%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : NUM853+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 01:41:50 PM UTC 2026
% Result : Theorem 0.09s 0.40s
% Output : CNFRefutation 0.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 9
% Syntax : Number of formulae : 34 ( 11 unt; 2 def)
% Number of atoms : 59 ( 7 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 50 ( 25 ~; 21 |; 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 : 32 ( 32 !; 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(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(f39,plain,
~ greater(vd486,vd488),
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f40,plain,
greater(vmul(vd486,vd487),vmul(vd488,vd487)),
inference(cnf_transformation,[status(thm)],[f3]) ).
fof(f41,plain,
! [Vd456,Vd465,Vd466] :
( less(vmul(Vd465,Vd456),vmul(Vd466,Vd456))
| ~ less(Vd465,Vd466) ),
inference(pre_NNF_transformation,[status(thm)],[f4]) ).
fof(f42,plain,
! [Vd465,Vd466] :
( ! [Vd456] : less(vmul(Vd465,Vd456),vmul(Vd466,Vd456))
| ~ less(Vd465,Vd466) ),
inference(miniscoping,[status(thm)],[f41]) ).
fof(f43,plain,
! [X0,X1,X2] :
( less(vmul(X0,X2),vmul(X1,X2))
| ~ less(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f42]) ).
fof(f67,plain,
! [Vd208,Vd209] :
( less(Vd209,Vd208)
| ~ greater(Vd208,Vd209) ),
inference(pre_NNF_transformation,[status(thm)],[f18]) ).
fof(f68,plain,
! [X0,X1] :
( less(X1,X0)
| ~ greater(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f67]) ).
fof(f69,plain,
! [X0,X1] :
( less(X0,X1)
| greater(X0,X1)
| X0 = X1 ),
inference(cnf_transformation,[status(thm)],[f19]) ).
fof(f70,plain,
! [X0,X1] :
( ~ less(X0,X1)
| X0 != X1 ),
inference(cnf_transformation,[status(thm)],[f20]) ).
fof(f71,plain,
! [X0,X1] :
( ~ less(X0,X1)
| ~ greater(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f21]) ).
fof(f106,plain,
! [X0] : ~ less(X0,X0),
inference(destructive_equality_resolution,[status(thm)],[f70]) ).
fof(f475,plain,
less(vmul(vd488,vd487),vmul(vd486,vd487)),
inference(resolution,[status(thm)],[f68,f40]) ).
fof(f550,plain,
( less(vd486,vd488)
| vd486 = vd488 ),
inference(resolution,[status(thm)],[f69,f39]) ).
fof(f555,definition,
( sQ0_spl
<=> vd486 = vd488 ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f556,plain,
( ~ sQ0_spl
| vd486 = vd488 ),
inference(component_clause,[status(thm)],[f555]) ).
fof(f558,definition,
( sQ1_spl
<=> less(vd486,vd488) ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f559,plain,
( ~ sQ1_spl
| less(vd486,vd488) ),
inference(component_clause,[status(thm)],[f558]) ).
fof(f561,plain,
( sQ1_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f550,f555,f558]) ).
fof(f574,plain,
~ less(vmul(vd486,vd487),vmul(vd488,vd487)),
inference(resolution,[status(thm)],[f71,f40]) ).
fof(f584,plain,
( ~ sQ0_spl
| less(vmul(vd486,vd487),vmul(vd486,vd487)) ),
inference(backward_demodulation,[status(thm)],[f556,f475]) ).
fof(f589,plain,
( ~ sQ0_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f584,f106]) ).
fof(f590,plain,
~ sQ0_spl,
inference(contradiction_clause,[status(thm)],[f589]) ).
fof(f618,plain,
! [X0] :
( ~ sQ1_spl
| less(vmul(vd486,X0),vmul(vd488,X0)) ),
inference(resolution,[status(thm)],[f559,f43]) ).
fof(f852,plain,
( ~ sQ1_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f574,f618]) ).
fof(f862,plain,
~ sQ1_spl,
inference(contradiction_clause,[status(thm)],[f852]) ).
fof(f863,plain,
$false,
inference(sat_refutation,[status(thm)],[f561,f590,f862]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM853+2 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.35 % Computer : n020.cluster.edu
% 0.08/0.35 % Model : x86_64 x86_64
% 0.08/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.35 % Memory : 8046.5625MB
% 0.08/0.35 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Mon Sep 21 03:14:17 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.37 % Drodi V4.1.1
% 0.09/0.40 % Refutation found
% 0.09/0.40 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.09/0.40 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.09/0.43 % Elapsed time: 0.062897 seconds
% 0.09/0.43 % CPU time: 0.249058 seconds
% 0.09/0.43 % Total memory used: 105.585 MB
% 0.09/0.43 % Net memory used: 105.293 MB
%------------------------------------------------------------------------------