%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SWV408+1 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n001.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Sep 24 02:47:36 PM UTC 2026
% Result : Theorem 0.10s 0.40s
% Output : CNFRefutation 0.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 9
% Syntax : Number of formulae : 42 ( 9 unt; 5 def)
% Number of atoms : 109 ( 11 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 109 ( 42 ~; 41 |; 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 : 55 ( 43 !; 12 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f8,axiom,
! [U] : ~ contains_slb(create_slb,U),
file('/export/starexec/sandbox2/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/sandbox2/benchmark/theBenchmark.p') ).
fof(f42,lemma,
! [U,V,W] :
( ( strictly_less_than(V,W)
& contains_slb(U,V) )
=> ( ? [X] :
( less_than(W,X)
& pair_in_list(update_slb(U,W),V,X) )
| pair_in_list(update_slb(U,W),V,W) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f43,conjecture,
! [U,V,W,X] :
( ( strictly_less_than(X,findmin_cpq_res(triple(U,V,W)))
& contains_slb(V,X) )
=> ( ? [Y] :
( less_than(findmin_pqp_res(U),Y)
& pair_in_list(update_slb(V,findmin_pqp_res(U)),X,Y) )
| pair_in_list(update_slb(V,findmin_pqp_res(U)),X,findmin_pqp_res(U)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f44,negated_conjecture,
~ ! [U,V,W,X] :
( ( strictly_less_than(X,findmin_cpq_res(triple(U,V,W)))
& contains_slb(V,X) )
=> ( ? [Y] :
( less_than(findmin_pqp_res(U),Y)
& pair_in_list(update_slb(V,findmin_pqp_res(U)),X,Y) )
| pair_in_list(update_slb(V,findmin_pqp_res(U)),X,findmin_pqp_res(U)) ) ),
inference(negated_conjecture,[status(cth)],[f43]) ).
fof(f58,plain,
! [X0] : ~ contains_slb(create_slb,X0),
inference(cnf_transformation,[status(thm)],[f8]) ).
fof(f140,plain,
! [U,V,W,X] :
( findmin_cpq_res(triple(U,V,W)) = findmin_pqp_res(U)
| V = create_slb ),
inference(pre_NNF_transformation,[status(thm)],[f39]) ).
fof(f141,plain,
! [V] :
( ! [U,W] : findmin_cpq_res(triple(U,V,W)) = findmin_pqp_res(U)
| V = create_slb ),
inference(miniscoping,[status(thm)],[f140]) ).
fof(f142,plain,
! [X0,X1,X2] :
( findmin_cpq_res(triple(X1,X0,X2)) = findmin_pqp_res(X1)
| X0 = create_slb ),
inference(cnf_transformation,[status(thm)],[f141]) ).
fof(f145,plain,
! [U,V,W] :
( ? [X] :
( less_than(W,X)
& pair_in_list(update_slb(U,W),V,X) )
| pair_in_list(update_slb(U,W),V,W)
| ~ strictly_less_than(V,W)
| ~ contains_slb(U,V) ),
inference(pre_NNF_transformation,[status(thm)],[f42]) ).
fof(f146,plain,
! [U,V,W] :
( ( less_than(W,sK0_skl(W,V,U))
& pair_in_list(update_slb(U,W),V,sK0_skl(W,V,U)) )
| pair_in_list(update_slb(U,W),V,W)
| ~ strictly_less_than(V,W)
| ~ contains_slb(U,V) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl]),skolemize(X,sK0_skl(W,V,U))],[f145]) ).
fof(f147,plain,
! [X0,X1,X2] :
( pair_in_list(update_slb(X0,X2),X1,sK0_skl(X2,X1,X0))
| pair_in_list(update_slb(X0,X2),X1,X2)
| ~ strictly_less_than(X1,X2)
| ~ contains_slb(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f146]) ).
