%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SWV406+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 : n014.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 0.14s 0.47s
% Output : CNFRefutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 24
% Syntax : Number of formulae : 130 ( 3 unt; 17 def)
% Number of atoms : 393 ( 20 equ)
% Maximal formula atoms : 12 ( 3 avg)
% Number of connectives : 438 ( 175 ~; 192 |; 33 &)
% ( 28 <=>; 9 =>; 0 <=; 1 <~>)
% Maximal formula depth : 14 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 24 ( 21 usr; 19 prp; 0-3 aty)
% Number of functors : 12 ( 12 usr; 9 con; 0-3 aty)
% Number of variables : 256 ( 233 !; 23 ?)
% 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(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(f25,axiom,
! [U,V,W,X,Y] :
( less_than(Y,X)
=> ( check_cpq(triple(U,insert_slb(V,pair(X,Y)),W))
<=> check_cpq(triple(U,V,W)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f26,axiom,
! [U,V,W,X,Y] :
( strictly_less_than(X,Y)
=> ( check_cpq(triple(U,insert_slb(V,pair(X,Y)),W))
<=> $false ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f42,conjecture,
! [U] :
( ! [V,W] :
( check_cpq(triple(V,U,W))
<=> ! [X,Y] :
( pair_in_list(U,X,Y)
=> less_than(Y,X) ) )
=> ! [Z,X1,X2,X3] :
( check_cpq(triple(Z,insert_slb(U,pair(X2,X3)),X1))
<=> ! [X4,X5] :
( pair_in_list(insert_slb(U,pair(X2,X3)),X4,X5)
=> less_than(X5,X4) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f43,negated_conjecture,
~ ! [U] :
( ! [V,W] :
( check_cpq(triple(V,U,W))
<=> ! [X,Y] :
( pair_in_list(U,X,Y)
=> less_than(Y,X) ) )
=> ! [Z,X1,X2,X3] :
( check_cpq(triple(Z,insert_slb(U,pair(X2,X3)),X1))
<=> ! [X4,X5] :
( pair_in_list(insert_slb(U,pair(X2,X3)),X4,X5)
=> less_than(X5,X4) ) ) ),
inference(negated_conjecture,[status(cth)],[f42]) ).
fof(f44,plain,
! [U,V,W] :
( less_than(U,W)
| ~ less_than(V,W)
| ~ less_than(U,V) ),
inference(pre_NNF_transformation,[status(thm)],[f1]) ).
fof(f45,plain,
! [U,W] :
( less_than(U,W)
| ! [V] :
( ~ less_than(V,W)
| ~ less_than(U,V) ) ),
inference(miniscoping,[status(thm)],[f44]) ).
fof(f46,plain,
! [X0,X1,X2] :
( less_than(X0,X2)
| ~ less_than(X1,X2)
| ~ less_than(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f45]) ).
fof(f47,plain,
! [X0,X1] :
( less_than(X1,X0)
| less_than(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f49,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(f50,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)],[f49]) ).
fof(f53,plain,
! [X0,X1] :
( less_than(X1,X0)
| ~ less_than(X0,X1)
| strictly_less_than(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f50]) ).
fof(f64,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(f65,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)],[f64]) ).
fof(f66,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)],[f65]) ).
fof(f67,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)],[f65]) ).
fof(f68,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)],[f65]) ).
fof(f69,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)],[f65]) ).
fof(f97,plain,
! [U,V,W,X,Y] :
( ( check_cpq(triple(U,insert_slb(V,pair(X,Y)),W))
<=> check_cpq(triple(U,V,W)) )
| ~ less_than(Y,X) ),
inference(pre_NNF_transformation,[status(thm)],[f25]) ).
