TSTP Solution File: KRS084+1 by Drodi---3.6.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Drodi---3.6.0
% Problem : KRS084+1 : TPTP v8.1.2. Released v3.1.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% Computer : n004.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 20:24:44 EDT 2024
% Result : Unsatisfiable 0.12s 0.35s
% Output : CNFRefutation 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 11
% Syntax : Number of formulae : 65 ( 10 unt; 0 def)
% Number of atoms : 208 ( 6 equ)
% Maximal formula atoms : 14 ( 3 avg)
% Number of connectives : 236 ( 93 ~; 89 |; 42 &)
% ( 9 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 13 ( 11 usr; 5 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 1 con; 0-2 aty)
% Number of variables : 88 ( 75 !; 13 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f18,axiom,
! [X] :
( cUnsatisfiable(X)
<=> ( ? [Y] :
( rinvF(X,Y)
& cd(Y) )
& ! [Y] :
( rinvR(X,Y)
=> ? [Z] :
( rinvF(Y,Z)
& cd(Z) ) )
& ~ cc(X) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f19,axiom,
! [X] :
( cd(X)
<=> ( ? [Y] :
( rf(X,Y)
& ~ cc(Y) )
& cc(X) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f20,axiom,
! [X,Y,Z] :
( ( rf(X,Y)
& rf(X,Z) )
=> Y = Z ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f21,axiom,
! [X,Y] :
( rinvF(X,Y)
<=> rf(Y,X) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f22,axiom,
! [X,Y] :
( rinvR(X,Y)
<=> rr(Y,X) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f24,axiom,
cUnsatisfiable(i2003_11_14_17_19_35232),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f25,axiom,
! [X,Y] :
( rf(X,Y)
=> rr(X,Y) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f78,plain,
! [X] :
( cUnsatisfiable(X)
<=> ( ? [Y] :
( rinvF(X,Y)
& cd(Y) )
& ! [Y] :
( ~ rinvR(X,Y)
| ? [Z] :
( rinvF(Y,Z)
& cd(Z) ) )
& ~ cc(X) ) ),
inference(pre_NNF_transformation,[status(esa)],[f18]) ).
fof(f79,plain,
! [X] :
( ( ~ cUnsatisfiable(X)
| ( ? [Y] :
( rinvF(X,Y)
& cd(Y) )
& ! [Y] :
( ~ rinvR(X,Y)
| ? [Z] :
( rinvF(Y,Z)
& cd(Z) ) )
& ~ cc(X) ) )
& ( cUnsatisfiable(X)
| ! [Y] :
( ~ rinvF(X,Y)
| ~ cd(Y) )
| ? [Y] :
( rinvR(X,Y)
& ! [Z] :
( ~ rinvF(Y,Z)
| ~ cd(Z) ) )
| cc(X) ) ),
inference(NNF_transformation,[status(esa)],[f78]) ).
fof(f80,plain,
( ! [X] :
( ~ cUnsatisfiable(X)
| ( ? [Y] :
( rinvF(X,Y)
& cd(Y) )
& ! [Y] :
( ~ rinvR(X,Y)
| ? [Z] :
( rinvF(Y,Z)
& cd(Z) ) )
& ~ cc(X) ) )
& ! [X] :
( cUnsatisfiable(X)
| ! [Y] :
( ~ rinvF(X,Y)
| ~ cd(Y) )
| ? [Y] :
( rinvR(X,Y)
& ! [Z] :
( ~ rinvF(Y,Z)
| ~ cd(Z) ) )
| cc(X) ) ),
inference(miniscoping,[status(esa)],[f79]) ).
fof(f81,plain,
( ! [X] :
( ~ cUnsatisfiable(X)
| ( rinvF(X,sk0_0(X))
& cd(sk0_0(X))
& ! [Y] :
( ~ rinvR(X,Y)
| ( rinvF(Y,sk0_1(Y,X))
& cd(sk0_1(Y,X)) ) )
& ~ cc(X) ) )
& ! [X] :
( cUnsatisfiable(X)
| ! [Y] :
( ~ rinvF(X,Y)
| ~ cd(Y) )
| ( rinvR(X,sk0_2(X))
& ! [Z] :
( ~ rinvF(sk0_2(X),Z)
| ~ cd(Z) ) )
| cc(X) ) ),
inference(skolemization,[status(esa)],[f80]) ).
