%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : RNG105+2 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n004.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 02:04:59 PM UTC 2026
% Result : Theorem 0.08s 0.41s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 11
% Syntax : Number of formulae : 60 ( 19 unt; 1 def)
% Number of atoms : 168 ( 40 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 189 ( 81 ~; 66 |; 37 &)
% ( 1 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 2 prp; 0-2 aty)
% Number of functors : 12 ( 12 usr; 9 con; 0-2 aty)
% Number of variables : 46 ( 39 !; 7 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f5,axiom,
! [W0,W1] :
( ( aElement0(W1)
& aElement0(W0) )
=> aElement0(sdtpldt0(W0,W1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f6,axiom,
! [W0,W1] :
( ( aElement0(W1)
& aElement0(W0) )
=> aElement0(sdtasdt0(W0,W1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f7,axiom,
! [W0,W1] :
( ( aElement0(W1)
& aElement0(W0) )
=> sdtpldt0(W0,W1) = sdtpldt0(W1,W0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
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/sandbox2/benchmark/theBenchmark.p') ).
fof(f38,hypothesis,
aElement0(xc),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f39,hypothesis,
( aElement0(xz)
& aElementOf0(xy,slsdtgt0(xc))
& ? [W0] :
( sdtasdt0(xc,W0) = xy
& aElement0(W0) )
& aElementOf0(xx,slsdtgt0(xc))
& ? [W0] :
( sdtasdt0(xc,W0) = xx
& aElement0(W0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f40,hypothesis,
( sdtasdt0(xc,xu) = xx
& aElement0(xu) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f41,hypothesis,
( sdtasdt0(xc,xv) = xy
& aElement0(xv) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f43,hypothesis,
sdtasdt0(xz,xx) = sdtasdt0(xc,sdtasdt0(xu,xz)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f44,conjecture,
( ( aElementOf0(sdtasdt0(xz,xx),slsdtgt0(xc))
| ? [W0] :
( sdtasdt0(xc,W0) = sdtasdt0(xz,xx)
& aElement0(W0) ) )
& ( aElementOf0(sdtpldt0(xx,xy),slsdtgt0(xc))
| ? [W0] :
( sdtasdt0(xc,W0) = sdtpldt0(xx,xy)
& aElement0(W0) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f45,negated_conjecture,
~ ( ( aElementOf0(sdtasdt0(xz,xx),slsdtgt0(xc))
| ? [W0] :
( sdtasdt0(xc,W0) = sdtasdt0(xz,xx)
& aElement0(W0) ) )
& ( aElementOf0(sdtpldt0(xx,xy),slsdtgt0(xc))
| ? [W0] :
( sdtasdt0(xc,W0) = sdtpldt0(xx,xy)
& aElement0(W0) ) ) ),
inference(negated_conjecture,[status(cth)],[f44]) ).
fof(f53,plain,
! [W0,W1] :
( aElement0(sdtpldt0(W0,W1))
| ~ aElement0(W1)
| ~ aElement0(W0) ),
inference(pre_NNF_transformation,[status(thm)],[f5]) ).
fof(f54,plain,
! [X0,X1] :
( aElement0(sdtpldt0(X0,X1))
| ~ aElement0(X1)
| ~ aElement0(X0) ),
inference(cnf_transformation,[status(thm)],[f53]) ).
fof(f55,plain,
! [W0,W1] :
( aElement0(sdtasdt0(W0,W1))
| ~ aElement0(W1)
| ~ aElement0(W0) ),
inference(pre_NNF_transformation,[status(thm)],[f6]) ).
fof(f56,plain,
! [X0,X1] :
( aElement0(sdtasdt0(X0,X1))
| ~ aElement0(X1)
| ~ aElement0(X0) ),
inference(cnf_transformation,[status(thm)],[f55]) ).
fof(f57,plain,
! [W0,W1] :
( sdtpldt0(W0,W1) = sdtpldt0(W1,W0)
| ~ aElement0(W1)
| ~ aElement0(W0) ),
inference(pre_NNF_transformation,[status(thm)],[f7]) ).
fof(f58,plain,
! [X0,X1] :
( sdtpldt0(X0,X1) = sdtpldt0(X1,X0)
| ~ aElement0(X1)
| ~ aElement0(X0) ),
inference(cnf_transformation,[status(thm)],[f57]) ).
fof(f74,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(f75,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)],[f74]) ).
fof(f196,plain,
aElement0(xc),
inference(cnf_transformation,[status(thm)],[f38]) ).
fof(f197,plain,
( aElement0(xz)
& aElementOf0(xy,slsdtgt0(xc))
& sdtasdt0(xc,sK21_skl) = xy
& aElement0(sK21_skl)
& aElementOf0(xx,slsdtgt0(xc))
& sdtasdt0(xc,sK20_skl) = xx
& aElement0(sK20_skl) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK20_skl,sK21_skl]),skolemize(W0,sK20_skl),skolemize(W0,sK21_skl)],[f39]) ).
