TSTP Solution File: RNG083+1 by Drodi---3.5.1
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Drodi---3.5.1
% 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 : n015.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 : Wed May 31 12:32:50 EDT 2023
% Result : Theorem 3.39s 0.84s
% Output : CNFRefutation 3.39s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 21
% Syntax : Number of formulae : 94 ( 19 unt; 0 def)
% Number of atoms : 215 ( 66 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 206 ( 85 ~; 86 |; 18 &)
% ( 8 <=>; 9 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 11 ( 9 usr; 9 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 55 (; 55 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f2,axiom,
aElement0(sz00),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f3,axiom,
aElement0(sz10),
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(f13,axiom,
! [W0] :
( aElement0(W0)
=> ( sdtasdt0(W0,sz10) = W0
& W0 = sdtasdt0(sz10,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(f15,axiom,
! [W0] :
( aElement0(W0)
=> ( sdtasdt0(smndt0(sz10),W0) = smndt0(W0)
& smndt0(W0) = sdtasdt0(W0,smndt0(sz10)) ) ),
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(f23,plain,
aElement0(sz10),
inference(cnf_transformation,[status(esa)],[f3]) ).
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(f38,plain,
! [X0] :
( ~ aElement0(X0)
| sdtpldt0(X0,smndt0(X0)) = sz00 ),
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(f44,plain,
! [W0] :
( ~ aElement0(W0)
| ( sdtasdt0(W0,sz10) = W0
& W0 = sdtasdt0(sz10,W0) ) ),
inference(pre_NNF_transformation,[status(esa)],[f13]) ).
fof(f45,plain,
! [X0] :
( ~ aElement0(X0)
| sdtasdt0(X0,sz10) = X0 ),
inference(cnf_transformation,[status(esa)],[f44]) ).
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(f50,plain,
! [W0] :
( ~ aElement0(W0)
| ( sdtasdt0(smndt0(sz10),W0) = smndt0(W0)
& smndt0(W0) = sdtasdt0(W0,smndt0(sz10)) ) ),
inference(pre_NNF_transformation,[status(esa)],[f15]) ).
fof(f51,plain,
! [X0] :
( ~ aElement0(X0)
| sdtasdt0(smndt0(sz10),X0) = smndt0(X0) ),
inference(cnf_transformation,[status(esa)],[f50]) ).
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(f70,plain,
! [X0] :
( ~ aElement0(X0)
| sdtasdt0(X0,xx) = sdtasdt0(xx,X0) ),
inference(resolution,[status(thm)],[f41,f53]) ).
fof(f73,plain,
sdtasdt0(sz00,xx) = sdtasdt0(xx,sz00),
inference(resolution,[status(thm)],[f70,f22]) ).
fof(f74,plain,
( sdtasdt0(sz00,xx) != sz00
| spl0_0 ),
inference(backward_demodulation,[status(thm)],[f73,f58]) ).
fof(f75,plain,
( spl0_2
<=> aElement0(xx) ),
introduced(split_symbol_definition) ).
fof(f77,plain,
( ~ aElement0(xx)
| spl0_2 ),
inference(component_clause,[status(thm)],[f75]) ).
fof(f78,plain,
( spl0_3
<=> aElement0(sz00) ),
introduced(split_symbol_definition) ).
fof(f80,plain,
( ~ aElement0(sz00)
| spl0_3 ),
inference(component_clause,[status(thm)],[f78]) ).
fof(f81,plain,
( spl0_4
<=> aElement0(sdtasdt0(sz00,xx)) ),
introduced(split_symbol_definition) ).
fof(f82,plain,
( aElement0(sdtasdt0(sz00,xx))
| ~ spl0_4 ),
inference(component_clause,[status(thm)],[f81]) ).
fof(f84,plain,
( ~ aElement0(xx)
| ~ aElement0(sz00)
| aElement0(sdtasdt0(sz00,xx)) ),
inference(paramodulation,[status(thm)],[f73,f29]) ).
fof(f85,plain,
( ~ spl0_2
| ~ spl0_3
| spl0_4 ),
inference(split_clause,[status(thm)],[f84,f75,f78,f81]) ).
fof(f86,plain,
( $false
| spl0_3 ),
inference(forward_subsumption_resolution,[status(thm)],[f80,f22]) ).
fof(f87,plain,
spl0_3,
inference(contradiction_clause,[status(thm)],[f86]) ).
