%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SWV409+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 : 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 02:47:36 PM UTC 2026
% Result : Theorem 0.18s 0.57s
% Output : CNFRefutation 0.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 14
% Syntax : Number of formulae : 73 ( 7 unt; 7 def)
% Number of atoms : 208 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 232 ( 97 ~; 97 |; 24 &)
% ( 8 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 5 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 12 ( 11 usr; 8 prp; 0-3 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-3 aty)
% Number of variables : 118 ( 108 !; 10 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [U,V,W] :
( ( less_than(V,W)
& less_than(U,V) )
=> less_than(U,W) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
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(f19,lemma,
! [U,V] :
( contains_slb(U,V)
=> ? [W] : pair_in_list(U,V,W) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f20,lemma,
! [U,V,W,X] :
( ( strictly_less_than(W,X)
& strictly_less_than(V,X)
& pair_in_list(U,V,W) )
=> pair_in_list(update_slb(U,X),V,X) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f21,lemma,
! [U,V,W,X] :
( ( less_than(X,W)
& strictly_less_than(V,X)
& pair_in_list(U,V,W) )
=> ? [Y] :
( less_than(X,Y)
& pair_in_list(update_slb(U,X),V,Y) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f22,conjecture,
! [U,V,W] :
( ( strictly_less_than(V,W)
& contains_slb(U,V) )
=> ( ? [X] :
( less_than(W,X)
& pair_in_list(update_slb(U,W),V,X) )
| pair_in_list(update_slb(U,W),V,W) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f23,negated_conjecture,
~ ! [U,V,W] :
( ( strictly_less_than(V,W)
& contains_slb(U,V) )
=> ( ? [X] :
( less_than(W,X)
& pair_in_list(update_slb(U,W),V,X) )
| pair_in_list(update_slb(U,W),V,W) ) ),
inference(negated_conjecture,[status(cth)],[f22]) ).
fof(f24,plain,
! [U,V,W] :
( less_than(U,W)
| ~ less_than(V,W)
| ~ less_than(U,V) ),
inference(pre_NNF_transformation,[status(thm)],[f1]) ).
fof(f25,plain,
! [U,W] :
( less_than(U,W)
| ! [V] :
( ~ less_than(V,W)
| ~ less_than(U,V) ) ),
inference(miniscoping,[status(thm)],[f24]) ).
fof(f26,plain,
! [X0,X1,X2] :
( less_than(X0,X2)
| ~ less_than(X1,X2)
| ~ less_than(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f25]) ).
fof(f27,plain,
! [X0,X1] :
( less_than(X1,X0)
| less_than(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f29,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(f30,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)],[f29]) ).
fof(f31,plain,
! [X0,X1] :
( less_than(X0,X1)
| ~ strictly_less_than(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f30]) ).
fof(f32,plain,
! [X0,X1] :
( ~ less_than(X1,X0)
| ~ strictly_less_than(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f30]) ).
fof(f33,plain,
! [X0,X1] :
( less_than(X1,X0)
| ~ less_than(X0,X1)
| strictly_less_than(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f30]) ).
fof(f65,plain,
! [U,V] :
( ? [W] : pair_in_list(U,V,W)
| ~ contains_slb(U,V) ),
inference(pre_NNF_transformation,[status(thm)],[f19]) ).
fof(f66,plain,
! [U,V] :
( pair_in_list(U,V,sK0_skl(V,U))
| ~ contains_slb(U,V) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl]),skolemize(W,sK0_skl(V,U))],[f65]) ).
fof(f67,plain,
! [X0,X1] :
( pair_in_list(X0,X1,sK0_skl(X1,X0))
| ~ contains_slb(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f66]) ).
fof(f68,plain,
! [U,V,W,X] :
( pair_in_list(update_slb(U,X),V,X)
| ~ strictly_less_than(W,X)
| ~ strictly_less_than(V,X)
| ~ pair_in_list(U,V,W) ),
inference(pre_NNF_transformation,[status(thm)],[f20]) ).
fof(f69,plain,
! [U,V,X] :
( pair_in_list(update_slb(U,X),V,X)
| ! [W] :
( ~ strictly_less_than(W,X)
| ~ strictly_less_than(V,X)
| ~ pair_in_list(U,V,W) ) ),
inference(miniscoping,[status(thm)],[f68]) ).
