%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : NUM853+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 : n014.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 01:41:50 PM UTC 2026
% Result : Theorem 0.12s 0.42s
% Output : CNFRefutation 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 9
% Syntax : Number of formulae : 34 ( 12 unt; 2 def)
% Number of atoms : 58 ( 7 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 49 ( 25 ~; 20 |; 0 &)
% ( 2 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 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 : 31 ( 31 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,conjecture,
greater(vd486,vd488),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f2,negated_conjecture,
~ greater(vd486,vd488),
inference(negated_conjecture,[status(cth)],[f1]) ).
fof(f3,axiom,
greater(vmul(vd486,vd487),vmul(vd488,vd487)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f4,axiom,
! [Vd456,Vd465,Vd466] :
( less(Vd465,Vd466)
=> less(vmul(Vd465,Vd456),vmul(Vd466,Vd456)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f34,axiom,
! [Vd208,Vd209] :
( greater(Vd208,Vd209)
=> less(Vd209,Vd208) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f35,axiom,
! [Vd203,Vd204] :
( less(Vd203,Vd204)
| greater(Vd203,Vd204)
| Vd203 = Vd204 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f36,axiom,
! [Vd203,Vd204] :
( ~ less(Vd203,Vd204)
| Vd203 != Vd204 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f37,axiom,
! [Vd203,Vd204] :
( ~ less(Vd203,Vd204)
| ~ greater(Vd203,Vd204) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f57,plain,
~ greater(vd486,vd488),
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f58,plain,
greater(vmul(vd486,vd487),vmul(vd488,vd487)),
inference(cnf_transformation,[status(thm)],[f3]) ).
fof(f59,plain,
! [Vd456,Vd465,Vd466] :
( less(vmul(Vd465,Vd456),vmul(Vd466,Vd456))
| ~ less(Vd465,Vd466) ),
inference(pre_NNF_transformation,[status(thm)],[f4]) ).
fof(f60,plain,
! [Vd465,Vd466] :
( ! [Vd456] : less(vmul(Vd465,Vd456),vmul(Vd466,Vd456))
| ~ less(Vd465,Vd466) ),
inference(miniscoping,[status(thm)],[f59]) ).
fof(f61,plain,
! [X0,X1,X2] :
( less(vmul(X0,X2),vmul(X1,X2))
| ~ less(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f60]) ).
fof(f133,plain,
! [Vd208,Vd209] :
( less(Vd209,Vd208)
| ~ greater(Vd208,Vd209) ),
inference(pre_NNF_transformation,[status(thm)],[f34]) ).
fof(f134,plain,
! [X0,X1] :
( less(X1,X0)
| ~ greater(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f133]) ).
fof(f135,plain,
! [X0,X1] :
( less(X0,X1)
| greater(X0,X1)
| X0 = X1 ),
inference(cnf_transformation,[status(thm)],[f35]) ).
fof(f136,plain,
! [X0,X1] :
( ~ less(X0,X1)
| X0 != X1 ),
inference(cnf_transformation,[status(thm)],[f36]) ).
fof(f137,plain,
! [X0,X1] :
( ~ less(X0,X1)
| ~ greater(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f37]) ).
fof(f177,plain,
! [X0] : ~ less(X0,X0),
inference(destructive_equality_resolution,[status(thm)],[f136]) ).
fof(f248,plain,
less(vmul(vd488,vd487),vmul(vd486,vd487)),
inference(resolution,[status(thm)],[f134,f58]) ).
fof(f253,plain,
~ less(vmul(vd486,vd487),vmul(vd488,vd487)),
inference(resolution,[status(thm)],[f137,f58]) ).
fof(f966,plain,
~ less(vd486,vd488),
inference(resolution,[status(thm)],[f253,f61]) ).
fof(f1645,plain,
( less(vd486,vd488)
| vd486 = vd488 ),
inference(resolution,[status(thm)],[f135,f57]) ).
fof(f1659,definition,
( sQ20_spl
<=> vd486 = vd488 ),
introduced(definition,[new_symbols(definition,[sQ20_spl])],[split_symbol_definition]) ).
fof(f1660,plain,
( ~ sQ20_spl
| vd486 = vd488 ),
inference(component_clause,[status(thm)],[f1659]) ).
fof(f1662,definition,
( sQ21_spl
<=> less(vd486,vd488) ),
introduced(definition,[new_symbols(definition,[sQ21_spl])],[split_symbol_definition]) ).
fof(f1663,plain,
( ~ sQ21_spl
| less(vd486,vd488) ),
inference(component_clause,[status(thm)],[f1662]) ).
fof(f1665,plain,
( sQ21_spl
| sQ20_spl ),
inference(split_clause,[status(thm)],[f1645,f1659,f1662]) ).
fof(f1684,plain,
( ~ sQ20_spl
| less(vmul(vd488,vd487),vmul(vd488,vd487)) ),
inference(backward_demodulation,[status(thm)],[f1660,f248]) ).
fof(f1690,plain,
( ~ sQ20_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1684,f177]) ).
fof(f1691,plain,
~ sQ20_spl,
inference(contradiction_clause,[status(thm)],[f1690]) ).
fof(f1712,plain,
( ~ sQ21_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f966,f1663]) ).
fof(f1713,plain,
~ sQ21_spl,
inference(contradiction_clause,[status(thm)],[f1712]) ).
fof(f1714,plain,
$false,
inference(sat_refutation,[status(thm)],[f1665,f1691,f1713]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM853+1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.36 % Computer : n014.cluster.edu
% 0.08/0.36 % Model : x86_64 x86_64
% 0.08/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.36 % Memory : 8046.5625MB
% 0.08/0.36 % OS : Linux 6.8.0-71-generic
% 0.12/0.36 % CPULimit : 300
% 0.12/0.36 % WCLimit : 300
% 0.12/0.36 % DateTime : Mon Sep 21 03:13:19 UTC 2026
% 0.12/0.36 % CPUTime :
% 0.12/0.38 % Drodi V4.1.1
% 0.12/0.42 % Refutation found
% 0.12/0.42 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.12/0.42 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.12/0.44 % Elapsed time: 0.078297 seconds
% 0.12/0.44 % CPU time: 0.296614 seconds
% 0.12/0.44 % Total memory used: 106.864 MB
% 0.12/0.44 % Net memory used: 106.440 MB
%------------------------------------------------------------------------------