TSTP Solution File: COM018+4 by Drodi---3.5.1
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Drodi---3.5.1
% Problem : COM018+4 : TPTP v8.1.2. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% Computer : n011.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 12:03:56 EDT 2023
% Result : Theorem 0.19s 0.40s
% Output : CNFRefutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 8
% Syntax : Number of formulae : 35 ( 9 unt; 0 def)
% Number of atoms : 249 ( 17 equ)
% Maximal formula atoms : 30 ( 7 avg)
% Number of connectives : 299 ( 85 ~; 97 |; 109 &)
% ( 3 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 21 ( 6 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 14 ( 12 usr; 4 prp; 0-3 aty)
% Number of functors : 11 ( 11 usr; 6 con; 0-2 aty)
% Number of variables : 62 (; 40 !; 22 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f14,axiom,
! [W0] :
( ( aRewritingSystem0(W0)
& isTerminating0(W0) )
=> ! [W1] :
( aElement0(W1)
=> ? [W2] : aNormalFormOfIn0(W2,W1,W0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f15,hypothesis,
aRewritingSystem0(xR),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f16,hypothesis,
( ! [W0,W1,W2] :
( ( aElement0(W0)
& aElement0(W1)
& aElement0(W2)
& aReductOfIn0(W1,W0,xR)
& aReductOfIn0(W2,W0,xR) )
=> ? [W3] :
( aElement0(W3)
& ( W1 = W3
| ( ( aReductOfIn0(W3,W1,xR)
| ? [W4] :
( aElement0(W4)
& aReductOfIn0(W4,W1,xR)
& sdtmndtplgtdt0(W4,xR,W3) ) )
& sdtmndtplgtdt0(W1,xR,W3) ) )
& sdtmndtasgtdt0(W1,xR,W3)
& ( W2 = W3
| ( ( aReductOfIn0(W3,W2,xR)
| ? [W4] :
( aElement0(W4)
& aReductOfIn0(W4,W2,xR)
& sdtmndtplgtdt0(W4,xR,W3) ) )
& sdtmndtplgtdt0(W2,xR,W3) ) )
& sdtmndtasgtdt0(W2,xR,W3) ) )
& isLocallyConfluent0(xR)
& ! [W0,W1] :
( ( aElement0(W0)
& aElement0(W1) )
=> ( ( aReductOfIn0(W1,W0,xR)
| ? [W2] :
( aElement0(W2)
& aReductOfIn0(W2,W0,xR)
& sdtmndtplgtdt0(W2,xR,W1) )
| sdtmndtplgtdt0(W0,xR,W1) )
=> iLess0(W1,W0) ) )
& isTerminating0(xR) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f22,hypothesis,
( aElement0(xw)
& ( xu = xw
| ( ( aReductOfIn0(xw,xu,xR)
| ? [W0] :
( aElement0(W0)
& aReductOfIn0(W0,xu,xR)
& sdtmndtplgtdt0(W0,xR,xw) ) )
& sdtmndtplgtdt0(xu,xR,xw) ) )
& sdtmndtasgtdt0(xu,xR,xw)
& ( xv = xw
| ( ( aReductOfIn0(xw,xv,xR)
| ? [W0] :
( aElement0(W0)
& aReductOfIn0(W0,xv,xR)
& sdtmndtplgtdt0(W0,xR,xw) ) )
& sdtmndtplgtdt0(xv,xR,xw) ) )
& sdtmndtasgtdt0(xv,xR,xw) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f23,conjecture,
? [W0] :
( ( aElement0(W0)
& ( xw = W0
| aReductOfIn0(W0,xw,xR)
| ? [W1] :
( aElement0(W1)
& aReductOfIn0(W1,xw,xR)
& sdtmndtplgtdt0(W1,xR,W0) )
| sdtmndtplgtdt0(xw,xR,W0)
| sdtmndtasgtdt0(xw,xR,W0) )
& ~ ? [W1] : aReductOfIn0(W1,W0,xR) )
| aNormalFormOfIn0(W0,xw,xR) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f24,negated_conjecture,
~ ? [W0] :
( ( aElement0(W0)
& ( xw = W0
| aReductOfIn0(W0,xw,xR)
| ? [W1] :
( aElement0(W1)
& aReductOfIn0(W1,xw,xR)
& sdtmndtplgtdt0(W1,xR,W0) )
| sdtmndtplgtdt0(xw,xR,W0)
| sdtmndtasgtdt0(xw,xR,W0) )
& ~ ? [W1] : aReductOfIn0(W1,W0,xR) )
| aNormalFormOfIn0(W0,xw,xR) ),
inference(negated_conjecture,[status(cth)],[f23]) ).
