%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SEU406+2 : TPTP v9.3.1. Released v3.4.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/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 02:20:26 PM UTC 2026
% Result : Theorem 0.62s 1.00s
% Output : CNFRefutation 0.62s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 3
% Syntax : Number of formulae : 37 ( 8 unt; 0 def)
% Number of atoms : 183 ( 16 equ)
% Maximal formula atoms : 14 ( 4 avg)
% Number of connectives : 244 ( 98 ~; 83 |; 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(f4434,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(f4435,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)],[f4434]) ).
fof(f4530,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(f4531,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)],[f4530]) ).
fof(f4532,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))],[f4531]) ).
fof(f4533,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)],[f4532]) ).
fof(f4548,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(f4549,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)],[f4548]) ).
fof(f4550,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))],[f4549]) ).
fof(f4553,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)],[f4550]) ).
fof(f18494,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)],[f4435]) ).
fof(f18495,plain,
( ( ~ r2_hidden(sK1190_skl,k4_xboole_0(sK1191_skl,sK1192_skl))
| ~ r2_hidden(sK1189_skl,sK1192_skl) )
& ( ~ r2_hidden(sK1190_skl,sK1192_skl)
| ~ r2_hidden(sK1189_skl,k4_xboole_0(sK1191_skl,sK1192_skl)) )
& ( ~ r2_hidden(sK1190_skl,sK1192_skl)
| ~ r2_hidden(sK1189_skl,sK1192_skl) )
& ( ~ r2_hidden(sK1190_skl,k4_xboole_0(sK1191_skl,sK1192_skl))
| ~ r2_hidden(sK1189_skl,k4_xboole_0(sK1191_skl,sK1192_skl)) )
& r2_hidden(sK1190_skl,k2_xboole_0(sK1191_skl,sK1192_skl))
& r2_hidden(sK1189_skl,k2_xboole_0(sK1191_skl,sK1192_skl)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1189_skl,sK1190_skl,sK1191_skl,sK1192_skl]),skolemize(A,sK1189_skl),skolemize(B,sK1190_skl),skolemize(C,sK1191_skl),skolemize(D,sK1192_skl)],[f18494]) ).
fof(f18496,plain,
r2_hidden(sK1189_skl,k2_xboole_0(sK1191_skl,sK1192_skl)),
inference(cnf_transformation,[status(thm)],[f18495]) ).
fof(f18497,plain,
r2_hidden(sK1190_skl,k2_xboole_0(sK1191_skl,sK1192_skl)),
inference(cnf_transformation,[status(thm)],[f18495]) ).
fof(f18498,plain,
( ~ r2_hidden(sK1190_skl,k4_xboole_0(sK1191_skl,sK1192_skl))
| ~ r2_hidden(sK1189_skl,k4_xboole_0(sK1191_skl,sK1192_skl)) ),
inference(cnf_transformation,[status(thm)],[f18495]) ).
fof(f18499,plain,
( ~ r2_hidden(sK1190_skl,sK1192_skl)
| ~ r2_hidden(sK1189_skl,sK1192_skl) ),
inference(cnf_transformation,[status(thm)],[f18495]) ).
fof(f18500,plain,
( ~ r2_hidden(sK1190_skl,sK1192_skl)
| ~ r2_hidden(sK1189_skl,k4_xboole_0(sK1191_skl,sK1192_skl)) ),
inference(cnf_transformation,[status(thm)],[f18495]) ).
fof(f18501,plain,
( ~ r2_hidden(sK1190_skl,k4_xboole_0(sK1191_skl,sK1192_skl))
| ~ r2_hidden(sK1189_skl,sK1192_skl) ),
inference(cnf_transformation,[status(thm)],[f18495]) ).
fof(f19866,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)],[f4533]) ).
fof(f19874,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)],[f4553]) ).
