%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SWV399+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 : n007.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 02:47:34 PM UTC 2026
% Result : Theorem 0.15s 0.45s
% Output : CNFRefutation 0.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 11
% Syntax : Number of formulae : 57 ( 5 unt; 5 def)
% Number of atoms : 142 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 142 ( 57 ~; 58 |; 16 &)
% ( 6 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 9 ( 8 usr; 6 prp; 0-3 aty)
% Number of functors : 5 ( 5 usr; 4 con; 0-2 aty)
% Number of variables : 88 ( 76 !; 12 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [U,V,W] :
( ( less_than(V,W)
& less_than(U,V) )
=> less_than(U,W) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
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(f19,lemma,
! [U,V,W,X] :
( ( less_than(X,W)
& pair_in_list(U,V,W) )
=> pair_in_list(update_slb(U,X),V,W) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f20,lemma,
! [U,V,W,X] :
( ( strictly_less_than(W,X)
& pair_in_list(U,V,W) )
=> pair_in_list(update_slb(U,X),V,X) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f21,conjecture,
! [U] :
( ? [V,W] :
( strictly_less_than(V,W)
& pair_in_list(U,V,W) )
=> ! [X] :
? [Y,Z] :
( strictly_less_than(Y,Z)
& pair_in_list(update_slb(U,X),Y,Z) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f22,negated_conjecture,
~ ! [U] :
( ? [V,W] :
( strictly_less_than(V,W)
& pair_in_list(U,V,W) )
=> ! [X] :
? [Y,Z] :
( strictly_less_than(Y,Z)
& pair_in_list(update_slb(U,X),Y,Z) ) ),
inference(negated_conjecture,[status(cth)],[f21]) ).
fof(f23,plain,
! [U,V,W] :
( less_than(U,W)
| ~ less_than(V,W)
| ~ less_than(U,V) ),
inference(pre_NNF_transformation,[status(thm)],[f1]) ).
fof(f24,plain,
! [U,W] :
( less_than(U,W)
| ! [V] :
( ~ less_than(V,W)
| ~ less_than(U,V) ) ),
inference(miniscoping,[status(thm)],[f23]) ).
fof(f25,plain,
! [X0,X1,X2] :
( less_than(X0,X2)
| ~ less_than(X1,X2)
| ~ less_than(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f24]) ).
fof(f26,plain,
! [X0,X1] :
( less_than(X1,X0)
| less_than(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f28,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(f29,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)],[f28]) ).
fof(f30,plain,
! [X0,X1] :
( less_than(X0,X1)
| ~ strictly_less_than(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f29]) ).
fof(f31,plain,
! [X0,X1] :
( ~ less_than(X1,X0)
| ~ strictly_less_than(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f29]) ).
fof(f32,plain,
! [X0,X1] :
( less_than(X1,X0)
| ~ less_than(X0,X1)
| strictly_less_than(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f29]) ).
fof(f64,plain,
! [U,V,W,X] :
( pair_in_list(update_slb(U,X),V,W)
| ~ less_than(X,W)
| ~ pair_in_list(U,V,W) ),
inference(pre_NNF_transformation,[status(thm)],[f19]) ).
fof(f65,plain,
! [X0,X1,X2,X3] :
( pair_in_list(update_slb(X0,X3),X1,X2)
| ~ less_than(X3,X2)
| ~ pair_in_list(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f64]) ).
fof(f66,plain,
! [U,V,W,X] :
( pair_in_list(update_slb(U,X),V,X)
| ~ strictly_less_than(W,X)
| ~ pair_in_list(U,V,W) ),
inference(pre_NNF_transformation,[status(thm)],[f20]) ).
fof(f67,plain,
! [U,V,X] :
( pair_in_list(update_slb(U,X),V,X)
| ! [W] :
( ~ strictly_less_than(W,X)
| ~ pair_in_list(U,V,W) ) ),
inference(miniscoping,[status(thm)],[f66]) ).
