%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : NUM841+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 : n001.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 23.11s 3.37s
% Output : CNFRefutation 23.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 16
% Syntax : Number of formulae : 83 ( 37 unt; 2 def)
% Number of atoms : 138 ( 55 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 111 ( 56 ~; 45 |; 3 &)
% ( 3 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 4 avg)
% Maximal term depth : 9 ( 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 : 137 ( 133 !; 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(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(f10,axiom,
! [Vd328,Vd329,Vd330] :
( vplus(Vd328,Vd330) = vplus(Vd329,Vd330)
=> Vd328 = Vd329 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f14,axiom,
! [Vd301,Vd302,Vd303] :
( greater(Vd301,Vd302)
=> greater(vplus(Vd301,Vd303),vplus(Vd302,Vd303)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f15,axiom,
! [Vd295,Vd296] : greater(vplus(Vd295,Vd296),Vd295),
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] :
( 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,
! [Vd193,Vd194] :
( greater(Vd194,Vd193)
<=> ? [Vd196] : Vd194 = vplus(Vd193,Vd196) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f21,axiom,
! [Vd120,Vd121] :
( ~ ? [Vd123] : Vd120 = vplus(Vd121,Vd123)
| Vd120 != Vd121 ),
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(thm)],[f2]) ).
fof(f33,plain,
greater(vd347,vd348),
inference(cnf_transformation,[status(thm)],[f7]) ).
fof(f34,plain,
greater(vd344,vd345),
inference(cnf_transformation,[status(thm)],[f8]) ).
fof(f38,plain,
! [Vd328,Vd329,Vd330] :
( Vd328 = Vd329
| vplus(Vd328,Vd330) != vplus(Vd329,Vd330) ),
inference(pre_NNF_transformation,[status(thm)],[f10]) ).
fof(f39,plain,
! [Vd328,Vd329] :
( Vd328 = Vd329
| ! [Vd330] : vplus(Vd328,Vd330) != vplus(Vd329,Vd330) ),
inference(miniscoping,[status(thm)],[f38]) ).
fof(f40,plain,
! [X0,X1,X2] :
( X0 = X2
| vplus(X0,X1) != vplus(X2,X1) ),
inference(cnf_transformation,[status(thm)],[f39]) ).
fof(f50,plain,
! [Vd301,Vd302,Vd303] :
( greater(vplus(Vd301,Vd303),vplus(Vd302,Vd303))
| ~ greater(Vd301,Vd302) ),
inference(pre_NNF_transformation,[status(thm)],[f14]) ).
fof(f51,plain,
! [Vd301,Vd302] :
( ! [Vd303] : greater(vplus(Vd301,Vd303),vplus(Vd302,Vd303))
| ~ greater(Vd301,Vd302) ),
inference(miniscoping,[status(thm)],[f50]) ).
fof(f52,plain,
! [X0,X1,X2] :
( greater(vplus(X0,X2),vplus(X1,X2))
| ~ greater(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f51]) ).
fof(f53,plain,
! [X0,X1] : greater(vplus(X0,X1),X0),
inference(cnf_transformation,[status(thm)],[f15]) ).
fof(f54,plain,
! [Vd226,Vd227] :
( greater(Vd227,Vd226)
| ~ less(Vd226,Vd227) ),
inference(pre_NNF_transformation,[status(thm)],[f16]) ).
fof(f55,plain,
! [X0,X1] :
( greater(X1,X0)
| ~ less(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f54]) ).
fof(f56,plain,
! [Vd208,Vd209] :
( less(Vd209,Vd208)
| ~ greater(Vd208,Vd209) ),
inference(pre_NNF_transformation,[status(thm)],[f17]) ).
fof(f57,plain,
! [X0,X1] :
( less(X1,X0)
| ~ greater(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f56]) ).
fof(f58,plain,
! [X0,X1] :
( less(X0,X1)
| greater(X0,X1)
| X0 = X1 ),
inference(cnf_transformation,[status(thm)],[f18]) ).