fof(f98,plain,
! [U,V,W,X,Y] :
( ( ( ~ check_cpq(triple(U,V,W))
| check_cpq(triple(U,insert_slb(V,pair(X,Y)),W)) )
& ( check_cpq(triple(U,V,W))
| ~ check_cpq(triple(U,insert_slb(V,pair(X,Y)),W)) ) )
| ~ less_than(Y,X) ),
inference(NNF_transformation,[status(thm)],[f97]) ).
fof(f99,plain,
! [X,Y] :
( ( ! [U,V,W] :
( ~ check_cpq(triple(U,V,W))
| check_cpq(triple(U,insert_slb(V,pair(X,Y)),W)) )
& ! [U,V,W] :
( check_cpq(triple(U,V,W))
| ~ check_cpq(triple(U,insert_slb(V,pair(X,Y)),W)) ) )
| ~ less_than(Y,X) ),
inference(miniscoping,[status(thm)],[f98]) ).
fof(f100,plain,
! [X0,X1,X2,X3,X4] :
( check_cpq(triple(X2,X3,X4))
| ~ check_cpq(triple(X2,insert_slb(X3,pair(X1,X0)),X4))
| ~ less_than(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f99]) ).
fof(f101,plain,
! [X0,X1,X2,X3,X4] :
( ~ check_cpq(triple(X2,X3,X4))
| check_cpq(triple(X2,insert_slb(X3,pair(X1,X0)),X4))
| ~ less_than(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f99]) ).
fof(f102,plain,
! [U,V,W,X,Y] :
( ( check_cpq(triple(U,insert_slb(V,pair(X,Y)),W))
<=> $false )
| ~ strictly_less_than(X,Y) ),
inference(pre_NNF_transformation,[status(thm)],[f26]) ).
fof(f103,plain,
! [U,V,W,X,Y] :
( ( ( $true
| check_cpq(triple(U,insert_slb(V,pair(X,Y)),W)) )
& ( $false
| ~ check_cpq(triple(U,insert_slb(V,pair(X,Y)),W)) ) )
| ~ strictly_less_than(X,Y) ),
inference(NNF_transformation,[status(thm)],[f102]) ).
fof(f104,plain,
! [X,Y] :
( ( ( $true
| ! [U,V,W] : check_cpq(triple(U,insert_slb(V,pair(X,Y)),W)) )
& ( $false
| ! [U,V,W] : ~ check_cpq(triple(U,insert_slb(V,pair(X,Y)),W)) ) )
| ~ strictly_less_than(X,Y) ),
inference(miniscoping,[status(thm)],[f103]) ).
fof(f105,plain,
! [X,Y] :
( ! [U,V,W] : ~ check_cpq(triple(U,insert_slb(V,pair(X,Y)),W))
| ~ strictly_less_than(X,Y) ),
inference(true_and_false_simplification,[status(thm)],[f104]) ).
fof(f106,plain,
! [X0,X1,X2,X3,X4] :
( ~ check_cpq(triple(X2,insert_slb(X3,pair(X0,X1)),X4))
| ~ strictly_less_than(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f105]) ).
fof(f144,plain,
? [U] :
( ? [Z,X1,X2,X3] :
( check_cpq(triple(Z,insert_slb(U,pair(X2,X3)),X1))
<~> ! [X4,X5] :
( less_than(X5,X4)
| ~ pair_in_list(insert_slb(U,pair(X2,X3)),X4,X5) ) )
& ! [V,W] :
( check_cpq(triple(V,U,W))
<=> ! [X,Y] :
( less_than(Y,X)
| ~ pair_in_list(U,X,Y) ) ) ),
inference(pre_NNF_transformation,[status(thm)],[f43]) ).
