%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SWV374+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 : n003.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 0.08s 0.38s
% Output : CNFRefutation 0.08s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 11
% Syntax : Number of formulae : 52 ( 8 unt; 4 def)
% Number of atoms : 139 ( 34 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 134 ( 47 ~; 60 |; 17 &)
% ( 6 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 11 ( 8 usr; 6 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 5 con; 0-3 aty)
% Number of variables : 80 ( 74 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f2,axiom,
! [U,V] :
( less_than(V,U)
| less_than(U,V) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f4,axiom,
! [U,V] :
( strictly_less_than(U,V)
<=> ( ~ less_than(V,U)
& less_than(U,V) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f28,axiom,
! [U,V] :
( ok(triple(U,V,bad))
<=> $false ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f34,axiom,
! [U,V] : findmin_cpq_eff(triple(U,create_slb,V)) = triple(U,create_slb,bad),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f35,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(f36,axiom,
! [U,V,W,X] :
( ( strictly_less_than(findmin_pqp_res(U),lookup_slb(V,findmin_pqp_res(U)))
& 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(f42,conjecture,
! [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,negated_conjecture,
~ ! [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 ) ),
inference(negated_conjecture,[status(cth)],[f42]) ).
fof(f47,plain,
! [X0,X1] :
( less_than(X1,X0)
| less_than(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f49,plain,
! [U,V] :
( ( less_than(V,U)
| ~ less_than(U,V)
| strictly_less_than(U,V) )
& ( ( ~ less_than(V,U)
& less_than(U,V) )
| ~ strictly_less_than(U,V) ) ),
inference(NNF_transformation,[status(thm)],[f4]) ).
fof(f50,plain,
( ! [U,V] :
( less_than(V,U)
| ~ less_than(U,V)
| strictly_less_than(U,V) )
& ! [U,V] :
( ( ~ less_than(V,U)
& less_than(U,V) )
| ~ strictly_less_than(U,V) ) ),
inference(miniscoping,[status(thm)],[f49]) ).
fof(f53,plain,
! [X0,X1] :
( less_than(X1,X0)
| ~ less_than(X0,X1)
| strictly_less_than(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f50]) ).
fof(f111,plain,
! [U,V] :
( ( $true
| ok(triple(U,V,bad)) )
& ( $false
| ~ ok(triple(U,V,bad)) ) ),
inference(NNF_transformation,[status(thm)],[f28]) ).
fof(f112,plain,
( ( $true
| ! [U,V] : ok(triple(U,V,bad)) )
& ( $false
| ! [U,V] : ~ ok(triple(U,V,bad)) ) ),
inference(miniscoping,[status(thm)],[f111]) ).
fof(f113,plain,
! [U,V] : ~ ok(triple(U,V,bad)),
inference(true_and_false_simplification,[status(thm)],[f112]) ).
fof(f114,plain,
! [X0,X1] : ~ ok(triple(X0,X1,bad)),
inference(cnf_transformation,[status(thm)],[f113]) ).
fof(f128,plain,
! [X0,X1] : findmin_cpq_eff(triple(X0,create_slb,X1)) = triple(X0,create_slb,bad),
inference(cnf_transformation,[status(thm)],[f34]) ).
fof(f129,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)],[f35]) ).
fof(f130,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)],[f129]) ).
fof(f131,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)],[f130]) ).
fof(f132,plain,
! [U,V,W,X] :
( findmin_cpq_eff(triple(U,V,W)) = triple(U,update_slb(V,findmin_pqp_res(U)),bad)
| ~ strictly_less_than(findmin_pqp_res(U),lookup_slb(V,findmin_pqp_res(U)))
| ~ contains_slb(V,findmin_pqp_res(U))
| V = create_slb ),
inference(pre_NNF_transformation,[status(thm)],[f36]) ).
fof(f133,plain,
! [U,V] :
( ! [W] : findmin_cpq_eff(triple(U,V,W)) = triple(U,update_slb(V,findmin_pqp_res(U)),bad)
| ~ strictly_less_than(findmin_pqp_res(U),lookup_slb(V,findmin_pqp_res(U)))
| ~ contains_slb(V,findmin_pqp_res(U))
| V = create_slb ),
inference(miniscoping,[status(thm)],[f132]) ).
fof(f134,plain,
! [X0,X1,X2] :
( findmin_cpq_eff(triple(X1,X0,X2)) = triple(X1,update_slb(X0,findmin_pqp_res(X1)),bad)
| ~ strictly_less_than(findmin_pqp_res(X1),lookup_slb(X0,findmin_pqp_res(X1)))
| ~ contains_slb(X0,findmin_pqp_res(X1))
| X0 = create_slb ),
inference(cnf_transformation,[status(thm)],[f133]) ).
fof(f144,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)],[f43]) ).
fof(f145,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)],[f144]) ).
fof(f146,plain,
( ( ~ less_than(lookup_slb(sK1_skl,findmin_pqp_res(sK0_skl)),findmin_pqp_res(sK0_skl))
| ~ contains_slb(sK1_skl,findmin_pqp_res(sK0_skl))
| sK1_skl = create_slb )
& ok(findmin_cpq_eff(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)],[f145]) ).
fof(f147,plain,
ok(findmin_cpq_eff(triple(sK0_skl,sK1_skl,sK2_skl))),
inference(cnf_transformation,[status(thm)],[f146]) ).
fof(f148,plain,
( ~ less_than(lookup_slb(sK1_skl,findmin_pqp_res(sK0_skl)),findmin_pqp_res(sK0_skl))
| ~ contains_slb(sK1_skl,findmin_pqp_res(sK0_skl))
| sK1_skl = create_slb ),
inference(cnf_transformation,[status(thm)],[f146]) ).
