TSTP Solution File: SWV153+1 by Drodi---3.6.0
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%------------------------------------------------------------------------------
% File : Drodi---3.6.0
% Problem : SWV153+1 : TPTP v8.1.2. Bugfixed v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% Computer : n006.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 20:46:07 EDT 2024
% Result : Theorem 0.19s 0.36s
% Output : CNFRefutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 7
% Syntax : Number of formulae : 39 ( 9 unt; 0 def)
% Number of atoms : 131 ( 32 equ)
% Maximal formula atoms : 15 ( 3 avg)
% Number of connectives : 135 ( 43 ~; 35 |; 41 &)
% ( 5 <=>; 11 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 4 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 8 ( 6 usr; 5 prp; 0-2 aty)
% Number of functors : 20 ( 20 usr; 12 con; 0-3 aty)
% Number of variables : 29 ( 28 !; 1 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f9,axiom,
! [X,Y] :
( ( leq(X,Y)
& X != Y )
=> gt(Y,X) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f10,axiom,
! [X,Y] :
( leq(X,pred(Y))
<=> gt(Y,X) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f53,conjecture,
( ( pv70 = sum(n0,n4,sqrt(times(minus(a_select3(center,tptp_sum_index,n0),a_select2(x,pv10)),minus(a_select3(center,tptp_sum_index,n0),a_select2(x,pv10)))))
& leq(n0,pv10)
& leq(n0,pv12)
& leq(pv10,n135299)
& leq(pv12,n4)
& ! [A] :
( ( leq(n0,A)
& leq(A,pred(pv12)) )
=> a_select3(q,pv10,A) = divide(sqrt(times(minus(a_select3(center,A,n0),a_select2(x,pv10)),minus(a_select3(center,A,n0),a_select2(x,pv10)))),sum(n0,n4,sqrt(times(minus(a_select3(center,tptp_sum_index,n0),a_select2(x,pv10)),minus(a_select3(center,tptp_sum_index,n0),a_select2(x,pv10)))))) )
& ! [B] :
( ( leq(n0,B)
& leq(B,pred(pv10)) )
=> sum(n0,n4,a_select3(q,B,tptp_sum_index)) = n1 ) )
=> ! [C] :
( ( leq(n0,C)
& leq(C,pv12) )
=> ( pv12 != C
=> a_select3(q,pv10,C) = divide(sqrt(times(minus(a_select3(center,C,n0),a_select2(x,pv10)),minus(a_select3(center,C,n0),a_select2(x,pv10)))),sum(n0,n4,sqrt(times(minus(a_select3(center,tptp_sum_index,n0),a_select2(x,pv10)),minus(a_select3(center,tptp_sum_index,n0),a_select2(x,pv10)))))) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f54,negated_conjecture,
~ ( ( pv70 = sum(n0,n4,sqrt(times(minus(a_select3(center,tptp_sum_index,n0),a_select2(x,pv10)),minus(a_select3(center,tptp_sum_index,n0),a_select2(x,pv10)))))
& leq(n0,pv10)
& leq(n0,pv12)
& leq(pv10,n135299)
& leq(pv12,n4)
& ! [A] :
( ( leq(n0,A)
& leq(A,pred(pv12)) )
=> a_select3(q,pv10,A) = divide(sqrt(times(minus(a_select3(center,A,n0),a_select2(x,pv10)),minus(a_select3(center,A,n0),a_select2(x,pv10)))),sum(n0,n4,sqrt(times(minus(a_select3(center,tptp_sum_index,n0),a_select2(x,pv10)),minus(a_select3(center,tptp_sum_index,n0),a_select2(x,pv10)))))) )
& ! [B] :
( ( leq(n0,B)
& leq(B,pred(pv10)) )
=> sum(n0,n4,a_select3(q,B,tptp_sum_index)) = n1 ) )
=> ! [C] :
( ( leq(n0,C)
& leq(C,pv12) )
=> ( pv12 != C
=> a_select3(q,pv10,C) = divide(sqrt(times(minus(a_select3(center,C,n0),a_select2(x,pv10)),minus(a_select3(center,C,n0),a_select2(x,pv10)))),sum(n0,n4,sqrt(times(minus(a_select3(center,tptp_sum_index,n0),a_select2(x,pv10)),minus(a_select3(center,tptp_sum_index,n0),a_select2(x,pv10)))))) ) ) ),
inference(negated_conjecture,[status(cth)],[f53]) ).
fof(f113,plain,
! [X,Y] :
( ~ leq(X,Y)
| X = Y
| gt(Y,X) ),
inference(pre_NNF_transformation,[status(esa)],[f9]) ).
fof(f114,plain,
! [X0,X1] :
( ~ leq(X0,X1)
| X0 = X1
| gt(X1,X0) ),
inference(cnf_transformation,[status(esa)],[f113]) ).
fof(f115,plain,
! [X,Y] :
( ( ~ leq(X,pred(Y))
| gt(Y,X) )
& ( leq(X,pred(Y))
| ~ gt(Y,X) ) ),
inference(NNF_transformation,[status(esa)],[f10]) ).