fof(f82,plain,
! [X0] :
( ~ cUnsatisfiable(X0)
| rinvF(X0,sk0_0(X0)) ),
inference(cnf_transformation,[status(esa)],[f81]) ).
fof(f83,plain,
! [X0] :
( ~ cUnsatisfiable(X0)
| cd(sk0_0(X0)) ),
inference(cnf_transformation,[status(esa)],[f81]) ).
fof(f84,plain,
! [X0,X1] :
( ~ cUnsatisfiable(X0)
| ~ rinvR(X0,X1)
| rinvF(X1,sk0_1(X1,X0)) ),
inference(cnf_transformation,[status(esa)],[f81]) ).
fof(f85,plain,
! [X0,X1] :
( ~ cUnsatisfiable(X0)
| ~ rinvR(X0,X1)
| cd(sk0_1(X1,X0)) ),
inference(cnf_transformation,[status(esa)],[f81]) ).
fof(f89,plain,
! [X] :
( ( ~ cd(X)
| ( ? [Y] :
( rf(X,Y)
& ~ cc(Y) )
& cc(X) ) )
& ( cd(X)
| ! [Y] :
( ~ rf(X,Y)
| cc(Y) )
| ~ cc(X) ) ),
inference(NNF_transformation,[status(esa)],[f19]) ).
fof(f90,plain,
( ! [X] :
( ~ cd(X)
| ( ? [Y] :
( rf(X,Y)
& ~ cc(Y) )
& cc(X) ) )
& ! [X] :
( cd(X)
| ! [Y] :
( ~ rf(X,Y)
| cc(Y) )
| ~ cc(X) ) ),
inference(miniscoping,[status(esa)],[f89]) ).
fof(f91,plain,
( ! [X] :
( ~ cd(X)
| ( rf(X,sk0_3(X))
& ~ cc(sk0_3(X))
& cc(X) ) )
& ! [X] :
( cd(X)
| ! [Y] :
( ~ rf(X,Y)
| cc(Y) )
| ~ cc(X) ) ),
inference(skolemization,[status(esa)],[f90]) ).
fof(f92,plain,
! [X0] :
( ~ cd(X0)
| rf(X0,sk0_3(X0)) ),
inference(cnf_transformation,[status(esa)],[f91]) ).
fof(f93,plain,
! [X0] :
( ~ cd(X0)
| ~ cc(sk0_3(X0)) ),
inference(cnf_transformation,[status(esa)],[f91]) ).
fof(f94,plain,
! [X0] :
( ~ cd(X0)
| cc(X0) ),
inference(cnf_transformation,[status(esa)],[f91]) ).
fof(f96,plain,
! [X,Y,Z] :
( ~ rf(X,Y)
| ~ rf(X,Z)
| Y = Z ),
inference(pre_NNF_transformation,[status(esa)],[f20]) ).
fof(f97,plain,
! [Y,Z] :
( ! [X] :
( ~ rf(X,Y)
| ~ rf(X,Z) )
| Y = Z ),
inference(miniscoping,[status(esa)],[f96]) ).
fof(f98,plain,
! [X0,X1,X2] :
( ~ rf(X0,X1)
| ~ rf(X0,X2)
| X1 = X2 ),
inference(cnf_transformation,[status(esa)],[f97]) ).
fof(f99,plain,
! [X,Y] :
( ( ~ rinvF(X,Y)
| rf(Y,X) )
& ( rinvF(X,Y)
| ~ rf(Y,X) ) ),
inference(NNF_transformation,[status(esa)],[f21]) ).
fof(f100,plain,
( ! [X,Y] :
( ~ rinvF(X,Y)
| rf(Y,X) )
& ! [X,Y] :
( rinvF(X,Y)
| ~ rf(Y,X) ) ),
inference(miniscoping,[status(esa)],[f99]) ).
fof(f101,plain,
! [X0,X1] :
( ~ rinvF(X0,X1)
| rf(X1,X0) ),
inference(cnf_transformation,[status(esa)],[f100]) ).
fof(f103,plain,
! [X,Y] :
( ( ~ rinvR(X,Y)
| rr(Y,X) )
& ( rinvR(X,Y)
| ~ rr(Y,X) ) ),
inference(NNF_transformation,[status(esa)],[f22]) ).