fof(f96,plain,
! [W0] :
( ~ aRewritingSystem0(W0)
| ~ isTerminating0(W0)
| ! [W1] :
( ~ aElement0(W1)
| ? [W2] : aNormalFormOfIn0(W2,W1,W0) ) ),
inference(pre_NNF_transformation,[status(esa)],[f14]) ).
fof(f97,plain,
! [W0] :
( ~ aRewritingSystem0(W0)
| ~ isTerminating0(W0)
| ! [W1] :
( ~ aElement0(W1)
| aNormalFormOfIn0(sk0_12(W1,W0),W1,W0) ) ),
inference(skolemization,[status(esa)],[f96]) ).
fof(f98,plain,
! [X0,X1] :
( ~ aRewritingSystem0(X0)
| ~ isTerminating0(X0)
| ~ aElement0(X1)
| aNormalFormOfIn0(sk0_12(X1,X0),X1,X0) ),
inference(cnf_transformation,[status(esa)],[f97]) ).
fof(f99,plain,
aRewritingSystem0(xR),
inference(cnf_transformation,[status(esa)],[f15]) ).
fof(f100,plain,
( ! [W0,W1,W2] :
( ~ aElement0(W0)
| ~ aElement0(W1)
| ~ aElement0(W2)
| ~ aReductOfIn0(W1,W0,xR)
| ~ aReductOfIn0(W2,W0,xR)
| ? [W3] :
( aElement0(W3)
& ( W1 = W3
| ( ( aReductOfIn0(W3,W1,xR)
| ? [W4] :
( aElement0(W4)
& aReductOfIn0(W4,W1,xR)
& sdtmndtplgtdt0(W4,xR,W3) ) )
& sdtmndtplgtdt0(W1,xR,W3) ) )
& sdtmndtasgtdt0(W1,xR,W3)
& ( W2 = W3
| ( ( aReductOfIn0(W3,W2,xR)
| ? [W4] :
( aElement0(W4)
& aReductOfIn0(W4,W2,xR)
& sdtmndtplgtdt0(W4,xR,W3) ) )
& sdtmndtplgtdt0(W2,xR,W3) ) )
& sdtmndtasgtdt0(W2,xR,W3) ) )
& isLocallyConfluent0(xR)
& ! [W0,W1] :
( ~ aElement0(W0)
| ~ aElement0(W1)
| ( ~ aReductOfIn0(W1,W0,xR)
& ! [W2] :
( ~ aElement0(W2)
| ~ aReductOfIn0(W2,W0,xR)
| ~ sdtmndtplgtdt0(W2,xR,W1) )
& ~ sdtmndtplgtdt0(W0,xR,W1) )
| iLess0(W1,W0) )
& isTerminating0(xR) ),
inference(pre_NNF_transformation,[status(esa)],[f16]) ).
fof(f101,plain,
( ! [W1,W2] :
( ! [W0] :
( ~ aElement0(W0)
| ~ aElement0(W1)
| ~ aElement0(W2)
| ~ aReductOfIn0(W1,W0,xR)
| ~ aReductOfIn0(W2,W0,xR) )
| ? [W3] :
( aElement0(W3)
& ( W1 = W3
| ( ( aReductOfIn0(W3,W1,xR)
| ? [W4] :
( aElement0(W4)
& aReductOfIn0(W4,W1,xR)
& sdtmndtplgtdt0(W4,xR,W3) ) )
& sdtmndtplgtdt0(W1,xR,W3) ) )
& sdtmndtasgtdt0(W1,xR,W3)
& ( W2 = W3
| ( ( aReductOfIn0(W3,W2,xR)
| ? [W4] :
( aElement0(W4)
& aReductOfIn0(W4,W2,xR)
& sdtmndtplgtdt0(W4,xR,W3) ) )
& sdtmndtplgtdt0(W2,xR,W3) ) )
& sdtmndtasgtdt0(W2,xR,W3) ) )
& isLocallyConfluent0(xR)
& ! [W0,W1] :
( ~ aElement0(W0)
| ~ aElement0(W1)
| ( ~ aReductOfIn0(W1,W0,xR)
& ! [W2] :
( ~ aElement0(W2)
| ~ aReductOfIn0(W2,W0,xR)
| ~ sdtmndtplgtdt0(W2,xR,W1) )
& ~ sdtmndtplgtdt0(W0,xR,W1) )
| iLess0(W1,W0) )
& isTerminating0(xR) ),
inference(miniscoping,[status(esa)],[f100]) ).
