TSTP Solution File: ALG226+2 by Drodi---3.6.0
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%------------------------------------------------------------------------------
% File : Drodi---3.6.0
% Problem : ALG226+2 : TPTP v8.1.2. Released v3.4.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% Computer : n029.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Apr 30 20:11:07 EDT 2024
% Result : Theorem 14.18s 2.50s
% Output : CNFRefutation 14.91s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 8
% Syntax : Number of formulae : 50 ( 13 unt; 0 def)
% Number of atoms : 136 ( 28 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 137 ( 51 ~; 45 |; 23 &)
% ( 7 <=>; 11 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 11 ( 9 usr; 6 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(B,A)
& m1_pboole(C,A) )
=> ( r6_pboole(A,B,C)
<=> B = C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f4730,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ( v2_relat_1(B)
& m1_pboole(B,A) )
=> 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] :
( ( v2_relat_1(B)
& m1_pboole(B,A) )
=> ! [C] :
( ( v2_relat_1(C)
& m1_pboole(C,A) )
=> ( ( k1_closure3(A,B) = k1_closure3(A,C)
& k7_relat_1(B,k1_closure3(A,B)) = k7_relat_1(C,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] :
( ( v2_relat_1(B)
& m1_pboole(B,A) )
=> ! [C] :
( ( v2_relat_1(C)
& m1_pboole(C,A) )
=> ( ( k1_closure3(A,B) = k1_closure3(A,C)
& k7_relat_1(B,k1_closure3(A,B)) = k7_relat_1(C,k1_closure3(A,C)) )
=> r6_pboole(A,B,C) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f4731]) ).
fof(f14066,plain,
! [A,B,C] :
( ~ m1_pboole(B,A)
| ~ m1_pboole(C,A)
| ( r6_pboole(A,B,C)
<=> B = C ) ),
inference(pre_NNF_transformation,[status(esa)],[f3148]) ).
fof(f14067,plain,
! [A,B,C] :
( ~ m1_pboole(B,A)
| ~ m1_pboole(C,A)
| ( ( ~ r6_pboole(A,B,C)
| B = C )
& ( r6_pboole(A,B,C)
| B != C ) ) ),
inference(NNF_transformation,[status(esa)],[f14066]) ).
fof(f14069,plain,
! [X0,X1,X2] :
( ~ m1_pboole(X0,X1)
| ~ m1_pboole(X2,X1)
| r6_pboole(X1,X0,X2)
| X0 != X2 ),
inference(cnf_transformation,[status(esa)],[f14067]) ).
fof(f19243,plain,
! [A] :
( v1_xboole_0(A)
| ! [B] :
( ~ v2_relat_1(B)
| ~ m1_pboole(B,A)
| B = k1_funct_4(k1_pboole(A),k7_relat_1(B,k1_closure3(A,B))) ) ),
inference(pre_NNF_transformation,[status(esa)],[f4730]) ).
fof(f19244,plain,
! [X0,X1] :
( v1_xboole_0(X0)
| ~ v2_relat_1(X1)
| ~ m1_pboole(X1,X0)
| X1 = k1_funct_4(k1_pboole(X0),k7_relat_1(X1,k1_closure3(X0,X1))) ),
inference(cnf_transformation,[status(esa)],[f19243]) ).
fof(f19245,plain,
? [A] :
( ~ v1_xboole_0(A)
& ? [B] :
( v2_relat_1(B)
& m1_pboole(B,A)
& ? [C] :
( v2_relat_1(C)
& m1_pboole(C,A)
& k1_closure3(A,B) = k1_closure3(A,C)
& k7_relat_1(B,k1_closure3(A,B)) = k7_relat_1(C,k1_closure3(A,C))
& ~ r6_pboole(A,B,C) ) ) ),
inference(pre_NNF_transformation,[status(esa)],[f4732]) ).
fof(f19246,plain,
( ~ v1_xboole_0(sk0_1314)
& v2_relat_1(sk0_1315)
& m1_pboole(sk0_1315,sk0_1314)
& v2_relat_1(sk0_1316)
& m1_pboole(sk0_1316,sk0_1314)
& k1_closure3(sk0_1314,sk0_1315) = k1_closure3(sk0_1314,sk0_1316)
& k7_relat_1(sk0_1315,k1_closure3(sk0_1314,sk0_1315)) = k7_relat_1(sk0_1316,k1_closure3(sk0_1314,sk0_1316))
& ~ r6_pboole(sk0_1314,sk0_1315,sk0_1316) ),
inference(skolemization,[status(esa)],[f19245]) ).
