%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SWV403+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 : n011.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 02:47:35 PM UTC 2026
% Result : Theorem 0.08s 0.53s
% Output : CNFRefutation 0.08s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 18
% Syntax : Number of formulae : 103 ( 14 unt; 10 def)
% Number of atoms : 299 ( 36 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 359 ( 163 ~; 149 |; 26 &)
% ( 12 <=>; 9 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 15 ( 13 usr; 11 prp; 0-3 aty)
% Number of functors : 10 ( 10 usr; 7 con; 0-2 aty)
% Number of variables : 230 ( 218 !; 12 ?)
% 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(f5,axiom,
! [U] : less_than(bottom,U),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f11,axiom,
! [U,V,W,X,Y] :
( pair_in_list(insert_slb(U,pair(V,X)),W,Y)
<=> ( ( X = Y
& V = W )
| pair_in_list(U,W,Y) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f17,axiom,
! [U,V,W,X] :
( strictly_less_than(X,W)
=> update_slb(insert_slb(U,pair(V,X)),W) = insert_slb(update_slb(U,W),pair(V,W)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f18,axiom,
! [U,V,W,X] :
( less_than(W,X)
=> update_slb(insert_slb(U,pair(V,X)),W) = insert_slb(update_slb(U,W),pair(V,X)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f19,conjecture,
! [U] :
( ! [V,W,X] :
( ( strictly_less_than(W,X)
& pair_in_list(U,V,W) )
=> pair_in_list(update_slb(U,X),V,X) )
=> ! [Y,Z,X1,X2,X3] :
( ( strictly_less_than(Z,X1)
& pair_in_list(insert_slb(U,pair(X2,X3)),Y,Z) )
=> pair_in_list(update_slb(insert_slb(U,pair(X2,X3)),X1),Y,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f20,negated_conjecture,
~ ! [U] :
( ! [V,W,X] :
( ( strictly_less_than(W,X)
& pair_in_list(U,V,W) )
=> pair_in_list(update_slb(U,X),V,X) )
=> ! [Y,Z,X1,X2,X3] :
( ( strictly_less_than(Z,X1)
& pair_in_list(insert_slb(U,pair(X2,X3)),Y,Z) )
=> pair_in_list(update_slb(insert_slb(U,pair(X2,X3)),X1),Y,X1) ) ),
inference(negated_conjecture,[status(cth)],[f19]) ).
fof(f21,plain,
! [U,V,W] :
( less_than(U,W)
| ~ less_than(V,W)
| ~ less_than(U,V) ),
inference(pre_NNF_transformation,[status(thm)],[f1]) ).
fof(f22,plain,
! [U,W] :
( less_than(U,W)
| ! [V] :
( ~ less_than(V,W)
| ~ less_than(U,V) ) ),
inference(miniscoping,[status(thm)],[f21]) ).
fof(f23,plain,
! [X0,X1,X2] :
( less_than(X0,X2)
| ~ less_than(X1,X2)
| ~ less_than(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f22]) ).
fof(f24,plain,
! [X0,X1] :
( less_than(X1,X0)
| less_than(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f26,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(f27,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)],[f26]) ).
fof(f29,plain,
! [X0,X1] :
( ~ less_than(X1,X0)
| ~ strictly_less_than(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f27]) ).
fof(f30,plain,
! [X0,X1] :
( less_than(X1,X0)
| ~ less_than(X0,X1)
| strictly_less_than(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f27]) ).
fof(f31,plain,
! [X0] : less_than(bottom,X0),
inference(cnf_transformation,[status(thm)],[f5]) ).
fof(f41,plain,
! [U,V,W,X,Y] :
( ( ( ( X != Y
| V != W )
& ~ pair_in_list(U,W,Y) )
| pair_in_list(insert_slb(U,pair(V,X)),W,Y) )
& ( ( X = Y
& V = W )
| pair_in_list(U,W,Y)
| ~ pair_in_list(insert_slb(U,pair(V,X)),W,Y) ) ),
inference(NNF_transformation,[status(thm)],[f11]) ).
fof(f42,plain,
( ! [U,V,W,X,Y] :
( ( ( X != Y
| V != W )
& ~ pair_in_list(U,W,Y) )
| pair_in_list(insert_slb(U,pair(V,X)),W,Y) )
& ! [U,V,W,X,Y] :
( ( X = Y
& V = W )
| pair_in_list(U,W,Y)
| ~ pair_in_list(insert_slb(U,pair(V,X)),W,Y) ) ),
inference(miniscoping,[status(thm)],[f41]) ).
