%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : NUM840+1 : TPTP v9.3.1. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n007.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 0.15s 0.39s
% Output : CNFRefutation 0.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 12
% Syntax : Number of formulae : 48 ( 11 unt; 3 def)
% Number of atoms : 99 ( 14 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 92 ( 41 ~; 40 |; 4 &)
% ( 4 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 8 ( 6 usr; 4 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 3 con; 0-2 aty)
% Number of variables : 52 ( 52 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,conjecture,
less(vd328,vd329),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f2,negated_conjecture,
~ less(vd328,vd329),
inference(negated_conjecture,[status(cth)],[f1]) ).
fof(f3,axiom,
less(vplus(vd328,vd330),vplus(vd329,vd330)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f6,axiom,
! [Vd301,Vd302,Vd303] :
( less(Vd301,Vd302)
=> less(vplus(Vd301,Vd303),vplus(Vd302,Vd303)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f15,axiom,
! [Vd249,Vd250] :
( leq(Vd250,Vd249)
<=> ( Vd250 = Vd249
| less(Vd250,Vd249) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f17,axiom,
! [Vd226,Vd227] :
( less(Vd226,Vd227)
=> greater(Vd227,Vd226) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f18,axiom,
! [Vd208,Vd209] :
( greater(Vd208,Vd209)
=> less(Vd209,Vd208) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f19,axiom,
! [Vd203,Vd204] :
( less(Vd203,Vd204)
| greater(Vd203,Vd204)
| Vd203 = Vd204 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f20,axiom,
! [Vd203,Vd204] :
( ~ less(Vd203,Vd204)
| Vd203 != Vd204 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f21,axiom,
! [Vd203,Vd204] :
( ~ less(Vd203,Vd204)
| ~ greater(Vd203,Vd204) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f41,plain,
~ less(vd328,vd329),
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f42,plain,
less(vplus(vd328,vd330),vplus(vd329,vd330)),
inference(cnf_transformation,[status(thm)],[f3]) ).
fof(f47,plain,
! [Vd301,Vd302,Vd303] :
( less(vplus(Vd301,Vd303),vplus(Vd302,Vd303))
| ~ less(Vd301,Vd302) ),
inference(pre_NNF_transformation,[status(thm)],[f6]) ).
fof(f48,plain,
! [Vd301,Vd302] :
( ! [Vd303] : less(vplus(Vd301,Vd303),vplus(Vd302,Vd303))
| ~ less(Vd301,Vd302) ),
inference(miniscoping,[status(thm)],[f47]) ).
fof(f49,plain,
! [X0,X1,X2] :
( less(vplus(X0,X2),vplus(X1,X2))
| ~ less(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f48]) ).
fof(f71,plain,
! [Vd249,Vd250] :
( ( ( Vd250 != Vd249
& ~ less(Vd250,Vd249) )
| leq(Vd250,Vd249) )
& ( Vd250 = Vd249
| less(Vd250,Vd249)
| ~ leq(Vd250,Vd249) ) ),
inference(NNF_transformation,[status(thm)],[f15]) ).
fof(f72,plain,
( ! [Vd249,Vd250] :
( ( Vd250 != Vd249
& ~ less(Vd250,Vd249) )
| leq(Vd250,Vd249) )
& ! [Vd249,Vd250] :
( Vd250 = Vd249
| less(Vd250,Vd249)
| ~ leq(Vd250,Vd249) ) ),
inference(miniscoping,[status(thm)],[f71]) ).
fof(f73,plain,
! [X0,X1] :
( X0 = X1
| less(X0,X1)
| ~ leq(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f72]) ).
fof(f74,plain,
! [X0,X1] :
( ~ less(X0,X1)
| leq(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f72]) ).
fof(f81,plain,
! [Vd226,Vd227] :
( greater(Vd227,Vd226)
| ~ less(Vd226,Vd227) ),
inference(pre_NNF_transformation,[status(thm)],[f17]) ).
fof(f82,plain,
! [X0,X1] :
( greater(X1,X0)
| ~ less(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f81]) ).
fof(f83,plain,
! [Vd208,Vd209] :
( less(Vd209,Vd208)
| ~ greater(Vd208,Vd209) ),
inference(pre_NNF_transformation,[status(thm)],[f18]) ).
fof(f84,plain,
! [X0,X1] :
( less(X1,X0)
| ~ greater(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f83]) ).
fof(f85,plain,
! [X0,X1] :
( less(X0,X1)
| greater(X0,X1)
| X0 = X1 ),
inference(cnf_transformation,[status(thm)],[f19]) ).
