%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SWV384+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 : 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 02:47:33 PM UTC 2026
% Result : Theorem 0.12s 0.41s
% Output : CNFRefutation 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 21
% Syntax : Number of formulae : 98 ( 8 unt; 14 def)
% Number of atoms : 313 ( 5 equ)
% Maximal formula atoms : 12 ( 3 avg)
% Number of connectives : 378 ( 163 ~; 156 |; 30 &)
% ( 17 <=>; 12 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 6 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 21 ( 18 usr; 15 prp; 0-6 aty)
% Number of functors : 17 ( 17 usr; 13 con; 0-3 aty)
% Number of variables : 252 ( 234 !; 18 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f2,axiom,
! [U,V] :
( less_than(V,U)
| less_than(U,V) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f25,axiom,
! [U,V,W,X,Y] :
( less_than(Y,X)
=> ( check_cpq(triple(U,insert_slb(V,pair(X,Y)),W))
<=> check_cpq(triple(U,V,W)) ) ),
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(f42,axiom,
( ! [U,V,W,X,Y,Z] :
( succ_cpq(triple(U,V,W),triple(X,Y,Z))
=> ( ( ~ ok(triple(X,Y,Z))
| ~ check_cpq(triple(X,Y,Z)) )
=> ( ~ ok(im_succ_cpq(triple(X,Y,Z)))
| ~ check_cpq(im_succ_cpq(triple(X,Y,Z))) ) ) )
=> ! [X1,X2,X3] :
( ( ~ ok(triple(X1,X2,X3))
| ~ check_cpq(triple(X1,X2,X3)) )
=> ! [X4,X5,X6] :
( succ_cpq(triple(X1,X2,X3),triple(X4,X5,X6))
=> ( ~ check_cpq(triple(X4,X5,X6))
| ~ ok(triple(X4,X5,X6)) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f43,lemma,
! [U,V,W] :
( ( ~ ok(triple(U,V,W))
| ~ check_cpq(triple(U,V,W)) )
=> ( ~ ok(im_succ_cpq(triple(U,V,W)))
| ~ check_cpq(im_succ_cpq(triple(U,V,W))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f44,conjecture,
! [U,V,W] :
( ( ~ ok(triple(U,V,W))
| ~ check_cpq(triple(U,V,W)) )
=> ! [X,Y,Z] :
( succ_cpq(triple(U,V,W),triple(X,Y,Z))
=> ( ~ check_cpq(triple(X,Y,Z))
| ~ ok(triple(X,Y,Z)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f45,negated_conjecture,
~ ! [U,V,W] :
( ( ~ ok(triple(U,V,W))
| ~ check_cpq(triple(U,V,W)) )
=> ! [X,Y,Z] :
( succ_cpq(triple(U,V,W),triple(X,Y,Z))
=> ( ~ check_cpq(triple(X,Y,Z))
| ~ ok(triple(X,Y,Z)) ) ) ),
inference(negated_conjecture,[status(cth)],[f44]) ).
fof(f49,plain,
! [X0,X1] :
( less_than(X1,X0)
| less_than(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f99,plain,
! [U,V,W,X,Y] :
( ( check_cpq(triple(U,insert_slb(V,pair(X,Y)),W))
<=> check_cpq(triple(U,V,W)) )
| ~ less_than(Y,X) ),
inference(pre_NNF_transformation,[status(thm)],[f25]) ).
fof(f100,plain,
! [U,V,W,X,Y] :
( ( ( ~ check_cpq(triple(U,V,W))
| check_cpq(triple(U,insert_slb(V,pair(X,Y)),W)) )
& ( check_cpq(triple(U,V,W))
| ~ check_cpq(triple(U,insert_slb(V,pair(X,Y)),W)) ) )
| ~ less_than(Y,X) ),
inference(NNF_transformation,[status(thm)],[f99]) ).
fof(f101,plain,
! [X,Y] :
( ( ! [U,V,W] :
( ~ check_cpq(triple(U,V,W))
| check_cpq(triple(U,insert_slb(V,pair(X,Y)),W)) )
& ! [U,V,W] :
( check_cpq(triple(U,V,W))
| ~ check_cpq(triple(U,insert_slb(V,pair(X,Y)),W)) ) )
| ~ less_than(Y,X) ),
inference(miniscoping,[status(thm)],[f100]) ).
