%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SEU406+4 : TPTP v9.3.1. Released v3.4.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n015.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 02:20:26 PM UTC 2026
% Result : Theorem 65.77s 20.35s
% Output : CNFRefutation 52.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 3
% Syntax : Number of formulae : 37 ( 9 unt; 0 def)
% Number of atoms : 181 ( 16 equ)
% Maximal formula atoms : 14 ( 4 avg)
% Number of connectives : 240 ( 96 ~; 81 |; 59 &)
% ( 4 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 6 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 4 con; 0-3 aty)
% Number of variables : 78 ( 70 !; 8 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f30,axiom,
! [A,B,C] :
( C = k2_xboole_0(A,B)
<=> ! [D] :
( r2_hidden(D,C)
<=> ( r2_hidden(D,B)
| r2_hidden(D,A) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f32,axiom,
! [A,B,C] :
( C = k4_xboole_0(A,B)
<=> ! [D] :
( r2_hidden(D,C)
<=> ( ~ r2_hidden(D,B)
& r2_hidden(D,A) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f66033,conjecture,
! [A,B,C,D] :
~ ( ~ ( r2_hidden(B,k4_xboole_0(C,D))
& r2_hidden(A,D) )
& ~ ( r2_hidden(B,D)
& r2_hidden(A,k4_xboole_0(C,D)) )
& ~ ( r2_hidden(B,D)
& r2_hidden(A,D) )
& ~ ( r2_hidden(B,k4_xboole_0(C,D))
& r2_hidden(A,k4_xboole_0(C,D)) )
& r2_hidden(B,k2_xboole_0(C,D))
& r2_hidden(A,k2_xboole_0(C,D)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f66034,negated_conjecture,
~ ! [A,B,C,D] :
~ ( ~ ( r2_hidden(B,k4_xboole_0(C,D))
& r2_hidden(A,D) )
& ~ ( r2_hidden(B,D)
& r2_hidden(A,k4_xboole_0(C,D)) )
& ~ ( r2_hidden(B,D)
& r2_hidden(A,D) )
& ~ ( r2_hidden(B,k4_xboole_0(C,D))
& r2_hidden(A,k4_xboole_0(C,D)) )
& r2_hidden(B,k2_xboole_0(C,D))
& r2_hidden(A,k2_xboole_0(C,D)) ),
inference(negated_conjecture,[status(cth)],[f66033]) ).
fof(f66129,plain,
! [A,B,C] :
( ( ? [D] :
( ( r2_hidden(D,B)
| r2_hidden(D,A)
| r2_hidden(D,C) )
& ( ( ~ r2_hidden(D,B)
& ~ r2_hidden(D,A) )
| ~ r2_hidden(D,C) ) )
| C = k2_xboole_0(A,B) )
& ( ! [D] :
( ( ( ~ r2_hidden(D,B)
& ~ r2_hidden(D,A) )
| r2_hidden(D,C) )
& ( r2_hidden(D,B)
| r2_hidden(D,A)
| ~ r2_hidden(D,C) ) )
| C != k2_xboole_0(A,B) ) ),
inference(NNF_transformation,[status(thm)],[f30]) ).
fof(f66130,plain,
( ! [A,B,C] :
( ? [D] :
( ( r2_hidden(D,B)
| r2_hidden(D,A)
| r2_hidden(D,C) )
& ( ( ~ r2_hidden(D,B)
& ~ r2_hidden(D,A) )
| ~ r2_hidden(D,C) ) )
| C = k2_xboole_0(A,B) )
& ! [A,B,C] :
( ( ! [D] :
( ( ~ r2_hidden(D,B)
& ~ r2_hidden(D,A) )
| r2_hidden(D,C) )
& ! [D] :
( r2_hidden(D,B)
| r2_hidden(D,A)
| ~ r2_hidden(D,C) ) )
| C != k2_xboole_0(A,B) ) ),
inference(miniscoping,[status(thm)],[f66129]) ).
