TSTP Solution File: NUM841+2 by Drodi---3.5.1
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%------------------------------------------------------------------------------
% File : Drodi---3.5.1
% Problem : NUM841+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 : Wed May 31 12:30:47 EDT 2023
% Result : Theorem 9.75s 1.62s
% Output : CNFRefutation 9.75s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 15
% Syntax : Number of formulae : 69 ( 28 unt; 0 def)
% Number of atoms : 119 ( 40 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 104 ( 54 ~; 41 |; 3 &)
% ( 3 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 3 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 4 con; 0-2 aty)
% Number of variables : 101 (; 97 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,conjecture,
greater(vplus(vd344,vd347),vplus(vd345,vd348)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f2,negated_conjecture,
~ greater(vplus(vd344,vd347),vplus(vd345,vd348)),
inference(negated_conjecture,[status(cth)],[f1]) ).
fof(f4,axiom,
greater(vplus(vd347,vd345),vplus(vd348,vd345)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f7,axiom,
greater(vd347,vd348),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f8,axiom,
greater(vd344,vd345),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f11,axiom,
! [Vd328,Vd329,Vd330] :
( greater(vplus(Vd328,Vd330),vplus(Vd329,Vd330))
=> greater(Vd328,Vd329) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f16,axiom,
! [Vd226,Vd227] :
( less(Vd226,Vd227)
=> greater(Vd227,Vd226) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f17,axiom,
! [Vd208,Vd209] :
( greater(Vd208,Vd209)
=> less(Vd209,Vd208) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f18,axiom,
! [Vd203,Vd204] :
( Vd203 = Vd204
| greater(Vd203,Vd204)
| less(Vd203,Vd204) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f19,axiom,
! [Vd203,Vd204] :
( ~ greater(Vd203,Vd204)
| ~ less(Vd203,Vd204) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f20,axiom,
! [Vd193,Vd194] :
( greater(Vd194,Vd193)
<=> ? [Vd196] : Vd194 = vplus(Vd193,Vd196) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f21,axiom,
! [Vd120,Vd121] :
( Vd120 != Vd121
| ~ ? [Vd123] : Vd120 = vplus(Vd121,Vd123) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f22,axiom,
! [Vd78,Vd79] : vplus(Vd79,Vd78) = vplus(Vd78,Vd79),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f25,axiom,
! [Vd46,Vd47,Vd48] : vplus(vplus(Vd46,Vd47),Vd48) = vplus(Vd46,vplus(Vd47,Vd48)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f28,plain,
~ greater(vplus(vd344,vd347),vplus(vd345,vd348)),
inference(cnf_transformation,[status(esa)],[f2]) ).
fof(f30,plain,
greater(vplus(vd347,vd345),vplus(vd348,vd345)),
inference(cnf_transformation,[status(esa)],[f4]) ).
fof(f33,plain,
greater(vd347,vd348),
inference(cnf_transformation,[status(esa)],[f7]) ).
fof(f34,plain,
greater(vd344,vd345),
inference(cnf_transformation,[status(esa)],[f8]) ).
fof(f41,plain,
! [Vd328,Vd329,Vd330] :
( ~ greater(vplus(Vd328,Vd330),vplus(Vd329,Vd330))
| greater(Vd328,Vd329) ),
inference(pre_NNF_transformation,[status(esa)],[f11]) ).
fof(f42,plain,
! [Vd328,Vd329] :
( ! [Vd330] : ~ greater(vplus(Vd328,Vd330),vplus(Vd329,Vd330))
| greater(Vd328,Vd329) ),
inference(miniscoping,[status(esa)],[f41]) ).
fof(f43,plain,
! [X0,X1,X2] :
( ~ greater(vplus(X0,X1),vplus(X2,X1))
| greater(X0,X2) ),
inference(cnf_transformation,[status(esa)],[f42]) ).
fof(f54,plain,
! [Vd226,Vd227] :
( ~ less(Vd226,Vd227)
| greater(Vd227,Vd226) ),
inference(pre_NNF_transformation,[status(esa)],[f16]) ).
fof(f55,plain,
! [X0,X1] :
( ~ less(X0,X1)
| greater(X1,X0) ),
inference(cnf_transformation,[status(esa)],[f54]) ).
fof(f56,plain,
! [Vd208,Vd209] :
( ~ greater(Vd208,Vd209)
| less(Vd209,Vd208) ),
inference(pre_NNF_transformation,[status(esa)],[f17]) ).
fof(f57,plain,
! [X0,X1] :
( ~ greater(X0,X1)
| less(X1,X0) ),
inference(cnf_transformation,[status(esa)],[f56]) ).
