TSTP Solution File: RNG083+1 by Drodi---3.6.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Drodi---3.6.0
% Problem : RNG083+1 : TPTP v8.1.2. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% Computer : n008.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Apr 30 20:37:55 EDT 2024
% Result : Theorem 0.14s 0.41s
% Output : CNFRefutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 12
% Syntax : Number of formulae : 66 ( 24 unt; 0 def)
% Number of atoms : 133 ( 55 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 113 ( 46 ~; 44 |; 14 &)
% ( 2 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 3 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 49 ( 49 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f2,axiom,
aElement0(sz00),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f4,axiom,
! [W0] :
( aElement0(W0)
=> aElement0(smndt0(W0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f6,axiom,
! [W0,W1] :
( ( aElement0(W0)
& aElement0(W1) )
=> aElement0(sdtasdt0(W0,W1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f8,axiom,
! [W0,W1,W2] :
( ( aElement0(W0)
& aElement0(W1)
& aElement0(W2) )
=> sdtpldt0(sdtpldt0(W0,W1),W2) = sdtpldt0(W0,sdtpldt0(W1,W2)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f9,axiom,
! [W0] :
( aElement0(W0)
=> ( sdtpldt0(W0,sz00) = W0
& W0 = sdtpldt0(sz00,W0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f10,axiom,
! [W0] :
( aElement0(W0)
=> ( sdtpldt0(W0,smndt0(W0)) = sz00
& sz00 = sdtpldt0(smndt0(W0),W0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f11,axiom,
! [W0,W1] :
( ( aElement0(W0)
& aElement0(W1) )
=> sdtasdt0(W0,W1) = sdtasdt0(W1,W0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f14,axiom,
! [W0,W1,W2] :
( ( aElement0(W0)
& aElement0(W1)
& aElement0(W2) )
=> ( sdtasdt0(W0,sdtpldt0(W1,W2)) = sdtpldt0(sdtasdt0(W0,W1),sdtasdt0(W0,W2))
& sdtasdt0(sdtpldt0(W1,W2),W0) = sdtpldt0(sdtasdt0(W1,W0),sdtasdt0(W2,W0)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f16,hypothesis,
aElement0(xx),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f17,conjecture,
( sdtasdt0(xx,sz00) = sz00
& sz00 = sdtasdt0(sz00,xx) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f18,negated_conjecture,
~ ( sdtasdt0(xx,sz00) = sz00
& sz00 = sdtasdt0(sz00,xx) ),
inference(negated_conjecture,[status(cth)],[f17]) ).
fof(f22,plain,
aElement0(sz00),
inference(cnf_transformation,[status(esa)],[f2]) ).
fof(f24,plain,
! [W0] :
( ~ aElement0(W0)
| aElement0(smndt0(W0)) ),
inference(pre_NNF_transformation,[status(esa)],[f4]) ).
fof(f25,plain,
! [X0] :
( ~ aElement0(X0)
| aElement0(smndt0(X0)) ),
inference(cnf_transformation,[status(esa)],[f24]) ).
fof(f28,plain,
! [W0,W1] :
( ~ aElement0(W0)
| ~ aElement0(W1)
| aElement0(sdtasdt0(W0,W1)) ),
inference(pre_NNF_transformation,[status(esa)],[f6]) ).
fof(f29,plain,
! [X0,X1] :
( ~ aElement0(X0)
| ~ aElement0(X1)
| aElement0(sdtasdt0(X0,X1)) ),
inference(cnf_transformation,[status(esa)],[f28]) ).
fof(f32,plain,
! [W0,W1,W2] :
( ~ aElement0(W0)
| ~ aElement0(W1)
| ~ aElement0(W2)
| sdtpldt0(sdtpldt0(W0,W1),W2) = sdtpldt0(W0,sdtpldt0(W1,W2)) ),
inference(pre_NNF_transformation,[status(esa)],[f8]) ).
