TSTP Solution File: NUM855+1 by Drodi---3.6.0
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%------------------------------------------------------------------------------
% File : Drodi---3.6.0
% Problem : NUM855+1 : TPTP v8.1.2. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% Computer : n024.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 6.52s 1.18s
% Output : CNFRefutation 6.52s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 20
% Syntax : Number of formulae : 79 ( 24 unt; 0 def)
% Number of atoms : 155 ( 24 equ)
% Maximal formula atoms : 6 ( 1 avg)
% Number of connectives : 135 ( 59 ~; 58 |; 9 &)
% ( 3 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 3 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 5 con; 0-2 aty)
% Number of variables : 114 ( 114 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,conjecture,
greater(vmul(vd508,vd511),vmul(vd509,vd512)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f2,negated_conjecture,
~ greater(vmul(vd508,vd511),vmul(vd509,vd512)),
inference(negated_conjecture,[status(cth)],[f1]) ).
fof(f3,axiom,
vmul(vd512,vd509) = vmul(vd509,vd512),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f4,axiom,
greater(vmul(vd511,vd509),vmul(vd512,vd509)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f5,axiom,
vmul(vd509,vd511) = vmul(vd511,vd509),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f6,axiom,
greater(vmul(vd508,vd511),vmul(vd509,vd511)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f8,axiom,
greater(vd508,vd509),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f11,axiom,
! [Vd486,Vd487,Vd488] :
( greater(vmul(Vd486,Vd487),vmul(Vd488,Vd487))
=> greater(Vd486,Vd488) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f17,axiom,
! [Vd418,Vd419] : vmul(Vd418,Vd419) = vmul(Vd419,Vd418),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f25,axiom,
! [Vd353,Vd354,Vd355,Vd356] :
( ( ( greater(Vd355,Vd356)
& geq(Vd353,Vd354) )
| ( geq(Vd355,Vd356)
& greater(Vd353,Vd354) ) )
=> greater(vplus(Vd353,Vd355),vplus(Vd354,Vd356)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f29,axiom,
! [Vd328,Vd329,Vd330] :
( greater(vplus(Vd328,Vd330),vplus(Vd329,Vd330))
=> greater(Vd328,Vd329) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f32,axiom,
! [Vd301,Vd302,Vd303] :
( greater(Vd301,Vd302)
=> greater(vplus(Vd301,Vd303),vplus(Vd302,Vd303)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f40,axiom,
! [Vd244,Vd245] :
( geq(Vd245,Vd244)
<=> ( greater(Vd245,Vd244)
| Vd245 = Vd244 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f41,axiom,
! [Vd226,Vd227] :
( less(Vd226,Vd227)
=> greater(Vd227,Vd226) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f42,axiom,
! [Vd208,Vd209] :
( greater(Vd208,Vd209)
=> less(Vd209,Vd208) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f43,axiom,
! [Vd203,Vd204] :
( Vd203 = Vd204
| greater(Vd203,Vd204)
| less(Vd203,Vd204) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f45,axiom,
! [Vd203,Vd204] :
( ~ greater(Vd203,Vd204)
| ~ less(Vd203,Vd204) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f55,axiom,
! [Vd78,Vd79] : vplus(Vd79,Vd78) = vplus(Vd78,Vd79),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f59,axiom,
! [Vd42,Vd43] :
( vplus(Vd42,vsucc(Vd43)) = vsucc(vplus(Vd42,Vd43))
& vplus(Vd42,v1) = vsucc(Vd42) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f65,plain,
~ greater(vmul(vd508,vd511),vmul(vd509,vd512)),
inference(cnf_transformation,[status(esa)],[f2]) ).
fof(f66,plain,
vmul(vd512,vd509) = vmul(vd509,vd512),
inference(cnf_transformation,[status(esa)],[f3]) ).
fof(f67,plain,
greater(vmul(vd511,vd509),vmul(vd512,vd509)),
inference(cnf_transformation,[status(esa)],[f4]) ).
fof(f68,plain,
vmul(vd509,vd511) = vmul(vd511,vd509),
inference(cnf_transformation,[status(esa)],[f5]) ).
