TSTP Solution File: NUM852+2 by Drodi---3.6.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Drodi---3.6.0
% Problem : NUM852+2 : TPTP v8.1.2. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% Computer : n026.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 20:35:57 EDT 2024
% Result : Theorem 3.22s 0.75s
% Output : CNFRefutation 3.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 19
% Syntax : Number of formulae : 85 ( 27 unt; 0 def)
% Number of atoms : 159 ( 50 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 140 ( 66 ~; 58 |; 6 &)
% ( 6 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 8 ( 6 usr; 5 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 3 con; 0-2 aty)
% Number of variables : 115 ( 109 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,conjecture,
greater(vmul(vd481,vd469),vmul(vd480,vd469)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f2,negated_conjecture,
~ greater(vmul(vd481,vd469),vmul(vd480,vd469)),
inference(negated_conjecture,[status(cth)],[f1]) ).
fof(f3,axiom,
greater(vd481,vd480),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f4,axiom,
less(vd480,vd481),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f7,axiom,
! [Vd470,Vd471] :
( greater(Vd470,Vd471)
=> vmul(vplus(Vd471,vskolem9(Vd470,Vd471)),vd469) = vplus(vmul(Vd471,vd469),vmul(vskolem9(Vd470,Vd471),vd469)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f9,axiom,
! [Vd470,Vd471] :
( greater(Vd470,Vd471)
=> Vd470 = vplus(Vd471,vskolem9(Vd470,Vd471)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f11,axiom,
! [Vd432,Vd433,Vd434] : vmul(Vd432,vplus(Vd433,Vd434)) = vplus(vmul(Vd432,Vd433),vmul(Vd432,Vd434)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f12,axiom,
! [Vd418,Vd419] : vmul(Vd418,Vd419) = vmul(Vd419,Vd418),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f14,axiom,
! [Vd226,Vd227] :
( less(Vd226,Vd227)
=> greater(Vd227,Vd226) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f15,axiom,
! [Vd208,Vd209] :
( greater(Vd208,Vd209)
=> less(Vd209,Vd208) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f16,axiom,
! [Vd203,Vd204] :
( Vd203 = Vd204
| greater(Vd203,Vd204)
| less(Vd203,Vd204) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f17,axiom,
! [Vd203,Vd204] :
( Vd203 != Vd204
| ~ less(Vd203,Vd204) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f18,axiom,
! [Vd203,Vd204] :
( ~ greater(Vd203,Vd204)
| ~ less(Vd203,Vd204) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f19,axiom,
! [Vd203,Vd204] :
( Vd203 != Vd204
| ~ greater(Vd203,Vd204) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f20,axiom,
! [Vd198,Vd199] :
( less(Vd199,Vd198)
<=> ? [Vd201] : Vd198 = vplus(Vd199,Vd201) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f21,axiom,
! [Vd193,Vd194] :
( greater(Vd194,Vd193)
<=> ? [Vd196] : Vd194 = vplus(Vd193,Vd196) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f22,plain,
~ greater(vmul(vd481,vd469),vmul(vd480,vd469)),
inference(cnf_transformation,[status(esa)],[f2]) ).
fof(f23,plain,
greater(vd481,vd480),
inference(cnf_transformation,[status(esa)],[f3]) ).
fof(f24,plain,
less(vd480,vd481),
inference(cnf_transformation,[status(esa)],[f4]) ).
fof(f29,plain,
! [Vd470,Vd471] :
( ~ greater(Vd470,Vd471)
| vmul(vplus(Vd471,vskolem9(Vd470,Vd471)),vd469) = vplus(vmul(Vd471,vd469),vmul(vskolem9(Vd470,Vd471),vd469)) ),
inference(pre_NNF_transformation,[status(esa)],[f7]) ).
fof(f30,plain,
! [X0,X1] :
( ~ greater(X0,X1)
| vmul(vplus(X1,vskolem9(X0,X1)),vd469) = vplus(vmul(X1,vd469),vmul(vskolem9(X0,X1),vd469)) ),
inference(cnf_transformation,[status(esa)],[f29]) ).
fof(f33,plain,
! [Vd470,Vd471] :
( ~ greater(Vd470,Vd471)
| Vd470 = vplus(Vd471,vskolem9(Vd470,Vd471)) ),
inference(pre_NNF_transformation,[status(esa)],[f9]) ).
fof(f34,plain,
! [X0,X1] :
( ~ greater(X0,X1)
| X0 = vplus(X1,vskolem9(X0,X1)) ),
inference(cnf_transformation,[status(esa)],[f33]) ).