fof(f68,plain,
! [X0,X1,X2,X3] :
( pair_in_list(update_slb(X0,X3),X1,X3)
| ~ strictly_less_than(X2,X3)
| ~ pair_in_list(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f67]) ).
fof(f69,plain,
? [U] :
( ? [X] :
! [Y,Z] :
( ~ strictly_less_than(Y,Z)
| ~ pair_in_list(update_slb(U,X),Y,Z) )
& ? [V,W] :
( strictly_less_than(V,W)
& pair_in_list(U,V,W) ) ),
inference(pre_NNF_transformation,[status(thm)],[f22]) ).
fof(f70,plain,
( ! [Y,Z] :
( ~ strictly_less_than(Y,Z)
| ~ pair_in_list(update_slb(sK0_skl,sK3_skl),Y,Z) )
& strictly_less_than(sK1_skl,sK2_skl)
& pair_in_list(sK0_skl,sK1_skl,sK2_skl) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl,sK1_skl,sK2_skl,sK3_skl]),skolemize(U,sK0_skl),skolemize(V,sK1_skl),skolemize(W,sK2_skl),skolemize(X,sK3_skl)],[f69]) ).
fof(f71,plain,
pair_in_list(sK0_skl,sK1_skl,sK2_skl),
inference(cnf_transformation,[status(thm)],[f70]) ).
fof(f72,plain,
strictly_less_than(sK1_skl,sK2_skl),
inference(cnf_transformation,[status(thm)],[f70]) ).
fof(f73,plain,
! [X0,X1] :
( ~ strictly_less_than(X0,X1)
| ~ pair_in_list(update_slb(sK0_skl,sK3_skl),X0,X1) ),
inference(cnf_transformation,[status(thm)],[f70]) ).
fof(f76,plain,
less_than(sK1_skl,sK2_skl),
inference(resolution,[status(thm)],[f30,f72]) ).
fof(f78,plain,
( less_than(sK2_skl,sK1_skl)
| strictly_less_than(sK1_skl,sK2_skl) ),
inference(resolution,[status(thm)],[f32,f76]) ).
fof(f79,definition,
( sQ0_spl
<=> strictly_less_than(sK1_skl,sK2_skl) ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f82,definition,
( sQ1_spl
<=> less_than(sK2_skl,sK1_skl) ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f83,plain,
( ~ sQ1_spl
| less_than(sK2_skl,sK1_skl) ),
inference(component_clause,[status(thm)],[f82]) ).
fof(f85,plain,
( sQ1_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f78,f79,f82]) ).
fof(f86,plain,
! [X0,X1] :
( ~ strictly_less_than(X0,X1)
| ~ less_than(sK3_skl,X1)
| ~ pair_in_list(sK0_skl,X0,X1) ),
inference(resolution,[status(thm)],[f65,f73]) ).
fof(f87,plain,
( ~ strictly_less_than(sK1_skl,sK2_skl)
| ~ less_than(sK3_skl,sK2_skl) ),
inference(resolution,[status(thm)],[f86,f71]) ).
fof(f88,definition,
( sQ2_spl
<=> less_than(sK3_skl,sK2_skl) ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f90,plain,
( sQ2_spl
| ~ less_than(sK3_skl,sK2_skl) ),
inference(component_clause,[status(thm)],[f88]) ).
fof(f91,plain,
( ~ sQ0_spl
| ~ sQ2_spl ),
inference(split_clause,[status(thm)],[f87,f88,f79]) ).
fof(f93,plain,
( ~ sQ1_spl
| ~ strictly_less_than(sK1_skl,sK2_skl) ),
inference(resolution,[status(thm)],[f83,f31]) ).
fof(f101,plain,
( ~ sQ1_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f93,f72]) ).
fof(f102,plain,
~ sQ1_spl,
inference(contradiction_clause,[status(thm)],[f101]) ).