fof(f102,plain,
! [X0,X1,X2,X3,X4] :
( check_cpq(triple(X2,X3,X4))
| ~ check_cpq(triple(X2,insert_slb(X3,pair(X1,X0)),X4))
| ~ less_than(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f101]) ).
fof(f103,plain,
! [X0,X1,X2,X3,X4] :
( ~ check_cpq(triple(X2,X3,X4))
| check_cpq(triple(X2,insert_slb(X3,pair(X1,X0)),X4))
| ~ less_than(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f101]) ).
fof(f113,plain,
! [U,V] :
( ( $true
| ok(triple(U,V,bad)) )
& ( $false
| ~ ok(triple(U,V,bad)) ) ),
inference(NNF_transformation,[status(thm)],[f28]) ).
fof(f114,plain,
( ( $true
| ! [U,V] : ok(triple(U,V,bad)) )
& ( $false
| ! [U,V] : ~ ok(triple(U,V,bad)) ) ),
inference(miniscoping,[status(thm)],[f113]) ).
fof(f115,plain,
! [U,V] : ~ ok(triple(U,V,bad)),
inference(true_and_false_simplification,[status(thm)],[f114]) ).
fof(f116,plain,
! [X0,X1] : ~ ok(triple(X0,X1,bad)),
inference(cnf_transformation,[status(thm)],[f115]) ).
fof(f117,plain,
! [U,V,W] :
( W = bad
| ok(triple(U,V,W)) ),
inference(pre_NNF_transformation,[status(thm)],[f29]) ).
fof(f118,plain,
! [W] :
( W = bad
| ! [U,V] : ok(triple(U,V,W)) ),
inference(miniscoping,[status(thm)],[f117]) ).
fof(f119,plain,
! [X0,X1,X2] :
( X2 = bad
| ok(triple(X0,X1,X2)) ),
inference(cnf_transformation,[status(thm)],[f118]) ).
fof(f146,plain,
( ! [X1,X2,X3] :
( ! [X4,X5,X6] :
( ~ check_cpq(triple(X4,X5,X6))
| ~ ok(triple(X4,X5,X6))
| ~ succ_cpq(triple(X1,X2,X3),triple(X4,X5,X6)) )
| ( ok(triple(X1,X2,X3))
& check_cpq(triple(X1,X2,X3)) ) )
| ? [U,V,W,X,Y,Z] :
( ok(im_succ_cpq(triple(X,Y,Z)))
& check_cpq(im_succ_cpq(triple(X,Y,Z)))
& ( ~ ok(triple(X,Y,Z))
| ~ check_cpq(triple(X,Y,Z)) )
& succ_cpq(triple(U,V,W),triple(X,Y,Z)) ) ),
inference(pre_NNF_transformation,[status(thm)],[f42]) ).
fof(f147,definition,
! [U,V,W,X,Y,Z] :
( sP0_prd(Z,Y,X,W,V,U)
<=> ( ok(im_succ_cpq(triple(X,Y,Z)))
& check_cpq(im_succ_cpq(triple(X,Y,Z)))
& ( ~ ok(triple(X,Y,Z))
| ~ check_cpq(triple(X,Y,Z)) )
& succ_cpq(triple(U,V,W),triple(X,Y,Z)) ) ),
introduced(definition,[new_symbols(definition,[sP0_prd])],[]) ).
fof(f148,plain,
( ! [X1,X2,X3] :
( ! [X4,X5,X6] :
( ~ check_cpq(triple(X4,X5,X6))
| ~ ok(triple(X4,X5,X6))
| ~ succ_cpq(triple(X1,X2,X3),triple(X4,X5,X6)) )
| ( ok(triple(X1,X2,X3))
& check_cpq(triple(X1,X2,X3)) ) )
| ? [U,V,W,X,Y,Z] : sP0_prd(Z,Y,X,W,V,U) ),
inference(formula_renaming,[status(thm)],[f146,f147]) ).