fof(f43,plain,
! [X0,X1,X2,X3,X4] :
( X1 = X3
| pair_in_list(X0,X3,X4)
| ~ pair_in_list(insert_slb(X0,pair(X1,X2)),X3,X4) ),
inference(cnf_transformation,[status(thm)],[f42]) ).
fof(f44,plain,
! [X0,X1,X2,X3,X4] :
( X2 = X4
| pair_in_list(X0,X3,X4)
| ~ pair_in_list(insert_slb(X0,pair(X1,X2)),X3,X4) ),
inference(cnf_transformation,[status(thm)],[f42]) ).
fof(f45,plain,
! [X0,X1,X2,X3,X4] :
( ~ pair_in_list(X0,X3,X4)
| pair_in_list(insert_slb(X0,pair(X1,X2)),X3,X4) ),
inference(cnf_transformation,[status(thm)],[f42]) ).
fof(f46,plain,
! [X0,X1,X2,X3,X4] :
( X2 != X4
| X1 != X3
| pair_in_list(insert_slb(X0,pair(X1,X2)),X3,X4) ),
inference(cnf_transformation,[status(thm)],[f42]) ).
fof(f56,plain,
! [U,V,W,X] :
( update_slb(insert_slb(U,pair(V,X)),W) = insert_slb(update_slb(U,W),pair(V,W))
| ~ strictly_less_than(X,W) ),
inference(pre_NNF_transformation,[status(thm)],[f17]) ).
fof(f57,plain,
! [W,X] :
( ! [U,V] : update_slb(insert_slb(U,pair(V,X)),W) = insert_slb(update_slb(U,W),pair(V,W))
| ~ strictly_less_than(X,W) ),
inference(miniscoping,[status(thm)],[f56]) ).
fof(f58,plain,
! [X0,X1,X2,X3] :
( update_slb(insert_slb(X2,pair(X3,X0)),X1) = insert_slb(update_slb(X2,X1),pair(X3,X1))
| ~ strictly_less_than(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f57]) ).
fof(f59,plain,
! [U,V,W,X] :
( update_slb(insert_slb(U,pair(V,X)),W) = insert_slb(update_slb(U,W),pair(V,X))
| ~ less_than(W,X) ),
inference(pre_NNF_transformation,[status(thm)],[f18]) ).
fof(f60,plain,
! [W,X] :
( ! [U,V] : update_slb(insert_slb(U,pair(V,X)),W) = insert_slb(update_slb(U,W),pair(V,X))
| ~ less_than(W,X) ),
inference(miniscoping,[status(thm)],[f59]) ).
fof(f61,plain,
! [X0,X1,X2,X3] :
( update_slb(insert_slb(X2,pair(X3,X1)),X0) = insert_slb(update_slb(X2,X0),pair(X3,X1))
| ~ less_than(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f60]) ).
fof(f62,plain,
? [U] :
( ? [Y,Z,X1,X2,X3] :
( ~ pair_in_list(update_slb(insert_slb(U,pair(X2,X3)),X1),Y,X1)
& strictly_less_than(Z,X1)
& pair_in_list(insert_slb(U,pair(X2,X3)),Y,Z) )
& ! [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(f63,plain,
? [U] :
( ? [Y,X1,X2,X3] :
( ~ pair_in_list(update_slb(insert_slb(U,pair(X2,X3)),X1),Y,X1)
& ? [Z] :
( strictly_less_than(Z,X1)
& pair_in_list(insert_slb(U,pair(X2,X3)),Y,Z) ) )
& ! [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)],[f62]) ).
fof(f64,plain,
( ~ pair_in_list(update_slb(insert_slb(sK0_skl,pair(sK3_skl,sK4_skl)),sK2_skl),sK1_skl,sK2_skl)
& strictly_less_than(sK5_skl,sK2_skl)
& pair_in_list(insert_slb(sK0_skl,pair(sK3_skl,sK4_skl)),sK1_skl,sK5_skl)
& ! [V,X] :
( pair_in_list(update_slb(sK0_skl,X),V,X)
| ! [W] :
( ~ strictly_less_than(W,X)
| ~ pair_in_list(sK0_skl,V,W) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl,sK1_skl,sK2_skl,sK3_skl,sK4_skl,sK5_skl]),skolemize(U,sK0_skl),skolemize(Y,sK1_skl),skolemize(X1,sK2_skl),skolemize(X2,sK3_skl),skolemize(X3,sK4_skl),skolemize(Z,sK5_skl)],[f63]) ).