fof(f58,plain,
! [X0,X1] :
( X0 = X1
| greater(X0,X1)
| less(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f18]) ).
fof(f59,plain,
! [X0,X1] :
( ~ greater(X0,X1)
| ~ less(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f19]) ).
fof(f60,plain,
! [Vd193,Vd194] :
( ( ~ greater(Vd194,Vd193)
| ? [Vd196] : Vd194 = vplus(Vd193,Vd196) )
& ( greater(Vd194,Vd193)
| ! [Vd196] : Vd194 != vplus(Vd193,Vd196) ) ),
inference(NNF_transformation,[status(esa)],[f20]) ).
fof(f61,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)],[f60]) ).
fof(f62,plain,
( ! [Vd193,Vd194] :
( ~ greater(Vd194,Vd193)
| Vd194 = vplus(Vd193,sk0_0(Vd194,Vd193)) )
& ! [Vd193,Vd194] :
( greater(Vd194,Vd193)
| ! [Vd196] : Vd194 != vplus(Vd193,Vd196) ) ),
inference(skolemization,[status(esa)],[f61]) ).
fof(f63,plain,
! [X0,X1] :
( ~ greater(X0,X1)
| X0 = vplus(X1,sk0_0(X0,X1)) ),
inference(cnf_transformation,[status(esa)],[f62]) ).
fof(f65,plain,
! [Vd120,Vd121] :
( Vd120 != Vd121
| ! [Vd123] : Vd120 != vplus(Vd121,Vd123) ),
inference(pre_NNF_transformation,[status(esa)],[f21]) ).
fof(f66,plain,
! [X0,X1,X2] :
( X0 != X1
| X0 != vplus(X1,X2) ),
inference(cnf_transformation,[status(esa)],[f65]) ).
fof(f67,plain,
! [X0,X1] : vplus(X0,X1) = vplus(X1,X0),
inference(cnf_transformation,[status(esa)],[f22]) ).
fof(f70,plain,
! [X0,X1,X2] : vplus(vplus(X0,X1),X2) = vplus(X0,vplus(X1,X2)),
inference(cnf_transformation,[status(esa)],[f25]) ).
fof(f76,plain,
! [X0,X1] : X0 != vplus(X0,X1),
inference(destructive_equality_resolution,[status(esa)],[f66]) ).
fof(f77,plain,
! [X0,X1] : X0 != vplus(X1,X0),
inference(paramodulation,[status(thm)],[f67,f76]) ).
fof(f99,plain,
greater(vplus(vd347,vd345),vplus(vd345,vd348)),
inference(forward_demodulation,[status(thm)],[f67,f30]) ).
fof(f112,plain,
! [X0,X1,X2] : vplus(X0,vplus(X1,X2)) = vplus(X1,vplus(X2,X0)),
inference(paramodulation,[status(thm)],[f67,f70]) ).
fof(f125,plain,
! [X0,X1,X2] : X0 != vplus(X1,vplus(X2,X0)),
inference(paramodulation,[status(thm)],[f70,f77]) ).
fof(f130,plain,
! [X0,X1,X2] : X0 != vplus(vplus(X1,X0),X2),
inference(paramodulation,[status(thm)],[f67,f125]) ).
fof(f139,plain,
! [X0,X1,X2] : X0 != vplus(vplus(X0,X1),X2),
inference(paramodulation,[status(thm)],[f67,f130]) ).
fof(f160,plain,
! [X0,X1,X2] :
( ~ greater(vplus(X0,X1),vplus(X2,X0))
| greater(X1,X2) ),
inference(paramodulation,[status(thm)],[f67,f43]) ).
fof(f282,plain,
! [X0,X1,X2] : vplus(X0,vplus(X1,X2)) = vplus(vplus(X2,X0),X1),
inference(paramodulation,[status(thm)],[f67,f112]) ).
fof(f2219,plain,
less(vd345,vd344),
inference(resolution,[status(thm)],[f57,f34]) ).
fof(f2261,plain,
vd344 = vplus(vd345,sk0_0(vd344,vd345)),
inference(resolution,[status(thm)],[f63,f34]) ).
fof(f2262,plain,
vd347 = vplus(vd348,sk0_0(vd347,vd348)),
inference(resolution,[status(thm)],[f63,f33]) ).
fof(f2700,plain,
! [X0,X1] :
( X0 = X1
| greater(X0,X1)
| greater(X1,X0) ),
inference(resolution,[status(thm)],[f58,f55]) ).