fof(f70,plain,
! [X0,X1,X2,X3] :
( pair_in_list(update_slb(X0,X3),X1,X3)
| ~ strictly_less_than(X2,X3)
| ~ strictly_less_than(X1,X3)
| ~ pair_in_list(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f69]) ).
fof(f71,plain,
! [U,V,W,X] :
( ? [Y] :
( less_than(X,Y)
& pair_in_list(update_slb(U,X),V,Y) )
| ~ less_than(X,W)
| ~ strictly_less_than(V,X)
| ~ pair_in_list(U,V,W) ),
inference(pre_NNF_transformation,[status(thm)],[f21]) ).
fof(f72,plain,
! [U,V,X] :
( ? [Y] :
( less_than(X,Y)
& pair_in_list(update_slb(U,X),V,Y) )
| ! [W] :
( ~ less_than(X,W)
| ~ strictly_less_than(V,X)
| ~ pair_in_list(U,V,W) ) ),
inference(miniscoping,[status(thm)],[f71]) ).
fof(f73,plain,
! [U,V,X] :
( ( less_than(X,sK1_skl(X,V,U))
& pair_in_list(update_slb(U,X),V,sK1_skl(X,V,U)) )
| ! [W] :
( ~ less_than(X,W)
| ~ strictly_less_than(V,X)
| ~ pair_in_list(U,V,W) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1_skl]),skolemize(Y,sK1_skl(X,V,U))],[f72]) ).
fof(f74,plain,
! [X0,X1,X2,X3] :
( pair_in_list(update_slb(X0,X3),X1,sK1_skl(X3,X1,X0))
| ~ less_than(X3,X2)
| ~ strictly_less_than(X1,X3)
| ~ pair_in_list(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f73]) ).
fof(f75,plain,
! [X0,X1,X2,X3] :
( less_than(X3,sK1_skl(X3,X1,X0))
| ~ less_than(X3,X2)
| ~ strictly_less_than(X1,X3)
| ~ pair_in_list(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f73]) ).
fof(f76,plain,
? [U,V,W] :
( ! [X] :
( ~ less_than(W,X)
| ~ pair_in_list(update_slb(U,W),V,X) )
& ~ pair_in_list(update_slb(U,W),V,W)
& strictly_less_than(V,W)
& contains_slb(U,V) ),
inference(pre_NNF_transformation,[status(thm)],[f23]) ).
fof(f77,plain,
( ! [X] :
( ~ less_than(sK4_skl,X)
| ~ pair_in_list(update_slb(sK2_skl,sK4_skl),sK3_skl,X) )
& ~ pair_in_list(update_slb(sK2_skl,sK4_skl),sK3_skl,sK4_skl)
& strictly_less_than(sK3_skl,sK4_skl)
& contains_slb(sK2_skl,sK3_skl) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2_skl,sK3_skl,sK4_skl]),skolemize(U,sK2_skl),skolemize(V,sK3_skl),skolemize(W,sK4_skl)],[f76]) ).
fof(f78,plain,
contains_slb(sK2_skl,sK3_skl),
inference(cnf_transformation,[status(thm)],[f77]) ).
fof(f79,plain,
strictly_less_than(sK3_skl,sK4_skl),
inference(cnf_transformation,[status(thm)],[f77]) ).
fof(f80,plain,
~ pair_in_list(update_slb(sK2_skl,sK4_skl),sK3_skl,sK4_skl),
inference(cnf_transformation,[status(thm)],[f77]) ).
fof(f81,plain,
! [X0] :
( ~ less_than(sK4_skl,X0)
| ~ pair_in_list(update_slb(sK2_skl,sK4_skl),sK3_skl,X0) ),
inference(cnf_transformation,[status(thm)],[f77]) ).
fof(f86,plain,
less_than(sK3_skl,sK4_skl),
inference(resolution,[status(thm)],[f31,f79]) ).
fof(f100,plain,
! [X0,X1] :
( less_than(X1,X0)
| strictly_less_than(X0,X1) ),
inference(forward_subsumption_resolution,[status(thm)],[f33,f27]) ).
fof(f103,plain,
! [X0,X1,X2] :
( less_than(X2,X0)
| ~ less_than(X2,X1)
| strictly_less_than(X0,X1) ),
inference(resolution,[status(thm)],[f100,f26]) ).
fof(f213,plain,
! [X0] :
( less_than(sK3_skl,X0)
| strictly_less_than(X0,sK4_skl) ),
inference(resolution,[status(thm)],[f103,f86]) ).