fof(f149,plain,
( ! [X1,X2,X3] :
( ! [X4,X5,X6] :
( ~ check_cpq(triple(X4,X5,X6))
| ~ ok(triple(X4,X5,X6))
| ~ succ_cpq(triple(X1,X2,X3),triple(X4,X5,X6)) )
| ( ok(triple(X1,X2,X3))
& check_cpq(triple(X1,X2,X3)) ) )
| sP0_prd(sK5_skl,sK4_skl,sK3_skl,sK2_skl,sK1_skl,sK0_skl) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl,sK1_skl,sK2_skl,sK3_skl,sK4_skl,sK5_skl]),skolemize(U,sK0_skl),skolemize(V,sK1_skl),skolemize(W,sK2_skl),skolemize(X,sK3_skl),skolemize(Y,sK4_skl),skolemize(Z,sK5_skl)],[f148]) ).
fof(f150,plain,
! [X0,X1,X2,X3,X4,X5] :
( ~ check_cpq(triple(X3,X4,X5))
| ~ ok(triple(X3,X4,X5))
| ~ succ_cpq(triple(X0,X1,X2),triple(X3,X4,X5))
| check_cpq(triple(X0,X1,X2))
| sP0_prd(sK5_skl,sK4_skl,sK3_skl,sK2_skl,sK1_skl,sK0_skl) ),
inference(cnf_transformation,[status(thm)],[f149]) ).
fof(f151,plain,
! [X0,X1,X2,X3,X4,X5] :
( ~ check_cpq(triple(X3,X4,X5))
| ~ ok(triple(X3,X4,X5))
| ~ succ_cpq(triple(X0,X1,X2),triple(X3,X4,X5))
| ok(triple(X0,X1,X2))
| sP0_prd(sK5_skl,sK4_skl,sK3_skl,sK2_skl,sK1_skl,sK0_skl) ),
inference(cnf_transformation,[status(thm)],[f149]) ).
fof(f152,plain,
! [U,V,W] :
( ~ ok(im_succ_cpq(triple(U,V,W)))
| ~ check_cpq(im_succ_cpq(triple(U,V,W)))
| ( ok(triple(U,V,W))
& check_cpq(triple(U,V,W)) ) ),
inference(pre_NNF_transformation,[status(thm)],[f43]) ).
fof(f153,plain,
! [X0,X1,X2] :
( ~ ok(im_succ_cpq(triple(X0,X1,X2)))
| ~ check_cpq(im_succ_cpq(triple(X0,X1,X2)))
| check_cpq(triple(X0,X1,X2)) ),
inference(cnf_transformation,[status(thm)],[f152]) ).
fof(f154,plain,
! [X0,X1,X2] :
( ~ ok(im_succ_cpq(triple(X0,X1,X2)))
| ~ check_cpq(im_succ_cpq(triple(X0,X1,X2)))
| ok(triple(X0,X1,X2)) ),
inference(cnf_transformation,[status(thm)],[f152]) ).
fof(f155,plain,
? [U,V,W] :
( ? [X,Y,Z] :
( check_cpq(triple(X,Y,Z))
& ok(triple(X,Y,Z))
& succ_cpq(triple(U,V,W),triple(X,Y,Z)) )
& ( ~ ok(triple(U,V,W))
| ~ check_cpq(triple(U,V,W)) ) ),
inference(pre_NNF_transformation,[status(thm)],[f45]) ).
fof(f156,plain,
( check_cpq(triple(sK9_skl,sK10_skl,sK11_skl))
& ok(triple(sK9_skl,sK10_skl,sK11_skl))
& succ_cpq(triple(sK6_skl,sK7_skl,sK8_skl),triple(sK9_skl,sK10_skl,sK11_skl))
& ( ~ ok(triple(sK6_skl,sK7_skl,sK8_skl))
| ~ check_cpq(triple(sK6_skl,sK7_skl,sK8_skl)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK6_skl,sK7_skl,sK8_skl,sK9_skl,sK10_skl,sK11_skl]),skolemize(U,sK6_skl),skolemize(V,sK7_skl),skolemize(W,sK8_skl),skolemize(X,sK9_skl),skolemize(Y,sK10_skl),skolemize(Z,sK11_skl)],[f155]) ).
fof(f157,plain,
( ~ ok(triple(sK6_skl,sK7_skl,sK8_skl))
| ~ check_cpq(triple(sK6_skl,sK7_skl,sK8_skl)) ),
inference(cnf_transformation,[status(thm)],[f156]) ).
fof(f158,plain,
succ_cpq(triple(sK6_skl,sK7_skl,sK8_skl),triple(sK9_skl,sK10_skl,sK11_skl)),
inference(cnf_transformation,[status(thm)],[f156]) ).
