%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : NUM842+2 : TPTP v9.3.1. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n020.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 01:41:48 PM UTC 2026
% Result : Theorem 0.12s 0.39s
% Output : CNFRefutation 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 16
% Syntax : Number of formulae : 60 ( 10 unt; 9 def)
% Number of atoms : 135 ( 16 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 132 ( 57 ~; 52 |; 11 &)
% ( 10 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 13 ( 11 usr; 10 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 4 con; 0-2 aty)
% Number of variables : 46 ( 46 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,conjecture,
greater(vplus(vd353,vd355),vplus(vd354,vd356)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f2,negated_conjecture,
~ greater(vplus(vd353,vd355),vplus(vd354,vd356)),
inference(negated_conjecture,[status(cth)],[f1]) ).
fof(f3,axiom,
( ( greater(vd353,vd354)
& geq(vd355,vd356) )
| ( geq(vd353,vd354)
& greater(vd355,vd356) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f4,axiom,
! [Vd337,Vd338,Vd340,Vd341] :
( ( greater(Vd337,Vd338)
& greater(Vd340,Vd341) )
=> greater(vplus(Vd337,Vd340),vplus(Vd338,Vd341)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f10,axiom,
! [Vd301,Vd302,Vd303] :
( greater(Vd301,Vd302)
=> greater(vplus(Vd301,Vd303),vplus(Vd302,Vd303)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f18,axiom,
! [Vd244,Vd245] :
( geq(Vd245,Vd244)
<=> ( Vd245 = Vd244
| greater(Vd245,Vd244) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f24,axiom,
! [Vd203,Vd204] :
( ~ greater(Vd203,Vd204)
| Vd203 != Vd204 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f33,axiom,
! [Vd78,Vd79] : vplus(Vd79,Vd78) = vplus(Vd78,Vd79),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f43,plain,
~ greater(vplus(vd353,vd355),vplus(vd354,vd356)),
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f44,definition,
( sP0_prd
<=> ( geq(vd353,vd354)
& greater(vd355,vd356) ) ),
introduced(definition,[new_symbols(definition,[sP0_prd])],[]) ).
fof(f45,plain,
( ( greater(vd353,vd354)
& geq(vd355,vd356) )
| sP0_prd ),
inference(formula_renaming,[status(thm)],[f3,f44]) ).
fof(f46,plain,
( geq(vd355,vd356)
| sP0_prd ),
inference(cnf_transformation,[status(thm)],[f45]) ).
fof(f47,plain,
( greater(vd353,vd354)
| sP0_prd ),
inference(cnf_transformation,[status(thm)],[f45]) ).
fof(f48,plain,
! [Vd337,Vd338,Vd340,Vd341] :
( greater(vplus(Vd337,Vd340),vplus(Vd338,Vd341))
| ~ greater(Vd337,Vd338)
| ~ greater(Vd340,Vd341) ),
inference(pre_NNF_transformation,[status(thm)],[f4]) ).
fof(f49,plain,
! [X0,X1,X2,X3] :
( greater(vplus(X2,X0),vplus(X3,X1))
| ~ greater(X2,X3)
| ~ greater(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f48]) ).
fof(f65,plain,
! [Vd301,Vd302,Vd303] :
( greater(vplus(Vd301,Vd303),vplus(Vd302,Vd303))
| ~ greater(Vd301,Vd302) ),
inference(pre_NNF_transformation,[status(thm)],[f10]) ).
fof(f66,plain,
! [Vd301,Vd302] :
( ! [Vd303] : greater(vplus(Vd301,Vd303),vplus(Vd302,Vd303))
| ~ greater(Vd301,Vd302) ),
inference(miniscoping,[status(thm)],[f65]) ).
fof(f67,plain,
! [X0,X1,X2] :
( greater(vplus(X0,X2),vplus(X1,X2))
| ~ greater(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f66]) ).
