TSTP Solution File: SWV408+2 by Drodi---3.6.0
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%------------------------------------------------------------------------------
% File : Drodi---3.6.0
% Problem : SWV408+2 : TPTP v8.1.2. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% Computer : n028.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 20:46:57 EDT 2024
% Result : Theorem 0.19s 0.56s
% Output : CNFRefutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 9
% Syntax : Number of formulae : 45 ( 4 unt; 0 def)
% Number of atoms : 120 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 127 ( 52 ~; 46 |; 20 &)
% ( 4 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 8 ( 7 usr; 4 prp; 0-3 aty)
% Number of functors : 9 ( 9 usr; 4 con; 0-3 aty)
% Number of variables : 79 ( 67 !; 12 ?)
% 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(f42,lemma,
! [U,V] :
( contains_slb(U,V)
=> ? [W] : pair_in_list(U,V,W) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f43,lemma,
! [U,V,W,X] :
( ( pair_in_list(U,V,W)
& strictly_less_than(W,X) )
=> pair_in_list(update_slb(U,X),V,X) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f44,lemma,
! [U,V,W,X] :
( ( pair_in_list(U,V,W)
& less_than(X,W) )
=> pair_in_list(update_slb(U,X),V,W) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f45,conjecture,
! [U,V,W,X] :
( ( contains_slb(V,X)
& strictly_less_than(X,findmin_cpq_res(triple(U,V,W))) )
=> ( pair_in_list(update_slb(V,findmin_pqp_res(U)),X,findmin_pqp_res(U))
| ? [Y] :
( pair_in_list(update_slb(V,findmin_pqp_res(U)),X,Y)
& less_than(findmin_pqp_res(U),Y) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f46,negated_conjecture,
~ ! [U,V,W,X] :
( ( contains_slb(V,X)
& strictly_less_than(X,findmin_cpq_res(triple(U,V,W))) )
=> ( pair_in_list(update_slb(V,findmin_pqp_res(U)),X,findmin_pqp_res(U))
| ? [Y] :
( pair_in_list(update_slb(V,findmin_pqp_res(U)),X,Y)
& less_than(findmin_pqp_res(U),Y) ) ) ),
inference(negated_conjecture,[status(cth)],[f45]) ).
fof(f50,plain,
! [X0,X1] :
( less_than(X0,X1)
| less_than(X1,X0) ),
inference(cnf_transformation,[status(esa)],[f2]) ).
fof(f52,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(f53,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)],[f52]) ).
fof(f56,plain,
! [X0,X1] :
( strictly_less_than(X0,X1)
| ~ less_than(X0,X1)
| less_than(X1,X0) ),
inference(cnf_transformation,[status(esa)],[f53]) ).
fof(f147,plain,
! [U,V] :
( ~ contains_slb(U,V)
| ? [W] : pair_in_list(U,V,W) ),
inference(pre_NNF_transformation,[status(esa)],[f42]) ).
fof(f148,plain,
! [U,V] :
( ~ contains_slb(U,V)
| pair_in_list(U,V,sk0_0(V,U)) ),
inference(skolemization,[status(esa)],[f147]) ).
fof(f149,plain,
! [X0,X1] :
( ~ contains_slb(X0,X1)
| pair_in_list(X0,X1,sk0_0(X1,X0)) ),
inference(cnf_transformation,[status(esa)],[f148]) ).
fof(f150,plain,
! [U,V,W,X] :
( ~ pair_in_list(U,V,W)
| ~ strictly_less_than(W,X)
| pair_in_list(update_slb(U,X),V,X) ),
inference(pre_NNF_transformation,[status(esa)],[f43]) ).
fof(f151,plain,
! [U,V,X] :
( ! [W] :
( ~ pair_in_list(U,V,W)
| ~ strictly_less_than(W,X) )
| pair_in_list(update_slb(U,X),V,X) ),
inference(miniscoping,[status(esa)],[f150]) ).