fof(f159,plain,
ok(triple(sK9_skl,sK10_skl,sK11_skl)),
inference(cnf_transformation,[status(thm)],[f156]) ).
fof(f160,plain,
check_cpq(triple(sK9_skl,sK10_skl,sK11_skl)),
inference(cnf_transformation,[status(thm)],[f156]) ).
fof(f161,plain,
! [U,V,W,X,Y,Z] :
( ( ~ ok(im_succ_cpq(triple(X,Y,Z)))
| ~ check_cpq(im_succ_cpq(triple(X,Y,Z)))
| ( ok(triple(X,Y,Z))
& check_cpq(triple(X,Y,Z)) )
| ~ succ_cpq(triple(U,V,W),triple(X,Y,Z))
| sP0_prd(Z,Y,X,W,V,U) )
& ( ( ok(im_succ_cpq(triple(X,Y,Z)))
& check_cpq(im_succ_cpq(triple(X,Y,Z)))
& ( ~ ok(triple(X,Y,Z))
| ~ check_cpq(triple(X,Y,Z)) )
& succ_cpq(triple(U,V,W),triple(X,Y,Z)) )
| ~ sP0_prd(Z,Y,X,W,V,U) ) ),
inference(NNF_transformation,[status(thm)],[f147]) ).
fof(f162,plain,
( ! [U,V,W,X,Y,Z] :
( ~ ok(im_succ_cpq(triple(X,Y,Z)))
| ~ check_cpq(im_succ_cpq(triple(X,Y,Z)))
| ( ok(triple(X,Y,Z))
& check_cpq(triple(X,Y,Z)) )
| ~ succ_cpq(triple(U,V,W),triple(X,Y,Z))
| sP0_prd(Z,Y,X,W,V,U) )
& ! [U,V,W,X,Y,Z] :
( ( ok(im_succ_cpq(triple(X,Y,Z)))
& check_cpq(im_succ_cpq(triple(X,Y,Z)))
& ( ~ ok(triple(X,Y,Z))
| ~ check_cpq(triple(X,Y,Z)) )
& succ_cpq(triple(U,V,W),triple(X,Y,Z)) )
| ~ sP0_prd(Z,Y,X,W,V,U) ) ),
inference(miniscoping,[status(thm)],[f161]) ).
fof(f164,plain,
! [X0,X1,X2,X3,X4,X5] :
( ~ ok(triple(X2,X1,X0))
| ~ check_cpq(triple(X2,X1,X0))
| ~ sP0_prd(X0,X1,X2,X3,X4,X5) ),
inference(cnf_transformation,[status(thm)],[f162]) ).
fof(f165,plain,
! [X0,X1,X2,X3,X4,X5] :
( check_cpq(im_succ_cpq(triple(X2,X1,X0)))
| ~ sP0_prd(X0,X1,X2,X3,X4,X5) ),
inference(cnf_transformation,[status(thm)],[f162]) ).
fof(f166,plain,
! [X0,X1,X2,X3,X4,X5] :
( ok(im_succ_cpq(triple(X2,X1,X0)))
| ~ sP0_prd(X0,X1,X2,X3,X4,X5) ),
inference(cnf_transformation,[status(thm)],[f162]) ).
fof(f169,definition,
( sQ0_spl
<=> sP0_prd(sK5_skl,sK4_skl,sK3_skl,sK2_skl,sK1_skl,sK0_skl) ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f170,plain,
( ~ sQ0_spl
| sP0_prd(sK5_skl,sK4_skl,sK3_skl,sK2_skl,sK1_skl,sK0_skl) ),
inference(component_clause,[status(thm)],[f169]) ).
fof(f172,definition,
! [X0,X1,X2,X3,X4,X5] :
( sQ1_spl
<=> ( ~ check_cpq(triple(X3,X4,X5))
| ~ ok(triple(X3,X4,X5))
| ~ succ_cpq(triple(X0,X1,X2),triple(X3,X4,X5))
| check_cpq(triple(X0,X1,X2)) ) ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f173,plain,
! [X0,X1,X2,X3,X4,X5] :
( ~ sQ1_spl
| ~ check_cpq(triple(X3,X4,X5))
| ~ ok(triple(X3,X4,X5))
| ~ succ_cpq(triple(X0,X1,X2),triple(X3,X4,X5))
| check_cpq(triple(X0,X1,X2)) ),
inference(component_clause,[status(thm)],[f172]) ).