fof(f65,plain,
! [X0,X1,X2] :
( pair_in_list(update_slb(sK0_skl,X2),X0,X2)
| ~ strictly_less_than(X1,X2)
| ~ pair_in_list(sK0_skl,X0,X1) ),
inference(cnf_transformation,[status(thm)],[f64]) ).
fof(f66,plain,
pair_in_list(insert_slb(sK0_skl,pair(sK3_skl,sK4_skl)),sK1_skl,sK5_skl),
inference(cnf_transformation,[status(thm)],[f64]) ).
fof(f67,plain,
strictly_less_than(sK5_skl,sK2_skl),
inference(cnf_transformation,[status(thm)],[f64]) ).
fof(f68,plain,
~ pair_in_list(update_slb(insert_slb(sK0_skl,pair(sK3_skl,sK4_skl)),sK2_skl),sK1_skl,sK2_skl),
inference(cnf_transformation,[status(thm)],[f64]) ).
fof(f69,plain,
! [X0,X1] :
( less_than(X1,X0)
| strictly_less_than(X0,X1) ),
inference(forward_subsumption_resolution,[status(thm)],[f30,f24]) ).
fof(f71,plain,
! [X0,X1,X2] : pair_in_list(insert_slb(X0,pair(X1,X2)),X1,X2),
inference(destructive_equality_resolution,[status(thm)],[f46]) ).
fof(f73,plain,
~ less_than(sK2_skl,sK5_skl),
inference(resolution,[status(thm)],[f29,f67]) ).
fof(f76,plain,
( sK3_skl = sK1_skl
| pair_in_list(sK0_skl,sK1_skl,sK5_skl) ),
inference(resolution,[status(thm)],[f43,f66]) ).
fof(f77,definition,
( sQ0_spl
<=> pair_in_list(sK0_skl,sK1_skl,sK5_skl) ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f78,plain,
( ~ sQ0_spl
| pair_in_list(sK0_skl,sK1_skl,sK5_skl) ),
inference(component_clause,[status(thm)],[f77]) ).
fof(f80,definition,
( sQ1_spl
<=> sK3_skl = sK1_skl ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f81,plain,
( ~ sQ1_spl
| sK3_skl = sK1_skl ),
inference(component_clause,[status(thm)],[f80]) ).
fof(f83,plain,
( sQ1_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f76,f77,f80]) ).
fof(f84,plain,
! [X0] :
( ~ less_than(X0,sK5_skl)
| ~ less_than(sK2_skl,X0) ),
inference(resolution,[status(thm)],[f23,f73]) ).
fof(f89,plain,
! [X0] :
( less_than(X0,sK2_skl)
| ~ less_than(X0,sK5_skl) ),
inference(resolution,[status(thm)],[f84,f24]) ).
fof(f92,plain,
! [X0,X1] :
( ~ less_than(X1,X0)
| ~ less_than(sK2_skl,X1)
| ~ less_than(X0,sK5_skl) ),
inference(resolution,[status(thm)],[f84,f23]) ).
fof(f96,plain,
! [X0] :
( less_than(sK5_skl,X0)
| less_than(X0,sK2_skl) ),
inference(resolution,[status(thm)],[f89,f24]) ).
fof(f99,plain,
! [X0,X1] :
( ~ less_than(X1,sK5_skl)
| ~ less_than(X0,X1)
| less_than(X0,sK2_skl) ),
inference(resolution,[status(thm)],[f89,f23]) ).
fof(f102,plain,
( less_than(sK5_skl,sK2_skl)
| less_than(sK5_skl,sK2_skl) ),
inference(resolution,[status(thm)],[f96,f89]) ).
fof(f103,definition,
( sQ2_spl
<=> less_than(sK5_skl,sK2_skl) ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f110,plain,
sQ2_spl,
inference(split_clause,[status(thm)],[f102,f103]) ).
fof(f117,plain,
! [X0,X1,X2] :
( ~ less_than(X2,X1)
| ~ less_than(sK2_skl,X2)
| ~ less_than(X1,X0)
| ~ less_than(X0,sK5_skl) ),
inference(resolution,[status(thm)],[f92,f23]) ).
fof(f119,definition,
! [X0] :
( sQ4_spl
<=> ( ~ less_than(sK2_skl,X0)
| ~ less_than(X0,sK5_skl) ) ),
introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition]) ).
