TSTP Solution File: SWV381+1 by Drodi---3.6.0
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%------------------------------------------------------------------------------
% File : Drodi---3.6.0
% 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 : n032.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 20:46:53 EDT 2024
% Result : Theorem 0.18s 0.54s
% Output : CNFRefutation 0.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 8
% Syntax : Number of formulae : 42 ( 6 unt; 0 def)
% Number of atoms : 117 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 127 ( 52 ~; 49 |; 17 &)
% ( 4 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 7 ( 6 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 3 con; 0-3 aty)
% Number of variables : 108 ( 102 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [U,V,W] :
( ( less_than(U,V)
& less_than(V,W) )
=> less_than(U,W) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f2,axiom,
! [U,V] :
( less_than(U,V)
| less_than(V,U) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f3,axiom,
! [U] : less_than(U,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(f67,plain,
! [U,V,W] :
( ~ less_than(U,V)
| ~ less_than(V,W)
| less_than(U,W) ),
inference(pre_NNF_transformation,[status(esa)],[f1]) ).
fof(f68,plain,
! [U,W] :
( ! [V] :
( ~ less_than(U,V)
| ~ less_than(V,W) )
| less_than(U,W) ),
inference(miniscoping,[status(esa)],[f67]) ).
fof(f69,plain,
! [X0,X1,X2] :
( ~ less_than(X0,X1)
| ~ less_than(X1,X2)
| less_than(X0,X2) ),
inference(cnf_transformation,[status(esa)],[f68]) ).
fof(f70,plain,
! [X0,X1] :
( less_than(X0,X1)
| less_than(X1,X0) ),
inference(cnf_transformation,[status(esa)],[f2]) ).
fof(f71,plain,
! [X0] : less_than(X0,X0),
inference(cnf_transformation,[status(esa)],[f3]) ).
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(f274,plain,
! [X0,X1] :
( strictly_less_than(X0,X1)
| less_than(X1,X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f76,f70]) ).
fof(f295,plain,
! [X0,X1,X2] :
( issmallestelement_pq(X0,X1)
| ~ less_than(X1,X2)
| ~ less_than(X2,sk0_0(X1,X0)) ),
inference(resolution,[status(thm)],[f92,f69]) ).
fof(f450,plain,
! [X0,X1,X2] :
( issmallestelement_pq(X0,X1)
| ~ less_than(X1,X2)
| strictly_less_than(sk0_0(X1,X0),X2) ),
inference(resolution,[status(thm)],[f295,f274]) ).
fof(f1485,plain,
! [X0] :
( ~ contains_cpq(triple(sk0_4,sk0_5,sk0_6),X0)
| ~ strictly_less_than(X0,findmin_cpq_res(triple(sk0_4,sk0_5,sk0_6))) ),
inference(resolution,[status(thm)],[f236,f239]) ).
fof(f1508,plain,
! [X0] :
( ~ strictly_less_than(X0,findmin_cpq_res(triple(sk0_4,sk0_5,sk0_6)))
| ~ contains_pq(i(triple(sk0_4,sk0_5,sk0_6)),X0) ),
inference(resolution,[status(thm)],[f1485,f234]) ).
fof(f1529,plain,
! [X0,X1] :
( ~ contains_pq(i(triple(sk0_4,sk0_5,sk0_6)),sk0_0(X0,X1))
| issmallestelement_pq(X1,X0)
| ~ less_than(X0,findmin_cpq_res(triple(sk0_4,sk0_5,sk0_6))) ),
inference(resolution,[status(thm)],[f1508,f450]) ).
fof(f1598,plain,
! [X0] :
( issmallestelement_pq(i(triple(sk0_4,sk0_5,sk0_6)),X0)
| ~ less_than(X0,findmin_cpq_res(triple(sk0_4,sk0_5,sk0_6)))
| issmallestelement_pq(i(triple(sk0_4,sk0_5,sk0_6)),X0) ),
inference(resolution,[status(thm)],[f1529,f91]) ).
fof(f1599,plain,
! [X0] :
( issmallestelement_pq(i(triple(sk0_4,sk0_5,sk0_6)),X0)
| ~ less_than(X0,findmin_cpq_res(triple(sk0_4,sk0_5,sk0_6))) ),
inference(duplicate_literals_removal,[status(esa)],[f1598]) ).
fof(f1608,plain,
issmallestelement_pq(i(triple(sk0_4,sk0_5,sk0_6)),findmin_cpq_res(triple(sk0_4,sk0_5,sk0_6))),
inference(resolution,[status(thm)],[f1599,f71]) ).
fof(f1609,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f1608,f240]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.13 % Problem : SWV381+1 : TPTP v8.1.2. Released v3.3.0.
% 0.10/0.14 % Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.11/0.35 % Computer : n032.cluster.edu
% 0.11/0.35 % Model : x86_64 x86_64
% 0.11/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.35 % Memory : 8042.1875MB
% 0.11/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.35 % CPULimit : 300
% 0.11/0.35 % WCLimit : 300
% 0.11/0.35 % DateTime : Tue Apr 30 00:43:50 EDT 2024
% 0.11/0.35 % CPUTime :
% 0.11/0.37 % Drodi V3.6.0
% 0.18/0.54 % Refutation found
% 0.18/0.54 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.18/0.54 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.18/0.56 % Elapsed time: 0.203481 seconds
% 0.18/0.56 % CPU time: 1.403191 seconds
% 0.18/0.56 % Total memory used: 91.388 MB
% 0.18/0.56 % Net memory used: 90.239 MB
%------------------------------------------------------------------------------