fof(f116,plain,
( ! [X,Y] :
( ~ leq(X,pred(Y))
| gt(Y,X) )
& ! [X,Y] :
( leq(X,pred(Y))
| ~ gt(Y,X) ) ),
inference(miniscoping,[status(esa)],[f115]) ).
fof(f118,plain,
! [X0,X1] :
( leq(X0,pred(X1))
| ~ gt(X1,X0) ),
inference(cnf_transformation,[status(esa)],[f116]) ).
fof(f251,plain,
( pv70 = sum(n0,n4,sqrt(times(minus(a_select3(center,tptp_sum_index,n0),a_select2(x,pv10)),minus(a_select3(center,tptp_sum_index,n0),a_select2(x,pv10)))))
& leq(n0,pv10)
& leq(n0,pv12)
& leq(pv10,n135299)
& leq(pv12,n4)
& ! [A] :
( ~ leq(n0,A)
| ~ leq(A,pred(pv12))
| a_select3(q,pv10,A) = divide(sqrt(times(minus(a_select3(center,A,n0),a_select2(x,pv10)),minus(a_select3(center,A,n0),a_select2(x,pv10)))),sum(n0,n4,sqrt(times(minus(a_select3(center,tptp_sum_index,n0),a_select2(x,pv10)),minus(a_select3(center,tptp_sum_index,n0),a_select2(x,pv10)))))) )
& ! [B] :
( ~ leq(n0,B)
| ~ leq(B,pred(pv10))
| sum(n0,n4,a_select3(q,B,tptp_sum_index)) = n1 )
& ? [C] :
( leq(n0,C)
& leq(C,pv12)
& pv12 != C
& a_select3(q,pv10,C) != divide(sqrt(times(minus(a_select3(center,C,n0),a_select2(x,pv10)),minus(a_select3(center,C,n0),a_select2(x,pv10)))),sum(n0,n4,sqrt(times(minus(a_select3(center,tptp_sum_index,n0),a_select2(x,pv10)),minus(a_select3(center,tptp_sum_index,n0),a_select2(x,pv10)))))) ) ),
inference(pre_NNF_transformation,[status(esa)],[f54]) ).
fof(f252,plain,
( pv70 = sum(n0,n4,sqrt(times(minus(a_select3(center,tptp_sum_index,n0),a_select2(x,pv10)),minus(a_select3(center,tptp_sum_index,n0),a_select2(x,pv10)))))
& leq(n0,pv10)
& leq(n0,pv12)
& leq(pv10,n135299)
& leq(pv12,n4)
& ! [A] :
( ~ leq(n0,A)
| ~ leq(A,pred(pv12))
| a_select3(q,pv10,A) = divide(sqrt(times(minus(a_select3(center,A,n0),a_select2(x,pv10)),minus(a_select3(center,A,n0),a_select2(x,pv10)))),sum(n0,n4,sqrt(times(minus(a_select3(center,tptp_sum_index,n0),a_select2(x,pv10)),minus(a_select3(center,tptp_sum_index,n0),a_select2(x,pv10)))))) )
& ! [B] :
( ~ leq(n0,B)
| ~ leq(B,pred(pv10))
| sum(n0,n4,a_select3(q,B,tptp_sum_index)) = n1 )
& leq(n0,sk0_23)
& leq(sk0_23,pv12)
& pv12 != sk0_23
& a_select3(q,pv10,sk0_23) != divide(sqrt(times(minus(a_select3(center,sk0_23,n0),a_select2(x,pv10)),minus(a_select3(center,sk0_23,n0),a_select2(x,pv10)))),sum(n0,n4,sqrt(times(minus(a_select3(center,tptp_sum_index,n0),a_select2(x,pv10)),minus(a_select3(center,tptp_sum_index,n0),a_select2(x,pv10)))))) ),
inference(skolemization,[status(esa)],[f251]) ).
fof(f253,plain,
pv70 = sum(n0,n4,sqrt(times(minus(a_select3(center,tptp_sum_index,n0),a_select2(x,pv10)),minus(a_select3(center,tptp_sum_index,n0),a_select2(x,pv10))))),
inference(cnf_transformation,[status(esa)],[f252]) ).
fof(f258,plain,
! [X0] :
( ~ leq(n0,X0)
| ~ leq(X0,pred(pv12))
| a_select3(q,pv10,X0) = divide(sqrt(times(minus(a_select3(center,X0,n0),a_select2(x,pv10)),minus(a_select3(center,X0,n0),a_select2(x,pv10)))),sum(n0,n4,sqrt(times(minus(a_select3(center,tptp_sum_index,n0),a_select2(x,pv10)),minus(a_select3(center,tptp_sum_index,n0),a_select2(x,pv10)))))) ),
inference(cnf_transformation,[status(esa)],[f252]) ).
fof(f260,plain,
leq(n0,sk0_23),
inference(cnf_transformation,[status(esa)],[f252]) ).
fof(f261,plain,
leq(sk0_23,pv12),
inference(cnf_transformation,[status(esa)],[f252]) ).