fof(f123,plain,
( sK4_skl = sK5_skl
| pair_in_list(sK0_skl,sK1_skl,sK5_skl) ),
inference(resolution,[status(thm)],[f44,f66]) ).
fof(f125,definition,
( sQ5_spl
<=> sK4_skl = sK5_skl ),
introduced(definition,[new_symbols(definition,[sQ5_spl])],[split_symbol_definition]) ).
fof(f126,plain,
( ~ sQ5_spl
| sK4_skl = sK5_skl ),
inference(component_clause,[status(thm)],[f125]) ).
fof(f128,plain,
( sQ5_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f123,f77,f125]) ).
fof(f131,plain,
! [X0,X1] :
( ~ less_than(sK2_skl,X1)
| ~ less_than(X1,sK5_skl)
| ~ less_than(X0,sK5_skl)
| ~ less_than(sK2_skl,X0) ),
inference(resolution,[status(thm)],[f99,f92]) ).
fof(f133,plain,
sQ4_spl,
inference(split_clause,[status(thm)],[f131,f119]) ).
fof(f143,plain,
! [X0,X1] : update_slb(insert_slb(X0,pair(X1,sK5_skl)),sK2_skl) = insert_slb(update_slb(X0,sK2_skl),pair(X1,sK2_skl)),
inference(resolution,[status(thm)],[f58,f67]) ).
fof(f144,plain,
! [X0,X1,X2,X3] :
( less_than(X3,X2)
| update_slb(insert_slb(X0,pair(X1,X2)),X3) = insert_slb(update_slb(X0,X3),pair(X1,X3)) ),
inference(resolution,[status(thm)],[f58,f69]) ).
fof(f148,plain,
! [X0,X1,X2] :
( less_than(X2,sK2_skl)
| ~ less_than(X2,X1)
| ~ less_than(X1,X0)
| ~ less_than(X0,sK5_skl) ),
inference(resolution,[status(thm)],[f117,f24]) ).
fof(f151,plain,
! [X0,X1,X2,X3] :
( ~ less_than(X3,X2)
| ~ less_than(sK2_skl,X3)
| ~ less_than(X2,X1)
| ~ less_than(X1,X0)
| ~ less_than(X0,sK5_skl) ),
inference(resolution,[status(thm)],[f117,f23]) ).
fof(f153,definition,
! [X0,X1] :
( sQ6_spl
<=> ( ~ less_than(sK2_skl,X1)
| ~ less_than(X1,X0)
| ~ less_than(X0,sK5_skl) ) ),
introduced(definition,[new_symbols(definition,[sQ6_spl])],[split_symbol_definition]) ).
fof(f158,plain,
! [X0,X1,X2,X3] :
( ~ less_than(sK2_skl,X3)
| ~ less_than(X3,X2)
| ~ less_than(X2,sK5_skl)
| ~ less_than(sK2_skl,X1)
| ~ less_than(X1,X0)
| ~ less_than(X0,sK5_skl) ),
inference(resolution,[status(thm)],[f148,f117]) ).
fof(f161,plain,
sQ6_spl,
inference(split_clause,[status(thm)],[f158,f153]) ).
fof(f164,plain,
! [X0,X1,X2] :
( ~ less_than(X2,X1)
| ~ less_than(sK2_skl,X2)
| ~ less_than(X1,X0)
| ~ less_than(X0,bottom) ),
inference(resolution,[status(thm)],[f151,f31]) ).
fof(f167,plain,
! [X0,X1,X2,X3] :
( less_than(sK5_skl,X1)
| ~ less_than(X3,X2)
| ~ less_than(sK2_skl,X3)
| ~ less_than(X2,X0)
| ~ less_than(X0,X1) ),
inference(resolution,[status(thm)],[f151,f24]) ).
fof(f172,definition,
! [X0,X1,X2] :
( sQ7_spl
<=> ( ~ less_than(X2,X1)
| ~ less_than(sK2_skl,X2)
| ~ less_than(X1,X0)
| ~ less_than(X0,sK5_skl) ) ),
introduced(definition,[new_symbols(definition,[sQ7_spl])],[split_symbol_definition]) ).
fof(f182,plain,
! [X0,X1,X2,X3] :
( ~ less_than(X3,bottom)
| ~ less_than(X1,X3)
| ~ less_than(X2,X0)
| ~ less_than(sK2_skl,X2)
| ~ less_than(X0,X1) ),
inference(resolution,[status(thm)],[f164,f23]) ).
