TSTP Solution File: NUM856+2 by Drodi---3.5.1
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%------------------------------------------------------------------------------
% File : Drodi---3.5.1
% Problem : NUM856+2 : TPTP v8.1.2. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% Computer : n019.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 : Wed May 31 12:30:52 EDT 2023
% Result : Theorem 1.83s 0.62s
% Output : CNFRefutation 1.83s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 14
% Syntax : Number of formulae : 64 ( 6 unt; 0 def)
% Number of atoms : 151 ( 14 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 149 ( 62 ~; 66 |; 10 &)
% ( 8 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 12 ( 10 usr; 9 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 4 con; 0-2 aty)
% Number of variables : 45 (; 45 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,conjecture,
greater(vmul(vd517,vd519),vmul(vd518,vd520)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f2,negated_conjecture,
~ greater(vmul(vd517,vd519),vmul(vd518,vd520)),
inference(negated_conjecture,[status(cth)],[f1]) ).
fof(f3,axiom,
( ( greater(vd519,vd520)
& geq(vd517,vd518) )
| ( geq(vd519,vd520)
& greater(vd517,vd518) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f4,axiom,
! [Vd501,Vd502,Vd504,Vd505] :
( ( greater(Vd504,Vd505)
& greater(Vd501,Vd502) )
=> greater(vmul(Vd501,Vd504),vmul(Vd502,Vd505)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f10,axiom,
! [Vd456,Vd457,Vd458] :
( greater(Vd457,Vd458)
=> greater(vmul(Vd457,Vd456),vmul(Vd458,Vd456)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f13,axiom,
! [Vd418,Vd419] : vmul(Vd418,Vd419) = vmul(Vd419,Vd418),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f36,axiom,
! [Vd244,Vd245] :
( geq(Vd245,Vd244)
<=> ( greater(Vd245,Vd244)
| Vd245 = Vd244 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f61,plain,
~ greater(vmul(vd517,vd519),vmul(vd518,vd520)),
inference(cnf_transformation,[status(esa)],[f2]) ).
fof(f62,plain,
( pd0_0
=> ( greater(vd519,vd520)
& geq(vd517,vd518) ) ),
introduced(predicate_definition,[f3]) ).
fof(f63,plain,
( pd0_0
| ( geq(vd519,vd520)
& greater(vd517,vd518) ) ),
inference(formula_renaming,[status(thm)],[f3,f62]) ).
fof(f64,plain,
( pd0_0
| geq(vd519,vd520) ),
inference(cnf_transformation,[status(esa)],[f63]) ).
fof(f65,plain,
( pd0_0
| greater(vd517,vd518) ),
inference(cnf_transformation,[status(esa)],[f63]) ).
fof(f66,plain,
! [Vd501,Vd502,Vd504,Vd505] :
( ~ greater(Vd504,Vd505)
| ~ greater(Vd501,Vd502)
| greater(vmul(Vd501,Vd504),vmul(Vd502,Vd505)) ),
inference(pre_NNF_transformation,[status(esa)],[f4]) ).
fof(f67,plain,
! [X0,X1,X2,X3] :
( ~ greater(X0,X1)
| ~ greater(X2,X3)
| greater(vmul(X2,X0),vmul(X3,X1)) ),
inference(cnf_transformation,[status(esa)],[f66]) ).
fof(f83,plain,
! [Vd456,Vd457,Vd458] :
( ~ greater(Vd457,Vd458)
| greater(vmul(Vd457,Vd456),vmul(Vd458,Vd456)) ),
inference(pre_NNF_transformation,[status(esa)],[f10]) ).
fof(f84,plain,
! [Vd457,Vd458] :
( ~ greater(Vd457,Vd458)
| ! [Vd456] : greater(vmul(Vd457,Vd456),vmul(Vd458,Vd456)) ),
inference(miniscoping,[status(esa)],[f83]) ).
fof(f85,plain,
! [X0,X1,X2] :
( ~ greater(X0,X1)
| greater(vmul(X0,X2),vmul(X1,X2)) ),
inference(cnf_transformation,[status(esa)],[f84]) ).
fof(f88,plain,
! [X0,X1] : vmul(X0,X1) = vmul(X1,X0),
inference(cnf_transformation,[status(esa)],[f13]) ).