fof(f88,plain,
( $false
| spl0_2 ),
inference(forward_subsumption_resolution,[status(thm)],[f77,f53]) ).
fof(f89,plain,
spl0_2,
inference(contradiction_clause,[status(thm)],[f88]) ).
fof(f93,plain,
( sdtpldt0(sdtasdt0(sz00,xx),sz00) = sdtasdt0(sz00,xx)
| ~ spl0_4 ),
inference(resolution,[status(thm)],[f82,f35]) ).
fof(f135,plain,
sdtasdt0(xx,sz10) = xx,
inference(resolution,[status(thm)],[f45,f53]) ).
fof(f137,plain,
( spl0_5
<=> aElement0(sz10) ),
introduced(split_symbol_definition) ).
fof(f139,plain,
( ~ aElement0(sz10)
| spl0_5 ),
inference(component_clause,[status(thm)],[f137]) ).
fof(f147,plain,
sdtpldt0(xx,smndt0(xx)) = sz00,
inference(resolution,[status(thm)],[f38,f53]) ).
fof(f163,plain,
! [X0,X1] :
( ~ aElement0(X0)
| ~ aElement0(X1)
| sdtpldt0(sdtpldt0(X0,xx),X1) = sdtpldt0(X0,sdtpldt0(xx,X1)) ),
inference(resolution,[status(thm)],[f33,f53]) ).
fof(f191,plain,
! [X0,X1] :
( ~ aElement0(X0)
| ~ aElement0(X1)
| sdtasdt0(X0,sdtpldt0(sz00,X1)) = sdtpldt0(sdtasdt0(X0,sz00),sdtasdt0(X0,X1)) ),
inference(resolution,[status(thm)],[f48,f22]) ).
fof(f229,plain,
sz10 = sdtpldt0(sz00,sz10),
inference(resolution,[status(thm)],[f23,f36]) ).
fof(f262,plain,
( spl0_7
<=> aElement0(smndt0(xx)) ),
introduced(split_symbol_definition) ).
fof(f263,plain,
( aElement0(smndt0(xx))
| ~ spl0_7 ),
inference(component_clause,[status(thm)],[f262]) ).
fof(f321,plain,
! [X0] :
( ~ aElement0(X0)
| sdtasdt0(X0,sdtpldt0(sz00,sz10)) = sdtpldt0(sdtasdt0(X0,sz00),sdtasdt0(X0,sz10)) ),
inference(resolution,[status(thm)],[f191,f23]) ).
fof(f322,plain,
! [X0] :
( ~ aElement0(X0)
| sdtasdt0(X0,sz10) = sdtpldt0(sdtasdt0(X0,sz00),sdtasdt0(X0,sz10)) ),
inference(forward_demodulation,[status(thm)],[f229,f321]) ).
fof(f335,plain,
sdtasdt0(xx,sz10) = sdtpldt0(sdtasdt0(xx,sz00),sdtasdt0(xx,sz10)),
inference(resolution,[status(thm)],[f322,f53]) ).
fof(f336,plain,
xx = sdtpldt0(sdtasdt0(xx,sz00),sdtasdt0(xx,sz10)),
inference(forward_demodulation,[status(thm)],[f135,f335]) ).
fof(f337,plain,
xx = sdtpldt0(sdtasdt0(sz00,xx),sdtasdt0(xx,sz10)),
inference(forward_demodulation,[status(thm)],[f73,f336]) ).
fof(f338,plain,
xx = sdtpldt0(sdtasdt0(sz00,xx),xx),
inference(forward_demodulation,[status(thm)],[f135,f337]) ).
fof(f689,plain,
( spl0_10
<=> aElement0(smndt0(sz10)) ),
introduced(split_symbol_definition) ).
fof(f691,plain,
( ~ aElement0(smndt0(sz10))
| spl0_10 ),
inference(component_clause,[status(thm)],[f689]) ).
fof(f730,plain,
( $false
| spl0_5 ),
inference(forward_subsumption_resolution,[status(thm)],[f139,f23]) ).
fof(f731,plain,
spl0_5,
inference(contradiction_clause,[status(thm)],[f730]) ).
fof(f913,plain,
sdtasdt0(smndt0(sz10),xx) = smndt0(xx),
inference(resolution,[status(thm)],[f51,f53]) ).