fof(f33,plain,
! [X0,X1,X2] :
( ~ aElement0(X0)
| ~ aElement0(X1)
| ~ aElement0(X2)
| sdtpldt0(sdtpldt0(X0,X1),X2) = sdtpldt0(X0,sdtpldt0(X1,X2)) ),
inference(cnf_transformation,[status(esa)],[f32]) ).
fof(f34,plain,
! [W0] :
( ~ aElement0(W0)
| ( sdtpldt0(W0,sz00) = W0
& W0 = sdtpldt0(sz00,W0) ) ),
inference(pre_NNF_transformation,[status(esa)],[f9]) ).
fof(f35,plain,
! [X0] :
( ~ aElement0(X0)
| sdtpldt0(X0,sz00) = X0 ),
inference(cnf_transformation,[status(esa)],[f34]) ).
fof(f36,plain,
! [X0] :
( ~ aElement0(X0)
| X0 = sdtpldt0(sz00,X0) ),
inference(cnf_transformation,[status(esa)],[f34]) ).
fof(f37,plain,
! [W0] :
( ~ aElement0(W0)
| ( sdtpldt0(W0,smndt0(W0)) = sz00
& sz00 = sdtpldt0(smndt0(W0),W0) ) ),
inference(pre_NNF_transformation,[status(esa)],[f10]) ).
fof(f39,plain,
! [X0] :
( ~ aElement0(X0)
| sz00 = sdtpldt0(smndt0(X0),X0) ),
inference(cnf_transformation,[status(esa)],[f37]) ).
fof(f40,plain,
! [W0,W1] :
( ~ aElement0(W0)
| ~ aElement0(W1)
| sdtasdt0(W0,W1) = sdtasdt0(W1,W0) ),
inference(pre_NNF_transformation,[status(esa)],[f11]) ).
fof(f41,plain,
! [X0,X1] :
( ~ aElement0(X0)
| ~ aElement0(X1)
| sdtasdt0(X0,X1) = sdtasdt0(X1,X0) ),
inference(cnf_transformation,[status(esa)],[f40]) ).
fof(f47,plain,
! [W0,W1,W2] :
( ~ aElement0(W0)
| ~ aElement0(W1)
| ~ aElement0(W2)
| ( sdtasdt0(W0,sdtpldt0(W1,W2)) = sdtpldt0(sdtasdt0(W0,W1),sdtasdt0(W0,W2))
& sdtasdt0(sdtpldt0(W1,W2),W0) = sdtpldt0(sdtasdt0(W1,W0),sdtasdt0(W2,W0)) ) ),
inference(pre_NNF_transformation,[status(esa)],[f14]) ).
fof(f48,plain,
! [X0,X1,X2] :
( ~ aElement0(X0)
| ~ aElement0(X1)
| ~ aElement0(X2)
| sdtasdt0(X0,sdtpldt0(X1,X2)) = sdtpldt0(sdtasdt0(X0,X1),sdtasdt0(X0,X2)) ),
inference(cnf_transformation,[status(esa)],[f47]) ).
fof(f53,plain,
aElement0(xx),
inference(cnf_transformation,[status(esa)],[f16]) ).
fof(f54,plain,
( sdtasdt0(xx,sz00) != sz00
| sz00 != sdtasdt0(sz00,xx) ),
inference(pre_NNF_transformation,[status(esa)],[f18]) ).
fof(f55,plain,
( sdtasdt0(xx,sz00) != sz00
| sz00 != sdtasdt0(sz00,xx) ),
inference(cnf_transformation,[status(esa)],[f54]) ).
fof(f56,plain,
( spl0_0
<=> sdtasdt0(xx,sz00) = sz00 ),
introduced(split_symbol_definition) ).
fof(f58,plain,
( sdtasdt0(xx,sz00) != sz00
| spl0_0 ),
inference(component_clause,[status(thm)],[f56]) ).
fof(f59,plain,
( spl0_1
<=> sz00 = sdtasdt0(sz00,xx) ),
introduced(split_symbol_definition) ).
fof(f61,plain,
( sz00 != sdtasdt0(sz00,xx)
| spl0_1 ),
inference(component_clause,[status(thm)],[f59]) ).
