%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SWV373+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 : n009.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 02:47:31 PM UTC 2026
% Result : Theorem 0.09s 0.38s
% Output : CNFRefutation 0.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 6
% Syntax : Number of formulae : 34 ( 8 unt; 2 def)
% Number of atoms : 70 ( 15 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 68 ( 32 ~; 19 |; 10 &)
% ( 3 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 8 ( 6 usr; 3 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 4 con; 0-3 aty)
% Number of variables : 62 ( 59 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f27,axiom,
! [U,V,W,X] :
( contains_cpq(triple(U,V,W),X)
<=> contains_slb(V,X) ),
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] :
( ok(findmin_cpq_eff(triple(U,V,W)))
=> ( less_than(lookup_slb(V,findmin_pqp_res(U)),findmin_pqp_res(U))
& contains_slb(V,findmin_pqp_res(U))
& V != create_slb ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f43,conjecture,
! [U,V,W] :
( ~ contains_cpq(triple(U,V,W),findmin_cpq_res(triple(U,V,W)))
=> ~ ok(findmin_cpq_eff(triple(U,V,W))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f44,negated_conjecture,
~ ! [U,V,W] :
( ~ contains_cpq(triple(U,V,W),findmin_cpq_res(triple(U,V,W)))
=> ~ ok(findmin_cpq_eff(triple(U,V,W))) ),
inference(negated_conjecture,[status(cth)],[f43]) ).
fof(f108,plain,
! [U,V,W,X] :
( ( ~ contains_slb(V,X)
| contains_cpq(triple(U,V,W),X) )
& ( contains_slb(V,X)
| ~ contains_cpq(triple(U,V,W),X) ) ),
inference(NNF_transformation,[status(thm)],[f27]) ).
fof(f109,plain,
( ! [V,X] :
( ~ contains_slb(V,X)
| ! [U,W] : contains_cpq(triple(U,V,W),X) )
& ! [V,X] :
( contains_slb(V,X)
| ! [U,W] : ~ contains_cpq(triple(U,V,W),X) ) ),
inference(miniscoping,[status(thm)],[f108]) ).
fof(f111,plain,
! [X0,X1,X2,X3] :
( ~ contains_slb(X1,X3)
| contains_cpq(triple(X0,X1,X2),X3) ),
inference(cnf_transformation,[status(thm)],[f109]) ).
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] :
( ( less_than(lookup_slb(V,findmin_pqp_res(U)),findmin_pqp_res(U))
& contains_slb(V,findmin_pqp_res(U))
& V != create_slb )
| ~ ok(findmin_cpq_eff(triple(U,V,W))) ),
inference(pre_NNF_transformation,[status(thm)],[f42]) ).
fof(f146,plain,
! [U,V] :
( ( less_than(lookup_slb(V,findmin_pqp_res(U)),findmin_pqp_res(U))
& contains_slb(V,findmin_pqp_res(U))
& V != create_slb )
| ! [W] : ~ ok(findmin_cpq_eff(triple(U,V,W))) ),
inference(miniscoping,[status(thm)],[f145]) ).
fof(f147,plain,
! [X0,X1,X2] :
( X1 != create_slb
| ~ ok(findmin_cpq_eff(triple(X0,X1,X2))) ),
inference(cnf_transformation,[status(thm)],[f146]) ).
fof(f148,plain,
! [X0,X1,X2] :
( contains_slb(X1,findmin_pqp_res(X0))
| ~ ok(findmin_cpq_eff(triple(X0,X1,X2))) ),
inference(cnf_transformation,[status(thm)],[f146]) ).
fof(f150,plain,
? [U,V,W] :
( ok(findmin_cpq_eff(triple(U,V,W)))
& ~ contains_cpq(triple(U,V,W),findmin_cpq_res(triple(U,V,W))) ),
inference(pre_NNF_transformation,[status(thm)],[f44]) ).