fof(f144,plain,
! [Vd244,Vd245] :
( ( ~ geq(Vd245,Vd244)
| greater(Vd245,Vd244)
| Vd245 = Vd244 )
& ( geq(Vd245,Vd244)
| ( ~ greater(Vd245,Vd244)
& Vd245 != Vd244 ) ) ),
inference(NNF_transformation,[status(esa)],[f36]) ).
fof(f145,plain,
( ! [Vd244,Vd245] :
( ~ geq(Vd245,Vd244)
| greater(Vd245,Vd244)
| Vd245 = Vd244 )
& ! [Vd244,Vd245] :
( geq(Vd245,Vd244)
| ( ~ greater(Vd245,Vd244)
& Vd245 != Vd244 ) ) ),
inference(miniscoping,[status(esa)],[f144]) ).
fof(f146,plain,
! [X0,X1] :
( ~ geq(X0,X1)
| greater(X0,X1)
| X0 = X1 ),
inference(cnf_transformation,[status(esa)],[f145]) ).
fof(f193,plain,
( ~ pd0_0
| ( greater(vd519,vd520)
& geq(vd517,vd518) ) ),
inference(pre_NNF_transformation,[status(esa)],[f62]) ).
fof(f194,plain,
( ~ pd0_0
| greater(vd519,vd520) ),
inference(cnf_transformation,[status(esa)],[f193]) ).
fof(f195,plain,
( ~ pd0_0
| geq(vd517,vd518) ),
inference(cnf_transformation,[status(esa)],[f193]) ).
fof(f196,plain,
( spl0_0
<=> pd0_0 ),
introduced(split_symbol_definition) ).
fof(f199,plain,
( spl0_1
<=> geq(vd519,vd520) ),
introduced(split_symbol_definition) ).
fof(f200,plain,
( geq(vd519,vd520)
| ~ spl0_1 ),
inference(component_clause,[status(thm)],[f199]) ).
fof(f202,plain,
( spl0_0
| spl0_1 ),
inference(split_clause,[status(thm)],[f64,f196,f199]) ).
fof(f203,plain,
( spl0_2
<=> greater(vd517,vd518) ),
introduced(split_symbol_definition) ).
fof(f204,plain,
( greater(vd517,vd518)
| ~ spl0_2 ),
inference(component_clause,[status(thm)],[f203]) ).
fof(f206,plain,
( spl0_0
| spl0_2 ),
inference(split_clause,[status(thm)],[f65,f196,f203]) ).
fof(f207,plain,
( spl0_3
<=> greater(vd519,vd520) ),
introduced(split_symbol_definition) ).
fof(f208,plain,
( greater(vd519,vd520)
| ~ spl0_3 ),
inference(component_clause,[status(thm)],[f207]) ).
fof(f210,plain,
( ~ spl0_0
| spl0_3 ),
inference(split_clause,[status(thm)],[f194,f196,f207]) ).
fof(f211,plain,
( spl0_4
<=> geq(vd517,vd518) ),
introduced(split_symbol_definition) ).
fof(f212,plain,
( geq(vd517,vd518)
| ~ spl0_4 ),
inference(component_clause,[status(thm)],[f211]) ).
fof(f214,plain,
( ~ spl0_0
| spl0_4 ),
inference(split_clause,[status(thm)],[f195,f196,f211]) ).
fof(f322,plain,
! [X0,X1] :
( ~ greater(X0,X1)
| greater(vmul(vd519,X0),vmul(vd520,X1))
| ~ spl0_3 ),
inference(resolution,[status(thm)],[f208,f67]) ).
fof(f323,plain,
! [X0] :
( greater(vmul(vd519,X0),vmul(vd520,X0))
| ~ spl0_3 ),
inference(resolution,[status(thm)],[f208,f85]) ).
fof(f327,plain,
! [X0] :
( greater(vmul(vd517,X0),vmul(vd518,X0))
| ~ spl0_2 ),
inference(resolution,[status(thm)],[f204,f85]) ).
fof(f351,plain,
! [X0] :
( greater(vmul(X0,vd519),vmul(vd520,X0))
| ~ spl0_3 ),
inference(paramodulation,[status(thm)],[f88,f323]) ).
fof(f374,plain,
! [X0] :
( greater(vmul(X0,vd519),vmul(X0,vd520))
| ~ spl0_3 ),
inference(paramodulation,[status(thm)],[f88,f351]) ).
fof(f425,plain,
( greater(vmul(vd519,vd517),vmul(vd520,vd518))
| ~ spl0_3
| ~ spl0_2 ),
inference(resolution,[status(thm)],[f322,f204]) ).