fof(f198,plain,
aElement0(sK20_skl),
inference(cnf_transformation,[status(thm)],[f197]) ).
fof(f199,plain,
sdtasdt0(xc,sK20_skl) = xx,
inference(cnf_transformation,[status(thm)],[f197]) ).
fof(f201,plain,
aElement0(sK21_skl),
inference(cnf_transformation,[status(thm)],[f197]) ).
fof(f202,plain,
sdtasdt0(xc,sK21_skl) = xy,
inference(cnf_transformation,[status(thm)],[f197]) ).
fof(f204,plain,
aElement0(xz),
inference(cnf_transformation,[status(thm)],[f197]) ).
fof(f205,plain,
aElement0(xu),
inference(cnf_transformation,[status(thm)],[f40]) ).
fof(f207,plain,
aElement0(xv),
inference(cnf_transformation,[status(thm)],[f41]) ).
fof(f208,plain,
sdtasdt0(xc,xv) = xy,
inference(cnf_transformation,[status(thm)],[f41]) ).
fof(f210,plain,
sdtasdt0(xz,xx) = sdtasdt0(xc,sdtasdt0(xu,xz)),
inference(cnf_transformation,[status(thm)],[f43]) ).
fof(f211,plain,
( ( ~ aElementOf0(sdtasdt0(xz,xx),slsdtgt0(xc))
& ! [W0] :
( sdtasdt0(xc,W0) != sdtasdt0(xz,xx)
| ~ aElement0(W0) ) )
| ( ~ aElementOf0(sdtpldt0(xx,xy),slsdtgt0(xc))
& ! [W0] :
( sdtasdt0(xc,W0) != sdtpldt0(xx,xy)
| ~ aElement0(W0) ) ) ),
inference(pre_NNF_transformation,[status(thm)],[f45]) ).
fof(f212,definition,
( sP3_prd
<=> ( ~ aElementOf0(sdtpldt0(xx,xy),slsdtgt0(xc))
& ! [W0] :
( sdtasdt0(xc,W0) != sdtpldt0(xx,xy)
| ~ aElement0(W0) ) ) ),
introduced(definition,[new_symbols(definition,[sP3_prd])],[]) ).
fof(f213,plain,
( ( ~ aElementOf0(sdtasdt0(xz,xx),slsdtgt0(xc))
& ! [W0] :
( sdtasdt0(xc,W0) != sdtasdt0(xz,xx)
| ~ aElement0(W0) ) )
| sP3_prd ),
inference(formula_renaming,[status(thm)],[f211,f212]) ).
fof(f214,plain,
! [X0] :
( sdtasdt0(xc,X0) != sdtasdt0(xz,xx)
| ~ aElement0(X0)
| sP3_prd ),
inference(cnf_transformation,[status(thm)],[f213]) ).
fof(f233,plain,
( ( aElementOf0(sdtpldt0(xx,xy),slsdtgt0(xc))
| ? [W0] :
( sdtasdt0(xc,W0) = sdtpldt0(xx,xy)
& aElement0(W0) )
| sP3_prd )
& ( ( ~ aElementOf0(sdtpldt0(xx,xy),slsdtgt0(xc))
& ! [W0] :
( sdtasdt0(xc,W0) != sdtpldt0(xx,xy)
| ~ aElement0(W0) ) )
| ~ sP3_prd ) ),
inference(NNF_transformation,[status(thm)],[f212]) ).
fof(f234,plain,
( ( aElementOf0(sdtpldt0(xx,xy),slsdtgt0(xc))
| ( sdtasdt0(xc,sK22_skl) = sdtpldt0(xx,xy)
& aElement0(sK22_skl) )
| sP3_prd )
& ( ( ~ aElementOf0(sdtpldt0(xx,xy),slsdtgt0(xc))
& ! [W0] :
( sdtasdt0(xc,W0) != sdtpldt0(xx,xy)
| ~ aElement0(W0) ) )
| ~ sP3_prd ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK22_skl]),skolemize(W0,sK22_skl)],[f233]) ).
fof(f235,plain,
! [X0] :
( sdtasdt0(xc,X0) != sdtpldt0(xx,xy)
| ~ aElement0(X0)
| ~ sP3_prd ),
inference(cnf_transformation,[status(thm)],[f234]) ).
fof(f256,plain,
! [X0] :
( sdtasdt0(xc,sdtpldt0(X0,sK20_skl)) = sdtpldt0(sdtasdt0(xc,X0),xx)
| ~ aElement0(sK20_skl)
| ~ aElement0(X0)
| ~ aElement0(xc) ),
inference(paramodulation,[status(thm)],[f199,f75]) ).
fof(f260,plain,
( aElement0(xx)
| ~ aElement0(sK20_skl)
| ~ aElement0(xc) ),
inference(paramodulation,[status(thm)],[f199,f56]) ).
