_tarski(k5_relat_1(A,C),k5_relat_1(B,C)) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f71086,conjecture,
! [A] :
( v1_relat_1(A)
=> ! [B] :
( v1_relat_1(B)
=> ! [C] :
( v1_relat_1(C)
=> r1_tarski(k5_relat_1(k3_xboole_0(A,B),C),k3_xboole_0(k5_relat_1(A,C),k5_relat_1(B,C))) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f71087,negated_conjecture,
~ ! [A] :
( v1_relat_1(A)
=> ! [B] :
( v1_relat_1(B)
=> ! [C] :
( v1_relat_1(C)
=> r1_tarski(k5_relat_1(k3_xboole_0(A,B),C),k3_xboole_0(k5_relat_1(A,C),k5_relat_1(B,C))) ) ) ),
inference(negated_conjecture,[status(cth)],[f71086]) ).
fof(f71296,plain,
! [X0,X1] : k3_xboole_0(X0,X1) = k3_xboole_0(X1,X0),
inference(cnf_transformation,[status(thm)],[f57]) ).
fof(f71347,plain,
! [X0,X1] : r1_tarski(k3_xboole_0(X0,X1),X0),
inference(cnf_transformation,[status(thm)],[f86]) ).
fof(f71351,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(f71352,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)],[f71351]) ).
fof(f72636,plain,
! [A,B] :
( v1_relat_1(k3_xboole_0(A,B))
| ~ v1_relat_1(B) ),
inference(pre_NNF_transformation,[status(thm)],[f708]) ).
fof(f72637,plain,
! [B] :
( ! [A] : v1_relat_1(k3_xboole_0(A,B))
| ~ v1_relat_1(B) ),
inference(miniscoping,[status(thm)],[f72636]) ).
fof(f72638,plain,
! [X0,X1] :
( v1_relat_1(k3_xboole_0(X1,X0))
| ~ v1_relat_1(X0) ),
inference(cnf_transformation,[status(thm)],[f72637]) ).
fof(f72754,plain,
! [A] :
( ! [B] :
( ! [C] :
( r1_tarski(k5_relat_1(A,C),k5_relat_1(B,C))
| ~ r1_tarski(A,B)
| ~ v1_relat_1(C) )
| ~ v1_relat_1(B) )
| ~ v1_relat_1(A) ),
inference(pre_NNF_transformation,[status(thm)],[f753]) ).
fof(f72755,plain,
! [X0,X1,X2] :
( r1_tarski(k5_relat_1(X0,X2),k5_relat_1(X1,X2))
| ~ r1_tarski(X0,X1)
| ~ v1_relat_1(X2)
| ~ v1_relat_1(X1)
| ~ v1_relat_1(X0) ),
inference(cnf_transformation,[status(thm)],[f72754]) ).
fof(f335918,plain,
? [A] :
( ? [B] :
( ? [C] :
( ~ r1_tarski(k5_relat_1(k3_xboole_0(A,B),C),k3_xboole_0(k5_relat_1(A,C),k5_relat_1(B,C)))
& v1_relat_1(C) )
& v1_relat_1(B) )
& v1_relat_1(A) ),
inference(pre_NNF_transformation,[status(thm)],[f71087]) ).
fof(f335919,plain,
( ~ r1_tarski(k5_relat_1(k3_xboole_0(sK23834_skl,sK23835_skl),sK23836_skl),k3_xboole_0(k5_relat_1(sK23834_skl,sK23836_skl),k5_relat_1(sK23835_skl,sK23836_skl)))
& v1_relat_1(sK23836_skl)
& v1_relat_1(sK23835_skl)
& v1_relat_1(sK23834_skl) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK23834_skl,sK23835_skl,sK23836_skl]),skolemize(A,sK23834_skl),skolemize(B,sK23835_skl),skolemize(C,sK23836_skl)],[f335918]) ).
fof(f335920,plain,
v1_relat_1(sK23834_skl),
inference(cnf_transformation,[status(thm)],[f335919]) ).
fof(f335921,plain,
v1_relat_1(sK23835_skl),
inference(cnf_transformation,[status(thm)],[f335919]) ).
fof(f335922,plain,
v1_relat_1(sK23836_skl),
inference(cnf_transformation,[status(thm)],[f335919]) ).
fof(f335923,plain,
~ r1_tarski(k5_relat_1(k3_xboole_0(sK23834_skl,sK23835_skl),sK23836_skl),k3_xboole_0(k5_relat_1(sK23834_skl,sK23836_skl),k5_relat_1(sK23835_skl,sK23836_skl))),
inference(cnf_transformation,[status(thm)],[f335919]) ).
fof(f412721,plain,
~ r1_tarski(k5_relat_1(k3_xboole_0(sK23834_skl,sK23835_skl),sK23836_skl),k3_xboole_0(k5_relat_1(sK23835_skl,sK23836_skl),k5_relat_1(sK23834_skl,sK23836_skl))),
inference(paramodulation,[status(thm)],[f71296,f335923]) ).
fof(f412724,plain,
! [X0,X1] : r1_tarski(k3_xboole_0(X0,X1),X1),
inference(paramodulation,[status(thm)],[f71296,f71347]) ).