fof(f145,plain,
? [U] :
( ? [Z,X1,X2,X3] :
( ( ? [X4,X5] :
( ~ less_than(X5,X4)
& pair_in_list(insert_slb(U,pair(X2,X3)),X4,X5) )
| ~ check_cpq(triple(Z,insert_slb(U,pair(X2,X3)),X1)) )
& ( ! [X4,X5] :
( less_than(X5,X4)
| ~ pair_in_list(insert_slb(U,pair(X2,X3)),X4,X5) )
| check_cpq(triple(Z,insert_slb(U,pair(X2,X3)),X1)) ) )
& ! [V,W] :
( ( ? [X,Y] :
( ~ less_than(Y,X)
& pair_in_list(U,X,Y) )
| check_cpq(triple(V,U,W)) )
& ( ! [X,Y] :
( less_than(Y,X)
| ~ pair_in_list(U,X,Y) )
| ~ check_cpq(triple(V,U,W)) ) ) ),
inference(NNF_transformation,[status(thm)],[f144]) ).
fof(f146,plain,
? [U] :
( ? [Z,X1,X2,X3] :
( ( ? [X4,X5] :
( ~ less_than(X5,X4)
& pair_in_list(insert_slb(U,pair(X2,X3)),X4,X5) )
| ~ check_cpq(triple(Z,insert_slb(U,pair(X2,X3)),X1)) )
& ( ! [X4,X5] :
( less_than(X5,X4)
| ~ pair_in_list(insert_slb(U,pair(X2,X3)),X4,X5) )
| check_cpq(triple(Z,insert_slb(U,pair(X2,X3)),X1)) ) )
& ( ? [X,Y] :
( ~ less_than(Y,X)
& pair_in_list(U,X,Y) )
| ! [V,W] : check_cpq(triple(V,U,W)) )
& ( ! [X,Y] :
( less_than(Y,X)
| ~ pair_in_list(U,X,Y) )
| ! [V,W] : ~ check_cpq(triple(V,U,W)) ) ),
inference(miniscoping,[status(thm)],[f145]) ).
fof(f147,plain,
( ( ( ~ less_than(sK8_skl,sK7_skl)
& pair_in_list(insert_slb(sK0_skl,pair(sK5_skl,sK6_skl)),sK7_skl,sK8_skl) )
| ~ check_cpq(triple(sK3_skl,insert_slb(sK0_skl,pair(sK5_skl,sK6_skl)),sK4_skl)) )
& ( ! [X4,X5] :
( less_than(X5,X4)
| ~ pair_in_list(insert_slb(sK0_skl,pair(sK5_skl,sK6_skl)),X4,X5) )
| check_cpq(triple(sK3_skl,insert_slb(sK0_skl,pair(sK5_skl,sK6_skl)),sK4_skl)) )
& ( ( ~ less_than(sK2_skl,sK1_skl)
& pair_in_list(sK0_skl,sK1_skl,sK2_skl) )
| ! [V,W] : check_cpq(triple(V,sK0_skl,W)) )
& ( ! [X,Y] :
( less_than(Y,X)
| ~ pair_in_list(sK0_skl,X,Y) )
| ! [V,W] : ~ check_cpq(triple(V,sK0_skl,W)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl,sK1_skl,sK2_skl,sK3_skl,sK4_skl,sK5_skl,sK6_skl,sK7_skl,sK8_skl]),skolemize(U,sK0_skl),skolemize(X,sK1_skl),skolemize(Y,sK2_skl),skolemize(Z,sK3_skl),skolemize(X1,sK4_skl),skolemize(X2,sK5_skl),skolemize(X3,sK6_skl),skolemize(X4,sK7_skl),skolemize(X5,sK8_skl)],[f146]) ).
fof(f148,plain,
! [X0,X1,X2,X3] :
( less_than(X3,X2)
| ~ pair_in_list(sK0_skl,X2,X3)
| ~ check_cpq(triple(X0,sK0_skl,X1)) ),
inference(cnf_transformation,[status(thm)],[f147]) ).
fof(f149,plain,
! [X0,X1] :
( pair_in_list(sK0_skl,sK1_skl,sK2_skl)
| check_cpq(triple(X0,sK0_skl,X1)) ),
inference(cnf_transformation,[status(thm)],[f147]) ).