fof(f175,plain,
( sQ1_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f150,f169,f172]) ).
fof(f176,definition,
! [X0,X1,X2,X3,X4,X5] :
( sQ2_spl
<=> ( ~ check_cpq(triple(X3,X4,X5))
| ~ ok(triple(X3,X4,X5))
| ~ succ_cpq(triple(X0,X1,X2),triple(X3,X4,X5))
| ok(triple(X0,X1,X2)) ) ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f177,plain,
! [X0,X1,X2,X3,X4,X5] :
( ~ sQ2_spl
| ~ check_cpq(triple(X3,X4,X5))
| ~ ok(triple(X3,X4,X5))
| ~ succ_cpq(triple(X0,X1,X2),triple(X3,X4,X5))
| ok(triple(X0,X1,X2)) ),
inference(component_clause,[status(thm)],[f176]) ).
fof(f179,plain,
( sQ2_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f151,f169,f176]) ).
fof(f180,definition,
( sQ3_spl
<=> check_cpq(triple(sK6_skl,sK7_skl,sK8_skl)) ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f182,plain,
( sQ3_spl
| ~ check_cpq(triple(sK6_skl,sK7_skl,sK8_skl)) ),
inference(component_clause,[status(thm)],[f180]) ).
fof(f183,definition,
( sQ4_spl
<=> ok(triple(sK6_skl,sK7_skl,sK8_skl)) ),
introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition]) ).
fof(f185,plain,
( sQ4_spl
| ~ ok(triple(sK6_skl,sK7_skl,sK8_skl)) ),
inference(component_clause,[status(thm)],[f183]) ).
fof(f186,plain,
( ~ sQ4_spl
| ~ sQ3_spl ),
inference(split_clause,[status(thm)],[f157,f180,f183]) ).
fof(f213,plain,
! [X0,X1,X2,X3,X4] :
( check_cpq(triple(X2,X3,X4))
| ~ less_than(X0,X1)
| ~ check_cpq(triple(X2,X3,X4))
| ~ less_than(X0,X1) ),
inference(resolution,[status(thm)],[f103,f102]) ).
fof(f214,definition,
! [X0,X1] :
( sQ5_spl
<=> ( ~ less_than(X0,X1)
| ~ less_than(X0,X1) ) ),
introduced(definition,[new_symbols(definition,[sQ5_spl])],[split_symbol_definition]) ).
fof(f215,plain,
! [X0,X1] :
( ~ sQ5_spl
| ~ less_than(X0,X1)
| ~ less_than(X0,X1) ),
inference(component_clause,[status(thm)],[f214]) ).
fof(f217,definition,
! [X2,X3,X4] :
( sQ6_spl
<=> ( check_cpq(triple(X2,X3,X4))
| ~ check_cpq(triple(X2,X3,X4)) ) ),
introduced(definition,[new_symbols(definition,[sQ6_spl])],[split_symbol_definition]) ).
fof(f220,plain,
( sQ6_spl
| sQ5_spl ),
inference(split_clause,[status(thm)],[f213,f214,f217]) ).
fof(f221,plain,
! [X0,X1] :
( ~ sQ5_spl
| ~ less_than(X0,X1) ),
inference(duplicate_literals_removal,[status(thm)],[f215]) ).
fof(f223,plain,
! [X0,X1] :
( ~ sQ5_spl
| less_than(X0,X1) ),
inference(backward_subsumption_resolution,[status(thm)],[f49,f221]) ).
fof(f227,plain,
( ~ sQ5_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f223,f221]) ).
fof(f228,plain,
~ sQ5_spl,
inference(contradiction_clause,[status(thm)],[f227]) ).
fof(f291,plain,
( ~ sQ0_spl
| ~ ok(triple(sK3_skl,sK4_skl,sK5_skl))
| ~ check_cpq(triple(sK3_skl,sK4_skl,sK5_skl)) ),
inference(resolution,[status(thm)],[f164,f170]) ).
fof(f292,definition,
( sQ10_spl
<=> check_cpq(triple(sK3_skl,sK4_skl,sK5_skl)) ),
introduced(definition,[new_symbols(definition,[sQ10_spl])],[split_symbol_definition]) ).