fof(f36,plain,
! [X0,X1,X2] : vmul(X0,vplus(X1,X2)) = vplus(vmul(X0,X1),vmul(X0,X2)),
inference(cnf_transformation,[status(esa)],[f11]) ).
fof(f37,plain,
! [X0,X1] : vmul(X0,X1) = vmul(X1,X0),
inference(cnf_transformation,[status(esa)],[f12]) ).
fof(f39,plain,
! [Vd226,Vd227] :
( ~ less(Vd226,Vd227)
| greater(Vd227,Vd226) ),
inference(pre_NNF_transformation,[status(esa)],[f14]) ).
fof(f40,plain,
! [X0,X1] :
( ~ less(X0,X1)
| greater(X1,X0) ),
inference(cnf_transformation,[status(esa)],[f39]) ).
fof(f41,plain,
! [Vd208,Vd209] :
( ~ greater(Vd208,Vd209)
| less(Vd209,Vd208) ),
inference(pre_NNF_transformation,[status(esa)],[f15]) ).
fof(f42,plain,
! [X0,X1] :
( ~ greater(X0,X1)
| less(X1,X0) ),
inference(cnf_transformation,[status(esa)],[f41]) ).
fof(f43,plain,
! [X0,X1] :
( X0 = X1
| greater(X0,X1)
| less(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f16]) ).
fof(f44,plain,
! [X0,X1] :
( X0 != X1
| ~ less(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f17]) ).
fof(f45,plain,
! [X0,X1] :
( ~ greater(X0,X1)
| ~ less(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f18]) ).
fof(f46,plain,
! [X0,X1] :
( X0 != X1
| ~ greater(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f19]) ).
fof(f47,plain,
! [Vd198,Vd199] :
( ( ~ less(Vd199,Vd198)
| ? [Vd201] : Vd198 = vplus(Vd199,Vd201) )
& ( less(Vd199,Vd198)
| ! [Vd201] : Vd198 != vplus(Vd199,Vd201) ) ),
inference(NNF_transformation,[status(esa)],[f20]) ).
fof(f48,plain,
( ! [Vd198,Vd199] :
( ~ less(Vd199,Vd198)
| ? [Vd201] : Vd198 = vplus(Vd199,Vd201) )
& ! [Vd198,Vd199] :
( less(Vd199,Vd198)
| ! [Vd201] : Vd198 != vplus(Vd199,Vd201) ) ),
inference(miniscoping,[status(esa)],[f47]) ).
fof(f49,plain,
( ! [Vd198,Vd199] :
( ~ less(Vd199,Vd198)
| Vd198 = vplus(Vd199,sk0_0(Vd199,Vd198)) )
& ! [Vd198,Vd199] :
( less(Vd199,Vd198)
| ! [Vd201] : Vd198 != vplus(Vd199,Vd201) ) ),
inference(skolemization,[status(esa)],[f48]) ).
fof(f50,plain,
! [X0,X1] :
( ~ less(X0,X1)
| X1 = vplus(X0,sk0_0(X0,X1)) ),
inference(cnf_transformation,[status(esa)],[f49]) ).
fof(f51,plain,
! [X0,X1,X2] :
( less(X0,X1)
| X1 != vplus(X0,X2) ),
inference(cnf_transformation,[status(esa)],[f49]) ).
fof(f52,plain,
! [Vd193,Vd194] :
( ( ~ greater(Vd194,Vd193)
| ? [Vd196] : Vd194 = vplus(Vd193,Vd196) )
& ( greater(Vd194,Vd193)
| ! [Vd196] : Vd194 != vplus(Vd193,Vd196) ) ),
inference(NNF_transformation,[status(esa)],[f21]) ).
fof(f53,plain,
( ! [Vd193,Vd194] :
( ~ greater(Vd194,Vd193)
| ? [Vd196] : Vd194 = vplus(Vd193,Vd196) )
& ! [Vd193,Vd194] :
( greater(Vd194,Vd193)
| ! [Vd196] : Vd194 != vplus(Vd193,Vd196) ) ),
inference(miniscoping,[status(esa)],[f52]) ).
fof(f54,plain,
( ! [Vd193,Vd194] :
( ~ greater(Vd194,Vd193)
| Vd194 = vplus(Vd193,sk0_1(Vd194,Vd193)) )
& ! [Vd193,Vd194] :
( greater(Vd194,Vd193)
| ! [Vd196] : Vd194 != vplus(Vd193,Vd196) ) ),
inference(skolemization,[status(esa)],[f53]) ).