fof(f66131,plain,
( ! [A,B,C] :
( ( ( r2_hidden(sK23_skl(C,B,A),B)
| r2_hidden(sK23_skl(C,B,A),A)
| r2_hidden(sK23_skl(C,B,A),C) )
& ( ( ~ r2_hidden(sK23_skl(C,B,A),B)
& ~ r2_hidden(sK23_skl(C,B,A),A) )
| ~ r2_hidden(sK23_skl(C,B,A),C) ) )
| C = k2_xboole_0(A,B) )
& ! [A,B,C] :
( ( ! [D] :
( ( ~ r2_hidden(D,B)
& ~ r2_hidden(D,A) )
| r2_hidden(D,C) )
& ! [D] :
( r2_hidden(D,B)
| r2_hidden(D,A)
| ~ r2_hidden(D,C) ) )
| C != k2_xboole_0(A,B) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK23_skl]),skolemize(D,sK23_skl(C,B,A))],[f66130]) ).
fof(f66132,plain,
! [X0,X1,X2,X3] :
( r2_hidden(X3,X2)
| r2_hidden(X3,X1)
| ~ r2_hidden(X3,X0)
| X0 != k2_xboole_0(X1,X2) ),
inference(cnf_transformation,[status(thm)],[f66131]) ).
fof(f66147,plain,
! [A,B,C] :
( ( ? [D] :
( ( ( ~ r2_hidden(D,B)
& r2_hidden(D,A) )
| r2_hidden(D,C) )
& ( r2_hidden(D,B)
| ~ r2_hidden(D,A)
| ~ r2_hidden(D,C) ) )
| C = k4_xboole_0(A,B) )
& ( ! [D] :
( ( r2_hidden(D,B)
| ~ r2_hidden(D,A)
| r2_hidden(D,C) )
& ( ( ~ r2_hidden(D,B)
& r2_hidden(D,A) )
| ~ r2_hidden(D,C) ) )
| C != k4_xboole_0(A,B) ) ),
inference(NNF_transformation,[status(thm)],[f32]) ).
fof(f66148,plain,
( ! [A,B,C] :
( ? [D] :
( ( ( ~ r2_hidden(D,B)
& r2_hidden(D,A) )
| r2_hidden(D,C) )
& ( r2_hidden(D,B)
| ~ r2_hidden(D,A)
| ~ r2_hidden(D,C) ) )
| C = k4_xboole_0(A,B) )
& ! [A,B,C] :
( ( ! [D] :
( r2_hidden(D,B)
| ~ r2_hidden(D,A)
| r2_hidden(D,C) )
& ! [D] :
( ( ~ r2_hidden(D,B)
& r2_hidden(D,A) )
| ~ r2_hidden(D,C) ) )
| C != k4_xboole_0(A,B) ) ),
inference(miniscoping,[status(thm)],[f66147]) ).
fof(f66149,plain,
( ! [A,B,C] :
( ( ( ( ~ r2_hidden(sK25_skl(C,B,A),B)
& r2_hidden(sK25_skl(C,B,A),A) )
| r2_hidden(sK25_skl(C,B,A),C) )
& ( r2_hidden(sK25_skl(C,B,A),B)
| ~ r2_hidden(sK25_skl(C,B,A),A)
| ~ r2_hidden(sK25_skl(C,B,A),C) ) )
| C = k4_xboole_0(A,B) )
& ! [A,B,C] :
( ( ! [D] :
( r2_hidden(D,B)
| ~ r2_hidden(D,A)
| r2_hidden(D,C) )
& ! [D] :
( ( ~ r2_hidden(D,B)
& r2_hidden(D,A) )
| ~ r2_hidden(D,C) ) )
| C != k4_xboole_0(A,B) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK25_skl]),skolemize(D,sK25_skl(C,B,A))],[f66148]) ).
fof(f66152,plain,
! [X0,X1,X2,X3] :
( r2_hidden(X3,X2)
| ~ r2_hidden(X3,X1)
| r2_hidden(X3,X0)
| X0 != k4_xboole_0(X1,X2) ),
inference(cnf_transformation,[status(thm)],[f66149]) ).
