%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : ALG226+3 : TPTP v9.3.1. Released v3.4.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n009.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 11:49:02 AM UTC 2026
% Result : Theorem 20.24s 5.08s
% Output : CNFRefutation 14.58s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 3
% Syntax : Number of formulae : 34 ( 14 unt; 0 def)
% Number of atoms : 99 ( 28 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 100 ( 35 ~; 29 |; 23 &)
% ( 2 <=>; 11 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-3 aty)
% Number of functors : 7 ( 7 usr; 3 con; 0-2 aty)
% Number of variables : 31 ( 28 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f5405,axiom,
! [A,B,C] :
( ( m1_pboole(C,A)
& m1_pboole(B,A) )
=> ( r6_pboole(A,B,C)
<=> B = C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f16950,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ( m1_pboole(B,A)
& v2_relat_1(B) )
=> B = k1_funct_4(k1_pboole(A),k7_relat_1(B,k1_closure3(A,B))) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f16951,conjecture,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ( m1_pboole(B,A)
& v2_relat_1(B) )
=> ! [C] :
( ( m1_pboole(C,A)
& v2_relat_1(C) )
=> ( ( k7_relat_1(B,k1_closure3(A,B)) = k7_relat_1(C,k1_closure3(A,C))
& k1_closure3(A,B) = k1_closure3(A,C) )
=> r6_pboole(A,B,C) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f16952,negated_conjecture,
~ ! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ( m1_pboole(B,A)
& v2_relat_1(B) )
=> ! [C] :
( ( m1_pboole(C,A)
& v2_relat_1(C) )
=> ( ( k7_relat_1(B,k1_closure3(A,B)) = k7_relat_1(C,k1_closure3(A,C))
& k1_closure3(A,B) = k1_closure3(A,C) )
=> r6_pboole(A,B,C) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f16951]) ).
fof(f33054,plain,
! [A,B,C] :
( ( r6_pboole(A,B,C)
<=> B = C )
| ~ m1_pboole(C,A)
| ~ m1_pboole(B,A) ),
inference(pre_NNF_transformation,[status(thm)],[f5405]) ).
fof(f33055,plain,
! [A,B,C] :
( ( ( B != C
| r6_pboole(A,B,C) )
& ( B = C
| ~ r6_pboole(A,B,C) ) )
| ~ m1_pboole(C,A)
| ~ m1_pboole(B,A) ),
inference(NNF_transformation,[status(thm)],[f33054]) ).
fof(f33057,plain,
! [X0,X1,X2] :
( X0 != X2
| r6_pboole(X1,X0,X2)
| ~ m1_pboole(X2,X1)
| ~ m1_pboole(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f33055]) ).
fof(f75975,plain,
! [A] :
( ! [B] :
( B = k1_funct_4(k1_pboole(A),k7_relat_1(B,k1_closure3(A,B)))
| ~ m1_pboole(B,A)
| ~ v2_relat_1(B) )
| v1_xboole_0(A) ),
inference(pre_NNF_transformation,[status(thm)],[f16950]) ).
fof(f75976,plain,
! [X0,X1] :
( X1 = k1_funct_4(k1_pboole(X0),k7_relat_1(X1,k1_closure3(X0,X1)))
| ~ m1_pboole(X1,X0)
| ~ v2_relat_1(X1)
| v1_xboole_0(X0) ),
inference(cnf_transformation,[status(thm)],[f75975]) ).
fof(f75977,plain,
? [A] :
( ? [B] :
( ? [C] :
( ~ r6_pboole(A,B,C)
& k7_relat_1(B,k1_closure3(A,B)) = k7_relat_1(C,k1_closure3(A,C))
& k1_closure3(A,B) = k1_closure3(A,C)
& m1_pboole(C,A)
& v2_relat_1(C) )
& m1_pboole(B,A)
& v2_relat_1(B) )
& ~ v1_xboole_0(A) ),
inference(pre_NNF_transformation,[status(thm)],[f16952]) ).
fof(f75978,plain,
( ~ r6_pboole(sK5437_skl,sK5438_skl,sK5439_skl)
& k7_relat_1(sK5438_skl,k1_closure3(sK5437_skl,sK5438_skl)) = k7_relat_1(sK5439_skl,k1_closure3(sK5437_skl,sK5439_skl))
& k1_closure3(sK5437_skl,sK5438_skl) = k1_closure3(sK5437_skl,sK5439_skl)
& m1_pboole(sK5439_skl,sK5437_skl)
& v2_relat_1(sK5439_skl)
& m1_pboole(sK5438_skl,sK5437_skl)
& v2_relat_1(sK5438_skl)
& ~ v1_xboole_0(sK5437_skl) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK5437_skl,sK5438_skl,sK5439_skl]),skolemize(A,sK5437_skl),skolemize(B,sK5438_skl),skolemize(C,sK5439_skl)],[f75977]) ).
fof(f75979,plain,
~ v1_xboole_0(sK5437_skl),
inference(cnf_transformation,[status(thm)],[f75978]) ).
fof(f75980,plain,
v2_relat_1(sK5438_skl),
inference(cnf_transformation,[status(thm)],[f75978]) ).
fof(f75981,plain,
m1_pboole(sK5438_skl,sK5437_skl),
inference(cnf_transformation,[status(thm)],[f75978]) ).
fof(f75982,plain,
v2_relat_1(sK5439_skl),
inference(cnf_transformation,[status(thm)],[f75978]) ).
fof(f75983,plain,
m1_pboole(sK5439_skl,sK5437_skl),
inference(cnf_transformation,[status(thm)],[f75978]) ).
