%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : RNG045+1 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n005.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 02:04:46 PM UTC 2026
% Result : Theorem 5.80s 6.17s
% Output : CNFRefutation 5.80s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 4
% Syntax : Number of formulae : 21 ( 15 unt; 0 def)
% Number of atoms : 38 ( 17 equ)
% Maximal formula atoms : 5 ( 1 avg)
% Number of connectives : 31 ( 14 ~; 9 |; 7 &)
% ( 0 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 4 con; 0-2 aty)
% Number of variables : 12 ( 12 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f15,axiom,
! [W0,W1,W2] :
( ( aScalar0(W2)
& aScalar0(W1)
& aScalar0(W0) )
=> ( sdtasdt0(sdtpldt0(W0,W1),W2) = sdtpldt0(sdtasdt0(W0,W2),sdtasdt0(W1,W2))
& sdtasdt0(W0,sdtpldt0(W1,W2)) = sdtpldt0(sdtasdt0(W0,W1),sdtasdt0(W0,W2)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f16,hypothesis,
( aScalar0(xv)
& aScalar0(xu)
& aScalar0(xy)
& aScalar0(xx) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f17,hypothesis,
sdtasdt0(sdtpldt0(xx,xy),sdtpldt0(xu,xv)) = sdtpldt0(sdtasdt0(xx,sdtpldt0(xu,xv)),sdtasdt0(xy,sdtpldt0(xu,xv))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f18,conjecture,
sdtasdt0(sdtpldt0(xx,xy),sdtpldt0(xu,xv)) = sdtpldt0(sdtpldt0(sdtasdt0(xx,xu),sdtasdt0(xx,xv)),sdtpldt0(sdtasdt0(xy,xu),sdtasdt0(xy,xv))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f19,negated_conjecture,
sdtasdt0(sdtpldt0(xx,xy),sdtpldt0(xu,xv)) != sdtpldt0(sdtpldt0(sdtasdt0(xx,xu),sdtasdt0(xx,xv)),sdtpldt0(sdtasdt0(xy,xu),sdtasdt0(xy,xv))),
inference(negated_conjecture,[status(cth)],[f18]) ).
fof(f61,plain,
! [W0,W1,W2] :
( ( sdtasdt0(sdtpldt0(W0,W1),W2) = sdtpldt0(sdtasdt0(W0,W2),sdtasdt0(W1,W2))
& sdtasdt0(W0,sdtpldt0(W1,W2)) = sdtpldt0(sdtasdt0(W0,W1),sdtasdt0(W0,W2)) )
| ~ aScalar0(W2)
| ~ aScalar0(W1)
| ~ aScalar0(W0) ),
inference(pre_NNF_transformation,[status(thm)],[f15]) ).
fof(f62,plain,
! [X0,X1,X2] :
( sdtasdt0(X0,sdtpldt0(X1,X2)) = sdtpldt0(sdtasdt0(X0,X1),sdtasdt0(X0,X2))
| ~ aScalar0(X2)
| ~ aScalar0(X1)
| ~ aScalar0(X0) ),
inference(cnf_transformation,[status(thm)],[f61]) ).
fof(f64,plain,
aScalar0(xx),
inference(cnf_transformation,[status(thm)],[f16]) ).
fof(f65,plain,
aScalar0(xy),
inference(cnf_transformation,[status(thm)],[f16]) ).
fof(f66,plain,
aScalar0(xu),
inference(cnf_transformation,[status(thm)],[f16]) ).
fof(f67,plain,
aScalar0(xv),
inference(cnf_transformation,[status(thm)],[f16]) ).
fof(f68,plain,
sdtasdt0(sdtpldt0(xx,xy),sdtpldt0(xu,xv)) = sdtpldt0(sdtasdt0(xx,sdtpldt0(xu,xv)),sdtasdt0(xy,sdtpldt0(xu,xv))),
inference(cnf_transformation,[status(thm)],[f17]) ).
fof(f69,plain,
sdtasdt0(sdtpldt0(xx,xy),sdtpldt0(xu,xv)) != sdtpldt0(sdtpldt0(sdtasdt0(xx,xu),sdtasdt0(xx,xv)),sdtpldt0(sdtasdt0(xy,xu),sdtasdt0(xy,xv))),
inference(cnf_transformation,[status(thm)],[f19]) ).
fof(f151,plain,
! [X0,X1] :
( sdtasdt0(X0,sdtpldt0(xu,X1)) = sdtpldt0(sdtasdt0(X0,xu),sdtasdt0(X0,X1))
| ~ aScalar0(X1)
| ~ aScalar0(X0) ),
inference(resolution,[status(thm)],[f66,f62]) ).
fof(f224,plain,
! [X0] :
( sdtasdt0(X0,sdtpldt0(xu,xv)) = sdtpldt0(sdtasdt0(X0,xu),sdtasdt0(X0,xv))
| ~ aScalar0(X0) ),
inference(resolution,[status(thm)],[f67,f151]) ).
fof(f671,plain,
sdtasdt0(xx,sdtpldt0(xu,xv)) = sdtpldt0(sdtasdt0(xx,xu),sdtasdt0(xx,xv)),
inference(resolution,[status(thm)],[f224,f64]) ).
fof(f672,plain,
sdtasdt0(xy,sdtpldt0(xu,xv)) = sdtpldt0(sdtasdt0(xy,xu),sdtasdt0(xy,xv)),
inference(resolution,[status(thm)],[f224,f65]) ).
fof(f3117,plain,
sdtasdt0(sdtpldt0(xx,xy),sdtpldt0(xu,xv)) != sdtpldt0(sdtasdt0(xx,sdtpldt0(xu,xv)),sdtpldt0(sdtasdt0(xy,xu),sdtasdt0(xy,xv))),
inference(backward_demodulation,[status(thm)],[f671,f69]) ).
fof(f3118,plain,
sdtasdt0(sdtpldt0(xx,xy),sdtpldt0(xu,xv)) != sdtpldt0(sdtasdt0(xx,sdtpldt0(xu,xv)),sdtasdt0(xy,sdtpldt0(xu,xv))),
inference(forward_demodulation,[status(thm)],[f672,f3117]) ).
fof(f3119,plain,
sdtasdt0(sdtpldt0(xx,xy),sdtpldt0(xu,xv)) != sdtasdt0(sdtpldt0(xx,xy),sdtpldt0(xu,xv)),
inference(forward_demodulation,[status(thm)],[f68,f3118]) ).
fof(f3120,plain,
$false,
inference(trivial_equality_resolution,[status(thm)],[f3119]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : RNG045+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/5.37 % Computer : n005.cluster.edu
% 0.10/5.37 % Model : x86_64 x86_64
% 0.10/5.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/5.37 % Memory : 8046.5625MB
% 0.10/5.37 % OS : Linux 6.8.0-71-generic
% 0.10/5.37 % CPULimit : 300
% 0.10/5.37 % WCLimit : 300
% 0.10/5.37 % DateTime : Mon Sep 21 04:15:09 UTC 2026
% 0.10/5.37 % CPUTime :
% 0.10/5.38 % Drodi V4.1.1
% 5.80/6.17 % Refutation found
% 5.80/6.17 % SZS status Theorem for theBenchmark: Theorem is valid
% 5.80/6.17 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 5.80/6.20 % Elapsed time: 0.810963 seconds
% 5.80/6.20 % CPU time: 6.205663 seconds
% 5.80/6.20 % Total memory used: 196.093 MB
% 5.80/6.20 % Net memory used: 187.112 MB
%------------------------------------------------------------------------------