%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : RNG103+2 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n026.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 02:04:58 PM UTC 2026
% Result : Theorem 0.18s 0.51s
% Output : CNFRefutation 0.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 5
% Syntax : Number of formulae : 20 ( 11 unt; 0 def)
% Number of atoms : 40 ( 17 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 35 ( 15 ~; 13 |; 6 &)
% ( 0 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 5 con; 0-2 aty)
% Number of variables : 12 ( 12 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f14,axiom,
! [W0,W1,W2] :
( ( aElement0(W2)
& aElement0(W1)
& aElement0(W0) )
=> ( sdtasdt0(sdtpldt0(W1,W2),W0) = sdtpldt0(sdtasdt0(W1,W0),sdtasdt0(W2,W0))
& sdtasdt0(W0,sdtpldt0(W1,W2)) = sdtpldt0(sdtasdt0(W0,W1),sdtasdt0(W0,W2)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f38,hypothesis,
aElement0(xc),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f40,hypothesis,
( sdtasdt0(xc,xu) = xx
& aElement0(xu) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f41,hypothesis,
( sdtasdt0(xc,xv) = xy
& aElement0(xv) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f42,conjecture,
sdtpldt0(xx,xy) = sdtasdt0(xc,sdtpldt0(xu,xv)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f43,negated_conjecture,
sdtpldt0(xx,xy) != sdtasdt0(xc,sdtpldt0(xu,xv)),
inference(negated_conjecture,[status(cth)],[f42]) ).
fof(f72,plain,
! [W0,W1,W2] :
( ( sdtasdt0(sdtpldt0(W1,W2),W0) = sdtpldt0(sdtasdt0(W1,W0),sdtasdt0(W2,W0))
& sdtasdt0(W0,sdtpldt0(W1,W2)) = sdtpldt0(sdtasdt0(W0,W1),sdtasdt0(W0,W2)) )
| ~ aElement0(W2)
| ~ aElement0(W1)
| ~ aElement0(W0) ),
inference(pre_NNF_transformation,[status(thm)],[f14]) ).
fof(f73,plain,
! [X0,X1,X2] :
( sdtasdt0(X0,sdtpldt0(X1,X2)) = sdtpldt0(sdtasdt0(X0,X1),sdtasdt0(X0,X2))
| ~ aElement0(X2)
| ~ aElement0(X1)
| ~ aElement0(X0) ),
inference(cnf_transformation,[status(thm)],[f72]) ).
fof(f194,plain,
aElement0(xc),
inference(cnf_transformation,[status(thm)],[f38]) ).
fof(f203,plain,
aElement0(xu),
inference(cnf_transformation,[status(thm)],[f40]) ).
fof(f204,plain,
sdtasdt0(xc,xu) = xx,
inference(cnf_transformation,[status(thm)],[f40]) ).
fof(f205,plain,
aElement0(xv),
inference(cnf_transformation,[status(thm)],[f41]) ).
fof(f206,plain,
sdtasdt0(xc,xv) = xy,
inference(cnf_transformation,[status(thm)],[f41]) ).
fof(f207,plain,
sdtpldt0(xx,xy) != sdtasdt0(xc,sdtpldt0(xu,xv)),
inference(cnf_transformation,[status(thm)],[f43]) ).
fof(f251,plain,
! [X0] :
( sdtasdt0(xc,sdtpldt0(xu,X0)) = sdtpldt0(xx,sdtasdt0(xc,X0))
| ~ aElement0(X0)
| ~ aElement0(xu)
| ~ aElement0(xc) ),
inference(paramodulation,[status(thm)],[f204,f73]) ).
fof(f255,plain,
! [X0] :
( sdtasdt0(xc,sdtpldt0(xu,X0)) = sdtpldt0(xx,sdtasdt0(xc,X0))
| ~ aElement0(X0)
| ~ aElement0(xu) ),
inference(forward_subsumption_resolution,[status(thm)],[f251,f194]) ).
fof(f297,plain,
! [X0] :
( sdtasdt0(xc,sdtpldt0(xu,X0)) = sdtpldt0(xx,sdtasdt0(xc,X0))
| ~ aElement0(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f255,f203]) ).
fof(f300,plain,
( sdtasdt0(xc,sdtpldt0(xu,xv)) = sdtpldt0(xx,xy)
| ~ aElement0(xv) ),
inference(paramodulation,[status(thm)],[f206,f297]) ).
fof(f302,plain,
sdtasdt0(xc,sdtpldt0(xu,xv)) = sdtpldt0(xx,xy),
inference(forward_subsumption_resolution,[status(thm)],[f300,f205]) ).
fof(f352,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f302,f207]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : RNG103+2 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.06 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.18/0.44 % Computer : n026.cluster.edu
% 0.18/0.44 % Model : x86_64 x86_64
% 0.18/0.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.44 % Memory : 8046.5625MB
% 0.18/0.44 % OS : Linux 6.8.0-71-generic
% 0.18/0.44 % CPULimit : 300
% 0.18/0.44 % WCLimit : 300
% 0.18/0.44 % DateTime : Mon Sep 21 04:22:51 UTC 2026
% 0.18/0.45 % CPUTime :
% 0.18/0.48 % Drodi V4.1.1
% 0.18/0.51 % Refutation found
% 0.18/0.51 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.18/0.51 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.18/0.55 % Elapsed time: 0.098114 seconds
% 0.18/0.55 % CPU time: 0.147031 seconds
% 0.18/0.55 % Total memory used: 17.323 MB
% 0.18/0.55 % Net memory used: 17.247 MB
%------------------------------------------------------------------------------