fof(f148,plain,
! [X0,X1,X2] :
( less_than(X2,sK0_skl(X2,X1,X0))
| pair_in_list(update_slb(X0,X2),X1,X2)
| ~ strictly_less_than(X1,X2)
| ~ contains_slb(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f146]) ).
fof(f149,plain,
? [U,V,W,X] :
( ! [Y] :
( ~ less_than(findmin_pqp_res(U),Y)
| ~ pair_in_list(update_slb(V,findmin_pqp_res(U)),X,Y) )
& ~ pair_in_list(update_slb(V,findmin_pqp_res(U)),X,findmin_pqp_res(U))
& strictly_less_than(X,findmin_cpq_res(triple(U,V,W)))
& contains_slb(V,X) ),
inference(pre_NNF_transformation,[status(thm)],[f44]) ).
fof(f150,plain,
? [U,V,X] :
( ! [Y] :
( ~ less_than(findmin_pqp_res(U),Y)
| ~ pair_in_list(update_slb(V,findmin_pqp_res(U)),X,Y) )
& ~ pair_in_list(update_slb(V,findmin_pqp_res(U)),X,findmin_pqp_res(U))
& ? [W] : strictly_less_than(X,findmin_cpq_res(triple(U,V,W)))
& contains_slb(V,X) ),
inference(miniscoping,[status(thm)],[f149]) ).
fof(f151,plain,
( ! [Y] :
( ~ less_than(findmin_pqp_res(sK1_skl),Y)
| ~ pair_in_list(update_slb(sK2_skl,findmin_pqp_res(sK1_skl)),sK3_skl,Y) )
& ~ pair_in_list(update_slb(sK2_skl,findmin_pqp_res(sK1_skl)),sK3_skl,findmin_pqp_res(sK1_skl))
& strictly_less_than(sK3_skl,findmin_cpq_res(triple(sK1_skl,sK2_skl,sK4_skl)))
& contains_slb(sK2_skl,sK3_skl) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1_skl,sK2_skl,sK3_skl,sK4_skl]),skolemize(U,sK1_skl),skolemize(V,sK2_skl),skolemize(X,sK3_skl),skolemize(W,sK4_skl)],[f150]) ).
fof(f152,plain,
contains_slb(sK2_skl,sK3_skl),
inference(cnf_transformation,[status(thm)],[f151]) ).
fof(f153,plain,
strictly_less_than(sK3_skl,findmin_cpq_res(triple(sK1_skl,sK2_skl,sK4_skl))),
inference(cnf_transformation,[status(thm)],[f151]) ).
fof(f154,plain,
~ pair_in_list(update_slb(sK2_skl,findmin_pqp_res(sK1_skl)),sK3_skl,findmin_pqp_res(sK1_skl)),
inference(cnf_transformation,[status(thm)],[f151]) ).
fof(f155,plain,
! [X0] :
( ~ less_than(findmin_pqp_res(sK1_skl),X0)
| ~ pair_in_list(update_slb(sK2_skl,findmin_pqp_res(sK1_skl)),sK3_skl,X0) ),
inference(cnf_transformation,[status(thm)],[f151]) ).
fof(f162,plain,
( sK2_skl = create_slb
| strictly_less_than(sK3_skl,findmin_pqp_res(sK1_skl)) ),
inference(paramodulation,[status(thm)],[f142,f153]) ).
fof(f163,definition,
( sQ0_spl
<=> strictly_less_than(sK3_skl,findmin_pqp_res(sK1_skl)) ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f166,definition,
( sQ1_spl
<=> sK2_skl = create_slb ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f167,plain,
( ~ sQ1_spl
| sK2_skl = create_slb ),
inference(component_clause,[status(thm)],[f166]) ).
fof(f169,plain,
( sQ1_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f162,f163,f166]) ).
