%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SWV379+1 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n020.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 02:47:32 PM UTC 2026
% Result : Theorem 0.12s 0.39s
% Output : CNFRefutation 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 11
% Syntax : Number of formulae : 58 ( 11 unt; 2 def)
% Number of atoms : 149 ( 53 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 141 ( 50 ~; 67 |; 14 &)
% ( 4 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 5 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 9 ( 6 usr; 4 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 5 con; 0-3 aty)
% Number of variables : 120 ( 117 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f2,axiom,
! [U,V] :
( less_than(V,U)
| less_than(U,V) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f4,axiom,
! [U,V] :
( strictly_less_than(U,V)
<=> ( ~ less_than(V,U)
& less_than(U,V) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f28,axiom,
! [U,V] :
( ok(triple(U,V,bad))
<=> $false ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f29,axiom,
! [U,V,W] :
( ~ ok(triple(U,V,W))
=> W = bad ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f34,axiom,
! [U,V] : findmin_cpq_eff(triple(U,create_slb,V)) = triple(U,create_slb,bad),
file('/export/starexec/sandbox/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/sandbox/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/sandbox/benchmark/theBenchmark.p') ).
fof(f37,axiom,
! [U,V,W,X] :
( ( less_than(lookup_slb(V,findmin_pqp_res(U)),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)),W) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f42,conjecture,
! [U,V,W] :
( ~ ok(triple(U,V,W))
=> ~ ok(findmin_cpq_eff(triple(U,V,W))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f43,negated_conjecture,
~ ! [U,V,W] :
( ~ ok(triple(U,V,W))
=> ~ ok(findmin_cpq_eff(triple(U,V,W))) ),
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(f115,plain,
! [U,V,W] :
( W = bad
| ok(triple(U,V,W)) ),
inference(pre_NNF_transformation,[status(thm)],[f29]) ).
fof(f116,plain,
! [W] :
( W = bad
| ! [U,V] : ok(triple(U,V,W)) ),
inference(miniscoping,[status(thm)],[f115]) ).
fof(f117,plain,
! [X0,X1,X2] :
( X2 = bad
| ok(triple(X0,X1,X2)) ),
inference(cnf_transformation,[status(thm)],[f116]) ).
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(f135,plain,
! [U,V,W,X] :
( findmin_cpq_eff(triple(U,V,W)) = triple(U,update_slb(V,findmin_pqp_res(U)),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(pre_NNF_transformation,[status(thm)],[f37]) ).
fof(f136,plain,
! [U,V] :
( ! [W] : findmin_cpq_eff(triple(U,V,W)) = triple(U,update_slb(V,findmin_pqp_res(U)),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(miniscoping,[status(thm)],[f135]) ).
fof(f137,plain,
! [X0,X1,X2] :
( findmin_cpq_eff(triple(X1,X0,X2)) = triple(X1,update_slb(X0,findmin_pqp_res(X1)),X2)
| ~ less_than(lookup_slb(X0,findmin_pqp_res(X1)),findmin_pqp_res(X1))
| ~ contains_slb(X0,findmin_pqp_res(X1))
| X0 = create_slb ),
inference(cnf_transformation,[status(thm)],[f136]) ).
fof(f144,plain,
? [U,V,W] :
( ok(findmin_cpq_eff(triple(U,V,W)))
& ~ ok(triple(U,V,W)) ),
inference(pre_NNF_transformation,[status(thm)],[f43]) ).
fof(f145,plain,
( ok(findmin_cpq_eff(triple(sK0_skl,sK1_skl,sK2_skl)))
& ~ ok(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)],[f144]) ).
fof(f146,plain,
~ ok(triple(sK0_skl,sK1_skl,sK2_skl)),
inference(cnf_transformation,[status(thm)],[f145]) ).
fof(f147,plain,
ok(findmin_cpq_eff(triple(sK0_skl,sK1_skl,sK2_skl))),
inference(cnf_transformation,[status(thm)],[f145]) ).
fof(f150,plain,
sK2_skl = bad,
inference(resolution,[status(thm)],[f117,f146]) ).
fof(f152,plain,
ok(findmin_cpq_eff(triple(sK0_skl,sK1_skl,bad))),
inference(backward_demodulation,[status(thm)],[f150,f147]) ).
fof(f155,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(f173,plain,
! [X0,X1] :
( less_than(X1,X0)
| strictly_less_than(X0,X1) ),
inference(forward_subsumption_resolution,[status(thm)],[f53,f47]) ).
fof(f174,plain,
! [X0,X1,X2] :
( findmin_cpq_eff(triple(X0,X1,X2)) = triple(X0,update_slb(X1,findmin_pqp_res(X0)),X2)
| ~ contains_slb(X1,findmin_pqp_res(X0))
| X1 = create_slb
| strictly_less_than(findmin_pqp_res(X0),lookup_slb(X1,findmin_pqp_res(X0))) ),
inference(resolution,[status(thm)],[f173,f137]) ).