fof(f59,plain,
! [X0,X1] :
( ~ less(X0,X1)
| ~ greater(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f19]) ).
fof(f60,plain,
! [Vd193,Vd194] :
( ( ! [Vd196] : Vd194 != vplus(Vd193,Vd196)
| greater(Vd194,Vd193) )
& ( ? [Vd196] : Vd194 = vplus(Vd193,Vd196)
| ~ greater(Vd194,Vd193) ) ),
inference(NNF_transformation,[status(thm)],[f20]) ).
fof(f61,plain,
( ! [Vd193,Vd194] :
( ! [Vd196] : Vd194 != vplus(Vd193,Vd196)
| greater(Vd194,Vd193) )
& ! [Vd193,Vd194] :
( ? [Vd196] : Vd194 = vplus(Vd193,Vd196)
| ~ greater(Vd194,Vd193) ) ),
inference(miniscoping,[status(thm)],[f60]) ).
fof(f62,plain,
( ! [Vd193,Vd194] :
( ! [Vd196] : Vd194 != vplus(Vd193,Vd196)
| greater(Vd194,Vd193) )
& ! [Vd193,Vd194] :
( Vd194 = vplus(Vd193,sK0_skl(Vd194,Vd193))
| ~ greater(Vd194,Vd193) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl]),skolemize(Vd196,sK0_skl(Vd194,Vd193))],[f61]) ).
fof(f63,plain,
! [X0,X1] :
( X0 = vplus(X1,sK0_skl(X0,X1))
| ~ greater(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f62]) ).
fof(f65,plain,
! [Vd120,Vd121] :
( ! [Vd123] : Vd120 != vplus(Vd121,Vd123)
| Vd120 != Vd121 ),
inference(pre_NNF_transformation,[status(thm)],[f21]) ).
fof(f66,plain,
! [X0,X1,X2] :
( X0 != vplus(X1,X2)
| X0 != X1 ),
inference(cnf_transformation,[status(thm)],[f65]) ).
fof(f67,plain,
! [X0,X1] : vplus(X0,X1) = vplus(X1,X0),
inference(cnf_transformation,[status(thm)],[f22]) ).
fof(f70,plain,
! [X0,X1,X2] : vplus(vplus(X0,X1),X2) = vplus(X0,vplus(X1,X2)),
inference(cnf_transformation,[status(thm)],[f25]) ).
fof(f79,plain,
! [X0,X1] : X0 != vplus(X0,X1),
inference(destructive_equality_resolution,[status(thm)],[f66]) ).
fof(f97,plain,
! [X0,X1,X2] :
( X1 = X2
| vplus(X0,X1) != vplus(X2,X0) ),
inference(paramodulation,[status(thm)],[f67,f40]) ).
fof(f106,plain,
! [X0,X1,X2] :
( X1 = X2
| vplus(X0,X1) != vplus(X0,X2) ),
inference(paramodulation,[status(thm)],[f67,f97]) ).
fof(f131,plain,
! [X0] : greater(vplus(vd347,X0),vplus(vd348,X0)),
inference(resolution,[status(thm)],[f33,f52]) ).
fof(f132,plain,
! [X0] : greater(vplus(vd344,X0),vplus(vd345,X0)),
inference(resolution,[status(thm)],[f34,f52]) ).
fof(f133,plain,
vd344 = vplus(vd345,sK0_skl(vd344,vd345)),
inference(resolution,[status(thm)],[f63,f34]) ).
fof(f134,plain,
vd347 = vplus(vd348,sK0_skl(vd347,vd348)),
inference(resolution,[status(thm)],[f63,f33]) ).
fof(f138,plain,
! [X0,X1] : vplus(X0,X1) = vplus(X0,sK0_skl(vplus(X0,X1),X0)),
inference(resolution,[status(thm)],[f63,f53]) ).
fof(f199,plain,
! [X0] : greater(vplus(X0,vd347),vplus(vd348,X0)),
inference(paramodulation,[status(thm)],[f67,f131]) ).