fof(f149,definition,
( sQ0_spl
<=> sK1_skl = create_slb ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f150,plain,
( ~ sQ0_spl
| sK1_skl = create_slb ),
inference(component_clause,[status(thm)],[f149]) ).
fof(f152,definition,
( sQ1_spl
<=> contains_slb(sK1_skl,findmin_pqp_res(sK0_skl)) ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f154,plain,
( sQ1_spl
| ~ contains_slb(sK1_skl,findmin_pqp_res(sK0_skl)) ),
inference(component_clause,[status(thm)],[f152]) ).
fof(f155,definition,
( sQ2_spl
<=> less_than(lookup_slb(sK1_skl,findmin_pqp_res(sK0_skl)),findmin_pqp_res(sK0_skl)) ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f157,plain,
( sQ2_spl
| ~ less_than(lookup_slb(sK1_skl,findmin_pqp_res(sK0_skl)),findmin_pqp_res(sK0_skl)) ),
inference(component_clause,[status(thm)],[f155]) ).
fof(f158,plain,
( ~ sQ2_spl
| ~ sQ1_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f148,f149,f152,f155]) ).
fof(f178,plain,
! [X0,X1] :
( less_than(X1,X0)
| strictly_less_than(X0,X1) ),
inference(forward_subsumption_resolution,[status(thm)],[f53,f47]) ).
fof(f179,plain,
( sQ2_spl
| strictly_less_than(findmin_pqp_res(sK0_skl),lookup_slb(sK1_skl,findmin_pqp_res(sK0_skl))) ),
inference(resolution,[status(thm)],[f178,f157]) ).
fof(f229,plain,
! [X0] :
( sQ1_spl
| findmin_cpq_eff(triple(sK0_skl,sK1_skl,X0)) = triple(sK0_skl,update_slb(sK1_skl,findmin_pqp_res(sK0_skl)),bad)
| sK1_skl = create_slb ),
inference(resolution,[status(thm)],[f131,f154]) ).
fof(f232,definition,
! [X0] :
( sQ5_spl
<=> findmin_cpq_eff(triple(sK0_skl,sK1_skl,X0)) = triple(sK0_skl,update_slb(sK1_skl,findmin_pqp_res(sK0_skl)),bad) ),
introduced(definition,[new_symbols(definition,[sQ5_spl])],[split_symbol_definition]) ).
fof(f233,plain,
! [X0] :
( ~ sQ5_spl
| findmin_cpq_eff(triple(sK0_skl,sK1_skl,X0)) = triple(sK0_skl,update_slb(sK1_skl,findmin_pqp_res(sK0_skl)),bad) ),
inference(component_clause,[status(thm)],[f232]) ).
fof(f235,plain,
( sQ1_spl
| sQ5_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f229,f149,f232,f152]) ).
fof(f243,plain,
! [X0,X1,X2] :
( findmin_cpq_eff(triple(X1,X0,X2)) = triple(X1,update_slb(X0,findmin_pqp_res(X1)),bad)
| ~ strictly_less_than(findmin_pqp_res(X1),lookup_slb(X0,findmin_pqp_res(X1)))
| X0 = create_slb ),
inference(forward_subsumption_resolution,[status(thm)],[f134,f131]) ).
fof(f247,plain,
( ~ sQ0_spl
| ok(findmin_cpq_eff(triple(sK0_skl,create_slb,sK2_skl))) ),
inference(backward_demodulation,[status(thm)],[f150,f147]) ).
fof(f248,plain,
( ~ sQ0_spl
| ok(triple(sK0_skl,create_slb,bad)) ),
inference(forward_demodulation,[status(thm)],[f128,f247]) ).
fof(f249,plain,
( ~ sQ0_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f248,f114]) ).
fof(f250,plain,
~ sQ0_spl,
inference(contradiction_clause,[status(thm)],[f249]) ).
fof(f286,plain,
! [X0] :
( ~ sQ5_spl
| ~ ok(findmin_cpq_eff(triple(sK0_skl,sK1_skl,X0))) ),
inference(paramodulation,[status(thm)],[f233,f114]) ).
fof(f297,plain,
( ~ sQ5_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f147,f286]) ).
fof(f299,plain,
~ sQ5_spl,
inference(contradiction_clause,[status(thm)],[f297]) ).
fof(f310,plain,
! [X0] :
( sQ2_spl
| findmin_cpq_eff(triple(sK0_skl,sK1_skl,X0)) = triple(sK0_skl,update_slb(sK1_skl,findmin_pqp_res(sK0_skl)),bad)
| sK1_skl = create_slb ),
inference(resolution,[status(thm)],[f179,f243]) ).
fof(f314,plain,
( sQ2_spl
| sQ5_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f310,f149,f232,f155]) ).
fof(f315,plain,
$false,
inference(sat_refutation,[status(thm)],[f158,f235,f250,f299,f314]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWV374+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/0.35 % Computer : n003.cluster.edu
% 0.08/0.35 % Model : x86_64 x86_64
% 0.08/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.35 % Memory : 8046.5625MB
% 0.08/0.35 % OS : Linux 6.8.0-71-generic
% 0.08/0.35 % CPULimit : 300
% 0.08/0.35 % WCLimit : 300
% 0.08/0.35 % DateTime : Mon Sep 21 08:45:16 UTC 2026
% 0.08/0.36 % CPUTime :
% 0.08/0.37 % Drodi V4.1.1
% 0.08/0.38 % Refutation found
% 0.08/0.38 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.08/0.38 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.12/0.41 % Elapsed time: 0.048673 seconds
% 0.12/0.41 % CPU time: 0.113800 seconds
% 0.12/0.41 % Total memory used: 26.597 MB
% 0.12/0.41 % Net memory used: 26.547 MB
%------------------------------------------------------------------------------