%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SWV401+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 02:47:35 PM UTC 2026
% Result : Theorem 0.18s 0.47s
% Output : CNFRefutation 0.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 12
% Syntax : Number of formulae : 72 ( 6 unt; 6 def)
% Number of atoms : 193 ( 37 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 198 ( 77 ~; 83 |; 22 &)
% ( 8 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 11 ( 9 usr; 7 prp; 0-3 aty)
% Number of functors : 9 ( 9 usr; 6 con; 0-2 aty)
% Number of variables : 143 ( 137 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
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(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] :
( ( less_than(X,W)
& pair_in_list(U,V,W) )
=> pair_in_list(update_slb(U,X),V,W) )
=> ! [Y,Z,X1,X2,X3] :
( ( less_than(X1,Z)
& pair_in_list(insert_slb(U,pair(X2,X3)),Y,Z) )
=> pair_in_list(update_slb(insert_slb(U,pair(X2,X3)),X1),Y,Z) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f20,negated_conjecture,
~ ! [U] :
( ! [V,W,X] :
( ( less_than(X,W)
& pair_in_list(U,V,W) )
=> pair_in_list(update_slb(U,X),V,W) )
=> ! [Y,Z,X1,X2,X3] :
( ( less_than(X1,Z)
& pair_in_list(insert_slb(U,pair(X2,X3)),Y,Z) )
=> pair_in_list(update_slb(insert_slb(U,pair(X2,X3)),X1),Y,Z) ) ),
inference(negated_conjecture,[status(cth)],[f19]) ).
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(f30,plain,
! [X0,X1] :
( less_than(X1,X0)
| ~ less_than(X0,X1)
| strictly_less_than(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f27]) ).
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,Z)
& less_than(X1,Z)
& pair_in_list(insert_slb(U,pair(X2,X3)),Y,Z) )
& ! [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)],[f20]) ).
fof(f63,plain,
( ~ pair_in_list(update_slb(insert_slb(sK0_skl,pair(sK4_skl,sK5_skl)),sK3_skl),sK1_skl,sK2_skl)
& less_than(sK3_skl,sK2_skl)
& pair_in_list(insert_slb(sK0_skl,pair(sK4_skl,sK5_skl)),sK1_skl,sK2_skl)
& ! [V,W,X] :
( pair_in_list(update_slb(sK0_skl,X),V,W)
| ~ less_than(X,W)
| ~ 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(Z,sK2_skl),skolemize(X1,sK3_skl),skolemize(X2,sK4_skl),skolemize(X3,sK5_skl)],[f62]) ).
fof(f64,plain,
! [X0,X1,X2] :
( pair_in_list(update_slb(sK0_skl,X2),X0,X1)
| ~ less_than(X2,X1)
| ~ pair_in_list(sK0_skl,X0,X1) ),
inference(cnf_transformation,[status(thm)],[f63]) ).
fof(f65,plain,
pair_in_list(insert_slb(sK0_skl,pair(sK4_skl,sK5_skl)),sK1_skl,sK2_skl),
inference(cnf_transformation,[status(thm)],[f63]) ).
fof(f66,plain,
less_than(sK3_skl,sK2_skl),
inference(cnf_transformation,[status(thm)],[f63]) ).
fof(f67,plain,
~ pair_in_list(update_slb(insert_slb(sK0_skl,pair(sK4_skl,sK5_skl)),sK3_skl),sK1_skl,sK2_skl),
inference(cnf_transformation,[status(thm)],[f63]) ).
fof(f69,plain,
! [X0,X1,X2] : pair_in_list(insert_slb(X0,pair(X1,X2)),X1,X2),
inference(destructive_equality_resolution,[status(thm)],[f46]) ).
fof(f70,plain,
! [X0,X1] :
( less_than(X1,X0)
| strictly_less_than(X0,X1) ),
inference(forward_subsumption_resolution,[status(thm)],[f30,f24]) ).
fof(f71,plain,
( sK4_skl = sK1_skl
| pair_in_list(sK0_skl,sK1_skl,sK2_skl) ),
inference(resolution,[status(thm)],[f65,f43]) ).
fof(f72,definition,
( sQ0_spl
<=> pair_in_list(sK0_skl,sK1_skl,sK2_skl) ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f73,plain,
( ~ sQ0_spl
| pair_in_list(sK0_skl,sK1_skl,sK2_skl) ),
inference(component_clause,[status(thm)],[f72]) ).
fof(f75,definition,
( sQ1_spl
<=> sK4_skl = sK1_skl ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f76,plain,
( ~ sQ1_spl
| sK4_skl = sK1_skl ),
inference(component_clause,[status(thm)],[f75]) ).