fof(f183,plain,
! [X0,X1,X2,X3] :
( findmin_cpq_eff(triple(X0,X1,X3)) = triple(X0,update_slb(X1,findmin_pqp_res(X0)),bad)
| X1 = create_slb
| findmin_cpq_eff(triple(X0,X1,X2)) = triple(X0,update_slb(X1,findmin_pqp_res(X0)),X2)
| X1 = create_slb
| strictly_less_than(findmin_pqp_res(X0),lookup_slb(X1,findmin_pqp_res(X0))) ),
inference(resolution,[status(thm)],[f174,f131]) ).
fof(f184,plain,
! [X0,X1,X2,X3] :
( findmin_cpq_eff(triple(X0,X1,X3)) = triple(X0,update_slb(X1,findmin_pqp_res(X0)),bad)
| findmin_cpq_eff(triple(X0,X1,X2)) = triple(X0,update_slb(X1,findmin_pqp_res(X0)),X2)
| X1 = create_slb
| strictly_less_than(findmin_pqp_res(X0),lookup_slb(X1,findmin_pqp_res(X0))) ),
inference(duplicate_literals_removal,[status(thm)],[f183]) ).
fof(f185,plain,
! [X0,X1,X2,X3] :
( findmin_cpq_eff(triple(X1,X0,X3)) = triple(X1,update_slb(X0,findmin_pqp_res(X1)),bad)
| findmin_cpq_eff(triple(X1,X0,X2)) = triple(X1,update_slb(X0,findmin_pqp_res(X1)),X2)
| X0 = create_slb ),
inference(forward_subsumption_resolution,[status(thm)],[f184,f155]) ).
fof(f192,plain,
! [X0,X1,X2,X3] :
( findmin_cpq_eff(triple(X0,X1,X3)) = triple(X0,update_slb(X1,findmin_pqp_res(X0)),X3)
| X1 = create_slb
| ~ ok(findmin_cpq_eff(triple(X0,X1,X2))) ),
inference(paramodulation,[status(thm)],[f185,f114]) ).
fof(f218,plain,
! [X0] :
( findmin_cpq_eff(triple(sK0_skl,sK1_skl,X0)) = triple(sK0_skl,update_slb(sK1_skl,findmin_pqp_res(sK0_skl)),X0)
| sK1_skl = create_slb ),
inference(resolution,[status(thm)],[f192,f152]) ).
fof(f222,definition,
( sQ6_spl
<=> sK1_skl = create_slb ),
introduced(definition,[new_symbols(definition,[sQ6_spl])],[split_symbol_definition]) ).
fof(f223,plain,
( ~ sQ6_spl
| sK1_skl = create_slb ),
inference(component_clause,[status(thm)],[f222]) ).
fof(f225,definition,
! [X0] :
( sQ7_spl
<=> findmin_cpq_eff(triple(sK0_skl,sK1_skl,X0)) = triple(sK0_skl,update_slb(sK1_skl,findmin_pqp_res(sK0_skl)),X0) ),
introduced(definition,[new_symbols(definition,[sQ7_spl])],[split_symbol_definition]) ).
fof(f226,plain,
! [X0] :
( ~ sQ7_spl
| findmin_cpq_eff(triple(sK0_skl,sK1_skl,X0)) = triple(sK0_skl,update_slb(sK1_skl,findmin_pqp_res(sK0_skl)),X0) ),
inference(component_clause,[status(thm)],[f225]) ).
fof(f228,plain,
( sQ7_spl
| sQ6_spl ),
inference(split_clause,[status(thm)],[f218,f222,f225]) ).
fof(f234,plain,
( ~ sQ6_spl
| ok(findmin_cpq_eff(triple(sK0_skl,create_slb,bad))) ),
inference(backward_demodulation,[status(thm)],[f223,f152]) ).
fof(f235,plain,
( ~ sQ6_spl
| ok(triple(sK0_skl,create_slb,bad)) ),
inference(forward_demodulation,[status(thm)],[f128,f234]) ).
fof(f236,plain,
( ~ sQ6_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f235,f114]) ).
fof(f237,plain,
~ sQ6_spl,
inference(contradiction_clause,[status(thm)],[f236]) ).
fof(f242,plain,
( ~ sQ7_spl
| ~ ok(findmin_cpq_eff(triple(sK0_skl,sK1_skl,bad))) ),
inference(paramodulation,[status(thm)],[f226,f114]) ).
fof(f251,plain,
( ~ sQ7_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f242,f152]) ).
fof(f252,plain,
~ sQ7_spl,
inference(contradiction_clause,[status(thm)],[f251]) ).
fof(f253,plain,
$false,
inference(sat_refutation,[status(thm)],[f228,f237,f252]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWV379+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.35 % Computer : n020.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 08:44:47 UTC 2026
% 0.09/0.35 % CPUTime :
% 0.12/0.36 % Drodi V4.1.1
% 0.12/0.39 % Refutation found
% 0.12/0.39 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.12/0.39 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.12/0.41 % Elapsed time: 0.057125 seconds
% 0.12/0.41 % CPU time: 0.164635 seconds
% 0.12/0.41 % Total memory used: 103.844 MB
% 0.12/0.41 % Net memory used: 103.756 MB
%------------------------------------------------------------------------------