%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SWV372+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 : n026.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 0.15s 0.51s
% Output : CNFRefutation 0.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 11
% Syntax : Number of formulae : 54 ( 8 unt; 3 def)
% Number of atoms : 120 ( 24 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 107 ( 41 ~; 46 |; 9 &)
% ( 6 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 11 ( 8 usr; 5 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 5 con; 0-3 aty)
% Number of variables : 108 ( 105 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f39,axiom,
! [U,V,W,X] :
( contains_cpq(triple(U,V,W),X)
<=> contains_slb(V,X) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f40,axiom,
! [U,V] :
( ok(triple(U,V,bad))
<=> $false ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f46,axiom,
! [U,V] : findmin_cpq_eff(triple(U,create_slb,V)) = triple(U,create_slb,bad),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f47,axiom,
! [U,V,W,X] :
( ( ~ contains_slb(V,findmin_pqp_res(U))
& V != create_slb )
=> findmin_cpq_eff(triple(U,V,W)) = triple(U,update_slb(V,findmin_pqp_res(U)),bad) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f51,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(f63,lemma,
! [U,V,W,X] :
( contains_cpq(triple(U,V,W),X)
<=> contains_pq(i(triple(U,V,W)),X) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f65,lemma,
! [U,V,W] :
( ~ ok(triple(U,V,W))
=> ~ phi(triple(U,V,W)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f66,conjecture,
! [U,V,W] :
( phi(findmin_cpq_eff(triple(U,V,W)))
=> contains_pq(i(triple(U,V,W)),findmin_cpq_res(triple(U,V,W))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f67,negated_conjecture,
~ ! [U,V,W] :
( phi(findmin_cpq_eff(triple(U,V,W)))
=> contains_pq(i(triple(U,V,W)),findmin_cpq_res(triple(U,V,W))) ),
inference(negated_conjecture,[status(cth)],[f66]) ).
fof(f158,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)],[f39]) ).
fof(f159,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)],[f158]) ).
fof(f161,plain,
! [X0,X1,X2,X3] :
( ~ contains_slb(X1,X3)
| contains_cpq(triple(X0,X1,X2),X3) ),
inference(cnf_transformation,[status(thm)],[f159]) ).
fof(f162,plain,
! [U,V] :
( ( $true
| ok(triple(U,V,bad)) )
& ( $false
| ~ ok(triple(U,V,bad)) ) ),
inference(NNF_transformation,[status(thm)],[f40]) ).
fof(f163,plain,
( ( $true
| ! [U,V] : ok(triple(U,V,bad)) )
& ( $false
| ! [U,V] : ~ ok(triple(U,V,bad)) ) ),
inference(miniscoping,[status(thm)],[f162]) ).
fof(f164,plain,
! [U,V] : ~ ok(triple(U,V,bad)),
inference(true_and_false_simplification,[status(thm)],[f163]) ).
fof(f165,plain,
! [X0,X1] : ~ ok(triple(X0,X1,bad)),
inference(cnf_transformation,[status(thm)],[f164]) ).
fof(f179,plain,
! [X0,X1] : findmin_cpq_eff(triple(X0,create_slb,X1)) = triple(X0,create_slb,bad),
inference(cnf_transformation,[status(thm)],[f46]) ).
fof(f180,plain,
! [U,V,W,X] :
( findmin_cpq_eff(triple(U,V,W)) = triple(U,update_slb(V,findmin_pqp_res(U)),bad)
| contains_slb(V,findmin_pqp_res(U))
| V = create_slb ),
inference(pre_NNF_transformation,[status(thm)],[f47]) ).
fof(f181,plain,
! [U,V] :
( ! [W] : findmin_cpq_eff(triple(U,V,W)) = triple(U,update_slb(V,findmin_pqp_res(U)),bad)
| contains_slb(V,findmin_pqp_res(U))
| V = create_slb ),
inference(miniscoping,[status(thm)],[f180]) ).
