TSTP Solution File: SWV408+1 by Drodi---3.6.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Drodi---3.6.0
% Problem : SWV408+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 20:46:57 EDT 2024
% Result : Theorem 0.14s 0.39s
% Output : CNFRefutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 9
% Syntax : Number of formulae : 45 ( 9 unt; 0 def)
% Number of atoms : 119 ( 11 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 121 ( 47 ~; 48 |; 17 &)
% ( 5 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 11 ( 9 usr; 6 prp; 0-3 aty)
% Number of functors : 10 ( 10 usr; 5 con; 0-3 aty)
% Number of variables : 57 ( 45 !; 12 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f8,axiom,
! [U] : ~ contains_slb(create_slb,U),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f39,axiom,
! [U,V,W,X] :
( V != create_slb
=> findmin_cpq_res(triple(U,V,W)) = findmin_pqp_res(U) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f42,lemma,
! [U,V,W] :
( ( contains_slb(U,V)
& strictly_less_than(V,W) )
=> ( pair_in_list(update_slb(U,W),V,W)
| ? [X] :
( pair_in_list(update_slb(U,W),V,X)
& less_than(W,X) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f43,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(f44,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)],[f43]) ).
fof(f58,plain,
! [X0] : ~ contains_slb(create_slb,X0),
inference(cnf_transformation,[status(esa)],[f8]) ).
fof(f140,plain,
! [U,V,W,X] :
( V = create_slb
| findmin_cpq_res(triple(U,V,W)) = findmin_pqp_res(U) ),
inference(pre_NNF_transformation,[status(esa)],[f39]) ).
fof(f141,plain,
! [V] :
( V = create_slb
| ! [U,W] : findmin_cpq_res(triple(U,V,W)) = findmin_pqp_res(U) ),
inference(miniscoping,[status(esa)],[f140]) ).
fof(f142,plain,
! [X0,X1,X2] :
( X0 = create_slb
| findmin_cpq_res(triple(X1,X0,X2)) = findmin_pqp_res(X1) ),
inference(cnf_transformation,[status(esa)],[f141]) ).
fof(f145,plain,
! [U,V,W] :
( ~ contains_slb(U,V)
| ~ strictly_less_than(V,W)
| pair_in_list(update_slb(U,W),V,W)
| ? [X] :
( pair_in_list(update_slb(U,W),V,X)
& less_than(W,X) ) ),
inference(pre_NNF_transformation,[status(esa)],[f42]) ).
fof(f146,plain,
! [U,V,W] :
( ~ contains_slb(U,V)
| ~ strictly_less_than(V,W)
| pair_in_list(update_slb(U,W),V,W)
| ( pair_in_list(update_slb(U,W),V,sk0_0(W,V,U))
& less_than(W,sk0_0(W,V,U)) ) ),
inference(skolemization,[status(esa)],[f145]) ).
fof(f147,plain,
! [X0,X1,X2] :
( ~ contains_slb(X0,X1)
| ~ strictly_less_than(X1,X2)
| pair_in_list(update_slb(X0,X2),X1,X2)
| pair_in_list(update_slb(X0,X2),X1,sk0_0(X2,X1,X0)) ),
inference(cnf_transformation,[status(esa)],[f146]) ).
fof(f148,plain,
! [X0,X1,X2] :
( ~ contains_slb(X0,X1)
| ~ strictly_less_than(X1,X2)
| pair_in_list(update_slb(X0,X2),X1,X2)
| less_than(X2,sk0_0(X2,X1,X0)) ),
inference(cnf_transformation,[status(esa)],[f146]) ).
fof(f149,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)],[f44]) ).
fof(f150,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)],[f149]) ).
fof(f151,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)],[f150]) ).
fof(f152,plain,
contains_slb(sk0_2,sk0_3),
inference(cnf_transformation,[status(esa)],[f151]) ).
fof(f153,plain,
strictly_less_than(sk0_3,findmin_cpq_res(triple(sk0_1,sk0_2,sk0_4))),
inference(cnf_transformation,[status(esa)],[f151]) ).
fof(f154,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)],[f151]) ).
fof(f155,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)],[f151]) ).
fof(f170,plain,
( spl0_2
<=> strictly_less_than(sk0_3,findmin_pqp_res(sk0_1)) ),
introduced(split_symbol_definition) ).
fof(f171,plain,
( strictly_less_than(sk0_3,findmin_pqp_res(sk0_1))
| ~ spl0_2 ),
inference(component_clause,[status(thm)],[f170]) ).
fof(f173,plain,
( spl0_3
<=> sk0_2 = create_slb ),
introduced(split_symbol_definition) ).
fof(f174,plain,
( sk0_2 = create_slb
| ~ spl0_3 ),
inference(component_clause,[status(thm)],[f173]) ).
fof(f176,plain,
( strictly_less_than(sk0_3,findmin_pqp_res(sk0_1))
| sk0_2 = create_slb ),
inference(paramodulation,[status(thm)],[f142,f153]) ).
fof(f177,plain,
( spl0_2
| spl0_3 ),
inference(split_clause,[status(thm)],[f176,f170,f173]) ).
fof(f220,plain,
( contains_slb(create_slb,sk0_3)
| ~ spl0_3 ),
inference(backward_demodulation,[status(thm)],[f174,f152]) ).