fof(f19247,plain,
~ v1_xboole_0(sk0_1314),
inference(cnf_transformation,[status(esa)],[f19246]) ).
fof(f19248,plain,
v2_relat_1(sk0_1315),
inference(cnf_transformation,[status(esa)],[f19246]) ).
fof(f19249,plain,
m1_pboole(sk0_1315,sk0_1314),
inference(cnf_transformation,[status(esa)],[f19246]) ).
fof(f19250,plain,
v2_relat_1(sk0_1316),
inference(cnf_transformation,[status(esa)],[f19246]) ).
fof(f19251,plain,
m1_pboole(sk0_1316,sk0_1314),
inference(cnf_transformation,[status(esa)],[f19246]) ).
fof(f19252,plain,
k1_closure3(sk0_1314,sk0_1315) = k1_closure3(sk0_1314,sk0_1316),
inference(cnf_transformation,[status(esa)],[f19246]) ).
fof(f19253,plain,
k7_relat_1(sk0_1315,k1_closure3(sk0_1314,sk0_1315)) = k7_relat_1(sk0_1316,k1_closure3(sk0_1314,sk0_1316)),
inference(cnf_transformation,[status(esa)],[f19246]) ).
fof(f19254,plain,
~ r6_pboole(sk0_1314,sk0_1315,sk0_1316),
inference(cnf_transformation,[status(esa)],[f19246]) ).
fof(f23292,plain,
! [X2,X1] :
( ~ m1_pboole(X2,X1)
| ~ m1_pboole(X2,X1)
| r6_pboole(X1,X2,X2) ),
inference(destructive_equality_resolution,[status(esa)],[f14069]) ).
fof(f23293,plain,
! [X0,X1] :
( ~ m1_pboole(X0,X1)
| r6_pboole(X1,X0,X0) ),
inference(duplicate_literals_removal,[status(esa)],[f23292]) ).
fof(f23651,plain,
k7_relat_1(sk0_1315,k1_closure3(sk0_1314,sk0_1315)) = k7_relat_1(sk0_1316,k1_closure3(sk0_1314,sk0_1315)),
inference(forward_demodulation,[status(thm)],[f19252,f19253]) ).
fof(f23661,plain,
( spl0_663
<=> v1_xboole_0(sk0_1314) ),
introduced(split_symbol_definition) ).
fof(f23662,plain,
( v1_xboole_0(sk0_1314)
| ~ spl0_663 ),
inference(component_clause,[status(thm)],[f23661]) ).
fof(f23664,plain,
( spl0_664
<=> v2_relat_1(sk0_1316) ),
introduced(split_symbol_definition) ).
fof(f23666,plain,
( ~ v2_relat_1(sk0_1316)
| spl0_664 ),
inference(component_clause,[status(thm)],[f23664]) ).
fof(f23667,plain,
( spl0_665
<=> sk0_1316 = k1_funct_4(k1_pboole(sk0_1314),k7_relat_1(sk0_1316,k1_closure3(sk0_1314,sk0_1316))) ),
introduced(split_symbol_definition) ).
fof(f23668,plain,
( sk0_1316 = k1_funct_4(k1_pboole(sk0_1314),k7_relat_1(sk0_1316,k1_closure3(sk0_1314,sk0_1316)))
| ~ spl0_665 ),
inference(component_clause,[status(thm)],[f23667]) ).
fof(f23670,plain,
( v1_xboole_0(sk0_1314)
| ~ v2_relat_1(sk0_1316)
| sk0_1316 = k1_funct_4(k1_pboole(sk0_1314),k7_relat_1(sk0_1316,k1_closure3(sk0_1314,sk0_1316))) ),
inference(resolution,[status(thm)],[f19244,f19251]) ).
fof(f23671,plain,
( spl0_663
| ~ spl0_664
| spl0_665 ),
inference(split_clause,[status(thm)],[f23670,f23661,f23664,f23667]) ).
fof(f23672,plain,
( spl0_666
<=> v2_relat_1(sk0_1315) ),
introduced(split_symbol_definition) ).
fof(f23674,plain,
( ~ v2_relat_1(sk0_1315)
| spl0_666 ),
inference(component_clause,[status(thm)],[f23672]) ).
fof(f23675,plain,
( spl0_667
<=> sk0_1315 = k1_funct_4(k1_pboole(sk0_1314),k7_relat_1(sk0_1315,k1_closure3(sk0_1314,sk0_1315))) ),
introduced(split_symbol_definition) ).