fof(f152,plain,
! [X0,X1,X2,X3] :
( ~ pair_in_list(X0,X1,X2)
| ~ strictly_less_than(X2,X3)
| pair_in_list(update_slb(X0,X3),X1,X3) ),
inference(cnf_transformation,[status(esa)],[f151]) ).
fof(f153,plain,
! [U,V,W,X] :
( ~ pair_in_list(U,V,W)
| ~ less_than(X,W)
| pair_in_list(update_slb(U,X),V,W) ),
inference(pre_NNF_transformation,[status(esa)],[f44]) ).
fof(f154,plain,
! [X0,X1,X2,X3] :
( ~ pair_in_list(X0,X1,X2)
| ~ less_than(X3,X2)
| pair_in_list(update_slb(X0,X3),X1,X2) ),
inference(cnf_transformation,[status(esa)],[f153]) ).
fof(f155,plain,
? [U,V,W,X] :
( contains_slb(V,X)
& strictly_less_than(X,findmin_cpq_res(triple(U,V,W)))
& ~ pair_in_list(update_slb(V,findmin_pqp_res(U)),X,findmin_pqp_res(U))
& ! [Y] :
( ~ pair_in_list(update_slb(V,findmin_pqp_res(U)),X,Y)
| ~ less_than(findmin_pqp_res(U),Y) ) ),
inference(pre_NNF_transformation,[status(esa)],[f46]) ).
fof(f156,plain,
? [U,V,X] :
( contains_slb(V,X)
& ? [W] : strictly_less_than(X,findmin_cpq_res(triple(U,V,W)))
& ~ pair_in_list(update_slb(V,findmin_pqp_res(U)),X,findmin_pqp_res(U))
& ! [Y] :
( ~ pair_in_list(update_slb(V,findmin_pqp_res(U)),X,Y)
| ~ less_than(findmin_pqp_res(U),Y) ) ),
inference(miniscoping,[status(esa)],[f155]) ).
fof(f157,plain,
( contains_slb(sk0_2,sk0_3)
& strictly_less_than(sk0_3,findmin_cpq_res(triple(sk0_1,sk0_2,sk0_4)))
& ~ pair_in_list(update_slb(sk0_2,findmin_pqp_res(sk0_1)),sk0_3,findmin_pqp_res(sk0_1))
& ! [Y] :
( ~ pair_in_list(update_slb(sk0_2,findmin_pqp_res(sk0_1)),sk0_3,Y)
| ~ less_than(findmin_pqp_res(sk0_1),Y) ) ),
inference(skolemization,[status(esa)],[f156]) ).
fof(f158,plain,
contains_slb(sk0_2,sk0_3),
inference(cnf_transformation,[status(esa)],[f157]) ).
fof(f160,plain,
~ pair_in_list(update_slb(sk0_2,findmin_pqp_res(sk0_1)),sk0_3,findmin_pqp_res(sk0_1)),
inference(cnf_transformation,[status(esa)],[f157]) ).
fof(f161,plain,
! [X0] :
( ~ pair_in_list(update_slb(sk0_2,findmin_pqp_res(sk0_1)),sk0_3,X0)
| ~ less_than(findmin_pqp_res(sk0_1),X0) ),
inference(cnf_transformation,[status(esa)],[f157]) ).
fof(f167,plain,
! [X0,X1] :
( strictly_less_than(X0,X1)
| less_than(X1,X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f56,f50]) ).
fof(f366,plain,
! [X0] :
( ~ pair_in_list(sk0_2,sk0_3,X0)
| ~ strictly_less_than(X0,findmin_pqp_res(sk0_1)) ),
inference(resolution,[status(thm)],[f152,f160]) ).
fof(f383,plain,
! [X0] :
( ~ pair_in_list(sk0_2,sk0_3,X0)
| ~ less_than(findmin_pqp_res(sk0_1),X0)
| ~ less_than(findmin_pqp_res(sk0_1),X0) ),
inference(resolution,[status(thm)],[f154,f161]) ).