fof(f62,plain,
( ~ spl0_0
| ~ spl0_1 ),
inference(split_clause,[status(thm)],[f55,f56,f59]) ).
fof(f64,plain,
sdtpldt0(sz00,sz00) = sz00,
inference(resolution,[status(thm)],[f35,f22]) ).
fof(f65,plain,
! [X0] :
( ~ aElement0(X0)
| aElement0(sdtasdt0(xx,X0)) ),
inference(resolution,[status(thm)],[f29,f53]) ).
fof(f66,plain,
! [X0] :
( ~ aElement0(X0)
| aElement0(sdtasdt0(sz00,X0)) ),
inference(resolution,[status(thm)],[f29,f22]) ).
fof(f70,plain,
aElement0(sdtasdt0(xx,sz00)),
inference(resolution,[status(thm)],[f65,f22]) ).
fof(f76,plain,
sdtasdt0(xx,sz00) = sdtpldt0(sz00,sdtasdt0(xx,sz00)),
inference(resolution,[status(thm)],[f70,f36]) ).
fof(f81,plain,
aElement0(sdtasdt0(sz00,xx)),
inference(resolution,[status(thm)],[f66,f53]) ).
fof(f97,plain,
! [X0] :
( ~ aElement0(X0)
| sdtasdt0(X0,xx) = sdtasdt0(xx,X0) ),
inference(resolution,[status(thm)],[f41,f53]) ).
fof(f122,plain,
sdtasdt0(sz00,xx) = sdtasdt0(xx,sz00),
inference(resolution,[status(thm)],[f97,f22]) ).
fof(f124,plain,
aElement0(smndt0(sdtasdt0(sz00,xx))),
inference(resolution,[status(thm)],[f25,f81]) ).
fof(f182,plain,
sz00 = sdtpldt0(smndt0(sdtasdt0(sz00,xx)),sdtasdt0(sz00,xx)),
inference(resolution,[status(thm)],[f39,f81]) ).
fof(f189,plain,
( sdtasdt0(sz00,xx) != sz00
| spl0_0 ),
inference(backward_demodulation,[status(thm)],[f122,f58]) ).
fof(f197,plain,
sdtasdt0(sz00,xx) = sdtpldt0(sz00,sdtasdt0(xx,sz00)),
inference(forward_demodulation,[status(thm)],[f122,f76]) ).
fof(f198,plain,
sdtasdt0(sz00,xx) = sdtpldt0(sz00,sdtasdt0(sz00,xx)),
inference(forward_demodulation,[status(thm)],[f122,f197]) ).
fof(f314,plain,
! [X0,X1] :
( ~ aElement0(X0)
| ~ aElement0(X1)
| sdtpldt0(sdtpldt0(X0,X1),sdtasdt0(sz00,xx)) = sdtpldt0(X0,sdtpldt0(X1,sdtasdt0(sz00,xx))) ),
inference(resolution,[status(thm)],[f33,f81]) ).
fof(f377,plain,
! [X0] :
( ~ aElement0(X0)
| sdtasdt0(X0,sdtpldt0(sz00,sz00)) = sdtpldt0(sdtasdt0(X0,sz00),sdtasdt0(X0,sz00)) ),
inference(resolution,[status(thm)],[f48,f22]) ).
fof(f378,plain,
! [X0] :
( ~ aElement0(X0)
| sdtasdt0(X0,sz00) = sdtpldt0(sdtasdt0(X0,sz00),sdtasdt0(X0,sz00)) ),
inference(forward_demodulation,[status(thm)],[f64,f377]) ).
fof(f399,plain,
sdtasdt0(xx,sz00) = sdtpldt0(sdtasdt0(xx,sz00),sdtasdt0(xx,sz00)),
inference(resolution,[status(thm)],[f378,f53]) ).
fof(f400,plain,
sdtasdt0(sz00,xx) = sdtpldt0(sdtasdt0(xx,sz00),sdtasdt0(xx,sz00)),
inference(forward_demodulation,[status(thm)],[f122,f399]) ).