fof(f151,plain,
( ok(findmin_cpq_eff(triple(sK0_skl,sK1_skl,sK2_skl)))
& ~ contains_cpq(triple(sK0_skl,sK1_skl,sK2_skl),findmin_cpq_res(triple(sK0_skl,sK1_skl,sK2_skl))) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl,sK1_skl,sK2_skl]),skolemize(U,sK0_skl),skolemize(V,sK1_skl),skolemize(W,sK2_skl)],[f150]) ).
fof(f152,plain,
~ contains_cpq(triple(sK0_skl,sK1_skl,sK2_skl),findmin_cpq_res(triple(sK0_skl,sK1_skl,sK2_skl))),
inference(cnf_transformation,[status(thm)],[f151]) ).
fof(f153,plain,
ok(findmin_cpq_eff(triple(sK0_skl,sK1_skl,sK2_skl))),
inference(cnf_transformation,[status(thm)],[f151]) ).
fof(f156,plain,
! [X0,X1] : ~ ok(findmin_cpq_eff(triple(X0,create_slb,X1))),
inference(destructive_equality_resolution,[status(thm)],[f147]) ).
fof(f158,plain,
~ contains_slb(sK1_skl,findmin_cpq_res(triple(sK0_skl,sK1_skl,sK2_skl))),
inference(resolution,[status(thm)],[f111,f152]) ).
fof(f164,definition,
( sQ1_spl
<=> sK1_skl = create_slb ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f165,plain,
( ~ sQ1_spl
| sK1_skl = create_slb ),
inference(component_clause,[status(thm)],[f164]) ).
fof(f168,plain,
( sK1_skl = create_slb
| ~ contains_slb(sK1_skl,findmin_pqp_res(sK0_skl)) ),
inference(paramodulation,[status(thm)],[f142,f158]) ).
fof(f169,definition,
( sQ2_spl
<=> contains_slb(sK1_skl,findmin_pqp_res(sK0_skl)) ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f171,plain,
( sQ2_spl
| ~ contains_slb(sK1_skl,findmin_pqp_res(sK0_skl)) ),
inference(component_clause,[status(thm)],[f169]) ).
fof(f172,plain,
( sQ1_spl
| ~ sQ2_spl ),
inference(split_clause,[status(thm)],[f168,f169,f164]) ).
fof(f174,plain,
! [X0,X1] :
( ~ sQ1_spl
| ~ ok(findmin_cpq_eff(triple(X0,sK1_skl,X1))) ),
inference(backward_demodulation,[status(thm)],[f165,f156]) ).
fof(f175,plain,
( ~ sQ1_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f153,f174]) ).
fof(f176,plain,
~ sQ1_spl,
inference(contradiction_clause,[status(thm)],[f175]) ).
fof(f181,plain,
contains_slb(sK1_skl,findmin_pqp_res(sK0_skl)),
inference(resolution,[status(thm)],[f148,f153]) ).
fof(f182,plain,
( sQ2_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f181,f171]) ).
fof(f183,plain,
sQ2_spl,
inference(contradiction_clause,[status(thm)],[f182]) ).
fof(f184,plain,
$false,
inference(sat_refutation,[status(thm)],[f172,f176,f183]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWV373+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.35 % Computer : n009.cluster.edu
% 0.09/0.35 % Model : x86_64 x86_64
% 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.35 % Memory : 8046.5625MB
% 0.09/0.35 % OS : Linux 6.8.0-71-generic
% 0.09/0.35 % CPULimit : 300
% 0.09/0.35 % WCLimit : 300
% 0.09/0.35 % DateTime : Mon Sep 21 08:43:42 UTC 2026
% 0.09/0.35 % CPUTime :
% 0.09/0.37 % Drodi V4.1.1
% 0.09/0.38 % Refutation found
% 0.09/0.38 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.09/0.38 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.14/0.44 % Elapsed time: 0.082280 seconds
% 0.14/0.44 % CPU time: 0.110039 seconds
% 0.14/0.44 % Total memory used: 6.476 MB
% 0.14/0.44 % Net memory used: 6.473 MB
%------------------------------------------------------------------------------