fof(f78,plain,
( sQ1_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f71,f72,f75]) ).
fof(f79,plain,
! [X0] :
( ~ sQ0_spl
| pair_in_list(update_slb(sK0_skl,X0),sK1_skl,sK2_skl)
| ~ less_than(X0,sK2_skl) ),
inference(resolution,[status(thm)],[f73,f64]) ).
fof(f81,plain,
( sK5_skl = sK2_skl
| pair_in_list(sK0_skl,sK1_skl,sK2_skl) ),
inference(resolution,[status(thm)],[f44,f65]) ).
fof(f83,definition,
( sQ2_spl
<=> sK5_skl = sK2_skl ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f84,plain,
( ~ sQ2_spl
| sK5_skl = sK2_skl ),
inference(component_clause,[status(thm)],[f83]) ).
fof(f86,plain,
( sQ2_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f81,f72,f83]) ).
fof(f92,plain,
! [X0,X1] : update_slb(insert_slb(X0,pair(X1,sK2_skl)),sK3_skl) = insert_slb(update_slb(X0,sK3_skl),pair(X1,sK2_skl)),
inference(resolution,[status(thm)],[f61,f66]) ).
fof(f93,plain,
! [X0,X1,X2,X3] :
( strictly_less_than(X2,X3)
| update_slb(insert_slb(X0,pair(X1,X2)),X3) = insert_slb(update_slb(X0,X3),pair(X1,X2)) ),
inference(resolution,[status(thm)],[f61,f70]) ).
fof(f109,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)],[f58,f93]) ).
fof(f127,plain,
! [X0,X1] :
( update_slb(insert_slb(X0,pair(X1,sK5_skl)),sK3_skl) = insert_slb(update_slb(X0,sK3_skl),pair(X1,sK3_skl))
| ~ pair_in_list(insert_slb(update_slb(sK0_skl,sK3_skl),pair(sK4_skl,sK5_skl)),sK1_skl,sK2_skl) ),
inference(paramodulation,[status(thm)],[f109,f67]) ).
fof(f139,definition,
( sQ5_spl
<=> pair_in_list(insert_slb(update_slb(sK0_skl,sK3_skl),pair(sK4_skl,sK5_skl)),sK1_skl,sK2_skl) ),
introduced(definition,[new_symbols(definition,[sQ5_spl])],[split_symbol_definition]) ).
fof(f140,plain,
( ~ sQ5_spl
| pair_in_list(insert_slb(update_slb(sK0_skl,sK3_skl),pair(sK4_skl,sK5_skl)),sK1_skl,sK2_skl) ),
inference(component_clause,[status(thm)],[f139]) ).
fof(f141,plain,
( sQ5_spl
| ~ pair_in_list(insert_slb(update_slb(sK0_skl,sK3_skl),pair(sK4_skl,sK5_skl)),sK1_skl,sK2_skl) ),
inference(component_clause,[status(thm)],[f139]) ).
fof(f142,definition,
! [X0,X1] :
( sQ6_spl
<=> update_slb(insert_slb(X0,pair(X1,sK5_skl)),sK3_skl) = insert_slb(update_slb(X0,sK3_skl),pair(X1,sK3_skl)) ),
introduced(definition,[new_symbols(definition,[sQ6_spl])],[split_symbol_definition]) ).
fof(f143,plain,
! [X0,X1] :
( ~ sQ6_spl
| update_slb(insert_slb(X0,pair(X1,sK5_skl)),sK3_skl) = insert_slb(update_slb(X0,sK3_skl),pair(X1,sK3_skl)) ),
inference(component_clause,[status(thm)],[f142]) ).
fof(f145,plain,
( sQ6_spl
| ~ sQ5_spl ),
inference(split_clause,[status(thm)],[f127,f139,f142]) ).
fof(f177,plain,
( sQ5_spl
| ~ pair_in_list(update_slb(sK0_skl,sK3_skl),sK1_skl,sK2_skl) ),
inference(resolution,[status(thm)],[f141,f45]) ).
fof(f178,plain,
( ~ sQ0_spl
| sQ5_spl
| ~ less_than(sK3_skl,sK2_skl) ),
inference(resolution,[status(thm)],[f177,f79]) ).
fof(f179,plain,
( ~ sQ0_spl
| sQ5_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f178,f66]) ).
fof(f180,plain,
( ~ sQ0_spl
| sQ5_spl ),
inference(contradiction_clause,[status(thm)],[f179]) ).