fof(f295,definition,
( sQ11_spl
<=> ok(triple(sK3_skl,sK4_skl,sK5_skl)) ),
introduced(definition,[new_symbols(definition,[sQ11_spl])],[split_symbol_definition]) ).
fof(f298,plain,
( ~ sQ0_spl
| ~ sQ11_spl
| ~ sQ10_spl ),
inference(split_clause,[status(thm)],[f291,f292,f295,f169]) ).
fof(f300,plain,
( ~ sQ0_spl
| ok(im_succ_cpq(triple(sK3_skl,sK4_skl,sK5_skl))) ),
inference(resolution,[status(thm)],[f166,f170]) ).
fof(f324,plain,
( ~ sQ0_spl
| ~ check_cpq(im_succ_cpq(triple(sK3_skl,sK4_skl,sK5_skl)))
| ok(triple(sK3_skl,sK4_skl,sK5_skl)) ),
inference(resolution,[status(thm)],[f300,f154]) ).
fof(f325,plain,
( ~ sQ0_spl
| ~ check_cpq(im_succ_cpq(triple(sK3_skl,sK4_skl,sK5_skl)))
| check_cpq(triple(sK3_skl,sK4_skl,sK5_skl)) ),
inference(resolution,[status(thm)],[f300,f153]) ).
fof(f326,definition,
( sQ12_spl
<=> check_cpq(im_succ_cpq(triple(sK3_skl,sK4_skl,sK5_skl))) ),
introduced(definition,[new_symbols(definition,[sQ12_spl])],[split_symbol_definition]) ).
fof(f328,plain,
( sQ12_spl
| ~ check_cpq(im_succ_cpq(triple(sK3_skl,sK4_skl,sK5_skl))) ),
inference(component_clause,[status(thm)],[f326]) ).
fof(f329,plain,
( ~ sQ0_spl
| ~ sQ12_spl
| sQ11_spl ),
inference(split_clause,[status(thm)],[f324,f295,f326,f169]) ).
fof(f330,plain,
( ~ sQ0_spl
| ~ sQ12_spl
| sQ10_spl ),
inference(split_clause,[status(thm)],[f325,f292,f326,f169]) ).
fof(f331,plain,
! [X0,X1,X2] :
( sQ12_spl
| ~ sP0_prd(sK5_skl,sK4_skl,sK3_skl,X0,X1,X2) ),
inference(resolution,[status(thm)],[f328,f165]) ).
fof(f358,plain,
( ~ sQ0_spl
| sQ12_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f170,f331]) ).
fof(f359,plain,
( ~ sQ0_spl
| sQ12_spl ),
inference(contradiction_clause,[status(thm)],[f358]) ).
fof(f360,plain,
! [X0,X1,X2] :
( ~ sQ1_spl
| ~ check_cpq(triple(sK9_skl,sK10_skl,sK11_skl))
| ~ succ_cpq(triple(X0,X1,X2),triple(sK9_skl,sK10_skl,sK11_skl))
| check_cpq(triple(X0,X1,X2)) ),
inference(resolution,[status(thm)],[f173,f159]) ).
fof(f363,definition,
! [X0,X1,X2] :
( sQ15_spl
<=> ( ~ succ_cpq(triple(X0,X1,X2),triple(sK9_skl,sK10_skl,sK11_skl))
| check_cpq(triple(X0,X1,X2)) ) ),
introduced(definition,[new_symbols(definition,[sQ15_spl])],[split_symbol_definition]) ).
fof(f364,plain,
! [X0,X1,X2] :
( ~ sQ15_spl
| ~ succ_cpq(triple(X0,X1,X2),triple(sK9_skl,sK10_skl,sK11_skl))
| check_cpq(triple(X0,X1,X2)) ),
inference(component_clause,[status(thm)],[f363]) ).
fof(f366,definition,
( sQ16_spl
<=> check_cpq(triple(sK9_skl,sK10_skl,sK11_skl)) ),
introduced(definition,[new_symbols(definition,[sQ16_spl])],[split_symbol_definition]) ).
fof(f368,plain,
( sQ16_spl
| ~ check_cpq(triple(sK9_skl,sK10_skl,sK11_skl)) ),
inference(component_clause,[status(thm)],[f366]) ).