fof(f86,plain,
! [X0,X1] :
( ~ less(X0,X1)
| X0 != X1 ),
inference(cnf_transformation,[status(thm)],[f20]) ).
fof(f87,plain,
! [X0,X1] :
( ~ less(X0,X1)
| ~ greater(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f21]) ).
fof(f128,definition,
( sQ1_spl
<=> vd328 = vd329 ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f129,plain,
( ~ sQ1_spl
| vd328 = vd329 ),
inference(component_clause,[status(thm)],[f128]) ).
fof(f135,definition,
( sQ3_spl
<=> greater(vd328,vd329) ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f136,plain,
( ~ sQ3_spl
| greater(vd328,vd329) ),
inference(component_clause,[status(thm)],[f135]) ).
fof(f141,plain,
! [X0] : ~ less(X0,X0),
inference(destructive_equality_resolution,[status(thm)],[f86]) ).
fof(f252,plain,
greater(vplus(vd329,vd330),vplus(vd328,vd330)),
inference(resolution,[status(thm)],[f82,f42]) ).
fof(f263,plain,
! [X0,X1,X2] :
( ~ less(X0,X2)
| ~ greater(vplus(X0,X1),vplus(X2,X1)) ),
inference(resolution,[status(thm)],[f87,f49]) ).
fof(f471,plain,
( ~ sQ1_spl
| less(vplus(vd329,vd330),vplus(vd329,vd330)) ),
inference(backward_demodulation,[status(thm)],[f129,f42]) ).
fof(f473,plain,
( ~ sQ1_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f471,f141]) ).
fof(f474,plain,
~ sQ1_spl,
inference(contradiction_clause,[status(thm)],[f473]) ).
fof(f527,plain,
( ~ sQ3_spl
| less(vd329,vd328) ),
inference(resolution,[status(thm)],[f136,f84]) ).
fof(f533,plain,
( ~ sQ3_spl
| leq(vd329,vd328) ),
inference(resolution,[status(thm)],[f527,f74]) ).
fof(f552,plain,
( ~ sQ3_spl
| vd329 = vd328
| less(vd329,vd328) ),
inference(resolution,[status(thm)],[f533,f73]) ).
fof(f555,definition,
( sQ8_spl
<=> less(vd329,vd328) ),
introduced(definition,[new_symbols(definition,[sQ8_spl])],[split_symbol_definition]) ).
fof(f556,plain,
( ~ sQ8_spl
| less(vd329,vd328) ),
inference(component_clause,[status(thm)],[f555]) ).
fof(f558,plain,
( ~ sQ3_spl
| sQ1_spl
| sQ8_spl ),
inference(split_clause,[status(thm)],[f552,f555,f128,f135]) ).
fof(f576,plain,
( greater(vd328,vd329)
| vd328 = vd329 ),
inference(resolution,[status(thm)],[f85,f41]) ).
fof(f590,plain,
( sQ3_spl
| sQ1_spl ),
inference(split_clause,[status(thm)],[f576,f128,f135]) ).
fof(f1053,plain,
~ less(vd329,vd328),
inference(resolution,[status(thm)],[f263,f252]) ).
fof(f1067,plain,
( ~ sQ8_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1053,f556]) ).
fof(f1068,plain,
~ sQ8_spl,
inference(contradiction_clause,[status(thm)],[f1067]) ).
fof(f1069,plain,
$false,
inference(sat_refutation,[status(thm)],[f474,f558,f590,f1068]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : NUM840+1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.03 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.35 % Computer : n007.cluster.edu
% 0.09/0.35 % Model : x86_64 x86_64
% 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.35 % Memory : 8046.5625MB
% 0.09/0.35 % OS : Linux 6.8.0-71-generic
% 0.09/0.35 % CPULimit : 300
% 0.09/0.35 % WCLimit : 300
% 0.09/0.35 % DateTime : Mon Sep 21 03:10:35 UTC 2026
% 0.09/0.35 % CPUTime :
% 0.09/0.36 % Drodi V4.1.1
% 0.15/0.39 % Refutation found
% 0.15/0.39 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.15/0.39 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.15/0.43 % Elapsed time: 0.062324 seconds
% 0.15/0.43 % CPU time: 0.217948 seconds
% 0.15/0.43 % Total memory used: 104.182 MB
% 0.15/0.43 % Net memory used: 103.906 MB
%------------------------------------------------------------------------------