fof(f412969,plain,
( ~ r1_tarski(k5_relat_1(k3_xboole_0(sK23834_skl,sK23835_skl),sK23836_skl),k5_relat_1(sK23834_skl,sK23836_skl))
| ~ r1_tarski(k5_relat_1(k3_xboole_0(sK23834_skl,sK23835_skl),sK23836_skl),k5_relat_1(sK23835_skl,sK23836_skl)) ),
inference(resolution,[status(thm)],[f71352,f412721]) ).
fof(f412989,definition,
( sQ6603_spl
<=> r1_tarski(k5_relat_1(k3_xboole_0(sK23834_skl,sK23835_skl),sK23836_skl),k5_relat_1(sK23835_skl,sK23836_skl)) ),
introduced(definition,[new_symbols(definition,[sQ6603_spl])],[split_symbol_definition]) ).
fof(f412991,plain,
( sQ6603_spl
| ~ r1_tarski(k5_relat_1(k3_xboole_0(sK23834_skl,sK23835_skl),sK23836_skl),k5_relat_1(sK23835_skl,sK23836_skl)) ),
inference(component_clause,[status(thm)],[f412989]) ).
fof(f412992,definition,
( sQ6604_spl
<=> r1_tarski(k5_relat_1(k3_xboole_0(sK23834_skl,sK23835_skl),sK23836_skl),k5_relat_1(sK23834_skl,sK23836_skl)) ),
introduced(definition,[new_symbols(definition,[sQ6604_spl])],[split_symbol_definition]) ).
fof(f412994,plain,
( sQ6604_spl
| ~ r1_tarski(k5_relat_1(k3_xboole_0(sK23834_skl,sK23835_skl),sK23836_skl),k5_relat_1(sK23834_skl,sK23836_skl)) ),
inference(component_clause,[status(thm)],[f412992]) ).
fof(f412995,plain,
( ~ sQ6604_spl
| ~ sQ6603_spl ),
inference(split_clause,[status(thm)],[f412969,f412989,f412992]) ).
fof(f416572,plain,
( sQ6604_spl
| ~ r1_tarski(k3_xboole_0(sK23834_skl,sK23835_skl),sK23834_skl)
| ~ v1_relat_1(sK23836_skl)
| ~ v1_relat_1(sK23834_skl)
| ~ v1_relat_1(k3_xboole_0(sK23834_skl,sK23835_skl)) ),
inference(resolution,[status(thm)],[f72755,f412994]) ).
fof(f416573,plain,
( sQ6603_spl
| ~ r1_tarski(k3_xboole_0(sK23834_skl,sK23835_skl),sK23835_skl)
| ~ v1_relat_1(sK23836_skl)
| ~ v1_relat_1(sK23835_skl)
| ~ v1_relat_1(k3_xboole_0(sK23834_skl,sK23835_skl)) ),
inference(resolution,[status(thm)],[f72755,f412991]) ).
fof(f416582,definition,
( sQ6639_spl
<=> v1_relat_1(sK23834_skl) ),
introduced(definition,[new_symbols(definition,[sQ6639_spl])],[split_symbol_definition]) ).
fof(f416584,plain,
( sQ6639_spl
| ~ v1_relat_1(sK23834_skl) ),
inference(component_clause,[status(thm)],[f416582]) ).
fof(f416585,definition,
( sQ6640_spl
<=> v1_relat_1(sK23836_skl) ),
introduced(definition,[new_symbols(definition,[sQ6640_spl])],[split_symbol_definition]) ).
fof(f416587,plain,
( sQ6640_spl
| ~ v1_relat_1(sK23836_skl) ),
inference(component_clause,[status(thm)],[f416585]) ).
fof(f416588,definition,
( sQ6641_spl
<=> r1_tarski(k3_xboole_0(sK23835_skl,sK23834_skl),sK23834_skl) ),
introduced(definition,[new_symbols(definition,[sQ6641_spl])],[split_symbol_definition]) ).
fof(f416590,plain,
( sQ6641_spl
| ~ r1_tarski(k3_xboole_0(sK23835_skl,sK23834_skl),sK23834_skl) ),
inference(component_clause,[status(thm)],[f416588]) ).
fof(f416592,definition,
( sQ6642_spl
<=> v1_relat_1(sK23835_skl) ),
introduced(definition,[new_symbols(definition,[sQ6642_spl])],[split_symbol_definition]) ).
fof(f416594,plain,
( sQ6642_spl
| ~ v1_relat_1(sK23835_skl) ),
inference(component_clause,[status(thm)],[f416592]) ).
fof(f416595,definition,
( sQ6643_spl
<=> r1_tarski(k3_xboole_0(sK23835_skl,sK23834_skl),sK23835_skl) ),
introduced(definition,[new_symbols(definition,[sQ6643_spl])],[split_symbol_definition]) ).
fof(f416597,plain,
( sQ6643_spl
| ~ r1_tarski(k3_xboole_0(sK23835_skl,sK23834_skl),sK23835_skl) ),
inference(component_clause,[status(thm)],[f416595]) ).
