TSTP Solution File: SWV381+1 by Drodi---3.5.1
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%------------------------------------------------------------------------------
% File : Drodi---3.5.1
% Problem : SWV381+1 : TPTP v8.1.2. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% Computer : n018.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 12:41:32 EDT 2023
% Result : Theorem 1.64s 0.72s
% Output : CNFRefutation 2.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 8
% Syntax : Number of formulae : 42 ( 8 unt; 0 def)
% Number of atoms : 107 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 106 ( 41 ~; 39 |; 16 &)
% ( 6 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 9 ( 8 usr; 3 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 3 con; 0-3 aty)
% Number of variables : 84 (; 78 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f2,axiom,
! [U,V] :
( less_than(U,V)
| less_than(V,U) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f4,axiom,
! [U,V] :
( strictly_less_than(U,V)
<=> ( less_than(U,V)
& ~ less_than(V,U) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f10,axiom,
! [U,V] :
( issmallestelement_pq(U,V)
<=> ! [W] :
( contains_pq(U,W)
=> less_than(V,W) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f63,lemma,
! [U,V,W,X] :
( contains_cpq(triple(U,V,W),X)
<=> contains_pq(i(triple(U,V,W)),X) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f64,lemma,
! [U,V,W] :
( ? [X] :
( contains_cpq(triple(U,V,W),X)
& strictly_less_than(X,findmin_cpq_res(triple(U,V,W))) )
=> ~ phi(findmin_cpq_eff(triple(U,V,W))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f65,conjecture,
! [U,V,W] :
( phi(findmin_cpq_eff(triple(U,V,W)))
=> issmallestelement_pq(i(triple(U,V,W)),findmin_cpq_res(triple(U,V,W))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f66,negated_conjecture,
~ ! [U,V,W] :
( phi(findmin_cpq_eff(triple(U,V,W)))
=> issmallestelement_pq(i(triple(U,V,W)),findmin_cpq_res(triple(U,V,W))) ),
inference(negated_conjecture,[status(cth)],[f65]) ).
fof(f70,plain,
! [X0,X1] :
( less_than(X0,X1)
| less_than(X1,X0) ),
inference(cnf_transformation,[status(esa)],[f2]) ).
fof(f72,plain,
! [U,V] :
( ( ~ strictly_less_than(U,V)
| ( less_than(U,V)
& ~ less_than(V,U) ) )
& ( strictly_less_than(U,V)
| ~ less_than(U,V)
| less_than(V,U) ) ),
inference(NNF_transformation,[status(esa)],[f4]) ).
fof(f73,plain,
( ! [U,V] :
( ~ strictly_less_than(U,V)
| ( less_than(U,V)
& ~ less_than(V,U) ) )
& ! [U,V] :
( strictly_less_than(U,V)
| ~ less_than(U,V)
| less_than(V,U) ) ),
inference(miniscoping,[status(esa)],[f72]) ).
fof(f76,plain,
! [X0,X1] :
( strictly_less_than(X0,X1)
| ~ less_than(X0,X1)
| less_than(X1,X0) ),
inference(cnf_transformation,[status(esa)],[f73]) ).
fof(f86,plain,
! [U,V] :
( issmallestelement_pq(U,V)
<=> ! [W] :
( ~ contains_pq(U,W)
| less_than(V,W) ) ),
inference(pre_NNF_transformation,[status(esa)],[f10]) ).
fof(f87,plain,
! [U,V] :
( ( ~ issmallestelement_pq(U,V)
| ! [W] :
( ~ contains_pq(U,W)
| less_than(V,W) ) )
& ( issmallestelement_pq(U,V)
| ? [W] :
( contains_pq(U,W)
& ~ less_than(V,W) ) ) ),
inference(NNF_transformation,[status(esa)],[f86]) ).
fof(f88,plain,
( ! [U,V] :
( ~ issmallestelement_pq(U,V)
| ! [W] :
( ~ contains_pq(U,W)
| less_than(V,W) ) )
& ! [U,V] :
( issmallestelement_pq(U,V)
| ? [W] :
( contains_pq(U,W)
& ~ less_than(V,W) ) ) ),
inference(miniscoping,[status(esa)],[f87]) ).