fof(f150,plain,
! [X0,X1] :
( ~ less_than(sK2_skl,sK1_skl)
| check_cpq(triple(X0,sK0_skl,X1)) ),
inference(cnf_transformation,[status(thm)],[f147]) ).
fof(f151,plain,
! [X0,X1] :
( less_than(X1,X0)
| ~ pair_in_list(insert_slb(sK0_skl,pair(sK5_skl,sK6_skl)),X0,X1)
| check_cpq(triple(sK3_skl,insert_slb(sK0_skl,pair(sK5_skl,sK6_skl)),sK4_skl)) ),
inference(cnf_transformation,[status(thm)],[f147]) ).
fof(f152,plain,
( pair_in_list(insert_slb(sK0_skl,pair(sK5_skl,sK6_skl)),sK7_skl,sK8_skl)
| ~ check_cpq(triple(sK3_skl,insert_slb(sK0_skl,pair(sK5_skl,sK6_skl)),sK4_skl)) ),
inference(cnf_transformation,[status(thm)],[f147]) ).
fof(f153,plain,
( ~ less_than(sK8_skl,sK7_skl)
| ~ check_cpq(triple(sK3_skl,insert_slb(sK0_skl,pair(sK5_skl,sK6_skl)),sK4_skl)) ),
inference(cnf_transformation,[status(thm)],[f147]) ).
fof(f154,definition,
! [X0,X1] :
( sQ0_spl
<=> ~ check_cpq(triple(X0,sK0_skl,X1)) ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f155,plain,
! [X0,X1] :
( ~ sQ0_spl
| ~ check_cpq(triple(X0,sK0_skl,X1)) ),
inference(component_clause,[status(thm)],[f154]) ).
fof(f157,definition,
! [X2,X3] :
( sQ1_spl
<=> ( less_than(X3,X2)
| ~ pair_in_list(sK0_skl,X2,X3) ) ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f158,plain,
! [X0,X1] :
( ~ sQ1_spl
| less_than(X1,X0)
| ~ pair_in_list(sK0_skl,X0,X1) ),
inference(component_clause,[status(thm)],[f157]) ).
fof(f160,plain,
( sQ1_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f148,f154,f157]) ).
fof(f161,definition,
! [X0,X1] :
( sQ2_spl
<=> check_cpq(triple(X0,sK0_skl,X1)) ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f162,plain,
! [X0,X1] :
( ~ sQ2_spl
| check_cpq(triple(X0,sK0_skl,X1)) ),
inference(component_clause,[status(thm)],[f161]) ).
fof(f164,definition,
( sQ3_spl
<=> pair_in_list(sK0_skl,sK1_skl,sK2_skl) ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f165,plain,
( ~ sQ3_spl
| pair_in_list(sK0_skl,sK1_skl,sK2_skl) ),
inference(component_clause,[status(thm)],[f164]) ).
fof(f167,plain,
( sQ3_spl
| sQ2_spl ),
inference(split_clause,[status(thm)],[f149,f161,f164]) ).
fof(f168,definition,
( sQ4_spl
<=> less_than(sK2_skl,sK1_skl) ),
introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition]) ).
fof(f170,plain,
( sQ4_spl
| ~ less_than(sK2_skl,sK1_skl) ),
inference(component_clause,[status(thm)],[f168]) ).
fof(f171,plain,
( ~ sQ4_spl
| sQ2_spl ),
inference(split_clause,[status(thm)],[f150,f161,f168]) ).
fof(f172,definition,
( sQ5_spl
<=> check_cpq(triple(sK3_skl,insert_slb(sK0_skl,pair(sK5_skl,sK6_skl)),sK4_skl)) ),
introduced(definition,[new_symbols(definition,[sQ5_spl])],[split_symbol_definition]) ).
fof(f173,plain,
( ~ sQ5_spl
| check_cpq(triple(sK3_skl,insert_slb(sK0_skl,pair(sK5_skl,sK6_skl)),sK4_skl)) ),
inference(component_clause,[status(thm)],[f172]) ).