fof(f20924,plain,
( r2_hidden(sK1190_skl,sK1192_skl)
| r2_hidden(sK1190_skl,sK1191_skl) ),
inference(resolution,[status(thm)],[f19866,f18497]) ).
fof(f20925,plain,
( r2_hidden(sK1189_skl,sK1192_skl)
| r2_hidden(sK1189_skl,sK1191_skl) ),
inference(resolution,[status(thm)],[f19866,f18496]) ).
fof(f21032,plain,
( ~ r2_hidden(sK1190_skl,sK1192_skl)
| r2_hidden(sK1189_skl,sK1192_skl)
| ~ r2_hidden(sK1189_skl,sK1191_skl) ),
inference(resolution,[status(thm)],[f19874,f18500]) ).
fof(f21034,plain,
( ~ r2_hidden(sK1189_skl,sK1192_skl)
| r2_hidden(sK1190_skl,sK1192_skl)
| ~ r2_hidden(sK1190_skl,sK1191_skl) ),
inference(resolution,[status(thm)],[f19874,f18501]) ).
fof(f21035,plain,
( ~ r2_hidden(sK1189_skl,k4_xboole_0(sK1191_skl,sK1192_skl))
| r2_hidden(sK1190_skl,sK1192_skl)
| ~ r2_hidden(sK1190_skl,sK1191_skl) ),
inference(resolution,[status(thm)],[f19874,f18498]) ).
fof(f21042,plain,
( ~ r2_hidden(sK1190_skl,sK1192_skl)
| ~ r2_hidden(sK1189_skl,sK1191_skl) ),
inference(forward_subsumption_resolution,[status(thm)],[f21032,f18499]) ).
fof(f21043,plain,
( ~ r2_hidden(sK1189_skl,sK1192_skl)
| r2_hidden(sK1190_skl,sK1192_skl) ),
inference(forward_subsumption_resolution,[status(thm)],[f21034,f20924]) ).
fof(f21044,plain,
( ~ r2_hidden(sK1189_skl,k4_xboole_0(sK1191_skl,sK1192_skl))
| r2_hidden(sK1190_skl,sK1192_skl) ),
inference(forward_subsumption_resolution,[status(thm)],[f21035,f20924]) ).
fof(f21260,plain,
r2_hidden(sK1189_skl,sK1191_skl),
inference(backward_subsumption_resolution,[status(thm)],[f20925,f21261]) ).
fof(f21261,plain,
~ r2_hidden(sK1189_skl,sK1192_skl),
inference(forward_subsumption_resolution,[status(thm)],[f21043,f18499]) ).
fof(f21268,plain,
~ r2_hidden(sK1190_skl,sK1192_skl),
inference(backward_subsumption_resolution,[status(thm)],[f21042,f21260]) ).
fof(f21328,plain,
~ r2_hidden(sK1189_skl,k4_xboole_0(sK1191_skl,sK1192_skl)),
inference(forward_subsumption_resolution,[status(thm)],[f21044,f21268]) ).
fof(f21329,plain,
( r2_hidden(sK1189_skl,sK1192_skl)
| ~ r2_hidden(sK1189_skl,sK1191_skl) ),
inference(resolution,[status(thm)],[f21328,f19874]) ).
fof(f21330,plain,
r2_hidden(sK1189_skl,sK1192_skl),
inference(forward_subsumption_resolution,[status(thm)],[f21329,f21260]) ).
fof(f21331,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f21330,f21261]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU406+2 : TPTP v9.3.1. Released v3.4.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.36 % Computer : n002.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Mon Sep 21 06:23:49 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.56/0.81 % Drodi V4.1.1
% 0.62/1.00 % Refutation found
% 0.62/1.00 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.62/1.00 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.69/1.24 % Elapsed time: 0.843116 seconds
% 0.69/1.24 % CPU time: 2.273187 seconds
% 0.69/1.24 % Total memory used: 668.471 MB
% 0.69/1.24 % Net memory used: 663.693 MB
%------------------------------------------------------------------------------