fof(f102,plain,
( ! [W1,W2] :
( ! [W0] :
( ~ aElement0(W0)
| ~ aElement0(W1)
| ~ aElement0(W2)
| ~ aReductOfIn0(W1,W0,xR)
| ~ aReductOfIn0(W2,W0,xR) )
| ( aElement0(sk0_13(W2,W1))
& ( W1 = sk0_13(W2,W1)
| ( ( aReductOfIn0(sk0_13(W2,W1),W1,xR)
| ( aElement0(sk0_14(W2,W1))
& aReductOfIn0(sk0_14(W2,W1),W1,xR)
& sdtmndtplgtdt0(sk0_14(W2,W1),xR,sk0_13(W2,W1)) ) )
& sdtmndtplgtdt0(W1,xR,sk0_13(W2,W1)) ) )
& sdtmndtasgtdt0(W1,xR,sk0_13(W2,W1))
& ( W2 = sk0_13(W2,W1)
| ( ( aReductOfIn0(sk0_13(W2,W1),W2,xR)
| ( aElement0(sk0_15(W2,W1))
& aReductOfIn0(sk0_15(W2,W1),W2,xR)
& sdtmndtplgtdt0(sk0_15(W2,W1),xR,sk0_13(W2,W1)) ) )
& sdtmndtplgtdt0(W2,xR,sk0_13(W2,W1)) ) )
& sdtmndtasgtdt0(W2,xR,sk0_13(W2,W1)) ) )
& isLocallyConfluent0(xR)
& ! [W0,W1] :
( ~ aElement0(W0)
| ~ aElement0(W1)
| ( ~ aReductOfIn0(W1,W0,xR)
& ! [W2] :
( ~ aElement0(W2)
| ~ aReductOfIn0(W2,W0,xR)
| ~ sdtmndtplgtdt0(W2,xR,W1) )
& ~ sdtmndtplgtdt0(W0,xR,W1) )
| iLess0(W1,W0) )
& isTerminating0(xR) ),
inference(skolemization,[status(esa)],[f101]) ).
fof(f118,plain,
isTerminating0(xR),
inference(cnf_transformation,[status(esa)],[f102]) ).
fof(f206,plain,
( aElement0(xw)
& ( xu = xw
| ( ( aReductOfIn0(xw,xu,xR)
| ( aElement0(sk0_23)
& aReductOfIn0(sk0_23,xu,xR)
& sdtmndtplgtdt0(sk0_23,xR,xw) ) )
& sdtmndtplgtdt0(xu,xR,xw) ) )
& sdtmndtasgtdt0(xu,xR,xw)
& ( xv = xw
| ( ( aReductOfIn0(xw,xv,xR)
| ( aElement0(sk0_24)
& aReductOfIn0(sk0_24,xv,xR)
& sdtmndtplgtdt0(sk0_24,xR,xw) ) )
& sdtmndtplgtdt0(xv,xR,xw) ) )
& sdtmndtasgtdt0(xv,xR,xw) ),
inference(skolemization,[status(esa)],[f22]) ).
fof(f207,plain,
aElement0(xw),
inference(cnf_transformation,[status(esa)],[f206]) ).
fof(f218,plain,
! [W0] :
( ( ~ aElement0(W0)
| ( xw != W0
& ~ aReductOfIn0(W0,xw,xR)
& ! [W1] :
( ~ aElement0(W1)
| ~ aReductOfIn0(W1,xw,xR)
| ~ sdtmndtplgtdt0(W1,xR,W0) )
& ~ sdtmndtplgtdt0(xw,xR,W0)
& ~ sdtmndtasgtdt0(xw,xR,W0) )
| ? [W1] : aReductOfIn0(W1,W0,xR) )
& ~ aNormalFormOfIn0(W0,xw,xR) ),
inference(pre_NNF_transformation,[status(esa)],[f24]) ).
