%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SWV376+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 : n015.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 0.07s 0.37s
% Output : CNFRefutation 0.07s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 8
% Syntax : Number of formulae : 46 ( 9 unt; 3 def)
% Number of atoms : 117 ( 7 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 125 ( 54 ~; 44 |; 12 &)
% ( 4 <=>; 11 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 8 ( 5 usr; 5 prp; 0-2 aty)
% Number of functors : 15 ( 15 usr; 13 con; 0-3 aty)
% Number of variables : 127 ( 109 !; 18 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f28,axiom,
! [U,V] :
( ok(triple(U,V,bad))
<=> $false ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f29,axiom,
! [U,V,W] :
( ~ ok(triple(U,V,W))
=> W = bad ),
file('/export/starexec/sandbox2/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))
=> ~ ok(im_succ_cpq(triple(X,Y,Z))) ) )
=> ! [X1,X2,X3] :
( ~ ok(triple(X1,X2,X3))
=> ! [X4,X5,X6] :
( succ_cpq(triple(X1,X2,X3),triple(X4,X5,X6))
=> ~ ok(triple(X4,X5,X6)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f43,lemma,
! [U,V,W] :
( ~ ok(triple(U,V,W))
=> ~ ok(im_succ_cpq(triple(U,V,W))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f44,conjecture,
! [U,V,W] :
( ~ ok(triple(U,V,W))
=> ! [X,Y,Z] :
( succ_cpq(triple(U,V,W),triple(X,Y,Z))
=> ~ ok(triple(X,Y,Z)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f45,negated_conjecture,
~ ! [U,V,W] :
( ~ ok(triple(U,V,W))
=> ! [X,Y,Z] :
( succ_cpq(triple(U,V,W),triple(X,Y,Z))
=> ~ ok(triple(X,Y,Z)) ) ),
inference(negated_conjecture,[status(cth)],[f44]) ).
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] :
( ~ ok(triple(X4,X5,X6))
| ~ succ_cpq(triple(X1,X2,X3),triple(X4,X5,X6)) )
| ok(triple(X1,X2,X3)) )
| ? [U,V,W,X,Y,Z] :
( ok(im_succ_cpq(triple(X,Y,Z)))
& ~ ok(triple(X,Y,Z))
& succ_cpq(triple(U,V,W),triple(X,Y,Z)) ) ),
inference(pre_NNF_transformation,[status(thm)],[f42]) ).
fof(f147,plain,
( ! [X1,X2,X3] :
( ! [X4,X5,X6] :
( ~ ok(triple(X4,X5,X6))
| ~ succ_cpq(triple(X1,X2,X3),triple(X4,X5,X6)) )
| ok(triple(X1,X2,X3)) )
| ? [X,Y,Z] :
( ok(im_succ_cpq(triple(X,Y,Z)))
& ~ ok(triple(X,Y,Z))
& ? [U,V,W] : succ_cpq(triple(U,V,W),triple(X,Y,Z)) ) ),
inference(miniscoping,[status(thm)],[f146]) ).
fof(f148,plain,
( ! [X1,X2,X3] :
( ! [X4,X5,X6] :
( ~ ok(triple(X4,X5,X6))
| ~ succ_cpq(triple(X1,X2,X3),triple(X4,X5,X6)) )
| ok(triple(X1,X2,X3)) )
| ( ok(im_succ_cpq(triple(sK0_skl,sK1_skl,sK2_skl)))
& ~ ok(triple(sK0_skl,sK1_skl,sK2_skl))
& succ_cpq(triple(sK3_skl,sK4_skl,sK5_skl),triple(sK0_skl,sK1_skl,sK2_skl)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl,sK1_skl,sK2_skl,sK3_skl,sK4_skl,sK5_skl]),skolemize(X,sK0_skl),skolemize(Y,sK1_skl),skolemize(Z,sK2_skl),skolemize(U,sK3_skl),skolemize(V,sK4_skl),skolemize(W,sK5_skl)],[f147]) ).
fof(f150,plain,
! [X0,X1,X2,X3,X4,X5] :
( ~ ok(triple(X3,X4,X5))
| ~ succ_cpq(triple(X0,X1,X2),triple(X3,X4,X5))
| ok(triple(X0,X1,X2))
| ~ ok(triple(sK0_skl,sK1_skl,sK2_skl)) ),
inference(cnf_transformation,[status(thm)],[f148]) ).
fof(f151,plain,
! [X0,X1,X2,X3,X4,X5] :
( ~ ok(triple(X3,X4,X5))
| ~ succ_cpq(triple(X0,X1,X2),triple(X3,X4,X5))
| ok(triple(X0,X1,X2))
| ok(im_succ_cpq(triple(sK0_skl,sK1_skl,sK2_skl))) ),
inference(cnf_transformation,[status(thm)],[f148]) ).
fof(f152,plain,
! [U,V,W] :
( ~ ok(im_succ_cpq(triple(U,V,W)))
| ok(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)))
| ok(triple(X0,X1,X2)) ),
inference(cnf_transformation,[status(thm)],[f152]) ).
fof(f154,plain,
? [U,V,W] :
( ? [X,Y,Z] :
( ok(triple(X,Y,Z))
& succ_cpq(triple(U,V,W),triple(X,Y,Z)) )
& ~ ok(triple(U,V,W)) ),
inference(pre_NNF_transformation,[status(thm)],[f45]) ).