fof(f384,plain,
! [X0] :
( ~ pair_in_list(sk0_2,sk0_3,X0)
| ~ less_than(findmin_pqp_res(sk0_1),X0) ),
inference(duplicate_literals_removal,[status(esa)],[f383]) ).
fof(f393,plain,
( spl0_15
<=> contains_slb(sk0_2,sk0_3) ),
introduced(split_symbol_definition) ).
fof(f395,plain,
( ~ contains_slb(sk0_2,sk0_3)
| spl0_15 ),
inference(component_clause,[status(thm)],[f393]) ).
fof(f396,plain,
( spl0_16
<=> strictly_less_than(sk0_0(sk0_3,sk0_2),findmin_pqp_res(sk0_1)) ),
introduced(split_symbol_definition) ).
fof(f398,plain,
( ~ strictly_less_than(sk0_0(sk0_3,sk0_2),findmin_pqp_res(sk0_1))
| spl0_16 ),
inference(component_clause,[status(thm)],[f396]) ).
fof(f399,plain,
( ~ contains_slb(sk0_2,sk0_3)
| ~ strictly_less_than(sk0_0(sk0_3,sk0_2),findmin_pqp_res(sk0_1)) ),
inference(resolution,[status(thm)],[f149,f366]) ).
fof(f400,plain,
( ~ spl0_15
| ~ spl0_16 ),
inference(split_clause,[status(thm)],[f399,f393,f396]) ).
fof(f410,plain,
( $false
| spl0_15 ),
inference(forward_subsumption_resolution,[status(thm)],[f395,f158]) ).
fof(f411,plain,
spl0_15,
inference(contradiction_clause,[status(thm)],[f410]) ).
fof(f414,plain,
( less_than(findmin_pqp_res(sk0_1),sk0_0(sk0_3,sk0_2))
| spl0_16 ),
inference(resolution,[status(thm)],[f398,f167]) ).
fof(f496,plain,
( spl0_19
<=> less_than(findmin_pqp_res(sk0_1),sk0_0(sk0_3,sk0_2)) ),
introduced(split_symbol_definition) ).
fof(f498,plain,
( ~ less_than(findmin_pqp_res(sk0_1),sk0_0(sk0_3,sk0_2))
| spl0_19 ),
inference(component_clause,[status(thm)],[f496]) ).
fof(f499,plain,
( ~ less_than(findmin_pqp_res(sk0_1),sk0_0(sk0_3,sk0_2))
| ~ contains_slb(sk0_2,sk0_3) ),
inference(resolution,[status(thm)],[f384,f149]) ).
fof(f500,plain,
( ~ spl0_19
| ~ spl0_15 ),
inference(split_clause,[status(thm)],[f499,f496,f393]) ).
fof(f501,plain,
( $false
| spl0_16
| spl0_19 ),
inference(forward_subsumption_resolution,[status(thm)],[f498,f414]) ).
fof(f502,plain,
( spl0_16
| spl0_19 ),
inference(contradiction_clause,[status(thm)],[f501]) ).
fof(f503,plain,
$false,
inference(sat_refutation,[status(thm)],[f400,f411,f500,f502]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SWV408+2 : TPTP v8.1.2. Released v3.3.0.
% 0.03/0.13 % Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.13/0.34 % Computer : n028.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 01:10:14 EDT 2024
% 0.13/0.34 % CPUTime :
% 0.13/0.35 % Drodi V3.6.0
% 0.19/0.56 % Refutation found
% 0.19/0.56 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.19/0.56 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.19/0.58 % Elapsed time: 0.229093 seconds
% 0.19/0.58 % CPU time: 1.694497 seconds
% 0.19/0.58 % Total memory used: 71.972 MB
% 0.19/0.58 % Net memory used: 70.487 MB
%------------------------------------------------------------------------------