fof(f221,plain,
( $false
| ~ spl0_3 ),
inference(forward_subsumption_resolution,[status(thm)],[f220,f58]) ).
fof(f222,plain,
~ spl0_3,
inference(contradiction_clause,[status(thm)],[f221]) ).
fof(f921,plain,
( spl0_55
<=> contains_slb(sk0_2,sk0_3) ),
introduced(split_symbol_definition) ).
fof(f923,plain,
( ~ contains_slb(sk0_2,sk0_3)
| spl0_55 ),
inference(component_clause,[status(thm)],[f921]) ).
fof(f932,plain,
( $false
| spl0_55 ),
inference(forward_subsumption_resolution,[status(thm)],[f923,f152]) ).
fof(f933,plain,
spl0_55,
inference(contradiction_clause,[status(thm)],[f932]) ).
fof(f1127,plain,
! [X0] :
( ~ contains_slb(X0,sk0_3)
| pair_in_list(update_slb(X0,findmin_pqp_res(sk0_1)),sk0_3,findmin_pqp_res(sk0_1))
| pair_in_list(update_slb(X0,findmin_pqp_res(sk0_1)),sk0_3,sk0_0(findmin_pqp_res(sk0_1),sk0_3,X0))
| ~ spl0_2 ),
inference(resolution,[status(thm)],[f147,f171]) ).
fof(f1435,plain,
! [X0] :
( ~ contains_slb(X0,sk0_3)
| pair_in_list(update_slb(X0,findmin_pqp_res(sk0_1)),sk0_3,findmin_pqp_res(sk0_1))
| less_than(findmin_pqp_res(sk0_1),sk0_0(findmin_pqp_res(sk0_1),sk0_3,X0))
| ~ spl0_2 ),
inference(resolution,[status(thm)],[f148,f171]) ).
fof(f1871,plain,
( spl0_90
<=> pair_in_list(update_slb(sk0_2,findmin_pqp_res(sk0_1)),sk0_3,findmin_pqp_res(sk0_1)) ),
introduced(split_symbol_definition) ).
fof(f1872,plain,
( pair_in_list(update_slb(sk0_2,findmin_pqp_res(sk0_1)),sk0_3,findmin_pqp_res(sk0_1))
| ~ spl0_90 ),
inference(component_clause,[status(thm)],[f1871]) ).
fof(f1874,plain,
( spl0_91
<=> less_than(findmin_pqp_res(sk0_1),sk0_0(findmin_pqp_res(sk0_1),sk0_3,sk0_2)) ),
introduced(split_symbol_definition) ).
fof(f1877,plain,
( ~ contains_slb(sk0_2,sk0_3)
| pair_in_list(update_slb(sk0_2,findmin_pqp_res(sk0_1)),sk0_3,findmin_pqp_res(sk0_1))
| ~ less_than(findmin_pqp_res(sk0_1),sk0_0(findmin_pqp_res(sk0_1),sk0_3,sk0_2))
| ~ spl0_2 ),
inference(resolution,[status(thm)],[f1127,f155]) ).
fof(f1878,plain,
( ~ spl0_55
| spl0_90
| ~ spl0_91
| ~ spl0_2 ),
inference(split_clause,[status(thm)],[f1877,f921,f1871,f1874,f170]) ).
fof(f1902,plain,
( $false
| ~ spl0_90 ),
inference(forward_subsumption_resolution,[status(thm)],[f1872,f154]) ).
fof(f1903,plain,
~ spl0_90,
inference(contradiction_clause,[status(thm)],[f1902]) ).
fof(f1905,plain,
( ~ contains_slb(sk0_2,sk0_3)
| less_than(findmin_pqp_res(sk0_1),sk0_0(findmin_pqp_res(sk0_1),sk0_3,sk0_2))
| ~ spl0_2 ),
inference(resolution,[status(thm)],[f1435,f154]) ).
fof(f1906,plain,
( ~ spl0_55
| spl0_91
| ~ spl0_2 ),
inference(split_clause,[status(thm)],[f1905,f921,f1874,f170]) ).
fof(f1924,plain,
$false,
inference(sat_refutation,[status(thm)],[f177,f222,f933,f1878,f1903,f1906]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.09 % Problem : SWV408+1 : TPTP v8.1.2. Released v3.3.0.
% 0.08/0.09 % Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.09/0.28 % Computer : n032.cluster.edu
% 0.09/0.28 % Model : x86_64 x86_64
% 0.09/0.28 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.28 % Memory : 8042.1875MB
% 0.09/0.28 % OS : Linux 3.10.0-693.el7.x86_64
% 0.09/0.28 % CPULimit : 300
% 0.09/0.28 % WCLimit : 300
% 0.09/0.28 % DateTime : Tue Apr 30 01:00:05 EDT 2024
% 0.09/0.28 % CPUTime :
% 0.09/0.29 % Drodi V3.6.0
% 0.14/0.39 % Refutation found
% 0.14/0.39 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.14/0.39 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.14/0.40 % Elapsed time: 0.117249 seconds
% 0.14/0.40 % CPU time: 0.861077 seconds
% 0.14/0.40 % Total memory used: 70.104 MB
% 0.14/0.40 % Net memory used: 68.945 MB
%------------------------------------------------------------------------------