fof(f182,plain,
! [X0,X1,X2] :
( findmin_cpq_eff(triple(X1,X0,X2)) = triple(X1,update_slb(X0,findmin_pqp_res(X1)),bad)
| contains_slb(X0,findmin_pqp_res(X1))
| X0 = create_slb ),
inference(cnf_transformation,[status(thm)],[f181]) ).
fof(f190,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)],[f51]) ).
fof(f191,plain,
! [V] :
( ! [U,W] : findmin_cpq_res(triple(U,V,W)) = findmin_pqp_res(U)
| V = create_slb ),
inference(miniscoping,[status(thm)],[f190]) ).
fof(f192,plain,
! [X0,X1,X2] :
( findmin_cpq_res(triple(X1,X0,X2)) = findmin_pqp_res(X1)
| X0 = create_slb ),
inference(cnf_transformation,[status(thm)],[f191]) ).
fof(f232,plain,
! [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)
| ~ contains_cpq(triple(U,V,W),X) ) ),
inference(NNF_transformation,[status(thm)],[f63]) ).
fof(f233,plain,
( ! [U,V,W,X] :
( ~ contains_pq(i(triple(U,V,W)),X)
| contains_cpq(triple(U,V,W),X) )
& ! [U,V,W,X] :
( contains_pq(i(triple(U,V,W)),X)
| ~ contains_cpq(triple(U,V,W),X) ) ),
inference(miniscoping,[status(thm)],[f232]) ).
fof(f234,plain,
! [X0,X1,X2,X3] :
( contains_pq(i(triple(X0,X1,X2)),X3)
| ~ contains_cpq(triple(X0,X1,X2),X3) ),
inference(cnf_transformation,[status(thm)],[f233]) ).
fof(f238,plain,
! [U,V,W] :
( ~ phi(triple(U,V,W))
| ok(triple(U,V,W)) ),
inference(pre_NNF_transformation,[status(thm)],[f65]) ).
fof(f239,plain,
! [X0,X1,X2] :
( ~ phi(triple(X0,X1,X2))
| ok(triple(X0,X1,X2)) ),
inference(cnf_transformation,[status(thm)],[f238]) ).
fof(f240,plain,
? [U,V,W] :
( ~ contains_pq(i(triple(U,V,W)),findmin_cpq_res(triple(U,V,W)))
& phi(findmin_cpq_eff(triple(U,V,W))) ),
inference(pre_NNF_transformation,[status(thm)],[f67]) ).
fof(f241,plain,
( ~ contains_pq(i(triple(sK4_skl,sK5_skl,sK6_skl)),findmin_cpq_res(triple(sK4_skl,sK5_skl,sK6_skl)))
& phi(findmin_cpq_eff(triple(sK4_skl,sK5_skl,sK6_skl))) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4_skl,sK5_skl,sK6_skl]),skolemize(U,sK4_skl),skolemize(V,sK5_skl),skolemize(W,sK6_skl)],[f240]) ).
fof(f242,plain,
phi(findmin_cpq_eff(triple(sK4_skl,sK5_skl,sK6_skl))),
inference(cnf_transformation,[status(thm)],[f241]) ).
fof(f243,plain,
~ contains_pq(i(triple(sK4_skl,sK5_skl,sK6_skl)),findmin_cpq_res(triple(sK4_skl,sK5_skl,sK6_skl))),
inference(cnf_transformation,[status(thm)],[f241]) ).
fof(f247,plain,
( sK5_skl = create_slb
| ~ contains_pq(i(triple(sK4_skl,sK5_skl,sK6_skl)),findmin_pqp_res(sK4_skl)) ),
inference(paramodulation,[status(thm)],[f192,f243]) ).
fof(f248,definition,
( sQ0_spl
<=> contains_pq(i(triple(sK4_skl,sK5_skl,sK6_skl)),findmin_pqp_res(sK4_skl)) ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f250,plain,
( sQ0_spl
| ~ contains_pq(i(triple(sK4_skl,sK5_skl,sK6_skl)),findmin_pqp_res(sK4_skl)) ),
inference(component_clause,[status(thm)],[f248]) ).