fof(f310176,plain,
? [A,B,C,D] :
( ( ~ r2_hidden(B,k4_xboole_0(C,D))
| ~ r2_hidden(A,D) )
& ( ~ r2_hidden(B,D)
| ~ r2_hidden(A,k4_xboole_0(C,D)) )
& ( ~ r2_hidden(B,D)
| ~ r2_hidden(A,D) )
& ( ~ r2_hidden(B,k4_xboole_0(C,D))
| ~ r2_hidden(A,k4_xboole_0(C,D)) )
& r2_hidden(B,k2_xboole_0(C,D))
& r2_hidden(A,k2_xboole_0(C,D)) ),
inference(pre_NNF_transformation,[status(thm)],[f66034]) ).
fof(f310177,plain,
( ( ~ r2_hidden(sK22357_skl,k4_xboole_0(sK22358_skl,sK22359_skl))
| ~ r2_hidden(sK22356_skl,sK22359_skl) )
& ( ~ r2_hidden(sK22357_skl,sK22359_skl)
| ~ r2_hidden(sK22356_skl,k4_xboole_0(sK22358_skl,sK22359_skl)) )
& ( ~ r2_hidden(sK22357_skl,sK22359_skl)
| ~ r2_hidden(sK22356_skl,sK22359_skl) )
& ( ~ r2_hidden(sK22357_skl,k4_xboole_0(sK22358_skl,sK22359_skl))
| ~ r2_hidden(sK22356_skl,k4_xboole_0(sK22358_skl,sK22359_skl)) )
& r2_hidden(sK22357_skl,k2_xboole_0(sK22358_skl,sK22359_skl))
& r2_hidden(sK22356_skl,k2_xboole_0(sK22358_skl,sK22359_skl)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK22356_skl,sK22357_skl,sK22358_skl,sK22359_skl]),skolemize(A,sK22356_skl),skolemize(B,sK22357_skl),skolemize(C,sK22358_skl),skolemize(D,sK22359_skl)],[f310176]) ).
fof(f310178,plain,
r2_hidden(sK22356_skl,k2_xboole_0(sK22358_skl,sK22359_skl)),
inference(cnf_transformation,[status(thm)],[f310177]) ).
fof(f310179,plain,
r2_hidden(sK22357_skl,k2_xboole_0(sK22358_skl,sK22359_skl)),
inference(cnf_transformation,[status(thm)],[f310177]) ).
fof(f310180,plain,
( ~ r2_hidden(sK22357_skl,k4_xboole_0(sK22358_skl,sK22359_skl))
| ~ r2_hidden(sK22356_skl,k4_xboole_0(sK22358_skl,sK22359_skl)) ),
inference(cnf_transformation,[status(thm)],[f310177]) ).
fof(f310181,plain,
( ~ r2_hidden(sK22357_skl,sK22359_skl)
| ~ r2_hidden(sK22356_skl,sK22359_skl) ),
inference(cnf_transformation,[status(thm)],[f310177]) ).
fof(f310182,plain,
( ~ r2_hidden(sK22357_skl,sK22359_skl)
| ~ r2_hidden(sK22356_skl,k4_xboole_0(sK22358_skl,sK22359_skl)) ),
inference(cnf_transformation,[status(thm)],[f310177]) ).
fof(f310183,plain,
( ~ r2_hidden(sK22357_skl,k4_xboole_0(sK22358_skl,sK22359_skl))
| ~ r2_hidden(sK22356_skl,sK22359_skl) ),
inference(cnf_transformation,[status(thm)],[f310177]) ).
fof(f339361,plain,
! [X0,X1,X2] :
( r2_hidden(X0,X2)
| r2_hidden(X0,X1)
| ~ r2_hidden(X0,k2_xboole_0(X1,X2)) ),
inference(destructive_equality_resolution,[status(thm)],[f66132]) ).
fof(f339369,plain,
! [X0,X1,X2] :
( r2_hidden(X0,X2)
| ~ r2_hidden(X0,X1)
| r2_hidden(X0,k4_xboole_0(X1,X2)) ),
inference(destructive_equality_resolution,[status(thm)],[f66152]) ).
fof(f358382,plain,
( r2_hidden(sK22357_skl,sK22359_skl)
| r2_hidden(sK22357_skl,sK22358_skl) ),
inference(resolution,[status(thm)],[f339361,f310179]) ).