fof(f174,plain,
( sQ5_spl
| ~ check_cpq(triple(sK3_skl,insert_slb(sK0_skl,pair(sK5_skl,sK6_skl)),sK4_skl)) ),
inference(component_clause,[status(thm)],[f172]) ).
fof(f175,definition,
! [X0,X1] :
( sQ6_spl
<=> ( less_than(X1,X0)
| ~ pair_in_list(insert_slb(sK0_skl,pair(sK5_skl,sK6_skl)),X0,X1) ) ),
introduced(definition,[new_symbols(definition,[sQ6_spl])],[split_symbol_definition]) ).
fof(f176,plain,
! [X0,X1] :
( ~ sQ6_spl
| less_than(X1,X0)
| ~ pair_in_list(insert_slb(sK0_skl,pair(sK5_skl,sK6_skl)),X0,X1) ),
inference(component_clause,[status(thm)],[f175]) ).
fof(f178,plain,
( sQ6_spl
| sQ5_spl ),
inference(split_clause,[status(thm)],[f151,f172,f175]) ).
fof(f179,definition,
( sQ7_spl
<=> pair_in_list(insert_slb(sK0_skl,pair(sK5_skl,sK6_skl)),sK7_skl,sK8_skl) ),
introduced(definition,[new_symbols(definition,[sQ7_spl])],[split_symbol_definition]) ).
fof(f180,plain,
( ~ sQ7_spl
| pair_in_list(insert_slb(sK0_skl,pair(sK5_skl,sK6_skl)),sK7_skl,sK8_skl) ),
inference(component_clause,[status(thm)],[f179]) ).
fof(f182,plain,
( sQ7_spl
| ~ sQ5_spl ),
inference(split_clause,[status(thm)],[f152,f172,f179]) ).
fof(f183,definition,
( sQ8_spl
<=> less_than(sK8_skl,sK7_skl) ),
introduced(definition,[new_symbols(definition,[sQ8_spl])],[split_symbol_definition]) ).
fof(f185,plain,
( sQ8_spl
| ~ less_than(sK8_skl,sK7_skl) ),
inference(component_clause,[status(thm)],[f183]) ).
fof(f186,plain,
( ~ sQ8_spl
| ~ sQ5_spl ),
inference(split_clause,[status(thm)],[f153,f172,f183]) ).
fof(f188,plain,
! [X0,X1,X2] : pair_in_list(insert_slb(X0,pair(X1,X2)),X1,X2),
inference(destructive_equality_resolution,[status(thm)],[f69]) ).
fof(f189,plain,
( ~ sQ0_spl
| ~ sQ2_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f155,f162]) ).
fof(f190,plain,
( ~ sQ0_spl
| ~ sQ2_spl ),
inference(contradiction_clause,[status(thm)],[f189]) ).
fof(f192,plain,
( sQ4_spl
| less_than(sK1_skl,sK2_skl) ),
inference(resolution,[status(thm)],[f47,f170]) ).
fof(f193,plain,
( ~ sQ3_spl
| ~ sQ1_spl
| less_than(sK2_skl,sK1_skl) ),
inference(resolution,[status(thm)],[f158,f165]) ).
fof(f194,plain,
( ~ sQ3_spl
| ~ sQ1_spl
| sQ4_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f193,f170]) ).
fof(f195,plain,
( ~ sQ3_spl
| ~ sQ1_spl
| sQ4_spl ),
inference(contradiction_clause,[status(thm)],[f194]) ).
fof(f200,plain,
( ~ sQ7_spl
| sK5_skl = sK7_skl
| pair_in_list(sK0_skl,sK7_skl,sK8_skl) ),
inference(resolution,[status(thm)],[f66,f180]) ).