fof(f3725,plain,
~ greater(vd345,vd344),
inference(resolution,[status(thm)],[f2219,f59]) ).
fof(f5983,plain,
( spl0_14
<=> vplus(vd344,vd347) = vplus(vd345,vd348) ),
introduced(split_symbol_definition) ).
fof(f5984,plain,
( vplus(vd344,vd347) = vplus(vd345,vd348)
| ~ spl0_14 ),
inference(component_clause,[status(thm)],[f5983]) ).
fof(f5986,plain,
( spl0_15
<=> greater(vplus(vd345,vd348),vplus(vd344,vd347)) ),
introduced(split_symbol_definition) ).
fof(f5987,plain,
( greater(vplus(vd345,vd348),vplus(vd344,vd347))
| ~ spl0_15 ),
inference(component_clause,[status(thm)],[f5986]) ).
fof(f5989,plain,
( vplus(vd344,vd347) = vplus(vd345,vd348)
| greater(vplus(vd345,vd348),vplus(vd344,vd347)) ),
inference(resolution,[status(thm)],[f2700,f28]) ).
fof(f5990,plain,
( spl0_14
| spl0_15 ),
inference(split_clause,[status(thm)],[f5989,f5983,f5986]) ).
fof(f6607,plain,
( greater(vplus(vd347,vd345),vplus(vd344,vd347))
| ~ spl0_14 ),
inference(backward_demodulation,[status(thm)],[f5984,f99]) ).
fof(f6754,plain,
( vplus(vd345,vd348) = vplus(vplus(vd344,vd347),sk0_0(vplus(vd345,vd348),vplus(vd344,vd347)))
| ~ spl0_15 ),
inference(resolution,[status(thm)],[f5987,f63]) ).
fof(f6939,plain,
! [X0] :
( vplus(vd344,vd347) != vplus(vplus(vd345,vd348),X0)
| ~ spl0_15 ),
inference(paramodulation,[status(thm)],[f6754,f139]) ).
fof(f7130,plain,
( greater(vd345,vd344)
| ~ spl0_14 ),
inference(resolution,[status(thm)],[f6607,f160]) ).
fof(f7131,plain,
( $false
| ~ spl0_14 ),
inference(forward_subsumption_resolution,[status(thm)],[f7130,f3725]) ).
fof(f7132,plain,
~ spl0_14,
inference(contradiction_clause,[status(thm)],[f7131]) ).
fof(f7144,plain,
! [X0] :
( vplus(vd344,vd347) != vplus(vd348,vplus(X0,vd345))
| ~ spl0_15 ),
inference(paramodulation,[status(thm)],[f282,f6939]) ).
fof(f7176,plain,
! [X0,X1] :
( vplus(vd344,vd347) != vplus(vd348,vplus(X0,vplus(vd345,X1)))
| ~ spl0_15 ),
inference(paramodulation,[status(thm)],[f282,f7144]) ).
fof(f7423,plain,
! [X0] :
( vplus(vd344,vd347) != vplus(vd348,vplus(X0,vd344))
| ~ spl0_15 ),
inference(paramodulation,[status(thm)],[f2261,f7176]) ).
fof(f7440,plain,
! [X0] :
( vplus(vd344,vd347) != vplus(vd344,vplus(vd348,X0))
| ~ spl0_15 ),
inference(paramodulation,[status(thm)],[f112,f7423]) ).
fof(f7706,plain,
( vplus(vd344,vd347) != vplus(vd344,vd347)
| ~ spl0_15 ),
inference(paramodulation,[status(thm)],[f2262,f7440]) ).
fof(f7707,plain,
( $false
| ~ spl0_15 ),
inference(trivial_equality_resolution,[status(esa)],[f7706]) ).
fof(f7708,plain,
~ spl0_15,
inference(contradiction_clause,[status(thm)],[f7707]) ).
fof(f7709,plain,
$false,
inference(sat_refutation,[status(thm)],[f5990,f7132,f7708]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : NUM841+2 : TPTP v8.1.2. Released v4.1.0.
% 0.07/0.13 % Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.13/0.34 % Computer : n026.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Tue May 30 10:15:13 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.13/0.35 % Drodi V3.5.1
% 9.75/1.62 % Refutation found
% 9.75/1.62 % SZS status Theorem for theBenchmark: Theorem is valid
% 9.75/1.62 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 9.75/1.66 % Elapsed time: 1.304040 seconds
% 9.75/1.66 % CPU time: 10.222723 seconds
% 9.75/1.66 % Memory used: 163.886 MB
%------------------------------------------------------------------------------