fof(f56,plain,
! [X0,X1,X2] :
( greater(X0,X1)
| X0 != vplus(X1,X2) ),
inference(cnf_transformation,[status(esa)],[f54]) ).
fof(f57,plain,
! [X0] : ~ less(X0,X0),
inference(destructive_equality_resolution,[status(esa)],[f44]) ).
fof(f58,plain,
! [X0] : ~ greater(X0,X0),
inference(destructive_equality_resolution,[status(esa)],[f46]) ).
fof(f59,plain,
! [X0,X1] : less(X0,vplus(X0,X1)),
inference(destructive_equality_resolution,[status(esa)],[f51]) ).
fof(f60,plain,
! [X0,X1] : greater(vplus(X0,X1),X0),
inference(destructive_equality_resolution,[status(esa)],[f56]) ).
fof(f303,plain,
~ greater(vd480,vd481),
inference(resolution,[status(thm)],[f45,f24]) ).
fof(f304,plain,
! [X0,X1] : ~ greater(X0,vplus(X0,X1)),
inference(resolution,[status(thm)],[f45,f59]) ).
fof(f305,plain,
! [X0,X1] :
( X0 = X1
| greater(X0,X1)
| greater(X1,X0) ),
inference(resolution,[status(thm)],[f43,f40]) ).
fof(f306,plain,
( spl0_0
<=> vd480 = vd481 ),
introduced(split_symbol_definition) ).
fof(f307,plain,
( vd480 = vd481
| ~ spl0_0 ),
inference(component_clause,[status(thm)],[f306]) ).
fof(f309,plain,
( spl0_1
<=> greater(vd481,vd480) ),
introduced(split_symbol_definition) ).
fof(f310,plain,
( greater(vd481,vd480)
| ~ spl0_1 ),
inference(component_clause,[status(thm)],[f309]) ).
fof(f312,plain,
( vd480 = vd481
| greater(vd481,vd480) ),
inference(resolution,[status(thm)],[f305,f303]) ).
fof(f313,plain,
( spl0_0
| spl0_1 ),
inference(split_clause,[status(thm)],[f312,f306,f309]) ).
fof(f322,plain,
( spl0_4
<=> vmul(vd481,vd469) = vmul(vd480,vd469) ),
introduced(split_symbol_definition) ).
fof(f323,plain,
( vmul(vd481,vd469) = vmul(vd480,vd469)
| ~ spl0_4 ),
inference(component_clause,[status(thm)],[f322]) ).
fof(f325,plain,
( spl0_5
<=> greater(vmul(vd480,vd469),vmul(vd481,vd469)) ),
introduced(split_symbol_definition) ).
fof(f326,plain,
( greater(vmul(vd480,vd469),vmul(vd481,vd469))
| ~ spl0_5 ),
inference(component_clause,[status(thm)],[f325]) ).
fof(f328,plain,
( vmul(vd481,vd469) = vmul(vd480,vd469)
| greater(vmul(vd480,vd469),vmul(vd481,vd469)) ),
inference(resolution,[status(thm)],[f305,f22]) ).
fof(f329,plain,
( spl0_4
| spl0_5 ),
inference(split_clause,[status(thm)],[f328,f322,f325]) ).
fof(f340,plain,
( vmul(vd481,vd469) = vmul(vd469,vd480)
| ~ spl0_4 ),
inference(forward_demodulation,[status(thm)],[f37,f323]) ).
fof(f342,plain,
vd481 = vplus(vd480,vskolem9(vd481,vd480)),
inference(resolution,[status(thm)],[f34,f23]) ).
fof(f359,plain,
! [X0,X1] :
( ~ greater(X0,X1)
| vmul(vd469,vplus(X1,vskolem9(X0,X1))) = vplus(vmul(X1,vd469),vmul(vskolem9(X0,X1),vd469)) ),
inference(forward_demodulation,[status(thm)],[f37,f30]) ).
fof(f360,plain,
! [X0,X1] :
( ~ greater(X0,X1)
| vmul(vd469,vplus(X1,vskolem9(X0,X1))) = vplus(vmul(X1,vd469),vmul(vd469,vskolem9(X0,X1))) ),
inference(forward_demodulation,[status(thm)],[f37,f359]) ).
fof(f362,plain,
vmul(vd469,vplus(vd480,vskolem9(vd481,vd480))) = vplus(vmul(vd480,vd469),vmul(vd469,vskolem9(vd481,vd480))),
inference(resolution,[status(thm)],[f360,f23]) ).