fof(f183,plain,
( less_than(findmin_pqp_res(sK1_skl),sK0_skl(findmin_pqp_res(sK1_skl),sK3_skl,sK2_skl))
| ~ strictly_less_than(sK3_skl,findmin_pqp_res(sK1_skl))
| ~ contains_slb(sK2_skl,sK3_skl) ),
inference(resolution,[status(thm)],[f154,f148]) ).
fof(f186,definition,
( sQ4_spl
<=> contains_slb(sK2_skl,sK3_skl) ),
introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition]) ).
fof(f188,plain,
( sQ4_spl
| ~ contains_slb(sK2_skl,sK3_skl) ),
inference(component_clause,[status(thm)],[f186]) ).
fof(f189,definition,
( sQ5_spl
<=> less_than(findmin_pqp_res(sK1_skl),sK0_skl(findmin_pqp_res(sK1_skl),sK3_skl,sK2_skl)) ),
introduced(definition,[new_symbols(definition,[sQ5_spl])],[split_symbol_definition]) ).
fof(f192,plain,
( sQ5_spl
| ~ sQ0_spl
| ~ sQ4_spl ),
inference(split_clause,[status(thm)],[f183,f186,f163,f189]) ).
fof(f195,plain,
( ~ sQ1_spl
| contains_slb(create_slb,sK3_skl) ),
inference(backward_demodulation,[status(thm)],[f167,f152]) ).
fof(f203,plain,
( ~ sQ1_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f195,f58]) ).
fof(f204,plain,
~ sQ1_spl,
inference(contradiction_clause,[status(thm)],[f203]) ).
fof(f205,plain,
( sQ4_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f152,f188]) ).
fof(f206,plain,
sQ4_spl,
inference(contradiction_clause,[status(thm)],[f205]) ).
fof(f214,plain,
( pair_in_list(update_slb(sK2_skl,findmin_pqp_res(sK1_skl)),sK3_skl,findmin_pqp_res(sK1_skl))
| ~ strictly_less_than(sK3_skl,findmin_pqp_res(sK1_skl))
| ~ contains_slb(sK2_skl,sK3_skl)
| ~ less_than(findmin_pqp_res(sK1_skl),sK0_skl(findmin_pqp_res(sK1_skl),sK3_skl,sK2_skl)) ),
inference(resolution,[status(thm)],[f155,f147]) ).
fof(f218,definition,
( sQ6_spl
<=> pair_in_list(update_slb(sK2_skl,findmin_pqp_res(sK1_skl)),sK3_skl,findmin_pqp_res(sK1_skl)) ),
introduced(definition,[new_symbols(definition,[sQ6_spl])],[split_symbol_definition]) ).
fof(f219,plain,
( ~ sQ6_spl
| pair_in_list(update_slb(sK2_skl,findmin_pqp_res(sK1_skl)),sK3_skl,findmin_pqp_res(sK1_skl)) ),
inference(component_clause,[status(thm)],[f218]) ).
fof(f221,plain,
( sQ6_spl
| ~ sQ0_spl
| ~ sQ4_spl
| ~ sQ5_spl ),
inference(split_clause,[status(thm)],[f214,f189,f186,f163,f218]) ).
fof(f226,plain,
( ~ sQ6_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f219,f154]) ).
fof(f227,plain,
~ sQ6_spl,
inference(contradiction_clause,[status(thm)],[f226]) ).
fof(f228,plain,
$false,
inference(sat_refutation,[status(thm)],[f169,f192,f204,f206,f221,f227]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SWV408+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.03 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.36 % Computer : n001.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Mon Sep 21 08:50:59 UTC 2026
% 0.10/0.36 % CPUTime :
% 0.10/0.38 % Drodi V4.1.1
% 0.10/0.40 % Refutation found
% 0.10/0.40 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.10/0.40 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.10/0.45 % Elapsed time: 0.081221 seconds
% 0.10/0.45 % CPU time: 0.157558 seconds
% 0.10/0.45 % Total memory used: 26.664 MB
% 0.10/0.45 % Net memory used: 26.594 MB
%------------------------------------------------------------------------------