fof(f262,plain,
pv12 != sk0_23,
inference(cnf_transformation,[status(esa)],[f252]) ).
fof(f263,plain,
a_select3(q,pv10,sk0_23) != divide(sqrt(times(minus(a_select3(center,sk0_23,n0),a_select2(x,pv10)),minus(a_select3(center,sk0_23,n0),a_select2(x,pv10)))),sum(n0,n4,sqrt(times(minus(a_select3(center,tptp_sum_index,n0),a_select2(x,pv10)),minus(a_select3(center,tptp_sum_index,n0),a_select2(x,pv10)))))),
inference(cnf_transformation,[status(esa)],[f252]) ).
fof(f375,plain,
! [X0] :
( ~ leq(n0,X0)
| ~ leq(X0,pred(pv12))
| a_select3(q,pv10,X0) = divide(sqrt(times(minus(a_select3(center,X0,n0),a_select2(x,pv10)),minus(a_select3(center,X0,n0),a_select2(x,pv10)))),pv70) ),
inference(forward_demodulation,[status(thm)],[f253,f258]) ).
fof(f384,plain,
a_select3(q,pv10,sk0_23) != divide(sqrt(times(minus(a_select3(center,sk0_23,n0),a_select2(x,pv10)),minus(a_select3(center,sk0_23,n0),a_select2(x,pv10)))),pv70),
inference(forward_demodulation,[status(thm)],[f253,f263]) ).
fof(f385,plain,
( spl0_0
<=> leq(n0,sk0_23) ),
introduced(split_symbol_definition) ).
fof(f387,plain,
( ~ leq(n0,sk0_23)
| spl0_0 ),
inference(component_clause,[status(thm)],[f385]) ).
fof(f388,plain,
( spl0_1
<=> leq(sk0_23,pred(pv12)) ),
introduced(split_symbol_definition) ).
fof(f390,plain,
( ~ leq(sk0_23,pred(pv12))
| spl0_1 ),
inference(component_clause,[status(thm)],[f388]) ).
fof(f391,plain,
( ~ leq(n0,sk0_23)
| ~ leq(sk0_23,pred(pv12)) ),
inference(resolution,[status(thm)],[f384,f375]) ).
fof(f392,plain,
( ~ spl0_0
| ~ spl0_1 ),
inference(split_clause,[status(thm)],[f391,f385,f388]) ).
fof(f393,plain,
( $false
| spl0_0 ),
inference(forward_subsumption_resolution,[status(thm)],[f387,f260]) ).
fof(f394,plain,
spl0_0,
inference(contradiction_clause,[status(thm)],[f393]) ).
fof(f395,plain,
( ~ gt(pv12,sk0_23)
| spl0_1 ),
inference(resolution,[status(thm)],[f118,f390]) ).
fof(f401,plain,
( spl0_3
<=> sk0_23 = pv12 ),
introduced(split_symbol_definition) ).
fof(f402,plain,
( sk0_23 = pv12
| ~ spl0_3 ),
inference(component_clause,[status(thm)],[f401]) ).
fof(f1018,plain,
( spl0_68
<=> gt(pv12,sk0_23) ),
introduced(split_symbol_definition) ).
fof(f1019,plain,
( gt(pv12,sk0_23)
| ~ spl0_68 ),
inference(component_clause,[status(thm)],[f1018]) ).
fof(f1021,plain,
( sk0_23 = pv12
| gt(pv12,sk0_23) ),
inference(resolution,[status(thm)],[f114,f261]) ).
fof(f1022,plain,
( spl0_3
| spl0_68 ),
inference(split_clause,[status(thm)],[f1021,f401,f1018]) ).
fof(f1083,plain,
( $false
| ~ spl0_3 ),
inference(forward_subsumption_resolution,[status(thm)],[f402,f262]) ).
fof(f1084,plain,
~ spl0_3,
inference(contradiction_clause,[status(thm)],[f1083]) ).
fof(f1085,plain,
( $false
| spl0_1
| ~ spl0_68 ),
inference(forward_subsumption_resolution,[status(thm)],[f1019,f395]) ).
fof(f1086,plain,
( spl0_1
| ~ spl0_68 ),
inference(contradiction_clause,[status(thm)],[f1085]) ).
fof(f1087,plain,
$false,
inference(sat_refutation,[status(thm)],[f392,f394,f1022,f1084,f1086]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SWV153+1 : TPTP v8.1.2. Bugfixed v3.3.0.
% 0.03/0.13 % Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.13/0.34 % Computer : n006.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 Apr 30 00:38:20 EDT 2024
% 0.13/0.34 % CPUTime :
% 0.19/0.35 % Drodi V3.6.0
% 0.19/0.36 % Refutation found
% 0.19/0.36 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.19/0.36 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.19/0.38 % Elapsed time: 0.032158 seconds
% 0.19/0.38 % CPU time: 0.091772 seconds
% 0.19/0.38 % Total memory used: 17.251 MB
% 0.19/0.38 % Net memory used: 17.147 MB
%------------------------------------------------------------------------------