fof(f363,plain,
vmul(vd469,vd481) = vplus(vmul(vd480,vd469),vmul(vd469,vskolem9(vd481,vd480))),
inference(forward_demodulation,[status(thm)],[f342,f362]) ).
fof(f364,plain,
vmul(vd481,vd469) = vplus(vmul(vd480,vd469),vmul(vd469,vskolem9(vd481,vd480))),
inference(forward_demodulation,[status(thm)],[f37,f363]) ).
fof(f365,plain,
vmul(vd481,vd469) = vplus(vmul(vd469,vd480),vmul(vd469,vskolem9(vd481,vd480))),
inference(forward_demodulation,[status(thm)],[f37,f364]) ).
fof(f850,plain,
( less(vd481,vd481)
| ~ spl0_0 ),
inference(backward_demodulation,[status(thm)],[f307,f24]) ).
fof(f851,plain,
( $false
| ~ spl0_0 ),
inference(forward_subsumption_resolution,[status(thm)],[f850,f57]) ).
fof(f852,plain,
~ spl0_0,
inference(contradiction_clause,[status(thm)],[f851]) ).
fof(f859,plain,
( less(vd480,vd481)
| ~ spl0_1 ),
inference(resolution,[status(thm)],[f310,f42]) ).
fof(f860,plain,
( vd481 = vplus(vd480,sk0_0(vd480,vd481))
| ~ spl0_1 ),
inference(resolution,[status(thm)],[f859,f50]) ).
fof(f2144,plain,
( vmul(vd481,vd469) = vplus(vmul(vd481,vd469),vmul(vd469,vskolem9(vd481,vd480)))
| ~ spl0_4 ),
inference(forward_demodulation,[status(thm)],[f340,f365]) ).
fof(f2150,plain,
( greater(vmul(vd481,vd469),vmul(vd481,vd469))
| ~ spl0_4 ),
inference(paramodulation,[status(thm)],[f2144,f60]) ).
fof(f2151,plain,
( $false
| ~ spl0_4 ),
inference(forward_subsumption_resolution,[status(thm)],[f2150,f58]) ).
fof(f2152,plain,
~ spl0_4,
inference(contradiction_clause,[status(thm)],[f2151]) ).
fof(f2153,plain,
( greater(vmul(vd469,vd480),vmul(vd481,vd469))
| ~ spl0_5 ),
inference(forward_demodulation,[status(thm)],[f37,f326]) ).
fof(f2477,plain,
! [X0,X1,X2] : ~ greater(vmul(X0,X1),vmul(X0,vplus(X1,X2))),
inference(paramodulation,[status(thm)],[f36,f304]) ).
fof(f3199,plain,
! [X0,X1,X2] : ~ greater(vmul(X0,X1),vmul(vplus(X1,X2),X0)),
inference(paramodulation,[status(thm)],[f37,f2477]) ).
fof(f3396,plain,
! [X0] :
( ~ greater(vmul(X0,vd480),vmul(vd481,X0))
| ~ spl0_1 ),
inference(paramodulation,[status(thm)],[f860,f3199]) ).
fof(f4084,plain,
( $false
| ~ spl0_1
| ~ spl0_5 ),
inference(backward_subsumption_resolution,[status(thm)],[f2153,f3396]) ).
fof(f4085,plain,
( ~ spl0_1
| ~ spl0_5 ),
inference(contradiction_clause,[status(thm)],[f4084]) ).
fof(f4086,plain,
$false,
inference(sat_refutation,[status(thm)],[f313,f329,f852,f2152,f4085]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.09 % Problem : NUM852+2 : TPTP v8.1.2. Released v4.1.0.
% 0.04/0.10 % Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.08/0.30 % Computer : n026.cluster.edu
% 0.08/0.30 % Model : x86_64 x86_64
% 0.08/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.30 % Memory : 8042.1875MB
% 0.08/0.30 % OS : Linux 3.10.0-693.el7.x86_64
% 0.08/0.30 % CPULimit : 300
% 0.08/0.30 % WCLimit : 300
% 0.08/0.30 % DateTime : Mon Apr 29 21:01:49 EDT 2024
% 0.08/0.30 % CPUTime :
% 0.14/0.31 % Drodi V3.6.0
% 3.22/0.75 % Refutation found
% 3.22/0.75 % SZS status Theorem for theBenchmark: Theorem is valid
% 3.22/0.75 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 3.22/0.78 % Elapsed time: 0.464200 seconds
% 3.22/0.78 % CPU time: 3.532327 seconds
% 3.22/0.78 % Total memory used: 84.079 MB
% 3.22/0.78 % Net memory used: 83.747 MB
%------------------------------------------------------------------------------