fof(f89,plain,
( ! [U,V] :
( ~ issmallestelement_pq(U,V)
| ! [W] :
( ~ contains_pq(U,W)
| less_than(V,W) ) )
& ! [U,V] :
( issmallestelement_pq(U,V)
| ( contains_pq(U,sk0_0(V,U))
& ~ less_than(V,sk0_0(V,U)) ) ) ),
inference(skolemization,[status(esa)],[f88]) ).
fof(f91,plain,
! [X0,X1] :
( issmallestelement_pq(X0,X1)
| contains_pq(X0,sk0_0(X1,X0)) ),
inference(cnf_transformation,[status(esa)],[f89]) ).
fof(f92,plain,
! [X0,X1] :
( issmallestelement_pq(X0,X1)
| ~ less_than(X1,sk0_0(X1,X0)) ),
inference(cnf_transformation,[status(esa)],[f89]) ).
fof(f231,plain,
! [U,V,W,X] :
( ( ~ contains_cpq(triple(U,V,W),X)
| contains_pq(i(triple(U,V,W)),X) )
& ( contains_cpq(triple(U,V,W),X)
| ~ contains_pq(i(triple(U,V,W)),X) ) ),
inference(NNF_transformation,[status(esa)],[f63]) ).
fof(f232,plain,
( ! [U,V,W,X] :
( ~ contains_cpq(triple(U,V,W),X)
| contains_pq(i(triple(U,V,W)),X) )
& ! [U,V,W,X] :
( contains_cpq(triple(U,V,W),X)
| ~ contains_pq(i(triple(U,V,W)),X) ) ),
inference(miniscoping,[status(esa)],[f231]) ).
fof(f234,plain,
! [X0,X1,X2,X3] :
( contains_cpq(triple(X0,X1,X2),X3)
| ~ contains_pq(i(triple(X0,X1,X2)),X3) ),
inference(cnf_transformation,[status(esa)],[f232]) ).
fof(f235,plain,
! [U,V,W] :
( ! [X] :
( ~ contains_cpq(triple(U,V,W),X)
| ~ strictly_less_than(X,findmin_cpq_res(triple(U,V,W))) )
| ~ phi(findmin_cpq_eff(triple(U,V,W))) ),
inference(pre_NNF_transformation,[status(esa)],[f64]) ).
fof(f236,plain,
! [X0,X1,X2,X3] :
( ~ contains_cpq(triple(X0,X1,X2),X3)
| ~ strictly_less_than(X3,findmin_cpq_res(triple(X0,X1,X2)))
| ~ phi(findmin_cpq_eff(triple(X0,X1,X2))) ),
inference(cnf_transformation,[status(esa)],[f235]) ).
fof(f237,plain,
? [U,V,W] :
( phi(findmin_cpq_eff(triple(U,V,W)))
& ~ issmallestelement_pq(i(triple(U,V,W)),findmin_cpq_res(triple(U,V,W))) ),
inference(pre_NNF_transformation,[status(esa)],[f66]) ).
fof(f238,plain,
( phi(findmin_cpq_eff(triple(sk0_4,sk0_5,sk0_6)))
& ~ issmallestelement_pq(i(triple(sk0_4,sk0_5,sk0_6)),findmin_cpq_res(triple(sk0_4,sk0_5,sk0_6))) ),
inference(skolemization,[status(esa)],[f237]) ).
fof(f239,plain,
phi(findmin_cpq_eff(triple(sk0_4,sk0_5,sk0_6))),
inference(cnf_transformation,[status(esa)],[f238]) ).
fof(f240,plain,
~ issmallestelement_pq(i(triple(sk0_4,sk0_5,sk0_6)),findmin_cpq_res(triple(sk0_4,sk0_5,sk0_6))),
inference(cnf_transformation,[status(esa)],[f238]) ).
fof(f241,plain,
! [X0,X1] :
( strictly_less_than(X0,X1)
| less_than(X1,X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f76,f70]) ).
fof(f272,plain,
! [X0,X1] :
( issmallestelement_pq(X0,X1)
| strictly_less_than(sk0_0(X1,X0),X1) ),
inference(resolution,[status(thm)],[f92,f241]) ).