fof(f218,plain,
! [X0,X1,X2] :
( strictly_less_than(X1,X2)
| less_than(X2,X0)
| strictly_less_than(X0,X1) ),
inference(resolution,[status(thm)],[f103,f100]) ).
fof(f225,plain,
! [X0] :
( ~ strictly_less_than(X0,sK3_skl)
| strictly_less_than(X0,sK4_skl) ),
inference(resolution,[status(thm)],[f213,f32]) ).
fof(f227,definition,
( sQ9_spl
<=> strictly_less_than(sK3_skl,sK4_skl) ),
introduced(definition,[new_symbols(definition,[sQ9_spl])],[split_symbol_definition]) ).
fof(f312,plain,
! [X0] :
( ~ strictly_less_than(X0,sK4_skl)
| ~ strictly_less_than(sK3_skl,sK4_skl)
| ~ pair_in_list(sK2_skl,sK3_skl,X0) ),
inference(resolution,[status(thm)],[f70,f80]) ).
fof(f315,definition,
! [X0] :
( sQ12_spl
<=> ( ~ strictly_less_than(X0,sK4_skl)
| ~ pair_in_list(sK2_skl,sK3_skl,X0) ) ),
introduced(definition,[new_symbols(definition,[sQ12_spl])],[split_symbol_definition]) ).
fof(f316,plain,
! [X0] :
( ~ sQ12_spl
| ~ strictly_less_than(X0,sK4_skl)
| ~ pair_in_list(sK2_skl,sK3_skl,X0) ),
inference(component_clause,[status(thm)],[f315]) ).
fof(f318,plain,
( ~ sQ9_spl
| sQ12_spl ),
inference(split_clause,[status(thm)],[f312,f315,f227]) ).
fof(f361,plain,
! [X0,X1,X2] :
( ~ strictly_less_than(X0,X2)
| strictly_less_than(X1,X2)
| strictly_less_than(X0,X1) ),
inference(resolution,[status(thm)],[f218,f32]) ).
fof(f371,plain,
( ~ sQ12_spl
| ~ contains_slb(sK2_skl,sK3_skl)
| ~ strictly_less_than(sK0_skl(sK3_skl,sK2_skl),sK4_skl) ),
inference(resolution,[status(thm)],[f316,f67]) ).
fof(f372,definition,
( sQ16_spl
<=> strictly_less_than(sK0_skl(sK3_skl,sK2_skl),sK4_skl) ),
introduced(definition,[new_symbols(definition,[sQ16_spl])],[split_symbol_definition]) ).
fof(f374,plain,
( sQ16_spl
| ~ strictly_less_than(sK0_skl(sK3_skl,sK2_skl),sK4_skl) ),
inference(component_clause,[status(thm)],[f372]) ).
fof(f375,definition,
( sQ17_spl
<=> contains_slb(sK2_skl,sK3_skl) ),
introduced(definition,[new_symbols(definition,[sQ17_spl])],[split_symbol_definition]) ).
fof(f377,plain,
( sQ17_spl
| ~ contains_slb(sK2_skl,sK3_skl) ),
inference(component_clause,[status(thm)],[f375]) ).
fof(f378,plain,
( ~ sQ12_spl
| ~ sQ17_spl
| ~ sQ16_spl ),
inference(split_clause,[status(thm)],[f371,f372,f375,f315]) ).
fof(f386,plain,
! [X0] :
( strictly_less_than(X0,sK4_skl)
| strictly_less_than(sK3_skl,X0) ),
inference(resolution,[status(thm)],[f361,f79]) ).
fof(f390,plain,
( strictly_less_than(sK3_skl,sK4_skl)
| strictly_less_than(sK3_skl,sK4_skl) ),
inference(resolution,[status(thm)],[f386,f225]) ).
fof(f399,plain,
sQ9_spl,
inference(split_clause,[status(thm)],[f390,f227]) ).
fof(f411,plain,
! [X0] :
( ~ less_than(sK4_skl,sK1_skl(sK4_skl,sK3_skl,sK2_skl))
| ~ less_than(sK4_skl,X0)
| ~ strictly_less_than(sK3_skl,sK4_skl)
| ~ pair_in_list(sK2_skl,sK3_skl,X0) ),
inference(resolution,[status(thm)],[f74,f81]) ).