fof(f75984,plain,
k1_closure3(sK5437_skl,sK5438_skl) = k1_closure3(sK5437_skl,sK5439_skl),
inference(cnf_transformation,[status(thm)],[f75978]) ).
fof(f75985,plain,
k7_relat_1(sK5438_skl,k1_closure3(sK5437_skl,sK5438_skl)) = k7_relat_1(sK5439_skl,k1_closure3(sK5437_skl,sK5439_skl)),
inference(cnf_transformation,[status(thm)],[f75978]) ).
fof(f75986,plain,
~ r6_pboole(sK5437_skl,sK5438_skl,sK5439_skl),
inference(cnf_transformation,[status(thm)],[f75978]) ).
fof(f81197,plain,
! [X2,X1] :
( r6_pboole(X1,X2,X2)
| ~ m1_pboole(X2,X1)
| ~ m1_pboole(X2,X1) ),
inference(destructive_equality_resolution,[status(thm)],[f33057]) ).
fof(f81198,plain,
! [X0,X1] :
( r6_pboole(X1,X0,X0)
| ~ m1_pboole(X0,X1) ),
inference(duplicate_literals_removal,[status(thm)],[f81197]) ).
fof(f83947,plain,
k7_relat_1(sK5438_skl,k1_closure3(sK5437_skl,sK5438_skl)) = k7_relat_1(sK5439_skl,k1_closure3(sK5437_skl,sK5438_skl)),
inference(forward_demodulation,[status(thm)],[f75984,f75985]) ).
fof(f88711,plain,
( sK5439_skl = k1_funct_4(k1_pboole(sK5437_skl),k7_relat_1(sK5439_skl,k1_closure3(sK5437_skl,sK5439_skl)))
| ~ v2_relat_1(sK5439_skl)
| v1_xboole_0(sK5437_skl) ),
inference(resolution,[status(thm)],[f75976,f75983]) ).
fof(f88712,plain,
( sK5438_skl = k1_funct_4(k1_pboole(sK5437_skl),k7_relat_1(sK5438_skl,k1_closure3(sK5437_skl,sK5438_skl)))
| ~ v2_relat_1(sK5438_skl)
| v1_xboole_0(sK5437_skl) ),
inference(resolution,[status(thm)],[f75976,f75981]) ).
fof(f88713,plain,
( sK5439_skl = k1_funct_4(k1_pboole(sK5437_skl),k7_relat_1(sK5439_skl,k1_closure3(sK5437_skl,sK5438_skl)))
| ~ v2_relat_1(sK5439_skl)
| v1_xboole_0(sK5437_skl) ),
inference(forward_demodulation,[status(thm)],[f75984,f88711]) ).
fof(f88714,plain,
( sK5439_skl = k1_funct_4(k1_pboole(sK5437_skl),k7_relat_1(sK5438_skl,k1_closure3(sK5437_skl,sK5438_skl)))
| ~ v2_relat_1(sK5439_skl)
| v1_xboole_0(sK5437_skl) ),
inference(forward_demodulation,[status(thm)],[f83947,f88713]) ).
fof(f88715,plain,
( sK5439_skl = k1_funct_4(k1_pboole(sK5437_skl),k7_relat_1(sK5438_skl,k1_closure3(sK5437_skl,sK5438_skl)))
| ~ v2_relat_1(sK5439_skl) ),
inference(forward_subsumption_resolution,[status(thm)],[f88714,f75979]) ).
fof(f88716,plain,
( sK5438_skl = k1_funct_4(k1_pboole(sK5437_skl),k7_relat_1(sK5438_skl,k1_closure3(sK5437_skl,sK5438_skl)))
| ~ v2_relat_1(sK5438_skl) ),
inference(forward_subsumption_resolution,[status(thm)],[f88712,f75979]) ).
fof(f89153,plain,
sK5439_skl = k1_funct_4(k1_pboole(sK5437_skl),k7_relat_1(sK5438_skl,k1_closure3(sK5437_skl,sK5438_skl))),
inference(forward_subsumption_resolution,[status(thm)],[f88715,f75982]) ).
fof(f89343,plain,
( sK5438_skl = sK5439_skl
| ~ v2_relat_1(sK5438_skl) ),
inference(forward_demodulation,[status(thm)],[f89153,f88716]) ).
fof(f89385,plain,
~ r6_pboole(sK5437_skl,sK5438_skl,sK5438_skl),
inference(backward_demodulation,[status(thm)],[f89388,f75986]) ).
fof(f89388,plain,
sK5438_skl = sK5439_skl,
inference(forward_subsumption_resolution,[status(thm)],[f89343,f75980]) ).
fof(f89416,plain,
~ m1_pboole(sK5438_skl,sK5437_skl),
inference(resolution,[status(thm)],[f89385,f81198]) ).
fof(f89420,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f89416,f75981]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ALG226+3 : TPTP v9.3.1. Released v3.4.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n009.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Mon Sep 21 13:06:29 UTC 2026
% 0.09/0.36 % CPUTime :
% 2.47/2.73 % Drodi V4.1.1
% 20.24/5.08 % Refutation found
% 20.24/5.08 % SZS status Theorem for theBenchmark: Theorem is valid
% 20.24/5.08 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 3.16/5.45 % Elapsed time: 5.025166 seconds
% 3.16/5.45 % CPU time: 21.361049 seconds
% 3.16/5.45 % Total memory used: 4.578 GB
% 3.16/5.45 % Net memory used: 4.534 GB
%------------------------------------------------------------------------------