fof(f426,plain,
( greater(vmul(vd517,vd519),vmul(vd520,vd518))
| ~ spl0_3
| ~ spl0_2 ),
inference(forward_demodulation,[status(thm)],[f88,f425]) ).
fof(f427,plain,
( greater(vmul(vd517,vd519),vmul(vd518,vd520))
| ~ spl0_3
| ~ spl0_2 ),
inference(forward_demodulation,[status(thm)],[f88,f426]) ).
fof(f428,plain,
( $false
| ~ spl0_3
| ~ spl0_2 ),
inference(forward_subsumption_resolution,[status(thm)],[f427,f61]) ).
fof(f429,plain,
( ~ spl0_3
| ~ spl0_2 ),
inference(contradiction_clause,[status(thm)],[f428]) ).
fof(f451,plain,
! [X0] :
( greater(vmul(vd517,X0),vmul(X0,vd518))
| ~ spl0_2 ),
inference(paramodulation,[status(thm)],[f88,f327]) ).
fof(f1277,plain,
( spl0_7
<=> vd517 = vd518 ),
introduced(split_symbol_definition) ).
fof(f1278,plain,
( vd517 = vd518
| ~ spl0_7 ),
inference(component_clause,[status(thm)],[f1277]) ).
fof(f1280,plain,
( greater(vd517,vd518)
| vd517 = vd518
| ~ spl0_4 ),
inference(resolution,[status(thm)],[f146,f212]) ).
fof(f1281,plain,
( spl0_2
| spl0_7
| ~ spl0_4 ),
inference(split_clause,[status(thm)],[f1280,f203,f1277,f211]) ).
fof(f1282,plain,
( spl0_8
<=> vd519 = vd520 ),
introduced(split_symbol_definition) ).
fof(f1283,plain,
( vd519 = vd520
| ~ spl0_8 ),
inference(component_clause,[status(thm)],[f1282]) ).
fof(f1285,plain,
( greater(vd519,vd520)
| vd519 = vd520
| ~ spl0_1 ),
inference(resolution,[status(thm)],[f146,f200]) ).
fof(f1286,plain,
( spl0_3
| spl0_8
| ~ spl0_1 ),
inference(split_clause,[status(thm)],[f1285,f207,f1282,f199]) ).
fof(f2224,plain,
( ~ greater(vmul(vd517,vd519),vmul(vd517,vd520))
| ~ spl0_7 ),
inference(forward_demodulation,[status(thm)],[f1278,f61]) ).
fof(f2225,plain,
( $false
| ~ spl0_3
| ~ spl0_7 ),
inference(forward_subsumption_resolution,[status(thm)],[f2224,f374]) ).
fof(f2226,plain,
( ~ spl0_3
| ~ spl0_7 ),
inference(contradiction_clause,[status(thm)],[f2225]) ).
fof(f2542,plain,
( ~ greater(vmul(vd517,vd519),vmul(vd518,vd519))
| ~ spl0_8 ),
inference(forward_demodulation,[status(thm)],[f1283,f61]) ).
fof(f2543,plain,
( ~ greater(vmul(vd517,vd519),vmul(vd519,vd518))
| ~ spl0_8 ),
inference(forward_demodulation,[status(thm)],[f88,f2542]) ).
fof(f2544,plain,
( $false
| ~ spl0_2
| ~ spl0_8 ),
inference(forward_subsumption_resolution,[status(thm)],[f2543,f451]) ).
fof(f2545,plain,
( ~ spl0_2
| ~ spl0_8 ),
inference(contradiction_clause,[status(thm)],[f2544]) ).
fof(f2546,plain,
$false,
inference(sat_refutation,[status(thm)],[f202,f206,f210,f214,f429,f1281,f1286,f2226,f2545]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : NUM856+2 : TPTP v8.1.2. Released v4.1.0.
% 0.10/0.11 % Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.10/0.32 % Computer : n019.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 : Tue May 30 09:52:55 EDT 2023
% 0.10/0.32 % CPUTime :
% 0.16/0.33 % Drodi V3.5.1
% 1.83/0.62 % Refutation found
% 1.83/0.62 % SZS status Theorem for theBenchmark: Theorem is valid
% 1.83/0.62 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 1.83/0.64 % Elapsed time: 0.314355 seconds
% 1.83/0.64 % CPU time: 1.889308 seconds
% 1.83/0.64 % Memory used: 75.723 MB
%------------------------------------------------------------------------------