fof(f227,plain,
! [X0,X1,X2,X3,X4,X5] :
( update_slb(insert_slb(X4,pair(X5,X2)),X3) = insert_slb(update_slb(X4,X3),pair(X5,X2))
| update_slb(insert_slb(X0,pair(X1,X2)),X3) = insert_slb(update_slb(X0,X3),pair(X1,X3)) ),
inference(resolution,[status(thm)],[f144,f61]) ).
fof(f245,plain,
! [X0,X1,X2,X3,X4,X5] :
( ~ less_than(X5,X4)
| ~ less_than(sK2_skl,X5)
| ~ less_than(X4,X3)
| ~ less_than(X3,sK5_skl)
| ~ less_than(X2,X1)
| ~ less_than(sK2_skl,X2)
| ~ less_than(X1,X0)
| ~ less_than(X0,sK5_skl) ),
inference(resolution,[status(thm)],[f167,f151]) ).
fof(f248,definition,
! [X0,X1,X2] :
( sQ11_spl
<=> ( ~ less_than(X2,X1)
| ~ less_than(sK2_skl,X2)
| ~ less_than(X1,X0)
| ~ less_than(X0,bottom) ) ),
introduced(definition,[new_symbols(definition,[sQ11_spl])],[split_symbol_definition]) ).
fof(f254,plain,
sQ7_spl,
inference(split_clause,[status(thm)],[f245,f172]) ).
fof(f261,plain,
! [X0,X1,X2,X3] :
( less_than(X2,sK2_skl)
| ~ less_than(X3,bottom)
| ~ less_than(X1,X3)
| ~ less_than(X2,X0)
| ~ less_than(X0,X1) ),
inference(resolution,[status(thm)],[f182,f24]) ).
fof(f277,plain,
! [X0,X1,X2,X3,X4,X5] :
( ~ less_than(X5,bottom)
| ~ less_than(X4,X5)
| ~ less_than(sK2_skl,X3)
| ~ less_than(X3,X4)
| ~ less_than(X2,bottom)
| ~ less_than(X1,X2)
| ~ less_than(sK2_skl,X0)
| ~ less_than(X0,X1) ),
inference(resolution,[status(thm)],[f261,f182]) ).
fof(f282,plain,
sQ11_spl,
inference(split_clause,[status(thm)],[f277,f248]) ).
fof(f376,plain,
! [X0,X1] :
( update_slb(insert_slb(X0,pair(X1,sK4_skl)),sK2_skl) = insert_slb(update_slb(X0,sK2_skl),pair(X1,sK4_skl))
| ~ pair_in_list(insert_slb(update_slb(sK0_skl,sK2_skl),pair(sK3_skl,sK2_skl)),sK1_skl,sK2_skl) ),
inference(paramodulation,[status(thm)],[f227,f68]) ).
fof(f416,definition,
( sQ20_spl
<=> pair_in_list(insert_slb(update_slb(sK0_skl,sK2_skl),pair(sK3_skl,sK2_skl)),sK1_skl,sK2_skl) ),
introduced(definition,[new_symbols(definition,[sQ20_spl])],[split_symbol_definition]) ).
fof(f418,plain,
( sQ20_spl
| ~ pair_in_list(insert_slb(update_slb(sK0_skl,sK2_skl),pair(sK3_skl,sK2_skl)),sK1_skl,sK2_skl) ),
inference(component_clause,[status(thm)],[f416]) ).
fof(f419,definition,
! [X0,X1] :
( sQ21_spl
<=> update_slb(insert_slb(X0,pair(X1,sK4_skl)),sK2_skl) = insert_slb(update_slb(X0,sK2_skl),pair(X1,sK4_skl)) ),
introduced(definition,[new_symbols(definition,[sQ21_spl])],[split_symbol_definition]) ).
fof(f420,plain,
! [X0,X1] :
( ~ sQ21_spl
| update_slb(insert_slb(X0,pair(X1,sK4_skl)),sK2_skl) = insert_slb(update_slb(X0,sK2_skl),pair(X1,sK4_skl)) ),
inference(component_clause,[status(thm)],[f419]) ).
fof(f422,plain,
( sQ21_spl
| ~ sQ20_spl ),
inference(split_clause,[status(thm)],[f376,f416,f419]) ).
fof(f426,plain,
( sQ20_spl
| ~ pair_in_list(update_slb(sK0_skl,sK2_skl),sK1_skl,sK2_skl) ),
inference(resolution,[status(thm)],[f418,f45]) ).
