%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : NUM857+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 01:41:51 PM UTC 2026
% Result : Theorem 0.08s 0.38s
% Output : CNFRefutation 0.08s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 11
% Syntax : Number of formulae : 48 ( 12 unt; 6 def)
% Number of atoms : 108 ( 13 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 107 ( 47 ~; 45 |; 7 &)
% ( 7 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 10 ( 8 usr; 7 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 4 con; 0-2 aty)
% Number of variables : 31 ( 31 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,conjecture,
geq(vmul(vd526,vd529),vmul(vd527,vd530)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f2,negated_conjecture,
~ geq(vmul(vd526,vd529),vmul(vd527,vd530)),
inference(negated_conjecture,[status(cth)],[f1]) ).
fof(f3,axiom,
geq(vd529,vd530),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f4,axiom,
geq(vd526,vd527),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f5,axiom,
! [Vd517,Vd518,Vd519,Vd520] :
( ( ( greater(Vd517,Vd518)
& geq(Vd519,Vd520) )
| ( geq(Vd517,Vd518)
& greater(Vd519,Vd520) ) )
=> greater(vmul(Vd517,Vd519),vmul(Vd518,Vd520)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f38,axiom,
! [Vd244,Vd245] :
( geq(Vd245,Vd244)
<=> ( Vd245 = Vd244
| greater(Vd245,Vd244) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f63,plain,
~ geq(vmul(vd526,vd529),vmul(vd527,vd530)),
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f64,plain,
geq(vd529,vd530),
inference(cnf_transformation,[status(thm)],[f3]) ).
fof(f65,plain,
geq(vd526,vd527),
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f66,plain,
! [Vd517,Vd518,Vd519,Vd520] :
( greater(vmul(Vd517,Vd519),vmul(Vd518,Vd520))
| ( ( ~ greater(Vd517,Vd518)
| ~ geq(Vd519,Vd520) )
& ( ~ geq(Vd517,Vd518)
| ~ greater(Vd519,Vd520) ) ) ),
inference(pre_NNF_transformation,[status(thm)],[f5]) ).
fof(f67,plain,
! [X0,X1,X2,X3] :
( greater(vmul(X2,X0),vmul(X3,X1))
| ~ geq(X2,X3)
| ~ greater(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f66]) ).
fof(f68,plain,
! [X0,X1,X2,X3] :
( greater(vmul(X2,X0),vmul(X3,X1))
| ~ greater(X2,X3)
| ~ geq(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f66]) ).
fof(f147,plain,
! [Vd244,Vd245] :
( ( ( Vd245 != Vd244
& ~ greater(Vd245,Vd244) )
| geq(Vd245,Vd244) )
& ( Vd245 = Vd244
| greater(Vd245,Vd244)
| ~ geq(Vd245,Vd244) ) ),
inference(NNF_transformation,[status(thm)],[f38]) ).
fof(f148,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)],[f147]) ).
fof(f149,plain,
! [X0,X1] :
( X0 = X1
| greater(X0,X1)
| ~ geq(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f148]) ).
fof(f150,plain,
! [X0,X1] :
( ~ greater(X0,X1)
| geq(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f148]) ).
fof(f151,plain,
! [X0,X1] :
( X0 != X1
| geq(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f148]) ).
fof(f197,plain,
! [X0] : geq(X0,X0),
inference(destructive_equality_resolution,[status(thm)],[f151]) ).
fof(f274,plain,
~ greater(vmul(vd526,vd529),vmul(vd527,vd530)),
inference(resolution,[status(thm)],[f150,f63]) ).
fof(f276,plain,
( ~ greater(vd526,vd527)
| ~ geq(vd529,vd530) ),
inference(resolution,[status(thm)],[f274,f68]) ).
fof(f277,plain,
( ~ geq(vd526,vd527)
| ~ greater(vd529,vd530) ),
inference(resolution,[status(thm)],[f274,f67]) ).
fof(f279,definition,
( sQ2_spl
<=> greater(vd529,vd530) ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f281,plain,
( sQ2_spl
| ~ greater(vd529,vd530) ),
inference(component_clause,[status(thm)],[f279]) ).
fof(f282,definition,
( sQ3_spl
<=> greater(vd526,vd527) ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f284,plain,
( sQ3_spl
| ~ greater(vd526,vd527) ),
inference(component_clause,[status(thm)],[f282]) ).
fof(f286,definition,
( sQ4_spl
<=> geq(vd529,vd530) ),
introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition]) ).