fof(f191,plain,
( ~ sQ5_spl
| sK5_skl = sK2_skl
| pair_in_list(update_slb(sK0_skl,sK3_skl),sK1_skl,sK2_skl) ),
inference(resolution,[status(thm)],[f140,f44]) ).
fof(f192,plain,
( ~ sQ5_spl
| sK4_skl = sK1_skl
| pair_in_list(update_slb(sK0_skl,sK3_skl),sK1_skl,sK2_skl) ),
inference(resolution,[status(thm)],[f140,f43]) ).
fof(f193,definition,
( sQ11_spl
<=> pair_in_list(update_slb(sK0_skl,sK3_skl),sK1_skl,sK2_skl) ),
introduced(definition,[new_symbols(definition,[sQ11_spl])],[split_symbol_definition]) ).
fof(f194,plain,
( ~ sQ11_spl
| pair_in_list(update_slb(sK0_skl,sK3_skl),sK1_skl,sK2_skl) ),
inference(component_clause,[status(thm)],[f193]) ).
fof(f196,plain,
( ~ sQ5_spl
| sQ2_spl
| sQ11_spl ),
inference(split_clause,[status(thm)],[f191,f193,f83,f139]) ).
fof(f197,plain,
( ~ sQ5_spl
| sQ1_spl
| sQ11_spl ),
inference(split_clause,[status(thm)],[f192,f193,f75,f139]) ).
fof(f198,plain,
( ~ sQ1_spl
| ~ pair_in_list(update_slb(insert_slb(sK0_skl,pair(sK1_skl,sK5_skl)),sK3_skl),sK1_skl,sK2_skl) ),
inference(backward_demodulation,[status(thm)],[f76,f67]) ).
fof(f200,plain,
( ~ sQ1_spl
| ~ sQ2_spl
| ~ pair_in_list(update_slb(insert_slb(sK0_skl,pair(sK1_skl,sK2_skl)),sK3_skl),sK1_skl,sK2_skl) ),
inference(forward_demodulation,[status(thm)],[f84,f198]) ).
fof(f201,plain,
( ~ sQ1_spl
| ~ sQ2_spl
| ~ pair_in_list(insert_slb(update_slb(sK0_skl,sK3_skl),pair(sK1_skl,sK2_skl)),sK1_skl,sK2_skl) ),
inference(forward_demodulation,[status(thm)],[f92,f200]) ).
fof(f202,plain,
( ~ sQ1_spl
| ~ sQ2_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f201,f69]) ).
fof(f203,plain,
( ~ sQ1_spl
| ~ sQ2_spl ),
inference(contradiction_clause,[status(thm)],[f202]) ).
fof(f227,plain,
( ~ sQ6_spl
| ~ pair_in_list(insert_slb(update_slb(sK0_skl,sK3_skl),pair(sK4_skl,sK3_skl)),sK1_skl,sK2_skl) ),
inference(backward_demodulation,[status(thm)],[f143,f67]) ).
fof(f239,plain,
( ~ sQ6_spl
| ~ pair_in_list(update_slb(sK0_skl,sK3_skl),sK1_skl,sK2_skl) ),
inference(resolution,[status(thm)],[f227,f45]) ).
fof(f240,plain,
( ~ sQ6_spl
| ~ sQ11_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f239,f194]) ).
fof(f241,plain,
( ~ sQ6_spl
| ~ sQ11_spl ),
inference(contradiction_clause,[status(thm)],[f240]) ).
fof(f242,plain,
$false,
inference(sat_refutation,[status(thm)],[f78,f86,f145,f180,f196,f197,f203,f241]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SWV401+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.06 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.16/0.40 % Computer : n003.cluster.edu
% 0.16/0.40 % Model : x86_64 x86_64
% 0.16/0.40 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.40 % Memory : 8046.5625MB
% 0.16/0.40 % OS : Linux 6.8.0-71-generic
% 0.16/0.40 % CPULimit : 300
% 0.16/0.40 % WCLimit : 300
% 0.16/0.40 % DateTime : Mon Sep 21 08:46:31 UTC 2026
% 0.16/0.41 % CPUTime :
% 0.18/0.43 % Drodi V4.1.1
% 0.18/0.47 % Refutation found
% 0.18/0.47 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.18/0.47 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.18/0.51 % Elapsed time: 0.088481 seconds
% 0.18/0.51 % CPU time: 0.273567 seconds
% 0.18/0.51 % Total memory used: 46.947 MB
% 0.18/0.51 % Net memory used: 46.692 MB
%------------------------------------------------------------------------------