fof(f69,plain,
greater(vmul(vd508,vd511),vmul(vd509,vd511)),
inference(cnf_transformation,[status(esa)],[f6]) ).
fof(f71,plain,
greater(vd508,vd509),
inference(cnf_transformation,[status(esa)],[f8]) ).
fof(f78,plain,
! [Vd486,Vd487,Vd488] :
( ~ greater(vmul(Vd486,Vd487),vmul(Vd488,Vd487))
| greater(Vd486,Vd488) ),
inference(pre_NNF_transformation,[status(esa)],[f11]) ).
fof(f79,plain,
! [Vd486,Vd488] :
( ! [Vd487] : ~ greater(vmul(Vd486,Vd487),vmul(Vd488,Vd487))
| greater(Vd486,Vd488) ),
inference(miniscoping,[status(esa)],[f78]) ).
fof(f80,plain,
! [X0,X1,X2] :
( ~ greater(vmul(X0,X1),vmul(X2,X1))
| greater(X0,X2) ),
inference(cnf_transformation,[status(esa)],[f79]) ).
fof(f92,plain,
! [X0,X1] : vmul(X0,X1) = vmul(X1,X0),
inference(cnf_transformation,[status(esa)],[f17]) ).
fof(f105,plain,
! [Vd353,Vd354,Vd355,Vd356] :
( ( ( ~ greater(Vd355,Vd356)
| ~ geq(Vd353,Vd354) )
& ( ~ geq(Vd355,Vd356)
| ~ greater(Vd353,Vd354) ) )
| greater(vplus(Vd353,Vd355),vplus(Vd354,Vd356)) ),
inference(pre_NNF_transformation,[status(esa)],[f25]) ).
fof(f107,plain,
! [X0,X1,X2,X3] :
( ~ geq(X0,X1)
| ~ greater(X2,X3)
| greater(vplus(X2,X0),vplus(X3,X1)) ),
inference(cnf_transformation,[status(esa)],[f105]) ).
fof(f116,plain,
! [Vd328,Vd329,Vd330] :
( ~ greater(vplus(Vd328,Vd330),vplus(Vd329,Vd330))
| greater(Vd328,Vd329) ),
inference(pre_NNF_transformation,[status(esa)],[f29]) ).
fof(f117,plain,
! [Vd328,Vd329] :
( ! [Vd330] : ~ greater(vplus(Vd328,Vd330),vplus(Vd329,Vd330))
| greater(Vd328,Vd329) ),
inference(miniscoping,[status(esa)],[f116]) ).
fof(f118,plain,
! [X0,X1,X2] :
( ~ greater(vplus(X0,X1),vplus(X2,X1))
| greater(X0,X2) ),
inference(cnf_transformation,[status(esa)],[f117]) ).
fof(f125,plain,
! [Vd301,Vd302,Vd303] :
( ~ greater(Vd301,Vd302)
| greater(vplus(Vd301,Vd303),vplus(Vd302,Vd303)) ),
inference(pre_NNF_transformation,[status(esa)],[f32]) ).
fof(f126,plain,
! [Vd301,Vd302] :
( ~ greater(Vd301,Vd302)
| ! [Vd303] : greater(vplus(Vd301,Vd303),vplus(Vd302,Vd303)) ),
inference(miniscoping,[status(esa)],[f125]) ).
fof(f127,plain,
! [X0,X1,X2] :
( ~ greater(X0,X1)
| greater(vplus(X0,X2),vplus(X1,X2)) ),
inference(cnf_transformation,[status(esa)],[f126]) ).
fof(f148,plain,
! [Vd244,Vd245] :
( ( ~ geq(Vd245,Vd244)
| greater(Vd245,Vd244)
| Vd245 = Vd244 )
& ( geq(Vd245,Vd244)
| ( ~ greater(Vd245,Vd244)
& Vd245 != Vd244 ) ) ),
inference(NNF_transformation,[status(esa)],[f40]) ).
fof(f149,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)],[f148]) ).
fof(f151,plain,
! [X0,X1] :
( geq(X0,X1)
| ~ greater(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f149]) ).
fof(f153,plain,
! [Vd226,Vd227] :
( ~ less(Vd226,Vd227)
| greater(Vd227,Vd226) ),
inference(pre_NNF_transformation,[status(esa)],[f41]) ).