fof(f401,plain,
sdtasdt0(sz00,xx) = sdtpldt0(sdtasdt0(sz00,xx),sdtasdt0(xx,sz00)),
inference(forward_demodulation,[status(thm)],[f122,f400]) ).
fof(f402,plain,
sdtasdt0(sz00,xx) = sdtpldt0(sdtasdt0(sz00,xx),sdtasdt0(sz00,xx)),
inference(forward_demodulation,[status(thm)],[f122,f401]) ).
fof(f560,plain,
! [X0] :
( ~ aElement0(X0)
| sdtpldt0(sdtpldt0(X0,sdtasdt0(sz00,xx)),sdtasdt0(sz00,xx)) = sdtpldt0(X0,sdtpldt0(sdtasdt0(sz00,xx),sdtasdt0(sz00,xx))) ),
inference(resolution,[status(thm)],[f314,f81]) ).
fof(f561,plain,
! [X0] :
( ~ aElement0(X0)
| sdtpldt0(sdtpldt0(X0,sdtasdt0(sz00,xx)),sdtasdt0(sz00,xx)) = sdtpldt0(X0,sdtasdt0(sz00,xx)) ),
inference(forward_demodulation,[status(thm)],[f402,f560]) ).
fof(f641,plain,
sdtpldt0(sdtpldt0(smndt0(sdtasdt0(sz00,xx)),sdtasdt0(sz00,xx)),sdtasdt0(sz00,xx)) = sdtpldt0(smndt0(sdtasdt0(sz00,xx)),sdtasdt0(sz00,xx)),
inference(resolution,[status(thm)],[f561,f124]) ).
fof(f642,plain,
sdtpldt0(sz00,sdtasdt0(sz00,xx)) = sdtpldt0(smndt0(sdtasdt0(sz00,xx)),sdtasdt0(sz00,xx)),
inference(forward_demodulation,[status(thm)],[f182,f641]) ).
fof(f643,plain,
sdtasdt0(sz00,xx) = sdtpldt0(smndt0(sdtasdt0(sz00,xx)),sdtasdt0(sz00,xx)),
inference(forward_demodulation,[status(thm)],[f198,f642]) ).
fof(f644,plain,
sdtasdt0(sz00,xx) = sz00,
inference(forward_demodulation,[status(thm)],[f182,f643]) ).
fof(f645,plain,
( $false
| spl0_0 ),
inference(forward_subsumption_resolution,[status(thm)],[f644,f189]) ).
fof(f646,plain,
spl0_0,
inference(contradiction_clause,[status(thm)],[f645]) ).
fof(f654,plain,
( $false
| spl0_1 ),
inference(forward_subsumption_resolution,[status(thm)],[f644,f61]) ).
fof(f655,plain,
spl0_1,
inference(contradiction_clause,[status(thm)],[f654]) ).
fof(f656,plain,
$false,
inference(sat_refutation,[status(thm)],[f62,f646,f655]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.10 % Problem : RNG083+1 : TPTP v8.1.2. Released v4.0.0.
% 0.03/0.11 % Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.10/0.31 % Computer : n008.cluster.edu
% 0.10/0.31 % Model : x86_64 x86_64
% 0.10/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.31 % Memory : 8042.1875MB
% 0.10/0.31 % OS : Linux 3.10.0-693.el7.x86_64
% 0.10/0.32 % CPULimit : 300
% 0.10/0.32 % WCLimit : 300
% 0.10/0.32 % DateTime : Mon Apr 29 22:23:12 EDT 2024
% 0.10/0.32 % CPUTime :
% 0.10/0.32 % Drodi V3.6.0
% 0.14/0.41 % Refutation found
% 0.14/0.41 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.14/0.41 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.14/0.42 % Elapsed time: 0.100501 seconds
% 0.14/0.42 % CPU time: 0.710698 seconds
% 0.14/0.42 % Total memory used: 39.029 MB
% 0.14/0.42 % Net memory used: 34.994 MB
%------------------------------------------------------------------------------