fof(f298,plain,
! [X0] : less(vplus(vd345,X0),vplus(vd344,X0)),
inference(resolution,[status(thm)],[f57,f132]) ).
fof(f336,plain,
! [X0,X1,X2] : vplus(X0,vplus(X1,X2)) = vplus(X1,vplus(X2,X0)),
inference(paramodulation,[status(thm)],[f67,f70]) ).
fof(f370,plain,
! [X0,X1,X2] : vplus(X0,X1) != vplus(X0,vplus(X1,X2)),
inference(paramodulation,[status(thm)],[f70,f79]) ).
fof(f476,plain,
! [X0,X1,X2] : vplus(X0,X1) != vplus(vplus(X1,X2),X0),
inference(paramodulation,[status(thm)],[f67,f370]) ).
fof(f487,plain,
! [X0,X1,X2] : vplus(X0,X1) != vplus(X1,vplus(X2,X0)),
inference(forward_demodulation,[status(thm)],[f70,f476]) ).
fof(f600,plain,
! [X0,X1,X2] : vplus(X0,X1) != vplus(X1,vplus(X0,X2)),
inference(paramodulation,[status(thm)],[f67,f487]) ).
fof(f663,plain,
! [X0] : greater(vplus(X0,vd347),vplus(X0,vd348)),
inference(paramodulation,[status(thm)],[f67,f199]) ).
fof(f729,plain,
! [X0,X1] :
( greater(X1,X0)
| greater(X0,X1)
| X0 = X1 ),
inference(resolution,[status(thm)],[f58,f55]) ).
fof(f1034,plain,
! [X0] : ~ greater(vplus(vd345,X0),vplus(vd344,X0)),
inference(resolution,[status(thm)],[f298,f59]) ).
fof(f1233,plain,
( greater(vplus(vd345,vd348),vplus(vd344,vd347))
| vplus(vd344,vd347) = vplus(vd345,vd348) ),
inference(resolution,[status(thm)],[f729,f28]) ).
fof(f1270,definition,
( sQ0_spl
<=> vplus(vd344,vd347) = vplus(vd345,vd348) ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f1271,plain,
( ~ sQ0_spl
| vplus(vd344,vd347) = vplus(vd345,vd348) ),
inference(component_clause,[status(thm)],[f1270]) ).
fof(f1273,definition,
( sQ1_spl
<=> greater(vplus(vd345,vd348),vplus(vd344,vd347)) ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f1274,plain,
( ~ sQ1_spl
| greater(vplus(vd345,vd348),vplus(vd344,vd347)) ),
inference(component_clause,[status(thm)],[f1273]) ).
fof(f1276,plain,
( sQ1_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f1233,f1270,f1273]) ).
fof(f1372,plain,
! [X0] :
( ~ sQ1_spl
| greater(vplus(vplus(vd345,vd348),X0),vplus(vplus(vd344,vd347),X0)) ),
inference(resolution,[status(thm)],[f1274,f52]) ).
fof(f1374,plain,
! [X0] :
( ~ sQ1_spl
| greater(vplus(vd345,vplus(vd348,X0)),vplus(vplus(vd344,vd347),X0)) ),
inference(forward_demodulation,[status(thm)],[f70,f1372]) ).
fof(f1375,plain,
! [X0] :
( ~ sQ1_spl
| greater(vplus(vd345,vplus(vd348,X0)),vplus(vd344,vplus(vd347,X0))) ),
inference(forward_demodulation,[status(thm)],[f70,f1374]) ).
fof(f1541,plain,
! [X0,X1] : X0 = sK0_skl(vplus(X1,X0),X1),
inference(resolution,[status(thm)],[f138,f106]) ).
fof(f2108,plain,
( ~ sQ0_spl
| ~ greater(vplus(vd344,vd347),vplus(vd344,vd348)) ),
inference(paramodulation,[status(thm)],[f1271,f1034]) ).
fof(f2160,plain,
( ~ sQ0_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f2108,f663]) ).