fof(f251,definition,
( sQ1_spl
<=> sK5_skl = create_slb ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f252,plain,
( ~ sQ1_spl
| sK5_skl = create_slb ),
inference(component_clause,[status(thm)],[f251]) ).
fof(f254,plain,
( sQ1_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f247,f248,f251]) ).
fof(f372,plain,
( ~ sQ1_spl
| phi(findmin_cpq_eff(triple(sK4_skl,create_slb,sK6_skl))) ),
inference(backward_demodulation,[status(thm)],[f252,f242]) ).
fof(f431,plain,
( ~ sQ1_spl
| phi(triple(sK4_skl,create_slb,bad)) ),
inference(backward_demodulation,[status(thm)],[f179,f372]) ).
fof(f435,plain,
( ~ sQ1_spl
| ok(triple(sK4_skl,create_slb,bad)) ),
inference(resolution,[status(thm)],[f431,f239]) ).
fof(f436,plain,
( ~ sQ1_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f435,f165]) ).
fof(f437,plain,
~ sQ1_spl,
inference(contradiction_clause,[status(thm)],[f436]) ).
fof(f461,plain,
! [X0,X1,X2] :
( contains_slb(X1,findmin_pqp_res(X0))
| X1 = create_slb
| ~ phi(findmin_cpq_eff(triple(X0,X1,X2)))
| ok(triple(X0,update_slb(X1,findmin_pqp_res(X0)),bad)) ),
inference(paramodulation,[status(thm)],[f182,f239]) ).
fof(f479,plain,
! [X0,X1,X2] :
( contains_slb(X1,findmin_pqp_res(X0))
| X1 = create_slb
| ~ phi(findmin_cpq_eff(triple(X0,X1,X2))) ),
inference(forward_subsumption_resolution,[status(thm)],[f461,f165]) ).
fof(f524,plain,
( contains_slb(sK5_skl,findmin_pqp_res(sK4_skl))
| sK5_skl = create_slb ),
inference(resolution,[status(thm)],[f479,f242]) ).
fof(f530,definition,
( sQ22_spl
<=> contains_slb(sK5_skl,findmin_pqp_res(sK4_skl)) ),
introduced(definition,[new_symbols(definition,[sQ22_spl])],[split_symbol_definition]) ).
fof(f531,plain,
( ~ sQ22_spl
| contains_slb(sK5_skl,findmin_pqp_res(sK4_skl)) ),
inference(component_clause,[status(thm)],[f530]) ).
fof(f533,plain,
( sQ22_spl
| sQ1_spl ),
inference(split_clause,[status(thm)],[f524,f251,f530]) ).
fof(f647,plain,
( sQ0_spl
| ~ contains_cpq(triple(sK4_skl,sK5_skl,sK6_skl),findmin_pqp_res(sK4_skl)) ),
inference(resolution,[status(thm)],[f234,f250]) ).
fof(f703,plain,
( sQ0_spl
| ~ contains_slb(sK5_skl,findmin_pqp_res(sK4_skl)) ),
inference(resolution,[status(thm)],[f647,f161]) ).
fof(f704,plain,
( sQ0_spl
| ~ sQ22_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f703,f531]) ).
fof(f705,plain,
( sQ0_spl
| ~ sQ22_spl ),
inference(contradiction_clause,[status(thm)],[f704]) ).
fof(f706,plain,
$false,
inference(sat_refutation,[status(thm)],[f254,f437,f533,f705]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWV372+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.36 % Computer : n026.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 08:46:22 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.41 % Drodi V4.1.1
% 0.15/0.51 % Refutation found
% 0.15/0.51 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.15/0.51 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.15/0.54 % Elapsed time: 0.144531 seconds
% 0.15/0.54 % CPU time: 0.624798 seconds
% 0.15/0.54 % Total memory used: 104.014 MB
% 0.15/0.54 % Net memory used: 103.690 MB
%------------------------------------------------------------------------------