%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : NUM852+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 : n008.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 0.10s 0.47s
% Output : CNFRefutation 0.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 5
% Syntax : Number of formulae : 22 ( 11 unt; 0 def)
% Number of atoms : 39 ( 17 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 30 ( 13 ~; 11 |; 3 &)
% ( 1 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 3 con; 0-2 aty)
% Number of variables : 35 ( 32 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,conjecture,
greater(vmul(vd481,vd469),vmul(vd480,vd469)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f2,negated_conjecture,
~ greater(vmul(vd481,vd469),vmul(vd480,vd469)),
inference(negated_conjecture,[status(cth)],[f1]) ).
fof(f3,axiom,
greater(vd481,vd480),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f7,axiom,
! [Vd470,Vd471] :
( greater(Vd470,Vd471)
=> vmul(vplus(Vd471,vskolem9(Vd470,Vd471)),vd469) = vplus(vmul(Vd471,vd469),vmul(vskolem9(Vd470,Vd471),vd469)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f9,axiom,
! [Vd470,Vd471] :
( greater(Vd470,Vd471)
=> Vd470 = vplus(Vd471,vskolem9(Vd470,Vd471)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f21,axiom,
! [Vd193,Vd194] :
( greater(Vd194,Vd193)
<=> ? [Vd196] : Vd194 = vplus(Vd193,Vd196) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f22,plain,
~ greater(vmul(vd481,vd469),vmul(vd480,vd469)),
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f23,plain,
greater(vd481,vd480),
inference(cnf_transformation,[status(thm)],[f3]) ).
fof(f29,plain,
! [Vd470,Vd471] :
( vmul(vplus(Vd471,vskolem9(Vd470,Vd471)),vd469) = vplus(vmul(Vd471,vd469),vmul(vskolem9(Vd470,Vd471),vd469))
| ~ greater(Vd470,Vd471) ),
inference(pre_NNF_transformation,[status(thm)],[f7]) ).
fof(f30,plain,
! [X0,X1] :
( vmul(vplus(X1,vskolem9(X0,X1)),vd469) = vplus(vmul(X1,vd469),vmul(vskolem9(X0,X1),vd469))
| ~ greater(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f29]) ).
fof(f33,plain,
! [Vd470,Vd471] :
( Vd470 = vplus(Vd471,vskolem9(Vd470,Vd471))
| ~ greater(Vd470,Vd471) ),
inference(pre_NNF_transformation,[status(thm)],[f9]) ).
fof(f34,plain,
! [X0,X1] :
( X0 = vplus(X1,vskolem9(X0,X1))
| ~ greater(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f33]) ).
fof(f52,plain,
! [Vd193,Vd194] :
( ( ! [Vd196] : Vd194 != vplus(Vd193,Vd196)
| greater(Vd194,Vd193) )
& ( ? [Vd196] : Vd194 = vplus(Vd193,Vd196)
| ~ greater(Vd194,Vd193) ) ),
inference(NNF_transformation,[status(thm)],[f21]) ).
fof(f53,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)],[f52]) ).
fof(f54,plain,
( ! [Vd193,Vd194] :
( ! [Vd196] : Vd194 != vplus(Vd193,Vd196)
| greater(Vd194,Vd193) )
& ! [Vd193,Vd194] :
( Vd194 = vplus(Vd193,sK1_skl(Vd194,Vd193))
| ~ greater(Vd194,Vd193) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1_skl]),skolemize(Vd196,sK1_skl(Vd194,Vd193))],[f53]) ).
fof(f56,plain,
! [X0,X1,X2] :
( X0 != vplus(X1,X2)
| greater(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f54]) ).
fof(f60,plain,
! [X0,X1] : greater(vplus(X0,X1),X0),
inference(destructive_equality_resolution,[status(thm)],[f56]) ).
fof(f118,plain,
vmul(vplus(vd480,vskolem9(vd481,vd480)),vd469) = vplus(vmul(vd480,vd469),vmul(vskolem9(vd481,vd480),vd469)),
inference(resolution,[status(thm)],[f30,f23]) ).
fof(f122,plain,
vd481 = vplus(vd480,vskolem9(vd481,vd480)),
inference(resolution,[status(thm)],[f34,f23]) ).
fof(f230,plain,
vmul(vd481,vd469) = vplus(vmul(vd480,vd469),vmul(vskolem9(vd481,vd480),vd469)),
inference(forward_demodulation,[status(thm)],[f122,f118]) ).
fof(f235,plain,
greater(vmul(vd481,vd469),vmul(vd480,vd469)),
inference(paramodulation,[status(thm)],[f230,f60]) ).
fof(f237,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f235,f22]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM852+2 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.36 % Computer : n008.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Mon Sep 21 03:14:11 UTC 2026
% 0.10/0.36 % CPUTime :
% 0.10/0.37 % Drodi V4.1.1
% 0.10/0.47 % Refutation found
% 0.10/0.47 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.10/0.47 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.10/0.49 % Elapsed time: 0.108903 seconds
% 0.10/0.49 % CPU time: 0.641085 seconds
% 0.10/0.49 % Total memory used: 109.716 MB
% 0.10/0.49 % Net memory used: 109.376 MB
%------------------------------------------------------------------------------