fof(f2161,plain,
~ sQ0_spl,
inference(contradiction_clause,[status(thm)],[f2160]) ).
fof(f4462,plain,
! [X0,X1,X2] : vplus(X0,X1) = sK0_skl(vplus(X1,vplus(X2,X0)),X2),
inference(paramodulation,[status(thm)],[f336,f1541]) ).
fof(f4467,plain,
! [X0,X1,X2,X3] : vplus(X0,X1) != vplus(X1,vplus(X2,vplus(X0,X3))),
inference(paramodulation,[status(thm)],[f336,f600]) ).
fof(f8193,plain,
( ~ sQ1_spl
| greater(vplus(vd345,vd347),vplus(vd344,vplus(vd347,sK0_skl(vd347,vd348)))) ),
inference(paramodulation,[status(thm)],[f134,f1375]) ).
fof(f8202,plain,
! [X0] : vplus(sK0_skl(vd347,vd348),X0) = sK0_skl(vplus(X0,vd347),vd348),
inference(paramodulation,[status(thm)],[f134,f4462]) ).
fof(f10134,plain,
! [X0,X1] : vplus(vd345,X0) != vplus(X0,vplus(X1,vd344)),
inference(paramodulation,[status(thm)],[f133,f4467]) ).
fof(f10553,plain,
! [X0,X1] : vplus(vd345,X0) != vplus(vd344,vplus(X0,X1)),
inference(paramodulation,[status(thm)],[f336,f10134]) ).
fof(f15411,plain,
( ~ sQ1_spl
| vplus(vd345,vd347) = vplus(vplus(vd344,vplus(vd347,sK0_skl(vd347,vd348))),sK0_skl(vplus(vd345,vd347),vplus(vd344,vplus(vd347,sK0_skl(vd347,vd348))))) ),
inference(resolution,[status(thm)],[f8193,f63]) ).
fof(f15415,plain,
( ~ sQ1_spl
| vplus(vd345,vd347) = vplus(vd344,vplus(vplus(vd347,sK0_skl(vd347,vd348)),sK0_skl(vplus(vd345,vd347),vplus(vd344,vplus(vd347,sK0_skl(vd347,vd348)))))) ),
inference(forward_demodulation,[status(thm)],[f70,f15411]) ).
fof(f15416,plain,
( ~ sQ1_spl
| vplus(vd345,vd347) = vplus(vd344,vplus(vd347,vplus(sK0_skl(vd347,vd348),sK0_skl(vplus(vd345,vd347),vplus(vd344,vplus(vd347,sK0_skl(vd347,vd348))))))) ),
inference(forward_demodulation,[status(thm)],[f70,f15415]) ).
fof(f15417,plain,
( ~ sQ1_spl
| vplus(vd345,vd347) = vplus(vd344,vplus(vd347,sK0_skl(vplus(sK0_skl(vplus(vd345,vd347),vplus(vd344,vplus(vd347,sK0_skl(vd347,vd348)))),vd347),vd348))) ),
inference(forward_demodulation,[status(thm)],[f8202,f15416]) ).
fof(f15418,plain,
( ~ sQ1_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f15417,f10553]) ).
fof(f15419,plain,
~ sQ1_spl,
inference(contradiction_clause,[status(thm)],[f15418]) ).
fof(f15420,plain,
$false,
inference(sat_refutation,[status(thm)],[f1276,f2161,f15419]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM841+2 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.35 % Computer : n001.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 03:18:13 UTC 2026
% 0.09/0.35 % CPUTime :
% 0.13/0.37 % Drodi V4.1.1
% 23.11/3.37 % Refutation found
% 23.11/3.37 % SZS status Theorem for theBenchmark: Theorem is valid
% 23.11/3.37 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 4.16/3.42 % Elapsed time: 3.049115 seconds
% 4.16/3.42 % CPU time: 23.913461 seconds
% 4.16/3.42 % Total memory used: 291.164 MB
% 4.16/3.42 % Net memory used: 273.685 MB
%------------------------------------------------------------------------------