fof(f715,plain,
contains_pq(i(triple(sk0_4,sk0_5,sk0_6)),sk0_0(findmin_cpq_res(triple(sk0_4,sk0_5,sk0_6)),i(triple(sk0_4,sk0_5,sk0_6)))),
inference(resolution,[status(thm)],[f240,f91]) ).
fof(f717,plain,
strictly_less_than(sk0_0(findmin_cpq_res(triple(sk0_4,sk0_5,sk0_6)),i(triple(sk0_4,sk0_5,sk0_6))),findmin_cpq_res(triple(sk0_4,sk0_5,sk0_6))),
inference(resolution,[status(thm)],[f240,f272]) ).
fof(f789,plain,
contains_cpq(triple(sk0_4,sk0_5,sk0_6),sk0_0(findmin_cpq_res(triple(sk0_4,sk0_5,sk0_6)),i(triple(sk0_4,sk0_5,sk0_6)))),
inference(resolution,[status(thm)],[f715,f234]) ).
fof(f1142,plain,
( spl0_44
<=> strictly_less_than(sk0_0(findmin_cpq_res(triple(sk0_4,sk0_5,sk0_6)),i(triple(sk0_4,sk0_5,sk0_6))),findmin_cpq_res(triple(sk0_4,sk0_5,sk0_6))) ),
introduced(split_symbol_definition) ).
fof(f1144,plain,
( ~ strictly_less_than(sk0_0(findmin_cpq_res(triple(sk0_4,sk0_5,sk0_6)),i(triple(sk0_4,sk0_5,sk0_6))),findmin_cpq_res(triple(sk0_4,sk0_5,sk0_6)))
| spl0_44 ),
inference(component_clause,[status(thm)],[f1142]) ).
fof(f1145,plain,
( spl0_45
<=> phi(findmin_cpq_eff(triple(sk0_4,sk0_5,sk0_6))) ),
introduced(split_symbol_definition) ).
fof(f1147,plain,
( ~ phi(findmin_cpq_eff(triple(sk0_4,sk0_5,sk0_6)))
| spl0_45 ),
inference(component_clause,[status(thm)],[f1145]) ).
fof(f1148,plain,
( ~ strictly_less_than(sk0_0(findmin_cpq_res(triple(sk0_4,sk0_5,sk0_6)),i(triple(sk0_4,sk0_5,sk0_6))),findmin_cpq_res(triple(sk0_4,sk0_5,sk0_6)))
| ~ phi(findmin_cpq_eff(triple(sk0_4,sk0_5,sk0_6))) ),
inference(resolution,[status(thm)],[f789,f236]) ).
fof(f1149,plain,
( ~ spl0_44
| ~ spl0_45 ),
inference(split_clause,[status(thm)],[f1148,f1142,f1145]) ).
fof(f1157,plain,
( $false
| spl0_44 ),
inference(forward_subsumption_resolution,[status(thm)],[f1144,f717]) ).
fof(f1158,plain,
spl0_44,
inference(contradiction_clause,[status(thm)],[f1157]) ).
fof(f1159,plain,
( $false
| spl0_45 ),
inference(forward_subsumption_resolution,[status(thm)],[f1147,f239]) ).
fof(f1160,plain,
spl0_45,
inference(contradiction_clause,[status(thm)],[f1159]) ).
fof(f1161,plain,
$false,
inference(sat_refutation,[status(thm)],[f1149,f1158,f1160]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.10 % Problem : SWV381+1 : TPTP v8.1.2. Released v3.3.0.
% 0.00/0.11 % Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.10/0.31 % Computer : n018.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
% 0.10/0.31 % CPULimit : 300
% 0.10/0.31 % WCLimit : 300
% 0.10/0.31 % DateTime : Tue May 30 11:42:25 EDT 2023
% 0.16/0.31 % CPUTime :
% 0.16/0.32 % Drodi V3.5.1
% 1.64/0.72 % Refutation found
% 1.64/0.72 % SZS status Theorem for theBenchmark: Theorem is valid
% 1.64/0.72 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 2.09/0.76 % Elapsed time: 0.432784 seconds
% 2.09/0.76 % CPU time: 2.142943 seconds
% 2.09/0.76 % Memory used: 92.858 MB
%------------------------------------------------------------------------------