%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SEU406+3 : TPTP v9.3.1. Released v3.4.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n013.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 13.33s 4.63s
% Output : CNFRefutation 8.95s
% 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(f19023,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(f19024,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)],[f19023]) ).
fof(f19119,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(f19120,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)],[f19119]) ).
fof(f19121,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))],[f19120]) ).
fof(f19122,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)],[f19121]) ).
fof(f19137,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(f19138,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)],[f19137]) ).
fof(f19139,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))],[f19138]) ).
fof(f19142,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)],[f19139]) ).
fof(f89010,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)],[f19024]) ).
fof(f89011,plain,
( ( ~ r2_hidden(sK6518_skl,k4_xboole_0(sK6519_skl,sK6520_skl))
| ~ r2_hidden(sK6517_skl,sK6520_skl) )
& ( ~ r2_hidden(sK6518_skl,sK6520_skl)
| ~ r2_hidden(sK6517_skl,k4_xboole_0(sK6519_skl,sK6520_skl)) )
& ( ~ r2_hidden(sK6518_skl,sK6520_skl)
| ~ r2_hidden(sK6517_skl,sK6520_skl) )
& ( ~ r2_hidden(sK6518_skl,k4_xboole_0(sK6519_skl,sK6520_skl))
| ~ r2_hidden(sK6517_skl,k4_xboole_0(sK6519_skl,sK6520_skl)) )
& r2_hidden(sK6518_skl,k2_xboole_0(sK6519_skl,sK6520_skl))
& r2_hidden(sK6517_skl,k2_xboole_0(sK6519_skl,sK6520_skl)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK6517_skl,sK6518_skl,sK6519_skl,sK6520_skl]),skolemize(A,sK6517_skl),skolemize(B,sK6518_skl),skolemize(C,sK6519_skl),skolemize(D,sK6520_skl)],[f89010]) ).
fof(f89012,plain,
r2_hidden(sK6517_skl,k2_xboole_0(sK6519_skl,sK6520_skl)),
inference(cnf_transformation,[status(thm)],[f89011]) ).
fof(f89013,plain,
r2_hidden(sK6518_skl,k2_xboole_0(sK6519_skl,sK6520_skl)),
inference(cnf_transformation,[status(thm)],[f89011]) ).
fof(f89014,plain,
( ~ r2_hidden(sK6518_skl,k4_xboole_0(sK6519_skl,sK6520_skl))
| ~ r2_hidden(sK6517_skl,k4_xboole_0(sK6519_skl,sK6520_skl)) ),
inference(cnf_transformation,[status(thm)],[f89011]) ).
fof(f89015,plain,
( ~ r2_hidden(sK6518_skl,sK6520_skl)
| ~ r2_hidden(sK6517_skl,sK6520_skl) ),
inference(cnf_transformation,[status(thm)],[f89011]) ).
fof(f89016,plain,
( ~ r2_hidden(sK6518_skl,sK6520_skl)
| ~ r2_hidden(sK6517_skl,k4_xboole_0(sK6519_skl,sK6520_skl)) ),
inference(cnf_transformation,[status(thm)],[f89011]) ).
fof(f89017,plain,
( ~ r2_hidden(sK6518_skl,k4_xboole_0(sK6519_skl,sK6520_skl))
| ~ r2_hidden(sK6517_skl,sK6520_skl) ),
inference(cnf_transformation,[status(thm)],[f89011]) ).
fof(f95576,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)],[f19122]) ).
fof(f95584,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)],[f19142]) ).
fof(f100467,plain,
( r2_hidden(sK6518_skl,sK6520_skl)
| r2_hidden(sK6518_skl,sK6519_skl) ),
inference(resolution,[status(thm)],[f95576,f89013]) ).
fof(f100468,plain,
( r2_hidden(sK6517_skl,sK6520_skl)
| r2_hidden(sK6517_skl,sK6519_skl) ),
inference(resolution,[status(thm)],[f95576,f89012]) ).