fof(f88,plain,
! [Vd244,Vd245] :
( ( ( Vd245 != Vd244
& ~ greater(Vd245,Vd244) )
| geq(Vd245,Vd244) )
& ( Vd245 = Vd244
| greater(Vd245,Vd244)
| ~ geq(Vd245,Vd244) ) ),
inference(NNF_transformation,[status(thm)],[f18]) ).
fof(f89,plain,
( ! [Vd244,Vd245] :
( ( Vd245 != Vd244
& ~ greater(Vd245,Vd244) )
| geq(Vd245,Vd244) )
& ! [Vd244,Vd245] :
( Vd245 = Vd244
| greater(Vd245,Vd244)
| ~ geq(Vd245,Vd244) ) ),
inference(miniscoping,[status(thm)],[f88]) ).
fof(f90,plain,
! [X0,X1] :
( X0 = X1
| greater(X0,X1)
| ~ geq(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f89]) ).
fof(f100,plain,
! [X0,X1] :
( ~ greater(X0,X1)
| X0 != X1 ),
inference(cnf_transformation,[status(thm)],[f24]) ).
fof(f122,plain,
! [X0,X1] : vplus(X0,X1) = vplus(X1,X0),
inference(cnf_transformation,[status(thm)],[f33]) ).
fof(f137,plain,
( ( ~ geq(vd353,vd354)
| ~ greater(vd355,vd356)
| sP0_prd )
& ( ( geq(vd353,vd354)
& greater(vd355,vd356) )
| ~ sP0_prd ) ),
inference(NNF_transformation,[status(thm)],[f44]) ).
fof(f138,plain,
( greater(vd355,vd356)
| ~ sP0_prd ),
inference(cnf_transformation,[status(thm)],[f137]) ).
fof(f139,plain,
( geq(vd353,vd354)
| ~ sP0_prd ),
inference(cnf_transformation,[status(thm)],[f137]) ).
fof(f141,definition,
( sQ0_spl
<=> sP0_prd ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f144,definition,
( sQ1_spl
<=> geq(vd355,vd356) ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f145,plain,
( ~ sQ1_spl
| geq(vd355,vd356) ),
inference(component_clause,[status(thm)],[f144]) ).
fof(f147,plain,
( sQ1_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f46,f141,f144]) ).
fof(f148,definition,
( sQ2_spl
<=> greater(vd353,vd354) ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f151,plain,
( sQ2_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f47,f141,f148]) ).
fof(f152,definition,
( sQ3_spl
<=> greater(vd355,vd356) ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f155,plain,
( sQ3_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f138,f141,f152]) ).
fof(f156,definition,
( sQ4_spl
<=> geq(vd353,vd354) ),
introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition]) ).
fof(f157,plain,
( ~ sQ4_spl
| geq(vd353,vd354) ),
inference(component_clause,[status(thm)],[f156]) ).
fof(f159,plain,
( sQ4_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f139,f141,f156]) ).
fof(f164,plain,
! [X0] : ~ greater(X0,X0),
inference(destructive_equality_resolution,[status(thm)],[f100]) ).
fof(f170,plain,
( ~ greater(vd353,vd354)
| ~ greater(vd355,vd356) ),
inference(resolution,[status(thm)],[f49,f43]) ).
fof(f171,plain,
! [X0,X1] :
( ~ greater(X1,X1)
| ~ greater(X0,X0) ),
inference(resolution,[status(thm)],[f49,f164]) ).
fof(f172,plain,
( ~ sQ2_spl
| ~ sQ3_spl ),
inference(split_clause,[status(thm)],[f170,f152,f148]) ).
fof(f173,definition,
! [X0] :
( sQ5_spl
<=> ~ greater(X0,X0) ),
introduced(definition,[new_symbols(definition,[sQ5_spl])],[split_symbol_definition]) ).
fof(f176,plain,
sQ5_spl,
inference(split_clause,[status(thm)],[f171,f173]) ).