fof(f202,definition,
( sQ9_spl
<=> pair_in_list(sK0_skl,sK7_skl,sK8_skl) ),
introduced(definition,[new_symbols(definition,[sQ9_spl])],[split_symbol_definition]) ).
fof(f203,plain,
( ~ sQ9_spl
| pair_in_list(sK0_skl,sK7_skl,sK8_skl) ),
inference(component_clause,[status(thm)],[f202]) ).
fof(f205,definition,
( sQ10_spl
<=> sK5_skl = sK7_skl ),
introduced(definition,[new_symbols(definition,[sQ10_spl])],[split_symbol_definition]) ).
fof(f206,plain,
( ~ sQ10_spl
| sK5_skl = sK7_skl ),
inference(component_clause,[status(thm)],[f205]) ).
fof(f208,plain,
( ~ sQ7_spl
| sQ10_spl
| sQ9_spl ),
inference(split_clause,[status(thm)],[f200,f202,f205,f179]) ).
fof(f215,plain,
( ~ sQ1_spl
| ~ sQ9_spl
| less_than(sK8_skl,sK7_skl) ),
inference(resolution,[status(thm)],[f203,f158]) ).
fof(f216,plain,
( ~ sQ1_spl
| ~ sQ9_spl
| sQ8_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f215,f185]) ).
fof(f217,plain,
( ~ sQ1_spl
| ~ sQ9_spl
| sQ8_spl ),
inference(contradiction_clause,[status(thm)],[f216]) ).
fof(f218,plain,
! [X0,X1] :
( less_than(X1,X0)
| strictly_less_than(X0,X1) ),
inference(forward_subsumption_resolution,[status(thm)],[f53,f47]) ).
fof(f365,plain,
! [X0,X1,X2,X3,X4] :
( check_cpq(triple(X2,X3,X4))
| ~ less_than(X0,X1)
| ~ check_cpq(triple(X2,X3,X4))
| ~ less_than(X0,X1) ),
inference(resolution,[status(thm)],[f101,f100]) ).
fof(f369,definition,
( sQ19_spl
<=> check_cpq(triple(sK3_skl,sK0_skl,sK4_skl)) ),
introduced(definition,[new_symbols(definition,[sQ19_spl])],[split_symbol_definition]) ).
fof(f370,plain,
( ~ sQ19_spl
| check_cpq(triple(sK3_skl,sK0_skl,sK4_skl)) ),
inference(component_clause,[status(thm)],[f369]) ).
fof(f371,plain,
( sQ19_spl
| ~ check_cpq(triple(sK3_skl,sK0_skl,sK4_skl)) ),
inference(component_clause,[status(thm)],[f369]) ).
fof(f373,definition,
! [X0,X1] :
( sQ20_spl
<=> ( ~ less_than(X0,X1)
| ~ less_than(X0,X1) ) ),
introduced(definition,[new_symbols(definition,[sQ20_spl])],[split_symbol_definition]) ).
fof(f374,plain,
! [X0,X1] :
( ~ sQ20_spl
| ~ less_than(X0,X1)
| ~ less_than(X0,X1) ),
inference(component_clause,[status(thm)],[f373]) ).
fof(f376,definition,
! [X2,X3,X4] :
( sQ21_spl
<=> ( check_cpq(triple(X2,X3,X4))
| ~ check_cpq(triple(X2,X3,X4)) ) ),
introduced(definition,[new_symbols(definition,[sQ21_spl])],[split_symbol_definition]) ).
fof(f379,plain,
( sQ21_spl
| sQ20_spl ),
inference(split_clause,[status(thm)],[f365,f373,f376]) ).
fof(f380,plain,
! [X0,X1] :
( ~ sQ20_spl
| ~ less_than(X0,X1) ),
inference(duplicate_literals_removal,[status(thm)],[f374]) ).
fof(f381,plain,
( sQ19_spl
| ~ sQ2_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f371,f162]) ).
fof(f382,plain,
( sQ19_spl
| ~ sQ2_spl ),
inference(contradiction_clause,[status(thm)],[f381]) ).