fof(f104,plain,
( ! [X,Y] :
( ~ rinvR(X,Y)
| rr(Y,X) )
& ! [X,Y] :
( rinvR(X,Y)
| ~ rr(Y,X) ) ),
inference(miniscoping,[status(esa)],[f103]) ).
fof(f106,plain,
! [X0,X1] :
( rinvR(X0,X1)
| ~ rr(X1,X0) ),
inference(cnf_transformation,[status(esa)],[f104]) ).
fof(f110,plain,
cUnsatisfiable(i2003_11_14_17_19_35232),
inference(cnf_transformation,[status(esa)],[f24]) ).
fof(f111,plain,
! [X,Y] :
( ~ rf(X,Y)
| rr(X,Y) ),
inference(pre_NNF_transformation,[status(esa)],[f25]) ).
fof(f112,plain,
! [X0,X1] :
( ~ rf(X0,X1)
| rr(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f111]) ).
fof(f113,plain,
rinvF(i2003_11_14_17_19_35232,sk0_0(i2003_11_14_17_19_35232)),
inference(resolution,[status(thm)],[f82,f110]) ).
fof(f114,plain,
cd(sk0_0(i2003_11_14_17_19_35232)),
inference(resolution,[status(thm)],[f83,f110]) ).
fof(f115,plain,
cc(sk0_0(i2003_11_14_17_19_35232)),
inference(resolution,[status(thm)],[f114,f94]) ).
fof(f117,plain,
rf(sk0_0(i2003_11_14_17_19_35232),i2003_11_14_17_19_35232),
inference(resolution,[status(thm)],[f113,f101]) ).
fof(f118,plain,
( spl0_0
<=> cUnsatisfiable(i2003_11_14_17_19_35232) ),
introduced(split_symbol_definition) ).
fof(f120,plain,
( ~ cUnsatisfiable(i2003_11_14_17_19_35232)
| spl0_0 ),
inference(component_clause,[status(thm)],[f118]) ).
fof(f139,plain,
rr(sk0_0(i2003_11_14_17_19_35232),i2003_11_14_17_19_35232),
inference(resolution,[status(thm)],[f117,f112]) ).
fof(f146,plain,
rinvR(i2003_11_14_17_19_35232,sk0_0(i2003_11_14_17_19_35232)),
inference(resolution,[status(thm)],[f139,f106]) ).
fof(f163,plain,
( spl0_7
<=> rinvF(sk0_0(i2003_11_14_17_19_35232),sk0_1(sk0_0(i2003_11_14_17_19_35232),i2003_11_14_17_19_35232)) ),
introduced(split_symbol_definition) ).
fof(f164,plain,
( rinvF(sk0_0(i2003_11_14_17_19_35232),sk0_1(sk0_0(i2003_11_14_17_19_35232),i2003_11_14_17_19_35232))
| ~ spl0_7 ),
inference(component_clause,[status(thm)],[f163]) ).
fof(f166,plain,
( ~ cUnsatisfiable(i2003_11_14_17_19_35232)
| rinvF(sk0_0(i2003_11_14_17_19_35232),sk0_1(sk0_0(i2003_11_14_17_19_35232),i2003_11_14_17_19_35232)) ),
inference(resolution,[status(thm)],[f84,f146]) ).
fof(f167,plain,
( ~ spl0_0
| spl0_7 ),
inference(split_clause,[status(thm)],[f166,f118,f163]) ).
fof(f168,plain,
( spl0_8
<=> cd(sk0_1(sk0_0(i2003_11_14_17_19_35232),i2003_11_14_17_19_35232)) ),
introduced(split_symbol_definition) ).
fof(f169,plain,
( cd(sk0_1(sk0_0(i2003_11_14_17_19_35232),i2003_11_14_17_19_35232))
| ~ spl0_8 ),
inference(component_clause,[status(thm)],[f168]) ).
fof(f171,plain,
( ~ cUnsatisfiable(i2003_11_14_17_19_35232)
| cd(sk0_1(sk0_0(i2003_11_14_17_19_35232),i2003_11_14_17_19_35232)) ),
inference(resolution,[status(thm)],[f85,f146]) ).
fof(f172,plain,
( ~ spl0_0
| spl0_8 ),
inference(split_clause,[status(thm)],[f171,f118,f168]) ).