fof(f154,plain,
! [X0,X1] :
( ~ less(X0,X1)
| greater(X1,X0) ),
inference(cnf_transformation,[status(esa)],[f153]) ).
fof(f155,plain,
! [Vd208,Vd209] :
( ~ greater(Vd208,Vd209)
| less(Vd209,Vd208) ),
inference(pre_NNF_transformation,[status(esa)],[f42]) ).
fof(f156,plain,
! [X0,X1] :
( ~ greater(X0,X1)
| less(X1,X0) ),
inference(cnf_transformation,[status(esa)],[f155]) ).
fof(f157,plain,
! [X0,X1] :
( X0 = X1
| greater(X0,X1)
| less(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f43]) ).
fof(f159,plain,
! [X0,X1] :
( ~ greater(X0,X1)
| ~ less(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f45]) ).
fof(f182,plain,
! [X0,X1] : vplus(X0,X1) = vplus(X1,X0),
inference(cnf_transformation,[status(esa)],[f55]) ).
fof(f186,plain,
( ! [Vd42,Vd43] : vplus(Vd42,vsucc(Vd43)) = vsucc(vplus(Vd42,Vd43))
& ! [Vd42] : vplus(Vd42,v1) = vsucc(Vd42) ),
inference(miniscoping,[status(esa)],[f59]) ).
fof(f188,plain,
! [X0] : vplus(X0,v1) = vsucc(X0),
inference(cnf_transformation,[status(esa)],[f186]) ).
fof(f204,plain,
greater(vmul(vd511,vd509),vmul(vd509,vd512)),
inference(forward_demodulation,[status(thm)],[f66,f67]) ).
fof(f227,plain,
greater(vmul(vd508,vd511),vmul(vd511,vd509)),
inference(backward_demodulation,[status(thm)],[f68,f69]) ).
fof(f286,plain,
! [X0,X1,X2] :
( ~ greater(vmul(X0,X1),vmul(X2,X0))
| greater(X1,X2) ),
inference(paramodulation,[status(thm)],[f92,f80]) ).
fof(f946,plain,
! [X0,X1,X2] :
( ~ greater(vplus(X0,X1),vplus(X1,X2))
| greater(X0,X2) ),
inference(paramodulation,[status(thm)],[f182,f118]) ).
fof(f998,plain,
! [X0,X1] :
( ~ greater(X0,X1)
| greater(vplus(X0,v1),vsucc(X1)) ),
inference(paramodulation,[status(thm)],[f188,f127]) ).
fof(f999,plain,
! [X0,X1] :
( ~ greater(X0,X1)
| greater(vsucc(X0),vsucc(X1)) ),
inference(forward_demodulation,[status(thm)],[f188,f998]) ).
fof(f1081,plain,
! [X0,X1] :
( X0 = X1
| greater(X0,X1)
| greater(X1,X0) ),
inference(resolution,[status(thm)],[f157,f154]) ).
fof(f1104,plain,
( spl0_12
<=> vmul(vd509,vd512) = vmul(vd508,vd511) ),
introduced(split_symbol_definition) ).
fof(f1105,plain,
( vmul(vd509,vd512) = vmul(vd508,vd511)
| ~ spl0_12 ),
inference(component_clause,[status(thm)],[f1104]) ).
fof(f1107,plain,
( spl0_13
<=> greater(vmul(vd509,vd512),vmul(vd508,vd511)) ),
introduced(split_symbol_definition) ).
fof(f1108,plain,
( greater(vmul(vd509,vd512),vmul(vd508,vd511))
| ~ spl0_13 ),
inference(component_clause,[status(thm)],[f1107]) ).
fof(f1110,plain,
( vmul(vd509,vd512) = vmul(vd508,vd511)
| greater(vmul(vd509,vd512),vmul(vd508,vd511)) ),
inference(resolution,[status(thm)],[f1081,f65]) ).
fof(f1111,plain,
( spl0_12
| spl0_13 ),
inference(split_clause,[status(thm)],[f1110,f1104,f1107]) ).