fof(f384,plain,
! [X0,X1] :
( ~ sQ20_spl
| less_than(X0,X1) ),
inference(backward_subsumption_resolution,[status(thm)],[f47,f380]) ).
fof(f389,plain,
( ~ sQ20_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f384,f380]) ).
fof(f390,plain,
~ sQ20_spl,
inference(contradiction_clause,[status(thm)],[f389]) ).
fof(f485,plain,
( sQ5_spl
| ~ check_cpq(triple(sK3_skl,sK0_skl,sK4_skl))
| ~ less_than(sK6_skl,sK5_skl) ),
inference(resolution,[status(thm)],[f174,f101]) ).
fof(f486,definition,
( sQ22_spl
<=> less_than(sK6_skl,sK5_skl) ),
introduced(definition,[new_symbols(definition,[sQ22_spl])],[split_symbol_definition]) ).
fof(f488,plain,
( sQ22_spl
| ~ less_than(sK6_skl,sK5_skl) ),
inference(component_clause,[status(thm)],[f486]) ).
fof(f489,plain,
( sQ5_spl
| ~ sQ19_spl
| ~ sQ22_spl ),
inference(split_clause,[status(thm)],[f485,f486,f369,f172]) ).
fof(f513,plain,
! [X0,X1] :
( ~ sQ6_spl
| ~ pair_in_list(sK0_skl,X1,X0)
| less_than(X0,X1) ),
inference(resolution,[status(thm)],[f176,f68]) ).
fof(f514,plain,
( ~ sQ6_spl
| less_than(sK6_skl,sK5_skl) ),
inference(resolution,[status(thm)],[f176,f188]) ).
fof(f515,plain,
( ~ sQ6_spl
| sQ22_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f514,f488]) ).
fof(f516,plain,
( ~ sQ6_spl
| sQ22_spl ),
inference(contradiction_clause,[status(thm)],[f515]) ).
fof(f520,plain,
! [X0] :
( sQ4_spl
| less_than(X0,sK2_skl)
| ~ less_than(X0,sK1_skl) ),
inference(resolution,[status(thm)],[f192,f46]) ).
fof(f523,plain,
( sQ8_spl
| strictly_less_than(sK7_skl,sK8_skl) ),
inference(resolution,[status(thm)],[f185,f218]) ).
fof(f551,plain,
( ~ sQ5_spl
| ~ sQ10_spl
| check_cpq(triple(sK3_skl,insert_slb(sK0_skl,pair(sK7_skl,sK6_skl)),sK4_skl)) ),
inference(forward_demodulation,[status(thm)],[f206,f173]) ).
fof(f555,plain,
( ~ sQ6_spl
| sQ1_spl ),
inference(split_clause,[status(thm)],[f513,f157,f175]) ).
fof(f577,plain,
( ~ sQ5_spl
| ~ sQ10_spl
| ~ strictly_less_than(sK7_skl,sK6_skl) ),
inference(resolution,[status(thm)],[f551,f106]) ).
fof(f617,definition,
( sQ25_spl
<=> sK6_skl = sK8_skl ),
introduced(definition,[new_symbols(definition,[sQ25_spl])],[split_symbol_definition]) ).
fof(f618,plain,
( ~ sQ25_spl
| sK6_skl = sK8_skl ),
inference(component_clause,[status(thm)],[f617]) ).
fof(f633,plain,
( ~ sQ5_spl
| ~ sQ10_spl
| ~ sQ25_spl
| ~ strictly_less_than(sK7_skl,sK8_skl) ),
inference(forward_demodulation,[status(thm)],[f618,f577]) ).
fof(f634,plain,
( ~ sQ5_spl
| ~ sQ10_spl
| ~ sQ25_spl
| sQ8_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f633,f523]) ).