fof(f23676,plain,
( sk0_1315 = k1_funct_4(k1_pboole(sk0_1314),k7_relat_1(sk0_1315,k1_closure3(sk0_1314,sk0_1315)))
| ~ spl0_667 ),
inference(component_clause,[status(thm)],[f23675]) ).
fof(f23678,plain,
( v1_xboole_0(sk0_1314)
| ~ v2_relat_1(sk0_1315)
| sk0_1315 = k1_funct_4(k1_pboole(sk0_1314),k7_relat_1(sk0_1315,k1_closure3(sk0_1314,sk0_1315))) ),
inference(resolution,[status(thm)],[f19244,f19249]) ).
fof(f23679,plain,
( spl0_663
| ~ spl0_666
| spl0_667 ),
inference(split_clause,[status(thm)],[f23678,f23661,f23672,f23675]) ).
fof(f23680,plain,
( $false
| spl0_666 ),
inference(forward_subsumption_resolution,[status(thm)],[f23674,f19248]) ).
fof(f23681,plain,
spl0_666,
inference(contradiction_clause,[status(thm)],[f23680]) ).
fof(f23682,plain,
( $false
| spl0_664 ),
inference(forward_subsumption_resolution,[status(thm)],[f23666,f19250]) ).
fof(f23683,plain,
spl0_664,
inference(contradiction_clause,[status(thm)],[f23682]) ).
fof(f23684,plain,
( $false
| ~ spl0_663 ),
inference(forward_subsumption_resolution,[status(thm)],[f23662,f19247]) ).
fof(f23685,plain,
~ spl0_663,
inference(contradiction_clause,[status(thm)],[f23684]) ).
fof(f23686,plain,
( sk0_1316 = k1_funct_4(k1_pboole(sk0_1314),k7_relat_1(sk0_1316,k1_closure3(sk0_1314,sk0_1315)))
| ~ spl0_665 ),
inference(forward_demodulation,[status(thm)],[f19252,f23668]) ).
fof(f23687,plain,
( sk0_1316 = k1_funct_4(k1_pboole(sk0_1314),k7_relat_1(sk0_1315,k1_closure3(sk0_1314,sk0_1315)))
| ~ spl0_665 ),
inference(forward_demodulation,[status(thm)],[f23651,f23686]) ).
fof(f23688,plain,
( sk0_1316 = sk0_1315
| ~ spl0_667
| ~ spl0_665 ),
inference(forward_demodulation,[status(thm)],[f23676,f23687]) ).
fof(f23689,plain,
( ~ r6_pboole(sk0_1314,sk0_1315,sk0_1315)
| ~ spl0_667
| ~ spl0_665 ),
inference(backward_demodulation,[status(thm)],[f23688,f19254]) ).
fof(f23692,plain,
( ~ m1_pboole(sk0_1315,sk0_1314)
| ~ spl0_667
| ~ spl0_665 ),
inference(resolution,[status(thm)],[f23689,f23293]) ).
fof(f23693,plain,
( $false
| ~ spl0_667
| ~ spl0_665 ),
inference(forward_subsumption_resolution,[status(thm)],[f23692,f19249]) ).
fof(f23694,plain,
( ~ spl0_667
| ~ spl0_665 ),
inference(contradiction_clause,[status(thm)],[f23693]) ).
fof(f23695,plain,
$false,
inference(sat_refutation,[status(thm)],[f23671,f23679,f23681,f23683,f23685,f23694]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.09/0.11 % Problem : ALG226+2 : TPTP v8.1.2. Released v3.4.0.
% 0.09/0.12 % Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.10/0.32 % Computer : n029.cluster.edu
% 0.10/0.32 % Model : x86_64 x86_64
% 0.10/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.32 % Memory : 8042.1875MB
% 0.10/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.10/0.32 % CPULimit : 300
% 0.10/0.32 % WCLimit : 300
% 0.10/0.32 % DateTime : Mon Apr 29 23:53:05 EDT 2024
% 0.10/0.32 % CPUTime :
% 0.46/0.70 % Drodi V3.6.0
% 14.18/2.50 % Refutation found
% 14.18/2.50 % SZS status Theorem for theBenchmark: Theorem is valid
% 14.18/2.50 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 14.91/2.61 % Elapsed time: 2.272036 seconds
% 14.91/2.61 % CPU time: 14.838939 seconds
% 14.91/2.61 % Total memory used: 744.704 MB
% 14.91/2.61 % Net memory used: 739.151 MB
%------------------------------------------------------------------------------