fof(f103,plain,
! [X0,X1] :
( ~ strictly_less_than(X0,sK3_skl)
| ~ strictly_less_than(X1,sK3_skl)
| ~ pair_in_list(sK0_skl,X0,X1) ),
inference(resolution,[status(thm)],[f68,f73]) ).
fof(f114,plain,
! [X0,X1] :
( less_than(X1,X0)
| strictly_less_than(X0,X1) ),
inference(backward_subsumption_resolution,[status(thm)],[f32,f26]) ).
fof(f120,plain,
( sQ2_spl
| strictly_less_than(sK2_skl,sK3_skl) ),
inference(resolution,[status(thm)],[f114,f90]) ).
fof(f125,plain,
! [X0] :
( less_than(X0,sK2_skl)
| ~ less_than(X0,sK1_skl) ),
inference(resolution,[status(thm)],[f25,f76]) ).
fof(f139,plain,
! [X0] :
( strictly_less_than(sK1_skl,X0)
| less_than(X0,sK2_skl) ),
inference(resolution,[status(thm)],[f125,f114]) ).
fof(f144,plain,
( ~ strictly_less_than(sK1_skl,sK3_skl)
| ~ strictly_less_than(sK2_skl,sK3_skl) ),
inference(resolution,[status(thm)],[f103,f71]) ).
fof(f145,definition,
( sQ5_spl
<=> strictly_less_than(sK2_skl,sK3_skl) ),
introduced(definition,[new_symbols(definition,[sQ5_spl])],[split_symbol_definition]) ).
fof(f147,plain,
( sQ5_spl
| ~ strictly_less_than(sK2_skl,sK3_skl) ),
inference(component_clause,[status(thm)],[f145]) ).
fof(f148,definition,
( sQ6_spl
<=> strictly_less_than(sK1_skl,sK3_skl) ),
introduced(definition,[new_symbols(definition,[sQ6_spl])],[split_symbol_definition]) ).
fof(f150,plain,
( sQ6_spl
| ~ strictly_less_than(sK1_skl,sK3_skl) ),
inference(component_clause,[status(thm)],[f148]) ).
fof(f151,plain,
( ~ sQ6_spl
| ~ sQ5_spl ),
inference(split_clause,[status(thm)],[f144,f145,f148]) ).
fof(f152,plain,
( sQ5_spl
| sQ2_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f147,f120]) ).
fof(f153,plain,
( sQ5_spl
| sQ2_spl ),
inference(contradiction_clause,[status(thm)],[f152]) ).
fof(f176,plain,
( sQ2_spl
| strictly_less_than(sK1_skl,sK3_skl) ),
inference(resolution,[status(thm)],[f139,f90]) ).
fof(f180,plain,
( sQ2_spl
| sQ6_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f176,f150]) ).
fof(f181,plain,
( sQ2_spl
| sQ6_spl ),
inference(contradiction_clause,[status(thm)],[f180]) ).
fof(f182,plain,
$false,
inference(sat_refutation,[status(thm)],[f85,f91,f102,f151,f153,f181]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SWV399+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.06 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.15/0.41 % Computer : n007.cluster.edu
% 0.15/0.41 % Model : x86_64 x86_64
% 0.15/0.41 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.41 % Memory : 8046.5625MB
% 0.15/0.41 % OS : Linux 6.8.0-71-generic
% 0.15/0.41 % CPULimit : 300
% 0.15/0.41 % WCLimit : 300
% 0.15/0.41 % DateTime : Mon Sep 21 08:42:50 UTC 2026
% 0.15/0.42 % CPUTime :
% 0.15/0.43 % Drodi V4.1.1
% 0.15/0.45 % Refutation found
% 0.15/0.45 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.15/0.45 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.15/0.55 % Elapsed time: 0.121822 seconds
% 0.15/0.55 % CPU time: 0.104942 seconds
% 0.15/0.55 % Total memory used: 3.258 MB
% 0.15/0.55 % Net memory used: 3.250 MB
%------------------------------------------------------------------------------