fof(f155,plain,
( 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)) ),
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)],[f154]) ).
fof(f156,plain,
~ ok(triple(sK6_skl,sK7_skl,sK8_skl)),
inference(cnf_transformation,[status(thm)],[f155]) ).
fof(f157,plain,
succ_cpq(triple(sK6_skl,sK7_skl,sK8_skl),triple(sK9_skl,sK10_skl,sK11_skl)),
inference(cnf_transformation,[status(thm)],[f155]) ).
fof(f158,plain,
ok(triple(sK9_skl,sK10_skl,sK11_skl)),
inference(cnf_transformation,[status(thm)],[f155]) ).
fof(f162,definition,
! [X0,X1,X2,X3,X4,X5] :
( sQ1_spl
<=> ( ~ 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,[sQ1_spl])],[split_symbol_definition]) ).
fof(f163,plain,
! [X0,X1,X2,X3,X4,X5] :
( ~ sQ1_spl
| ~ 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)],[f162]) ).
fof(f166,definition,
( sQ2_spl
<=> ok(triple(sK0_skl,sK1_skl,sK2_skl)) ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f168,plain,
( sQ2_spl
| ~ ok(triple(sK0_skl,sK1_skl,sK2_skl)) ),
inference(component_clause,[status(thm)],[f166]) ).
fof(f169,plain,
( sQ1_spl
| ~ sQ2_spl ),
inference(split_clause,[status(thm)],[f150,f166,f162]) ).
fof(f170,definition,
( sQ3_spl
<=> ok(im_succ_cpq(triple(sK0_skl,sK1_skl,sK2_skl))) ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f171,plain,
( ~ sQ3_spl
| ok(im_succ_cpq(triple(sK0_skl,sK1_skl,sK2_skl))) ),
inference(component_clause,[status(thm)],[f170]) ).
fof(f173,plain,
( sQ1_spl
| sQ3_spl ),
inference(split_clause,[status(thm)],[f151,f170,f162]) ).
fof(f179,plain,
! [X0,X1,X2] :
( ~ sQ1_spl
| ~ succ_cpq(triple(X0,X1,X2),triple(sK9_skl,sK10_skl,sK11_skl))
| ok(triple(X0,X1,X2)) ),
inference(resolution,[status(thm)],[f163,f158]) ).
fof(f180,plain,
( ~ sQ1_spl
| ~ succ_cpq(triple(sK6_skl,sK7_skl,sK8_skl),triple(sK9_skl,sK10_skl,sK11_skl)) ),
inference(resolution,[status(thm)],[f179,f156]) ).
fof(f182,plain,
( ~ sQ1_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f180,f157]) ).
fof(f183,plain,
~ sQ1_spl,
inference(contradiction_clause,[status(thm)],[f182]) ).
fof(f196,plain,
sK8_skl = bad,
inference(resolution,[status(thm)],[f119,f156]) ).
fof(f198,plain,
! [X0,X1,X2] :
( X2 = sK8_skl
| ok(triple(X0,X1,X2)) ),
inference(backward_demodulation,[status(thm)],[f196,f119]) ).
fof(f199,plain,
! [X0,X1] : ~ ok(triple(X0,X1,sK8_skl)),
inference(backward_demodulation,[status(thm)],[f196,f116]) ).
fof(f202,plain,
( sQ2_spl
| sK2_skl = sK8_skl ),
inference(resolution,[status(thm)],[f168,f198]) ).
fof(f203,plain,
! [X0,X1] :
( sQ2_spl
| ~ ok(triple(X0,X1,sK2_skl)) ),
inference(backward_demodulation,[status(thm)],[f202,f199]) ).
fof(f279,plain,
( ~ sQ3_spl
| ok(triple(sK0_skl,sK1_skl,sK2_skl)) ),
inference(resolution,[status(thm)],[f153,f171]) ).
fof(f281,plain,
( ~ sQ3_spl
| sQ2_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f279,f203]) ).
fof(f282,plain,
( ~ sQ3_spl
| sQ2_spl ),
inference(contradiction_clause,[status(thm)],[f281]) ).
fof(f283,plain,
$false,
inference(sat_refutation,[status(thm)],[f169,f173,f183,f282]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SWV376+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.03 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.07/0.34 % Computer : n015.cluster.edu
% 0.07/0.34 % Model : x86_64 x86_64
% 0.07/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.34 % Memory : 8046.5625MB
% 0.07/0.34 % OS : Linux 6.8.0-71-generic
% 0.07/0.34 % CPULimit : 300
% 0.07/0.34 % WCLimit : 300
% 0.07/0.34 % DateTime : Mon Sep 21 08:46:51 UTC 2026
% 0.07/0.34 % CPUTime :
% 0.07/0.35 % Drodi V4.1.1
% 0.07/0.37 % Refutation found
% 0.07/0.37 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.07/0.37 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.12/0.40 % Elapsed time: 0.057851 seconds
% 0.12/0.40 % CPU time: 0.134911 seconds
% 0.12/0.40 % Total memory used: 27.545 MB
% 0.12/0.40 % Net memory used: 27.427 MB
%------------------------------------------------------------------------------