fof(f413,definition,
! [X0] :
( sQ18_spl
<=> ( ~ less_than(sK4_skl,X0)
| ~ pair_in_list(sK2_skl,sK3_skl,X0) ) ),
introduced(definition,[new_symbols(definition,[sQ18_spl])],[split_symbol_definition]) ).
fof(f414,plain,
! [X0] :
( ~ sQ18_spl
| ~ less_than(sK4_skl,X0)
| ~ pair_in_list(sK2_skl,sK3_skl,X0) ),
inference(component_clause,[status(thm)],[f413]) ).
fof(f416,definition,
( sQ19_spl
<=> less_than(sK4_skl,sK1_skl(sK4_skl,sK3_skl,sK2_skl)) ),
introduced(definition,[new_symbols(definition,[sQ19_spl])],[split_symbol_definition]) ).
fof(f418,plain,
( sQ19_spl
| ~ less_than(sK4_skl,sK1_skl(sK4_skl,sK3_skl,sK2_skl)) ),
inference(component_clause,[status(thm)],[f416]) ).
fof(f419,plain,
( ~ sQ19_spl
| ~ sQ9_spl
| sQ18_spl ),
inference(split_clause,[status(thm)],[f411,f413,f227,f416]) ).
fof(f430,plain,
( ~ sQ18_spl
| ~ contains_slb(sK2_skl,sK3_skl)
| ~ less_than(sK4_skl,sK0_skl(sK3_skl,sK2_skl)) ),
inference(resolution,[status(thm)],[f414,f67]) ).
fof(f431,definition,
( sQ20_spl
<=> less_than(sK4_skl,sK0_skl(sK3_skl,sK2_skl)) ),
introduced(definition,[new_symbols(definition,[sQ20_spl])],[split_symbol_definition]) ).
fof(f433,plain,
( sQ20_spl
| ~ less_than(sK4_skl,sK0_skl(sK3_skl,sK2_skl)) ),
inference(component_clause,[status(thm)],[f431]) ).
fof(f434,plain,
( ~ sQ18_spl
| ~ sQ17_spl
| ~ sQ20_spl ),
inference(split_clause,[status(thm)],[f430,f431,f375,f413]) ).
fof(f435,plain,
( sQ17_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f377,f78]) ).
fof(f436,plain,
sQ17_spl,
inference(contradiction_clause,[status(thm)],[f435]) ).
fof(f443,plain,
( sQ20_spl
| strictly_less_than(sK0_skl(sK3_skl,sK2_skl),sK4_skl) ),
inference(resolution,[status(thm)],[f433,f100]) ).
fof(f445,plain,
( sQ20_spl
| sQ16_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f443,f374]) ).
fof(f446,plain,
( sQ20_spl
| sQ16_spl ),
inference(contradiction_clause,[status(thm)],[f445]) ).
fof(f451,plain,
! [X0] :
( sQ19_spl
| ~ less_than(sK4_skl,X0)
| ~ strictly_less_than(sK3_skl,sK4_skl)
| ~ pair_in_list(sK2_skl,sK3_skl,X0) ),
inference(resolution,[status(thm)],[f418,f75]) ).
fof(f459,plain,
( sQ19_spl
| ~ sQ9_spl
| sQ18_spl ),
inference(split_clause,[status(thm)],[f451,f413,f227,f416]) ).
fof(f460,plain,
$false,
inference(sat_refutation,[status(thm)],[f318,f378,f399,f419,f434,f436,f446,f459]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SWV409+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.06 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.18/0.47 % Computer : n003.cluster.edu
% 0.18/0.47 % Model : x86_64 x86_64
% 0.18/0.47 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.47 % Memory : 8046.5625MB
% 0.18/0.47 % OS : Linux 6.8.0-71-generic
% 0.18/0.47 % CPULimit : 300
% 0.18/0.47 % WCLimit : 300
% 0.18/0.47 % DateTime : Mon Sep 21 08:46:45 UTC 2026
% 0.18/0.48 % CPUTime :
% 0.18/0.51 % Drodi V4.1.1
% 0.18/0.57 % Refutation found
% 0.18/0.57 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.18/0.57 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.22/0.61 % Elapsed time: 0.120858 seconds
% 0.22/0.61 % CPU time: 0.389000 seconds
% 0.22/0.61 % Total memory used: 64.349 MB
% 0.22/0.61 % Net memory used: 63.952 MB
%------------------------------------------------------------------------------