fof(f358383,plain,
( r2_hidden(sK22356_skl,sK22359_skl)
| r2_hidden(sK22356_skl,sK22358_skl) ),
inference(resolution,[status(thm)],[f339361,f310178]) ).
fof(f358469,plain,
( ~ r2_hidden(sK22356_skl,sK22359_skl)
| r2_hidden(sK22357_skl,sK22359_skl)
| ~ r2_hidden(sK22357_skl,sK22358_skl) ),
inference(resolution,[status(thm)],[f339369,f310183]) ).
fof(f358471,plain,
( ~ r2_hidden(sK22357_skl,k4_xboole_0(sK22358_skl,sK22359_skl))
| r2_hidden(sK22356_skl,sK22359_skl)
| ~ r2_hidden(sK22356_skl,sK22358_skl) ),
inference(resolution,[status(thm)],[f339369,f310180]) ).
fof(f358479,plain,
( ~ r2_hidden(sK22356_skl,sK22359_skl)
| r2_hidden(sK22357_skl,sK22359_skl) ),
inference(forward_subsumption_resolution,[status(thm)],[f358469,f358382]) ).
fof(f358480,plain,
( ~ r2_hidden(sK22357_skl,k4_xboole_0(sK22358_skl,sK22359_skl))
| ~ r2_hidden(sK22356_skl,sK22358_skl) ),
inference(forward_subsumption_resolution,[status(thm)],[f358471,f310183]) ).
fof(f358495,plain,
r2_hidden(sK22356_skl,sK22358_skl),
inference(backward_subsumption_resolution,[status(thm)],[f358383,f358496]) ).
fof(f358496,plain,
~ r2_hidden(sK22356_skl,sK22359_skl),
inference(forward_subsumption_resolution,[status(thm)],[f358479,f310181]) ).
fof(f358683,plain,
~ r2_hidden(sK22357_skl,k4_xboole_0(sK22358_skl,sK22359_skl)),
inference(forward_subsumption_resolution,[status(thm)],[f358480,f358495]) ).
fof(f358684,plain,
( r2_hidden(sK22357_skl,sK22359_skl)
| ~ r2_hidden(sK22357_skl,sK22358_skl) ),
inference(resolution,[status(thm)],[f358683,f339369]) ).
fof(f358685,plain,
r2_hidden(sK22357_skl,sK22359_skl),
inference(forward_subsumption_resolution,[status(thm)],[f358684,f358382]) ).
fof(f358686,plain,
~ r2_hidden(sK22356_skl,k4_xboole_0(sK22358_skl,sK22359_skl)),
inference(backward_subsumption_resolution,[status(thm)],[f310182,f358685]) ).
fof(f358797,plain,
( r2_hidden(sK22356_skl,sK22359_skl)
| ~ r2_hidden(sK22356_skl,sK22358_skl) ),
inference(resolution,[status(thm)],[f358686,f339369]) ).
fof(f358798,plain,
r2_hidden(sK22356_skl,sK22359_skl),
inference(forward_subsumption_resolution,[status(thm)],[f358797,f358495]) ).
fof(f358799,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f358798,f358496]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU406+4 : TPTP v9.3.1. Released v3.4.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.36 % Computer : n015.cluster.edu
% 0.08/0.36 % Model : x86_64 x86_64
% 0.08/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.36 % Memory : 8046.5625MB
% 0.08/0.36 % OS : Linux 6.8.0-71-generic
% 0.08/0.36 % CPULimit : 300
% 0.08/0.36 % WCLimit : 300
% 0.08/0.36 % DateTime : Mon Sep 21 06:24:33 UTC 2026
% 0.08/0.36 % CPUTime :
% 13.36/13.63 % Drodi V4.1.1
% 65.77/20.35 % Refutation found
% 65.77/20.35 % SZS status Theorem for theBenchmark: Theorem is valid
% 65.77/20.35 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 17.58/22.06 % Elapsed time: 21.244892 seconds
% 17.58/22.06 % CPU time: 68.049988 seconds
% 17.58/22.06 % Total memory used: 20.724 GB
% 17.58/22.06 % Net memory used: 20.573 GB
%------------------------------------------------------------------------------