%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : NUM851+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 : n009.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 0.40s
% Output : CNFRefutation 0.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 5
% Syntax : Number of formulae : 17 ( 17 unt; 0 def)
% Number of atoms : 17 ( 16 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 6 ( 6 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Maximal term depth : 3 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 4 con; 0-2 aty)
% Number of variables : 13 ( 13 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,conjecture,
vmul(vplus(vd471,vd473),vd469) = vplus(vmul(vd471,vd469),vmul(vd473,vd469)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f2,negated_conjecture,
vmul(vplus(vd471,vd473),vd469) != vplus(vmul(vd471,vd469),vmul(vd473,vd469)),
inference(negated_conjecture,[status(cth)],[f1]) ).
fof(f3,axiom,
vmul(vd470,vd469) = vmul(vplus(vd471,vd473),vd469),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f4,axiom,
vd470 = vplus(vd471,vd473),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f7,axiom,
! [Vd432,Vd433,Vd434] : vmul(Vd432,vplus(Vd433,Vd434)) = vplus(vmul(Vd432,Vd433),vmul(Vd432,Vd434)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f8,axiom,
! [Vd418,Vd419] : vmul(Vd418,Vd419) = vmul(Vd419,Vd418),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f29,plain,
vmul(vplus(vd471,vd473),vd469) != vplus(vmul(vd471,vd469),vmul(vd473,vd469)),
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f30,plain,
vmul(vd470,vd469) = vmul(vplus(vd471,vd473),vd469),
inference(cnf_transformation,[status(thm)],[f3]) ).
fof(f31,plain,
vd470 = vplus(vd471,vd473),
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f34,plain,
! [X0,X1,X2] : vmul(X0,vplus(X1,X2)) = vplus(vmul(X0,X1),vmul(X0,X2)),
inference(cnf_transformation,[status(thm)],[f7]) ).
fof(f35,plain,
! [X0,X1] : vmul(X0,X1) = vmul(X1,X0),
inference(cnf_transformation,[status(thm)],[f8]) ).
fof(f73,plain,
vmul(vd470,vd469) != vplus(vmul(vd471,vd469),vmul(vd473,vd469)),
inference(backward_demodulation,[status(thm)],[f30,f29]) ).
fof(f107,plain,
! [X0,X1,X2] : vmul(X0,vplus(X1,X2)) = vplus(vmul(X1,X0),vmul(X0,X2)),
inference(paramodulation,[status(thm)],[f35,f34]) ).
fof(f110,plain,
vmul(vd470,vd469) != vplus(vmul(vd471,vd469),vmul(vd469,vd473)),
inference(paramodulation,[status(thm)],[f35,f73]) ).
fof(f116,plain,
vmul(vd470,vd469) != vmul(vd469,vplus(vd471,vd473)),
inference(forward_demodulation,[status(thm)],[f107,f110]) ).
fof(f117,plain,
vmul(vd470,vd469) != vmul(vd469,vd470),
inference(forward_demodulation,[status(thm)],[f31,f116]) ).
fof(f118,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f117,f35]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM851+2 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.37 % Computer : n009.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Mon Sep 21 03:13:28 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.38 % Drodi V4.1.1
% 0.10/0.40 % Refutation found
% 0.10/0.40 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.10/0.40 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.10/0.43 % Elapsed time: 0.047150 seconds
% 0.10/0.43 % CPU time: 0.131521 seconds
% 0.10/0.43 % Total memory used: 63.775 MB
% 0.10/0.43 % Net memory used: 63.660 MB
%------------------------------------------------------------------------------