%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : ALG226+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 : 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 1.08s 2.19s
% Output : CNFRefutation 9.14s
% 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(f3148,axiom,
! [A,B,C] :
( ( m1_pboole(C,A)
& m1_pboole(B,A) )
=> ( r6_pboole(A,B,C)
<=> B = C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f4730,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/sandbox/benchmark/theBenchmark.p') ).
fof(f4731,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/sandbox/benchmark/theBenchmark.p') ).
fof(f4732,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)],[f4731]) ).
fof(f14066,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)],[f3148]) ).
fof(f14067,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)],[f14066]) ).
fof(f14069,plain,
! [X0,X1,X2] :
( X0 != X2
| r6_pboole(X1,X0,X2)
| ~ m1_pboole(X2,X1)
| ~ m1_pboole(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f14067]) ).
fof(f19243,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)],[f4730]) ).
fof(f19244,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)],[f19243]) ).
fof(f19245,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)],[f4732]) ).
fof(f19246,plain,
( ~ r6_pboole(sK1314_skl,sK1315_skl,sK1316_skl)
& k7_relat_1(sK1315_skl,k1_closure3(sK1314_skl,sK1315_skl)) = k7_relat_1(sK1316_skl,k1_closure3(sK1314_skl,sK1316_skl))
& k1_closure3(sK1314_skl,sK1315_skl) = k1_closure3(sK1314_skl,sK1316_skl)
& m1_pboole(sK1316_skl,sK1314_skl)
& v2_relat_1(sK1316_skl)
& m1_pboole(sK1315_skl,sK1314_skl)
& v2_relat_1(sK1315_skl)
& ~ v1_xboole_0(sK1314_skl) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1314_skl,sK1315_skl,sK1316_skl]),skolemize(A,sK1314_skl),skolemize(B,sK1315_skl),skolemize(C,sK1316_skl)],[f19245]) ).
fof(f19247,plain,
~ v1_xboole_0(sK1314_skl),
inference(cnf_transformation,[status(thm)],[f19246]) ).
fof(f19248,plain,
v2_relat_1(sK1315_skl),
inference(cnf_transformation,[status(thm)],[f19246]) ).
fof(f19249,plain,
m1_pboole(sK1315_skl,sK1314_skl),
inference(cnf_transformation,[status(thm)],[f19246]) ).
fof(f19250,plain,
v2_relat_1(sK1316_skl),
inference(cnf_transformation,[status(thm)],[f19246]) ).
fof(f19251,plain,
m1_pboole(sK1316_skl,sK1314_skl),
inference(cnf_transformation,[status(thm)],[f19246]) ).
fof(f19252,plain,
k1_closure3(sK1314_skl,sK1315_skl) = k1_closure3(sK1314_skl,sK1316_skl),
inference(cnf_transformation,[status(thm)],[f19246]) ).
fof(f19253,plain,
k7_relat_1(sK1315_skl,k1_closure3(sK1314_skl,sK1315_skl)) = k7_relat_1(sK1316_skl,k1_closure3(sK1314_skl,sK1316_skl)),
inference(cnf_transformation,[status(thm)],[f19246]) ).
fof(f19254,plain,
~ r6_pboole(sK1314_skl,sK1315_skl,sK1316_skl),
inference(cnf_transformation,[status(thm)],[f19246]) ).
fof(f21098,plain,
! [X2,X1] :
( r6_pboole(X1,X2,X2)
| ~ m1_pboole(X2,X1)
| ~ m1_pboole(X2,X1) ),
inference(destructive_equality_resolution,[status(thm)],[f14069]) ).
fof(f21099,plain,
! [X0,X1] :
( r6_pboole(X1,X0,X0)
| ~ m1_pboole(X0,X1) ),
inference(duplicate_literals_removal,[status(thm)],[f21098]) ).
fof(f21554,plain,
k7_relat_1(sK1315_skl,k1_closure3(sK1314_skl,sK1315_skl)) = k7_relat_1(sK1316_skl,k1_closure3(sK1314_skl,sK1315_skl)),
inference(forward_demodulation,[status(thm)],[f19252,f19253]) ).