fof(f288,plain,
( sQ4_spl
| ~ geq(vd529,vd530) ),
inference(component_clause,[status(thm)],[f286]) ).
fof(f289,plain,
( ~ sQ3_spl
| ~ sQ4_spl ),
inference(split_clause,[status(thm)],[f276,f286,f282]) ).
fof(f290,definition,
( sQ5_spl
<=> geq(vd526,vd527) ),
introduced(definition,[new_symbols(definition,[sQ5_spl])],[split_symbol_definition]) ).
fof(f292,plain,
( sQ5_spl
| ~ geq(vd526,vd527) ),
inference(component_clause,[status(thm)],[f290]) ).
fof(f293,plain,
( ~ sQ5_spl
| ~ sQ2_spl ),
inference(split_clause,[status(thm)],[f277,f279,f290]) ).
fof(f301,plain,
( sQ2_spl
| vd529 = vd530
| ~ geq(vd529,vd530) ),
inference(resolution,[status(thm)],[f281,f149]) ).
fof(f302,definition,
( sQ8_spl
<=> vd529 = vd530 ),
introduced(definition,[new_symbols(definition,[sQ8_spl])],[split_symbol_definition]) ).
fof(f303,plain,
( ~ sQ8_spl
| vd529 = vd530 ),
inference(component_clause,[status(thm)],[f302]) ).
fof(f305,plain,
( sQ2_spl
| sQ8_spl
| ~ sQ4_spl ),
inference(split_clause,[status(thm)],[f301,f286,f302,f279]) ).
fof(f306,plain,
( sQ4_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f288,f64]) ).
fof(f307,plain,
sQ4_spl,
inference(contradiction_clause,[status(thm)],[f306]) ).
fof(f311,plain,
( ~ sQ8_spl
| ~ geq(vmul(vd526,vd529),vmul(vd527,vd529)) ),
inference(backward_demodulation,[status(thm)],[f303,f63]) ).
fof(f313,plain,
( sQ3_spl
| vd526 = vd527
| ~ geq(vd526,vd527) ),
inference(resolution,[status(thm)],[f284,f149]) ).
fof(f314,definition,
( sQ9_spl
<=> vd526 = vd527 ),
introduced(definition,[new_symbols(definition,[sQ9_spl])],[split_symbol_definition]) ).
fof(f315,plain,
( ~ sQ9_spl
| vd526 = vd527 ),
inference(component_clause,[status(thm)],[f314]) ).
fof(f317,plain,
( sQ3_spl
| sQ9_spl
| ~ sQ5_spl ),
inference(split_clause,[status(thm)],[f313,f290,f314,f282]) ).
fof(f318,plain,
( sQ5_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f292,f65]) ).
fof(f319,plain,
sQ5_spl,
inference(contradiction_clause,[status(thm)],[f318]) ).
fof(f322,plain,
( ~ sQ8_spl
| ~ sQ9_spl
| ~ geq(vmul(vd526,vd529),vmul(vd526,vd529)) ),
inference(backward_demodulation,[status(thm)],[f315,f311]) ).
fof(f325,plain,
( ~ sQ8_spl
| ~ sQ9_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f322,f197]) ).
fof(f326,plain,
( ~ sQ8_spl
| ~ sQ9_spl ),
inference(contradiction_clause,[status(thm)],[f325]) ).
fof(f327,plain,
$false,
inference(sat_refutation,[status(thm)],[f289,f293,f305,f307,f317,f319,f326]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM857+2 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/0.34 % Computer : n001.cluster.edu
% 0.08/0.34 % Model : x86_64 x86_64
% 0.08/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.34 % Memory : 8046.5625MB
% 0.08/0.34 % OS : Linux 6.8.0-71-generic
% 0.08/0.34 % CPULimit : 300
% 0.08/0.34 % WCLimit : 300
% 0.08/0.34 % DateTime : Mon Sep 21 03:19:13 UTC 2026
% 0.08/0.34 % CPUTime :
% 0.08/0.36 % Drodi V4.1.1
% 0.08/0.38 % Refutation found
% 0.08/0.38 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.08/0.38 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.13/0.42 % Elapsed time: 0.061796 seconds
% 0.13/0.42 % CPU time: 0.177017 seconds
% 0.13/0.42 % Total memory used: 104.191 MB
% 0.13/0.42 % Net memory used: 104.090 MB
%------------------------------------------------------------------------------