fof(f187,plain,
( rf(sk0_1(sk0_0(i2003_11_14_17_19_35232),i2003_11_14_17_19_35232),sk0_3(sk0_1(sk0_0(i2003_11_14_17_19_35232),i2003_11_14_17_19_35232)))
| ~ spl0_8 ),
inference(resolution,[status(thm)],[f169,f92]) ).
fof(f190,plain,
( rf(sk0_1(sk0_0(i2003_11_14_17_19_35232),i2003_11_14_17_19_35232),sk0_0(i2003_11_14_17_19_35232))
| ~ spl0_7 ),
inference(resolution,[status(thm)],[f164,f101]) ).
fof(f204,plain,
! [X0] :
( ~ rf(sk0_1(sk0_0(i2003_11_14_17_19_35232),i2003_11_14_17_19_35232),X0)
| sk0_0(i2003_11_14_17_19_35232) = X0
| ~ spl0_7 ),
inference(resolution,[status(thm)],[f190,f98]) ).
fof(f247,plain,
( sk0_0(i2003_11_14_17_19_35232) = sk0_3(sk0_1(sk0_0(i2003_11_14_17_19_35232),i2003_11_14_17_19_35232))
| ~ spl0_8
| ~ spl0_7 ),
inference(resolution,[status(thm)],[f187,f204]) ).
fof(f251,plain,
( spl0_19
<=> cc(sk0_3(sk0_1(sk0_0(i2003_11_14_17_19_35232),i2003_11_14_17_19_35232))) ),
introduced(split_symbol_definition) ).
fof(f252,plain,
( cc(sk0_3(sk0_1(sk0_0(i2003_11_14_17_19_35232),i2003_11_14_17_19_35232)))
| ~ spl0_19 ),
inference(component_clause,[status(thm)],[f251]) ).
fof(f253,plain,
( ~ cc(sk0_3(sk0_1(sk0_0(i2003_11_14_17_19_35232),i2003_11_14_17_19_35232)))
| spl0_19 ),
inference(component_clause,[status(thm)],[f251]) ).
fof(f273,plain,
( ~ cd(sk0_1(sk0_0(i2003_11_14_17_19_35232),i2003_11_14_17_19_35232))
| ~ spl0_19 ),
inference(resolution,[status(thm)],[f252,f93]) ).
fof(f274,plain,
( $false
| ~ spl0_8
| ~ spl0_19 ),
inference(forward_subsumption_resolution,[status(thm)],[f273,f169]) ).
fof(f275,plain,
( ~ spl0_8
| ~ spl0_19 ),
inference(contradiction_clause,[status(thm)],[f274]) ).
fof(f278,plain,
( ~ cc(sk0_0(i2003_11_14_17_19_35232))
| ~ spl0_8
| ~ spl0_7
| spl0_19 ),
inference(backward_demodulation,[status(thm)],[f247,f253]) ).
fof(f279,plain,
( $false
| ~ spl0_8
| ~ spl0_7
| spl0_19 ),
inference(forward_subsumption_resolution,[status(thm)],[f278,f115]) ).
fof(f280,plain,
( ~ spl0_8
| ~ spl0_7
| spl0_19 ),
inference(contradiction_clause,[status(thm)],[f279]) ).
fof(f281,plain,
( $false
| spl0_0 ),
inference(forward_subsumption_resolution,[status(thm)],[f120,f110]) ).
fof(f282,plain,
spl0_0,
inference(contradiction_clause,[status(thm)],[f281]) ).
fof(f283,plain,
$false,
inference(sat_refutation,[status(thm)],[f167,f172,f275,f280,f282]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.11 % Problem : KRS084+1 : TPTP v8.1.2. Released v3.1.0.
% 0.10/0.12 % Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.12/0.33 % Computer : n004.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Mon Apr 29 23:51:48 EDT 2024
% 0.12/0.34 % CPUTime :
% 0.12/0.34 % Drodi V3.6.0
% 0.12/0.35 % Refutation found
% 0.12/0.35 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.12/0.35 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.12/0.35 % Elapsed time: 0.013517 seconds
% 0.12/0.35 % CPU time: 0.033533 seconds
% 0.12/0.35 % Total memory used: 1.120 MB
% 0.12/0.35 % Net memory used: 1.071 MB
%------------------------------------------------------------------------------