fof(f219,plain,
( ! [W0] :
( ~ aElement0(W0)
| ( xw != W0
& ~ aReductOfIn0(W0,xw,xR)
& ! [W1] :
( ~ aElement0(W1)
| ~ aReductOfIn0(W1,xw,xR)
| ~ sdtmndtplgtdt0(W1,xR,W0) )
& ~ sdtmndtplgtdt0(xw,xR,W0)
& ~ sdtmndtasgtdt0(xw,xR,W0) )
| ? [W1] : aReductOfIn0(W1,W0,xR) )
& ! [W0] : ~ aNormalFormOfIn0(W0,xw,xR) ),
inference(miniscoping,[status(esa)],[f218]) ).
fof(f220,plain,
( ! [W0] :
( ~ aElement0(W0)
| ( xw != W0
& ~ aReductOfIn0(W0,xw,xR)
& ! [W1] :
( ~ aElement0(W1)
| ~ aReductOfIn0(W1,xw,xR)
| ~ sdtmndtplgtdt0(W1,xR,W0) )
& ~ sdtmndtplgtdt0(xw,xR,W0)
& ~ sdtmndtasgtdt0(xw,xR,W0) )
| aReductOfIn0(sk0_25(W0),W0,xR) )
& ! [W0] : ~ aNormalFormOfIn0(W0,xw,xR) ),
inference(skolemization,[status(esa)],[f219]) ).
fof(f226,plain,
! [X0] : ~ aNormalFormOfIn0(X0,xw,xR),
inference(cnf_transformation,[status(esa)],[f220]) ).
fof(f386,plain,
( spl0_33
<=> aRewritingSystem0(xR) ),
introduced(split_symbol_definition) ).
fof(f388,plain,
( ~ aRewritingSystem0(xR)
| spl0_33 ),
inference(component_clause,[status(thm)],[f386]) ).
fof(f399,plain,
( spl0_36
<=> aElement0(xw) ),
introduced(split_symbol_definition) ).
fof(f401,plain,
( ~ aElement0(xw)
| spl0_36 ),
inference(component_clause,[status(thm)],[f399]) ).
fof(f427,plain,
( $false
| spl0_33 ),
inference(forward_subsumption_resolution,[status(thm)],[f388,f99]) ).
fof(f428,plain,
spl0_33,
inference(contradiction_clause,[status(thm)],[f427]) ).
fof(f429,plain,
( $false
| spl0_36 ),
inference(forward_subsumption_resolution,[status(thm)],[f401,f207]) ).
fof(f430,plain,
spl0_36,
inference(contradiction_clause,[status(thm)],[f429]) ).
fof(f1114,plain,
( spl0_128
<=> isTerminating0(xR) ),
introduced(split_symbol_definition) ).
fof(f1116,plain,
( ~ isTerminating0(xR)
| spl0_128 ),
inference(component_clause,[status(thm)],[f1114]) ).
fof(f1772,plain,
( ~ aRewritingSystem0(xR)
| ~ isTerminating0(xR)
| ~ aElement0(xw) ),
inference(resolution,[status(thm)],[f98,f226]) ).
fof(f1773,plain,
( ~ spl0_33
| ~ spl0_128
| ~ spl0_36 ),
inference(split_clause,[status(thm)],[f1772,f386,f1114,f399]) ).
fof(f1780,plain,
( $false
| spl0_128 ),
inference(forward_subsumption_resolution,[status(thm)],[f1116,f118]) ).
fof(f1781,plain,
spl0_128,
inference(contradiction_clause,[status(thm)],[f1780]) ).
fof(f1782,plain,
$false,
inference(sat_refutation,[status(thm)],[f428,f430,f1773,f1781]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : COM018+4 : TPTP v8.1.2. Released v4.0.0.
% 0.07/0.13 % Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.13/0.34 % Computer : n011.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Tue May 30 11:48:42 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.13/0.35 % Drodi V3.5.1
% 0.19/0.40 % Refutation found
% 0.19/0.40 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.19/0.40 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.19/0.42 % Elapsed time: 0.071412 seconds
% 0.19/0.42 % CPU time: 0.404317 seconds
% 0.19/0.42 % Memory used: 29.154 MB
%------------------------------------------------------------------------------