fof(f416599,definition,
( sQ6644_spl
<=> v1_relat_1(k3_xboole_0(sK23834_skl,sK23835_skl)) ),
introduced(definition,[new_symbols(definition,[sQ6644_spl])],[split_symbol_definition]) ).
fof(f416601,plain,
( sQ6644_spl
| ~ v1_relat_1(k3_xboole_0(sK23834_skl,sK23835_skl)) ),
inference(component_clause,[status(thm)],[f416599]) ).
fof(f416602,definition,
( sQ6645_spl
<=> r1_tarski(k3_xboole_0(sK23834_skl,sK23835_skl),sK23834_skl) ),
introduced(definition,[new_symbols(definition,[sQ6645_spl])],[split_symbol_definition]) ).
fof(f416604,plain,
( sQ6645_spl
| ~ r1_tarski(k3_xboole_0(sK23834_skl,sK23835_skl),sK23834_skl) ),
inference(component_clause,[status(thm)],[f416602]) ).
fof(f416605,plain,
( sQ6604_spl
| ~ sQ6645_spl
| ~ sQ6640_spl
| ~ sQ6639_spl
| ~ sQ6644_spl ),
inference(split_clause,[status(thm)],[f416572,f416599,f416582,f416585,f416602,f412992]) ).
fof(f416606,definition,
( sQ6646_spl
<=> r1_tarski(k3_xboole_0(sK23834_skl,sK23835_skl),sK23835_skl) ),
introduced(definition,[new_symbols(definition,[sQ6646_spl])],[split_symbol_definition]) ).
fof(f416608,plain,
( sQ6646_spl
| ~ r1_tarski(k3_xboole_0(sK23834_skl,sK23835_skl),sK23835_skl) ),
inference(component_clause,[status(thm)],[f416606]) ).
fof(f416609,plain,
( sQ6603_spl
| ~ sQ6646_spl
| ~ sQ6640_spl
| ~ sQ6642_spl
| ~ sQ6644_spl ),
inference(split_clause,[status(thm)],[f416573,f416599,f416592,f416585,f416606,f412989]) ).
fof(f416610,plain,
( sQ6640_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f416587,f335922]) ).
fof(f416611,plain,
sQ6640_spl,
inference(contradiction_clause,[status(thm)],[f416610]) ).
fof(f416612,plain,
( sQ6642_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f416594,f335921]) ).
fof(f416613,plain,
sQ6642_spl,
inference(contradiction_clause,[status(thm)],[f416612]) ).
fof(f416614,plain,
( sQ6639_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f416584,f335920]) ).
fof(f416615,plain,
sQ6639_spl,
inference(contradiction_clause,[status(thm)],[f416614]) ).
fof(f416616,plain,
( sQ6646_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f416608,f412724]) ).
fof(f416617,plain,
sQ6646_spl,
inference(contradiction_clause,[status(thm)],[f416616]) ).
fof(f416618,plain,
( sQ6645_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f416604,f71347]) ).
fof(f416619,plain,
sQ6645_spl,
inference(contradiction_clause,[status(thm)],[f416618]) ).
fof(f416620,plain,
( sQ6643_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f416597,f71347]) ).
fof(f416621,plain,
sQ6643_spl,
inference(contradiction_clause,[status(thm)],[f416620]) ).
fof(f416622,plain,
( sQ6641_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f416590,f412724]) ).
fof(f416623,plain,
sQ6641_spl,
inference(contradiction_clause,[status(thm)],[f416622]) ).
fof(f416758,plain,
( sQ6644_spl
| ~ v1_relat_1(sK23835_skl) ),
inference(resolution,[status(thm)],[f416601,f72638]) ).
fof(f416762,plain,
( sQ6644_spl
| ~ sQ6642_spl ),
inference(split_clause,[status(thm)],[f416758,f416592,f416599]) ).
fof(f416764,plain,
$false,
inference(sat_refutation,[status(thm)],[f412995,f416605,f416609,f416611,f416613,f416615,f416617,f416619,f416621,f416623,f416762]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU418+4 : TPTP v9.3.1. Released v3.4.0.
% 0.00/0.03 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/0.33 % Computer : n012.cluster.edu
% 0.08/0.33 % Model : x86_64 x86_64
% 0.08/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.33 % Memory : 8046.5625MB
% 0.08/0.33 % OS : Linux 6.8.0-71-generic
% 0.08/0.33 % CPULimit : 300
% 0.08/0.33 % WCLimit : 300
% 0.08/0.33 % DateTime : Mon Sep 21 06:25:02 UTC 2026
% 0.08/0.34 % CPUTime :
% 13.45/13.75 % Drodi V4.1.1
% 70.32/21.60 % Refutation found
% 70.32/21.60 % SZS status Theorem for theBenchmark: Theorem is valid
% 70.32/21.60 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 37.46/23.53 % Elapsed time: 22.725866 seconds
% 37.46/23.53 % CPU time: 73.454659 seconds
% 37.46/23.53 % Total memory used: 21.781 GB
% 37.46/23.53 % Net memory used: 21.633 GB
%------------------------------------------------------------------------------