fof(f24183,plain,
( sK1316_skl = k1_funct_4(k1_pboole(sK1314_skl),k7_relat_1(sK1316_skl,k1_closure3(sK1314_skl,sK1316_skl)))
| ~ v2_relat_1(sK1316_skl)
| v1_xboole_0(sK1314_skl) ),
inference(resolution,[status(thm)],[f19244,f19251]) ).
fof(f24184,plain,
( sK1315_skl = k1_funct_4(k1_pboole(sK1314_skl),k7_relat_1(sK1315_skl,k1_closure3(sK1314_skl,sK1315_skl)))
| ~ v2_relat_1(sK1315_skl)
| v1_xboole_0(sK1314_skl) ),
inference(resolution,[status(thm)],[f19244,f19249]) ).
fof(f24185,plain,
( sK1316_skl = k1_funct_4(k1_pboole(sK1314_skl),k7_relat_1(sK1316_skl,k1_closure3(sK1314_skl,sK1315_skl)))
| ~ v2_relat_1(sK1316_skl)
| v1_xboole_0(sK1314_skl) ),
inference(forward_demodulation,[status(thm)],[f19252,f24183]) ).
fof(f24186,plain,
( sK1316_skl = k1_funct_4(k1_pboole(sK1314_skl),k7_relat_1(sK1315_skl,k1_closure3(sK1314_skl,sK1315_skl)))
| ~ v2_relat_1(sK1316_skl)
| v1_xboole_0(sK1314_skl) ),
inference(forward_demodulation,[status(thm)],[f21554,f24185]) ).
fof(f24187,plain,
( sK1316_skl = k1_funct_4(k1_pboole(sK1314_skl),k7_relat_1(sK1315_skl,k1_closure3(sK1314_skl,sK1315_skl)))
| ~ v2_relat_1(sK1316_skl) ),
inference(forward_subsumption_resolution,[status(thm)],[f24186,f19247]) ).
fof(f24188,plain,
( sK1315_skl = k1_funct_4(k1_pboole(sK1314_skl),k7_relat_1(sK1315_skl,k1_closure3(sK1314_skl,sK1315_skl)))
| ~ v2_relat_1(sK1315_skl) ),
inference(forward_subsumption_resolution,[status(thm)],[f24184,f19247]) ).
fof(f24606,plain,
sK1316_skl = k1_funct_4(k1_pboole(sK1314_skl),k7_relat_1(sK1315_skl,k1_closure3(sK1314_skl,sK1315_skl))),
inference(forward_subsumption_resolution,[status(thm)],[f24187,f19250]) ).
fof(f24692,plain,
( sK1315_skl = sK1316_skl
| ~ v2_relat_1(sK1315_skl) ),
inference(forward_demodulation,[status(thm)],[f24606,f24188]) ).
fof(f24728,plain,
~ r6_pboole(sK1314_skl,sK1315_skl,sK1315_skl),
inference(backward_demodulation,[status(thm)],[f24732,f19254]) ).
fof(f24732,plain,
sK1315_skl = sK1316_skl,
inference(forward_subsumption_resolution,[status(thm)],[f24692,f19248]) ).
fof(f24783,plain,
~ m1_pboole(sK1315_skl,sK1314_skl),
inference(resolution,[status(thm)],[f24728,f21099]) ).
fof(f24786,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f24783,f19249]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ALG226+2 : TPTP v9.3.1. Released v3.4.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.17/0.42 % Computer : n009.cluster.edu
% 0.17/0.42 % Model : x86_64 x86_64
% 0.17/0.42 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.42 % Memory : 8046.5625MB
% 0.17/0.42 % OS : Linux 6.8.0-71-generic
% 0.17/0.42 % CPULimit : 300
% 0.17/0.42 % WCLimit : 300
% 0.17/0.42 % DateTime : Mon Sep 21 13:06:43 UTC 2026
% 0.17/0.43 % CPUTime :
% 0.67/1.03 % Drodi V4.1.1
% 1.08/2.19 % Refutation found
% 1.08/2.19 % SZS status Theorem for theBenchmark: Theorem is valid
% 1.08/2.19 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 9.14/2.33 % Elapsed time: 1.869550 seconds
% 9.14/2.33 % CPU time: 9.885928 seconds
% 9.14/2.33 % Total memory used: 791.892 MB
% 9.14/2.33 % Net memory used: 778.482 MB
%------------------------------------------------------------------------------