fof(f920,plain,
( ~ aElement0(smndt0(sz10))
| ~ aElement0(xx)
| aElement0(smndt0(xx)) ),
inference(paramodulation,[status(thm)],[f913,f29]) ).
fof(f921,plain,
( ~ spl0_10
| ~ spl0_2
| spl0_7 ),
inference(split_clause,[status(thm)],[f920,f689,f75,f262]) ).
fof(f922,plain,
( ~ aElement0(sz10)
| spl0_10 ),
inference(resolution,[status(thm)],[f691,f25]) ).
fof(f923,plain,
( ~ spl0_5
| spl0_10 ),
inference(split_clause,[status(thm)],[f922,f137,f689]) ).
fof(f1012,plain,
! [X0] :
( ~ aElement0(X0)
| sdtpldt0(sdtpldt0(X0,xx),smndt0(xx)) = sdtpldt0(X0,sdtpldt0(xx,smndt0(xx)))
| ~ spl0_7 ),
inference(resolution,[status(thm)],[f263,f163]) ).
fof(f1013,plain,
! [X0] :
( ~ aElement0(X0)
| sdtpldt0(sdtpldt0(X0,xx),smndt0(xx)) = sdtpldt0(X0,sz00)
| ~ spl0_7 ),
inference(forward_demodulation,[status(thm)],[f147,f1012]) ).
fof(f1041,plain,
( sdtpldt0(sdtpldt0(sdtasdt0(sz00,xx),xx),smndt0(xx)) = sdtpldt0(sdtasdt0(sz00,xx),sz00)
| ~ spl0_7
| ~ spl0_4 ),
inference(resolution,[status(thm)],[f1013,f82]) ).
fof(f1042,plain,
( sdtpldt0(xx,smndt0(xx)) = sdtpldt0(sdtasdt0(sz00,xx),sz00)
| ~ spl0_7
| ~ spl0_4 ),
inference(forward_demodulation,[status(thm)],[f338,f1041]) ).
fof(f1043,plain,
( sz00 = sdtpldt0(sdtasdt0(sz00,xx),sz00)
| ~ spl0_7
| ~ spl0_4 ),
inference(forward_demodulation,[status(thm)],[f147,f1042]) ).
fof(f1050,plain,
( sz00 = sdtasdt0(sz00,xx)
| ~ spl0_7
| ~ spl0_4 ),
inference(backward_demodulation,[status(thm)],[f1043,f93]) ).
fof(f1051,plain,
( $false
| spl0_0
| ~ spl0_7
| ~ spl0_4 ),
inference(forward_subsumption_resolution,[status(thm)],[f1050,f74]) ).
fof(f1052,plain,
( spl0_0
| ~ spl0_7
| ~ spl0_4 ),
inference(contradiction_clause,[status(thm)],[f1051]) ).
fof(f1055,plain,
( $false
| spl0_1
| ~ spl0_7
| ~ spl0_4 ),
inference(forward_subsumption_resolution,[status(thm)],[f1050,f61]) ).
fof(f1056,plain,
( spl0_1
| ~ spl0_7
| ~ spl0_4 ),
inference(contradiction_clause,[status(thm)],[f1055]) ).
fof(f1057,plain,
$false,
inference(sat_refutation,[status(thm)],[f62,f85,f87,f89,f731,f921,f923,f1052,f1056]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.09 % Problem : RNG083+1 : TPTP v8.1.2. Released v4.0.0.
% 0.04/0.10 % Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.10/0.30 % Computer : n015.cluster.edu
% 0.10/0.30 % Model : x86_64 x86_64
% 0.10/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.30 % Memory : 8042.1875MB
% 0.10/0.30 % OS : Linux 3.10.0-693.el7.x86_64
% 0.10/0.30 % CPULimit : 300
% 0.10/0.30 % WCLimit : 300
% 0.10/0.30 % DateTime : Tue May 30 10:51:49 EDT 2023
% 0.10/0.30 % CPUTime :
% 0.10/0.30 % Drodi V3.5.1
% 3.39/0.84 % Refutation found
% 3.39/0.84 % SZS status Theorem for theBenchmark: Theorem is valid
% 3.39/0.84 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 3.39/0.86 % Elapsed time: 0.553823 seconds
% 3.39/0.86 % CPU time: 3.725141 seconds
% 3.39/0.86 % Memory used: 76.718 MB
%------------------------------------------------------------------------------