fof(f182,plain,
~ greater(vplus(vd353,vd355),vplus(vd356,vd354)),
inference(paramodulation,[status(thm)],[f122,f43]) ).
fof(f256,plain,
~ greater(vplus(vd355,vd353),vplus(vd356,vd354)),
inference(paramodulation,[status(thm)],[f122,f182]) ).
fof(f544,definition,
( sQ10_spl
<=> vd356 = vd355 ),
introduced(definition,[new_symbols(definition,[sQ10_spl])],[split_symbol_definition]) ).
fof(f545,plain,
( ~ sQ10_spl
| vd356 = vd355 ),
inference(component_clause,[status(thm)],[f544]) ).
fof(f551,definition,
( sQ12_spl
<=> vd354 = vd353 ),
introduced(definition,[new_symbols(definition,[sQ12_spl])],[split_symbol_definition]) ).
fof(f552,plain,
( ~ sQ12_spl
| vd354 = vd353 ),
inference(component_clause,[status(thm)],[f551]) ).
fof(f558,plain,
( ~ sQ4_spl
| vd353 = vd354
| greater(vd353,vd354) ),
inference(resolution,[status(thm)],[f90,f157]) ).
fof(f563,plain,
( ~ sQ4_spl
| sQ12_spl
| sQ2_spl ),
inference(split_clause,[status(thm)],[f558,f148,f551,f156]) ).
fof(f567,plain,
( ~ sQ12_spl
| ~ greater(vplus(vd355,vd354),vplus(vd356,vd354)) ),
inference(backward_demodulation,[status(thm)],[f552,f256]) ).
fof(f572,plain,
( ~ sQ12_spl
| ~ greater(vd355,vd356) ),
inference(resolution,[status(thm)],[f567,f67]) ).
fof(f580,plain,
( ~ sQ12_spl
| ~ sQ3_spl ),
inference(split_clause,[status(thm)],[f572,f152,f551]) ).
fof(f603,plain,
( ~ sQ1_spl
| vd355 = vd356
| greater(vd355,vd356) ),
inference(resolution,[status(thm)],[f145,f90]) ).
fof(f605,plain,
( ~ sQ1_spl
| sQ10_spl
| sQ3_spl ),
inference(split_clause,[status(thm)],[f603,f152,f544,f144]) ).
fof(f607,plain,
( ~ sQ10_spl
| ~ greater(vplus(vd353,vd356),vplus(vd354,vd356)) ),
inference(backward_demodulation,[status(thm)],[f545,f43]) ).
fof(f627,plain,
( ~ sQ10_spl
| ~ greater(vd353,vd354) ),
inference(resolution,[status(thm)],[f607,f67]) ).
fof(f637,plain,
( ~ sQ10_spl
| ~ sQ2_spl ),
inference(split_clause,[status(thm)],[f627,f148,f544]) ).
fof(f642,plain,
$false,
inference(sat_refutation,[status(thm)],[f147,f151,f155,f159,f172,f176,f563,f580,f605,f637]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : NUM842+2 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.03 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.07/0.36 % Computer : n020.cluster.edu
% 0.07/0.36 % Model : x86_64 x86_64
% 0.07/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.36 % Memory : 8046.5625MB
% 0.07/0.36 % OS : Linux 6.8.0-71-generic
% 0.07/0.36 % CPULimit : 300
% 0.07/0.36 % WCLimit : 300
% 0.07/0.36 % DateTime : Mon Sep 21 03:13:47 UTC 2026
% 0.12/0.36 % CPUTime :
% 0.12/0.38 % Drodi V4.1.1
% 0.12/0.39 % Refutation found
% 0.12/0.39 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.12/0.39 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.12/0.42 % Elapsed time: 0.054368 seconds
% 0.12/0.42 % CPU time: 0.155847 seconds
% 0.12/0.42 % Total memory used: 74.659 MB
% 0.12/0.42 % Net memory used: 74.568 MB
%------------------------------------------------------------------------------