%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : NUM839+2 : TPTP v9.3.1. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n018.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Sep 24 01:41:47 PM UTC 2026
% Result : Theorem 0.10s 0.39s
% Output : CNFRefutation 0.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 10
% Syntax : Number of formulae : 38 ( 9 unt; 2 def)
% Number of atoms : 70 ( 8 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 62 ( 30 ~; 27 |; 0 &)
% ( 2 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 3 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 3 con; 0-2 aty)
% Number of variables : 43 ( 43 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,conjecture,
greater(vd328,vd329),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f2,negated_conjecture,
~ greater(vd328,vd329),
inference(negated_conjecture,[status(cth)],[f1]) ).
fof(f3,axiom,
greater(vplus(vd328,vd330),vplus(vd329,vd330)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f6,axiom,
! [Vd301,Vd302,Vd303] :
( greater(Vd301,Vd302)
=> greater(vplus(Vd301,Vd303),vplus(Vd302,Vd303)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f15,axiom,
! [Vd226,Vd227] :
( less(Vd226,Vd227)
=> greater(Vd227,Vd226) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f16,axiom,
! [Vd208,Vd209] :
( greater(Vd208,Vd209)
=> less(Vd209,Vd208) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f17,axiom,
! [Vd203,Vd204] :
( less(Vd203,Vd204)
| greater(Vd203,Vd204)
| Vd203 = Vd204 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f19,axiom,
! [Vd203,Vd204] :
( ~ less(Vd203,Vd204)
| ~ greater(Vd203,Vd204) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f20,axiom,
! [Vd203,Vd204] :
( ~ greater(Vd203,Vd204)
| Vd203 != Vd204 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f37,plain,
~ greater(vd328,vd329),
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f38,plain,
greater(vplus(vd328,vd330),vplus(vd329,vd330)),
inference(cnf_transformation,[status(thm)],[f3]) ).
fof(f45,plain,
! [Vd301,Vd302,Vd303] :
( greater(vplus(Vd301,Vd303),vplus(Vd302,Vd303))
| ~ greater(Vd301,Vd302) ),
inference(pre_NNF_transformation,[status(thm)],[f6]) ).
fof(f46,plain,
! [Vd301,Vd302] :
( ! [Vd303] : greater(vplus(Vd301,Vd303),vplus(Vd302,Vd303))
| ~ greater(Vd301,Vd302) ),
inference(miniscoping,[status(thm)],[f45]) ).
fof(f47,plain,
! [X0,X1,X2] :
( greater(vplus(X0,X2),vplus(X1,X2))
| ~ greater(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f46]) ).
fof(f73,plain,
! [Vd226,Vd227] :
( greater(Vd227,Vd226)
| ~ less(Vd226,Vd227) ),
inference(pre_NNF_transformation,[status(thm)],[f15]) ).
fof(f74,plain,
! [X0,X1] :
( greater(X1,X0)
| ~ less(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f73]) ).
fof(f75,plain,
! [Vd208,Vd209] :
( less(Vd209,Vd208)
| ~ greater(Vd208,Vd209) ),
inference(pre_NNF_transformation,[status(thm)],[f16]) ).
fof(f76,plain,
! [X0,X1] :
( less(X1,X0)
| ~ greater(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f75]) ).
fof(f77,plain,
! [X0,X1] :
( less(X0,X1)
| greater(X0,X1)
| X0 = X1 ),
inference(cnf_transformation,[status(thm)],[f17]) ).
fof(f79,plain,
! [X0,X1] :
( ~ less(X0,X1)
| ~ greater(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f19]) ).
fof(f80,plain,
! [X0,X1] :
( ~ greater(X0,X1)
| X0 != X1 ),
inference(cnf_transformation,[status(thm)],[f20]) ).
fof(f117,plain,
! [X0] : ~ greater(X0,X0),
inference(destructive_equality_resolution,[status(thm)],[f80]) ).
fof(f124,plain,
! [X0,X1] :
( ~ greater(X1,X0)
| ~ greater(X0,X1) ),
inference(resolution,[status(thm)],[f79,f76]) ).
fof(f128,plain,
! [X0,X1] :
( greater(X1,X0)
| greater(X0,X1)
| X0 = X1 ),
inference(resolution,[status(thm)],[f77,f74]) ).
fof(f129,plain,
( greater(vd329,vd328)
| vd329 = vd328 ),
inference(resolution,[status(thm)],[f128,f37]) ).
fof(f133,definition,
( sQ0_spl
<=> vd329 = vd328 ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f134,plain,
( ~ sQ0_spl
| vd329 = vd328 ),
inference(component_clause,[status(thm)],[f133]) ).
fof(f136,definition,
( sQ1_spl
<=> greater(vd329,vd328) ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f137,plain,
( ~ sQ1_spl
| greater(vd329,vd328) ),
inference(component_clause,[status(thm)],[f136]) ).
fof(f139,plain,
( sQ1_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f129,f133,f136]) ).
fof(f140,plain,
( ~ sQ0_spl
| greater(vplus(vd329,vd330),vplus(vd329,vd330)) ),
inference(backward_demodulation,[status(thm)],[f134,f38]) ).
fof(f142,plain,
( ~ sQ0_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f140,f117]) ).
fof(f143,plain,
~ sQ0_spl,
inference(contradiction_clause,[status(thm)],[f142]) ).
fof(f150,plain,
! [X0] :
( ~ sQ1_spl
| greater(vplus(vd329,X0),vplus(vd328,X0)) ),
inference(resolution,[status(thm)],[f137,f47]) ).
fof(f162,plain,
! [X0] :
( ~ sQ1_spl
| ~ greater(vplus(vd328,X0),vplus(vd329,X0)) ),
inference(resolution,[status(thm)],[f150,f124]) ).
fof(f163,plain,
( ~ sQ1_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f38,f162]) ).
fof(f165,plain,
~ sQ1_spl,
inference(contradiction_clause,[status(thm)],[f163]) ).
fof(f166,plain,
$false,
inference(sat_refutation,[status(thm)],[f139,f143,f165]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM839+2 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.36 % Computer : n018.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Mon Sep 21 03:14:15 UTC 2026
% 0.10/0.36 % CPUTime :
% 0.10/0.37 % Drodi V4.1.1
% 0.10/0.39 % Refutation found
% 0.10/0.39 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.10/0.39 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.10/0.41 % Elapsed time: 0.044141 seconds
% 0.10/0.41 % CPU time: 0.125675 seconds
% 0.10/0.41 % Total memory used: 64.156 MB
% 0.10/0.41 % Net memory used: 64.088 MB
%------------------------------------------------------------------------------