fof(f1171,plain,
! [X0,X1] :
( ~ greater(X0,X1)
| less(vsucc(X1),vsucc(X0)) ),
inference(resolution,[status(thm)],[f999,f156]) ).
fof(f1668,plain,
( greater(vmul(vd511,vd509),vmul(vd508,vd511))
| ~ spl0_12 ),
inference(backward_demodulation,[status(thm)],[f1105,f204]) ).
fof(f1777,plain,
( less(vmul(vd508,vd511),vmul(vd511,vd509))
| ~ spl0_12 ),
inference(resolution,[status(thm)],[f1668,f156]) ).
fof(f1795,plain,
( ~ greater(vmul(vd508,vd511),vmul(vd511,vd509))
| ~ spl0_12 ),
inference(resolution,[status(thm)],[f1777,f159]) ).
fof(f1796,plain,
( $false
| ~ spl0_12 ),
inference(forward_subsumption_resolution,[status(thm)],[f1795,f227]) ).
fof(f1797,plain,
~ spl0_12,
inference(contradiction_clause,[status(thm)],[f1796]) ).
fof(f1803,plain,
( geq(vmul(vd509,vd512),vmul(vd508,vd511))
| ~ spl0_13 ),
inference(resolution,[status(thm)],[f1108,f151]) ).
fof(f1981,plain,
! [X0,X1] :
( ~ greater(X0,X1)
| ~ greater(vsucc(X1),vsucc(X0)) ),
inference(resolution,[status(thm)],[f1171,f159]) ).
fof(f2298,plain,
! [X0,X1] :
( ~ greater(X0,X1)
| ~ greater(X1,X0) ),
inference(resolution,[status(thm)],[f1981,f999]) ).
fof(f2329,plain,
~ greater(vd509,vd508),
inference(resolution,[status(thm)],[f2298,f71]) ).
fof(f3287,plain,
! [X0,X1,X2] :
( greater(X0,X1)
| ~ geq(X2,X1)
| ~ greater(X0,X2) ),
inference(resolution,[status(thm)],[f946,f107]) ).
fof(f3316,plain,
! [X0] :
( greater(X0,vmul(vd508,vd511))
| ~ greater(X0,vmul(vd509,vd512))
| ~ spl0_13 ),
inference(resolution,[status(thm)],[f3287,f1803]) ).
fof(f3854,plain,
( greater(vmul(vd511,vd509),vmul(vd508,vd511))
| ~ spl0_13 ),
inference(resolution,[status(thm)],[f3316,f204]) ).
fof(f3890,plain,
( greater(vd509,vd508)
| ~ spl0_13 ),
inference(resolution,[status(thm)],[f3854,f286]) ).
fof(f3891,plain,
( $false
| ~ spl0_13 ),
inference(forward_subsumption_resolution,[status(thm)],[f3890,f2329]) ).
fof(f3892,plain,
~ spl0_13,
inference(contradiction_clause,[status(thm)],[f3891]) ).
fof(f3893,plain,
$false,
inference(sat_refutation,[status(thm)],[f1111,f1797,f3892]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.09 % Problem : NUM855+1 : TPTP v8.1.2. Released v4.1.0.
% 0.00/0.10 % Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.09/0.29 % Computer : n024.cluster.edu
% 0.09/0.29 % Model : x86_64 x86_64
% 0.09/0.29 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.29 % Memory : 8042.1875MB
% 0.09/0.29 % OS : Linux 3.10.0-693.el7.x86_64
% 0.09/0.29 % CPULimit : 300
% 0.09/0.29 % WCLimit : 300
% 0.09/0.29 % DateTime : Mon Apr 29 20:49:36 EDT 2024
% 0.09/0.29 % CPUTime :
% 0.09/0.30 % Drodi V3.6.0
% 6.52/1.18 % Refutation found
% 6.52/1.18 % SZS status Theorem for theBenchmark: Theorem is valid
% 6.52/1.18 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 6.91/1.21 % Elapsed time: 0.900186 seconds
% 6.91/1.21 % CPU time: 7.028816 seconds
% 6.91/1.21 % Total memory used: 128.840 MB
% 6.91/1.21 % Net memory used: 127.103 MB
%------------------------------------------------------------------------------