fof(f427,plain,
! [X0] :
( sQ20_spl
| ~ strictly_less_than(X0,sK2_skl)
| ~ pair_in_list(sK0_skl,sK1_skl,X0) ),
inference(resolution,[status(thm)],[f426,f65]) ).
fof(f428,plain,
( ~ sQ0_spl
| sQ20_spl
| ~ strictly_less_than(sK5_skl,sK2_skl) ),
inference(resolution,[status(thm)],[f427,f78]) ).
fof(f429,plain,
( ~ sQ0_spl
| sQ20_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f428,f67]) ).
fof(f430,plain,
( ~ sQ0_spl
| sQ20_spl ),
inference(contradiction_clause,[status(thm)],[f429]) ).
fof(f431,plain,
( ~ sQ1_spl
| ~ pair_in_list(update_slb(insert_slb(sK0_skl,pair(sK1_skl,sK4_skl)),sK2_skl),sK1_skl,sK2_skl) ),
inference(backward_demodulation,[status(thm)],[f81,f68]) ).
fof(f438,plain,
! [X0,X1] :
( ~ sQ5_spl
| update_slb(insert_slb(X0,pair(X1,sK4_skl)),sK2_skl) = insert_slb(update_slb(X0,sK2_skl),pair(X1,sK2_skl)) ),
inference(backward_demodulation,[status(thm)],[f126,f143]) ).
fof(f486,plain,
( ~ sQ21_spl
| ~ pair_in_list(insert_slb(update_slb(sK0_skl,sK2_skl),pair(sK3_skl,sK4_skl)),sK1_skl,sK2_skl) ),
inference(forward_demodulation,[status(thm)],[f420,f68]) ).
fof(f497,plain,
( ~ sQ21_spl
| ~ pair_in_list(update_slb(sK0_skl,sK2_skl),sK1_skl,sK2_skl) ),
inference(resolution,[status(thm)],[f486,f45]) ).
fof(f543,plain,
! [X0] :
( ~ sQ21_spl
| ~ strictly_less_than(X0,sK2_skl)
| ~ pair_in_list(sK0_skl,sK1_skl,X0) ),
inference(resolution,[status(thm)],[f497,f65]) ).
fof(f544,plain,
( ~ sQ0_spl
| ~ sQ21_spl
| ~ strictly_less_than(sK5_skl,sK2_skl) ),
inference(resolution,[status(thm)],[f543,f78]) ).
fof(f545,plain,
( ~ sQ0_spl
| ~ sQ21_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f544,f67]) ).
fof(f546,plain,
( ~ sQ0_spl
| ~ sQ21_spl ),
inference(contradiction_clause,[status(thm)],[f545]) ).
fof(f548,plain,
( ~ sQ1_spl
| ~ sQ5_spl
| ~ pair_in_list(insert_slb(update_slb(sK0_skl,sK2_skl),pair(sK1_skl,sK2_skl)),sK1_skl,sK2_skl) ),
inference(forward_demodulation,[status(thm)],[f438,f431]) ).
fof(f549,plain,
( ~ sQ1_spl
| ~ sQ5_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f548,f71]) ).
fof(f550,plain,
( ~ sQ1_spl
| ~ sQ5_spl ),
inference(contradiction_clause,[status(thm)],[f549]) ).
fof(f551,plain,
$false,
inference(sat_refutation,[status(thm)],[f83,f110,f128,f133,f161,f254,f282,f422,f430,f546,f550]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWV403+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.36 % Computer : n011.cluster.edu
% 0.08/0.36 % Model : x86_64 x86_64
% 0.08/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.36 % Memory : 8046.5625MB
% 0.08/0.36 % OS : Linux 6.8.0-71-generic
% 0.08/0.36 % CPULimit : 300
% 0.08/0.36 % WCLimit : 300
% 0.08/0.36 % DateTime : Mon Sep 21 08:44:42 UTC 2026
% 0.08/0.36 % CPUTime :
% 0.08/0.37 % Drodi V4.1.1
% 0.08/0.53 % Refutation found
% 0.08/0.53 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.08/0.53 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 1.04/0.55 % Elapsed time: 0.177662 seconds
% 1.04/0.55 % CPU time: 1.129920 seconds
% 1.04/0.55 % Total memory used: 117.949 MB
% 1.04/0.55 % Net memory used: 115.938 MB
%------------------------------------------------------------------------------