fof(f635,plain,
( ~ sQ5_spl
| ~ sQ10_spl
| ~ sQ25_spl
| sQ8_spl ),
inference(contradiction_clause,[status(thm)],[f634]) ).
fof(f711,plain,
! [X0] :
( sQ4_spl
| less_than(sK1_skl,X0)
| less_than(X0,sK2_skl) ),
inference(resolution,[status(thm)],[f520,f47]) ).
fof(f727,plain,
( ~ sQ7_spl
| sK6_skl = sK8_skl
| pair_in_list(sK0_skl,sK7_skl,sK8_skl) ),
inference(resolution,[status(thm)],[f180,f67]) ).
fof(f729,plain,
( ~ sQ7_spl
| sQ25_spl
| sQ9_spl ),
inference(split_clause,[status(thm)],[f727,f202,f617,f179]) ).
fof(f733,plain,
( sQ4_spl
| less_than(sK1_skl,sK2_skl)
| less_than(sK1_skl,sK2_skl) ),
inference(resolution,[status(thm)],[f711,f520]) ).
fof(f739,definition,
( sQ37_spl
<=> less_than(sK1_skl,sK2_skl) ),
introduced(definition,[new_symbols(definition,[sQ37_spl])],[split_symbol_definition]) ).
fof(f742,plain,
( sQ4_spl
| sQ37_spl ),
inference(split_clause,[status(thm)],[f733,f739,f168]) ).
fof(f772,plain,
( ~ sQ5_spl
| ~ strictly_less_than(sK5_skl,sK6_skl) ),
inference(resolution,[status(thm)],[f173,f106]) ).
fof(f773,plain,
( ~ sQ5_spl
| check_cpq(triple(sK3_skl,sK0_skl,sK4_skl))
| ~ less_than(sK6_skl,sK5_skl) ),
inference(resolution,[status(thm)],[f173,f100]) ).
fof(f774,plain,
( ~ sQ5_spl
| sQ19_spl
| ~ sQ22_spl ),
inference(split_clause,[status(thm)],[f773,f486,f369,f172]) ).
fof(f793,plain,
( sQ22_spl
| strictly_less_than(sK5_skl,sK6_skl) ),
inference(resolution,[status(thm)],[f488,f218]) ).
fof(f795,plain,
( sQ22_spl
| ~ sQ5_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f793,f772]) ).
fof(f796,plain,
( sQ22_spl
| ~ sQ5_spl ),
inference(contradiction_clause,[status(thm)],[f795]) ).
fof(f797,plain,
( ~ sQ19_spl
| ~ sQ0_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f370,f155]) ).
fof(f798,plain,
( ~ sQ19_spl
| ~ sQ0_spl ),
inference(contradiction_clause,[status(thm)],[f797]) ).
fof(f799,plain,
$false,
inference(sat_refutation,[status(thm)],[f160,f167,f171,f178,f182,f186,f190,f195,f208,f217,f379,f382,f390,f489,f516,f555,f635,f729,f742,f774,f796,f798]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : SWV406+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.05 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.14/0.42 % Computer : n014.cluster.edu
% 0.14/0.42 % Model : x86_64 x86_64
% 0.14/0.42 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.42 % Memory : 8046.5625MB
% 0.14/0.42 % OS : Linux 6.8.0-71-generic
% 0.14/0.42 % CPULimit : 300
% 0.14/0.42 % WCLimit : 300
% 0.14/0.42 % DateTime : Mon Sep 21 08:44:35 UTC 2026
% 0.14/0.42 % CPUTime :
% 0.14/0.43 % Drodi V4.1.1
% 0.14/0.47 % Refutation found
% 0.14/0.47 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.14/0.47 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.14/0.50 % Elapsed time: 0.067953 seconds
% 0.14/0.50 % CPU time: 0.301026 seconds
% 0.14/0.50 % Total memory used: 66.042 MB
% 0.14/0.50 % Net memory used: 65.644 MB
%------------------------------------------------------------------------------