fof(f369,plain,
( ~ sQ1_spl
| ~ sQ16_spl
| sQ15_spl ),
inference(split_clause,[status(thm)],[f360,f363,f366,f172]) ).
fof(f372,plain,
( sQ3_spl
| ~ sQ15_spl
| ~ succ_cpq(triple(sK6_skl,sK7_skl,sK8_skl),triple(sK9_skl,sK10_skl,sK11_skl)) ),
inference(resolution,[status(thm)],[f364,f182]) ).
fof(f375,plain,
( sQ3_spl
| ~ sQ15_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f372,f158]) ).
fof(f376,plain,
( sQ3_spl
| ~ sQ15_spl ),
inference(contradiction_clause,[status(thm)],[f375]) ).
fof(f377,plain,
( sQ16_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f368,f160]) ).
fof(f378,plain,
sQ16_spl,
inference(contradiction_clause,[status(thm)],[f377]) ).
fof(f383,plain,
( sQ4_spl
| sK8_skl = bad ),
inference(resolution,[status(thm)],[f185,f119]) ).
fof(f391,plain,
! [X0,X1] :
( sQ4_spl
| ~ ok(triple(X0,X1,sK8_skl)) ),
inference(backward_demodulation,[status(thm)],[f383,f116]) ).
fof(f408,plain,
! [X0,X1,X2] :
( ~ sQ2_spl
| ~ check_cpq(triple(sK9_skl,sK10_skl,sK11_skl))
| ~ succ_cpq(triple(X0,X1,X2),triple(sK9_skl,sK10_skl,sK11_skl))
| ok(triple(X0,X1,X2)) ),
inference(resolution,[status(thm)],[f177,f159]) ).
fof(f411,definition,
! [X0,X1,X2] :
( sQ18_spl
<=> ( ~ succ_cpq(triple(X0,X1,X2),triple(sK9_skl,sK10_skl,sK11_skl))
| ok(triple(X0,X1,X2)) ) ),
introduced(definition,[new_symbols(definition,[sQ18_spl])],[split_symbol_definition]) ).
fof(f412,plain,
! [X0,X1,X2] :
( ~ sQ18_spl
| ~ succ_cpq(triple(X0,X1,X2),triple(sK9_skl,sK10_skl,sK11_skl))
| ok(triple(X0,X1,X2)) ),
inference(component_clause,[status(thm)],[f411]) ).
fof(f414,plain,
( ~ sQ2_spl
| ~ sQ16_spl
| sQ18_spl ),
inference(split_clause,[status(thm)],[f408,f411,f366,f176]) ).
fof(f436,plain,
! [X0,X1] :
( sQ4_spl
| ~ sQ18_spl
| ~ succ_cpq(triple(X0,X1,sK8_skl),triple(sK9_skl,sK10_skl,sK11_skl)) ),
inference(resolution,[status(thm)],[f412,f391]) ).
fof(f449,plain,
( sQ4_spl
| ~ sQ18_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f158,f436]) ).
fof(f452,plain,
( sQ4_spl
| ~ sQ18_spl ),
inference(contradiction_clause,[status(thm)],[f449]) ).
fof(f453,plain,
$false,
inference(sat_refutation,[status(thm)],[f175,f179,f186,f220,f228,f298,f329,f330,f359,f369,f376,f378,f414,f452]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWV384+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.07/0.35 % Computer : n001.cluster.edu
% 0.07/0.35 % Model : x86_64 x86_64
% 0.07/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.35 % Memory : 8046.5625MB
% 0.07/0.35 % OS : Linux 6.8.0-71-generic
% 0.07/0.35 % CPULimit : 300
% 0.07/0.35 % WCLimit : 300
% 0.07/0.35 % DateTime : Mon Sep 21 08:49:58 UTC 2026
% 0.07/0.35 % CPUTime :
% 0.12/0.36 % Drodi V4.1.1
% 0.12/0.41 % Refutation found
% 0.12/0.41 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.12/0.41 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.12/0.44 % Elapsed time: 0.079213 seconds
% 0.12/0.44 % CPU time: 0.340829 seconds
% 0.12/0.44 % Total memory used: 108.997 MB
% 0.12/0.44 % Net memory used: 108.667 MB
%------------------------------------------------------------------------------