fof(f100575,plain,
( ~ r2_hidden(sK6518_skl,sK6520_skl)
| r2_hidden(sK6517_skl,sK6520_skl)
| ~ r2_hidden(sK6517_skl,sK6519_skl) ),
inference(resolution,[status(thm)],[f95584,f89016]) ).
fof(f100577,plain,
( ~ r2_hidden(sK6517_skl,sK6520_skl)
| r2_hidden(sK6518_skl,sK6520_skl)
| ~ r2_hidden(sK6518_skl,sK6519_skl) ),
inference(resolution,[status(thm)],[f95584,f89017]) ).
fof(f100578,plain,
( ~ r2_hidden(sK6517_skl,k4_xboole_0(sK6519_skl,sK6520_skl))
| r2_hidden(sK6518_skl,sK6520_skl)
| ~ r2_hidden(sK6518_skl,sK6519_skl) ),
inference(resolution,[status(thm)],[f95584,f89014]) ).
fof(f100585,plain,
( ~ r2_hidden(sK6518_skl,sK6520_skl)
| ~ r2_hidden(sK6517_skl,sK6519_skl) ),
inference(forward_subsumption_resolution,[status(thm)],[f100575,f89015]) ).
fof(f100586,plain,
( ~ r2_hidden(sK6517_skl,sK6520_skl)
| r2_hidden(sK6518_skl,sK6520_skl) ),
inference(forward_subsumption_resolution,[status(thm)],[f100577,f100467]) ).
fof(f100587,plain,
( ~ r2_hidden(sK6517_skl,k4_xboole_0(sK6519_skl,sK6520_skl))
| r2_hidden(sK6518_skl,sK6520_skl) ),
inference(forward_subsumption_resolution,[status(thm)],[f100578,f100467]) ).
fof(f100803,plain,
r2_hidden(sK6517_skl,sK6519_skl),
inference(backward_subsumption_resolution,[status(thm)],[f100468,f100804]) ).
fof(f100804,plain,
~ r2_hidden(sK6517_skl,sK6520_skl),
inference(forward_subsumption_resolution,[status(thm)],[f100586,f89015]) ).
fof(f100811,plain,
~ r2_hidden(sK6518_skl,sK6520_skl),
inference(backward_subsumption_resolution,[status(thm)],[f100585,f100803]) ).
fof(f100871,plain,
~ r2_hidden(sK6517_skl,k4_xboole_0(sK6519_skl,sK6520_skl)),
inference(forward_subsumption_resolution,[status(thm)],[f100587,f100811]) ).
fof(f100872,plain,
( r2_hidden(sK6517_skl,sK6520_skl)
| ~ r2_hidden(sK6517_skl,sK6519_skl) ),
inference(resolution,[status(thm)],[f100871,f95584]) ).
fof(f100873,plain,
r2_hidden(sK6517_skl,sK6520_skl),
inference(forward_subsumption_resolution,[status(thm)],[f100872,f100803]) ).
fof(f100874,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f100873,f100804]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU406+3 : TPTP v9.3.1. Released v3.4.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.07/0.34 % Computer : n013.cluster.edu
% 0.07/0.34 % Model : x86_64 x86_64
% 0.07/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.34 % Memory : 8046.5625MB
% 0.07/0.34 % OS : Linux 6.8.0-71-generic
% 0.07/0.34 % CPULimit : 300
% 0.07/0.34 % WCLimit : 300
% 0.07/0.34 % DateTime : Mon Sep 21 06:20:32 UTC 2026
% 0.07/0.34 % CPUTime :
% 2.96/3.26 % Drodi V4.1.1
% 13.33/4.63 % Refutation found
% 13.33/4.63 % SZS status Theorem for theBenchmark: Theorem is valid
% 13.33/4.63 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 3.38/5.35 % Elapsed time: 4.948590 seconds
% 3.38/5.35 % CPU time: 14.273267 seconds
% 3.38/5.35 % Total memory used: 5.314 GB
% 3.38/5.35 % Net memory used: 5.277 GB
%------------------------------------------------------------------------------