%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : NUM846+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 : 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 01:41:49 PM UTC 2026
% Result : Theorem 0.13s 0.38s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 5
% Syntax : Number of formulae : 18 ( 18 unt; 0 def)
% Number of atoms : 18 ( 17 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 6 ( 6 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 3 ( 2 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 4 ( 4 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,conjecture,
vplus(vmul(vd436,vplus(vd437,vd439)),vd436) = vplus(vplus(vmul(vd436,vd437),vmul(vd436,vd439)),vd436),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f2,negated_conjecture,
vplus(vmul(vd436,vplus(vd437,vd439)),vd436) != vplus(vplus(vmul(vd436,vd437),vmul(vd436,vd439)),vd436),
inference(negated_conjecture,[status(cth)],[f1]) ).
fof(f3,axiom,
vmul(vd436,vsucc(vplus(vd437,vd439))) = vplus(vmul(vd436,vplus(vd437,vd439)),vd436),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f4,axiom,
vmul(vd436,vplus(vd437,vsucc(vd439))) = vmul(vd436,vsucc(vplus(vd437,vd439))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f5,axiom,
vmul(vd436,vplus(vd437,vd439)) = vplus(vmul(vd436,vd437),vmul(vd436,vd439)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f15,axiom,
! [Vd78,Vd79] : vplus(Vd79,Vd78) = vplus(Vd78,Vd79),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f23,plain,
vplus(vmul(vd436,vplus(vd437,vd439)),vd436) != vplus(vplus(vmul(vd436,vd437),vmul(vd436,vd439)),vd436),
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f24,plain,
vmul(vd436,vsucc(vplus(vd437,vd439))) = vplus(vmul(vd436,vplus(vd437,vd439)),vd436),
inference(cnf_transformation,[status(thm)],[f3]) ).
fof(f25,plain,
vmul(vd436,vplus(vd437,vsucc(vd439))) = vmul(vd436,vsucc(vplus(vd437,vd439))),
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f26,plain,
vmul(vd436,vplus(vd437,vd439)) = vplus(vmul(vd436,vd437),vmul(vd436,vd439)),
inference(cnf_transformation,[status(thm)],[f5]) ).
fof(f40,plain,
! [X0,X1] : vplus(X0,X1) = vplus(X1,X0),
inference(cnf_transformation,[status(thm)],[f15]) ).
fof(f52,plain,
vmul(vd436,vsucc(vplus(vd437,vd439))) != vplus(vplus(vmul(vd436,vd437),vmul(vd436,vd439)),vd436),
inference(backward_demodulation,[status(thm)],[f24,f23]) ).
fof(f57,plain,
vmul(vd436,vsucc(vplus(vd437,vd439))) = vplus(vd436,vmul(vd436,vplus(vd437,vd439))),
inference(backward_demodulation,[status(thm)],[f40,f24]) ).
fof(f69,plain,
vmul(vd436,vplus(vd437,vsucc(vd439))) != vplus(vplus(vmul(vd436,vd437),vmul(vd436,vd439)),vd436),
inference(forward_demodulation,[status(thm)],[f25,f52]) ).
fof(f70,plain,
vmul(vd436,vplus(vd437,vsucc(vd439))) != vplus(vd436,vplus(vmul(vd436,vd437),vmul(vd436,vd439))),
inference(forward_demodulation,[status(thm)],[f40,f69]) ).
fof(f71,plain,
vmul(vd436,vplus(vd437,vsucc(vd439))) != vplus(vd436,vmul(vd436,vplus(vd437,vd439))),
inference(forward_demodulation,[status(thm)],[f26,f70]) ).
fof(f89,plain,
vmul(vd436,vplus(vd437,vsucc(vd439))) = vplus(vd436,vmul(vd436,vplus(vd437,vd439))),
inference(forward_demodulation,[status(thm)],[f25,f57]) ).
fof(f90,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f89,f71]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM846+2 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.34 % Computer : n014.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 03:12:49 UTC 2026
% 0.08/0.34 % CPUTime :
% 0.08/0.35 % Drodi V4.1.1
% 0.13/0.38 % Refutation found
% 0.13/0.38 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.13/0.38 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.13/0.40 % Elapsed time: 0.049298 seconds
% 0.13/0.40 % CPU time: 0.158390 seconds
% 0.13/0.40 % Total memory used: 102.049 MB
% 0.13/0.40 % Net memory used: 101.797 MB
%------------------------------------------------------------------------------