fof(f263,plain,
! [X0] :
( sdtasdt0(xc,sdtpldt0(X0,sK20_skl)) = sdtpldt0(sdtasdt0(xc,X0),xx)
| ~ aElement0(sK20_skl)
| ~ aElement0(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f256,f196]) ).
fof(f266,plain,
( aElement0(xx)
| ~ aElement0(sK20_skl) ),
inference(forward_subsumption_resolution,[status(thm)],[f260,f196]) ).
fof(f267,plain,
aElement0(xx),
inference(forward_subsumption_resolution,[status(thm)],[f266,f198]) ).
fof(f281,plain,
( aElement0(xy)
| ~ aElement0(sK21_skl)
| ~ aElement0(xc) ),
inference(paramodulation,[status(thm)],[f202,f56]) ).
fof(f287,plain,
( aElement0(xy)
| ~ aElement0(sK21_skl) ),
inference(forward_subsumption_resolution,[status(thm)],[f281,f196]) ).
fof(f313,plain,
aElement0(xy),
inference(forward_subsumption_resolution,[status(thm)],[f287,f201]) ).
fof(f334,plain,
! [X0] :
( sdtasdt0(xc,sdtpldt0(X0,sK20_skl)) = sdtpldt0(sdtasdt0(xc,X0),xx)
| ~ aElement0(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f263,f198]) ).
fof(f335,plain,
( sdtasdt0(xc,sdtpldt0(xv,sK20_skl)) = sdtpldt0(xy,xx)
| ~ aElement0(xv) ),
inference(paramodulation,[status(thm)],[f208,f334]) ).
fof(f339,plain,
sdtasdt0(xc,sdtpldt0(xv,sK20_skl)) = sdtpldt0(xy,xx),
inference(forward_subsumption_resolution,[status(thm)],[f335,f207]) ).
fof(f344,plain,
( sdtpldt0(xy,xx) != sdtpldt0(xx,xy)
| ~ aElement0(sdtpldt0(xv,sK20_skl))
| ~ sP3_prd ),
inference(paramodulation,[status(thm)],[f339,f235]) ).
fof(f458,plain,
( ~ aElement0(xx)
| ~ aElement0(xy)
| ~ aElement0(sdtpldt0(xv,sK20_skl))
| ~ sP3_prd ),
inference(resolution,[status(thm)],[f344,f58]) ).
fof(f460,plain,
( ~ aElement0(xx)
| ~ aElement0(sdtpldt0(xv,sK20_skl))
| ~ sP3_prd ),
inference(forward_subsumption_resolution,[status(thm)],[f458,f313]) ).
fof(f462,plain,
( ~ aElement0(sdtpldt0(xv,sK20_skl))
| ~ sP3_prd ),
inference(forward_subsumption_resolution,[status(thm)],[f460,f267]) ).
fof(f463,plain,
( ~ aElement0(sK20_skl)
| ~ aElement0(xv)
| ~ sP3_prd ),
inference(resolution,[status(thm)],[f462,f54]) ).
fof(f464,plain,
( ~ aElement0(sK20_skl)
| ~ sP3_prd ),
inference(forward_subsumption_resolution,[status(thm)],[f463,f207]) ).
fof(f470,plain,
! [X0] :
( sdtasdt0(xc,X0) != sdtasdt0(xz,xx)
| ~ aElement0(X0) ),
inference(backward_subsumption_resolution,[status(thm)],[f214,f472]) ).
fof(f472,plain,
~ sP3_prd,
inference(forward_subsumption_resolution,[status(thm)],[f464,f198]) ).
fof(f648,plain,
~ aElement0(sdtasdt0(xu,xz)),
inference(resolution,[status(thm)],[f210,f470]) ).
fof(f671,plain,
( ~ aElement0(xz)
| ~ aElement0(xu) ),
inference(resolution,[status(thm)],[f648,f56]) ).
fof(f672,plain,
~ aElement0(xz),
inference(forward_subsumption_resolution,[status(thm)],[f671,f205]) ).
fof(f673,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f672,f204]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : RNG105+2 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.03 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/0.36 % Computer : n004.cluster.edu
% 0.08/0.36 % Model : x86_64 x86_64
% 0.08/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.36 % Memory : 8046.5625MB
% 0.08/0.36 % OS : Linux 6.8.0-71-generic
% 0.08/0.36 % CPULimit : 300
% 0.08/0.36 % WCLimit : 300
% 0.08/0.36 % DateTime : Mon Sep 21 04:20:19 UTC 2026
% 0.08/0.36 % CPUTime :
% 0.08/0.38 % Drodi V4.1.1
% 0.08/0.41 % Refutation found
% 0.08/0.41 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.08/0.41 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.13/0.43 % Elapsed time: 0.063106 seconds
% 0.13/0.43 % CPU time: 0.204113 seconds
% 0.13/0.43 % Total memory used: 33.004 MB
% 0.13/0.43 % Net memory used: 32.816 MB
%------------------------------------------------------------------------------