%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SYN549+1 : TPTP v9.3.1. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n009.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 03:16:46 PM UTC 2026
% Result : Theorem 0.13s 0.43s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 21
% Syntax : Number of formulae : 130 ( 10 unt; 18 def)
% Number of atoms : 447 ( 0 equ)
% Maximal formula atoms : 12 ( 3 avg)
% Number of connectives : 546 ( 229 ~; 249 |; 43 &)
% ( 20 <=>; 3 =>; 0 <=; 2 <~>)
% Maximal formula depth : 12 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 22 ( 21 usr; 18 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 1 con; 0-2 aty)
% Number of variables : 150 ( 124 !; 26 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X] : reachable(X,X),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f2,axiom,
! [X,Y,Z] :
( ( reachable(Y,Z)
& reachable(X,Y) )
=> reachable(X,Z) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f3,conjecture,
? [X] :
( ! [Y] :
( reachable(X,Y)
=> ( ? [Z] :
( ( ? [V] :
( q(V)
& reachable(Z,V) )
| p(Z) )
& reachable(Y,Z) )
<=> ( ? [W] :
( q(W)
& reachable(Y,W) )
| ? [W] :
( p(W)
& reachable(Y,W) ) ) ) )
& reachable(initial_world,X) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f4,negated_conjecture,
~ ? [X] :
( ! [Y] :
( reachable(X,Y)
=> ( ? [Z] :
( ( ? [V] :
( q(V)
& reachable(Z,V) )
| p(Z) )
& reachable(Y,Z) )
<=> ( ? [W] :
( q(W)
& reachable(Y,W) )
| ? [W] :
( p(W)
& reachable(Y,W) ) ) ) )
& reachable(initial_world,X) ),
inference(negated_conjecture,[status(cth)],[f3]) ).
fof(f5,plain,
! [X0] : reachable(X0,X0),
inference(cnf_transformation,[status(thm)],[f1]) ).
fof(f6,plain,
! [X,Y,Z] :
( reachable(X,Z)
| ~ reachable(Y,Z)
| ~ reachable(X,Y) ),
inference(pre_NNF_transformation,[status(thm)],[f2]) ).
fof(f7,plain,
! [X,Z] :
( reachable(X,Z)
| ! [Y] :
( ~ reachable(Y,Z)
| ~ reachable(X,Y) ) ),
inference(miniscoping,[status(thm)],[f6]) ).
fof(f8,plain,
! [X0,X1,X2] :
( reachable(X0,X2)
| ~ reachable(X1,X2)
| ~ reachable(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f7]) ).
fof(f9,plain,
! [X] :
( ? [Y] :
( ( ? [Z] :
( ( ? [V] :
( q(V)
& reachable(Z,V) )
| p(Z) )
& reachable(Y,Z) )
<~> ( ? [W] :
( q(W)
& reachable(Y,W) )
| ? [W] :
( p(W)
& reachable(Y,W) ) ) )
& reachable(X,Y) )
| ~ reachable(initial_world,X) ),
inference(pre_NNF_transformation,[status(thm)],[f4]) ).
fof(f10,definition,
! [Y,Z] :
( sP0_prd(Z,Y)
<=> ( ( ? [V] :
( q(V)
& reachable(Z,V) )
| p(Z) )
& reachable(Y,Z) ) ),
introduced(definition,[new_symbols(definition,[sP0_prd])],[]) ).
fof(f11,plain,
! [X] :
( ? [Y] :
( ( ? [Z] : sP0_prd(Z,Y)
<~> ( ? [W] :
( q(W)
& reachable(Y,W) )
| ? [W] :
( p(W)
& reachable(Y,W) ) ) )
& reachable(X,Y) )
| ~ reachable(initial_world,X) ),
inference(formula_renaming,[status(thm)],[f9,f10]) ).
fof(f12,plain,
! [X] :
( ? [Y] :
( ( ( ! [W] :
( ~ q(W)
| ~ reachable(Y,W) )
& ! [W] :
( ~ p(W)
| ~ reachable(Y,W) ) )
| ! [Z] : ~ sP0_prd(Z,Y) )
& ( ? [W] :
( q(W)
& reachable(Y,W) )
| ? [W] :
( p(W)
& reachable(Y,W) )
| ? [Z] : sP0_prd(Z,Y) )
& reachable(X,Y) )
| ~ reachable(initial_world,X) ),
inference(NNF_transformation,[status(thm)],[f11]) ).
fof(f13,plain,
! [X] :
( ( ( ( ! [W] :
( ~ q(W)
| ~ reachable(sK0_skl(X),W) )
& ! [W] :
( ~ p(W)
| ~ reachable(sK0_skl(X),W) ) )
| ! [Z] : ~ sP0_prd(Z,sK0_skl(X)) )
& ( ( q(sK3_skl(X))
& reachable(sK0_skl(X),sK3_skl(X)) )
| ( p(sK2_skl(X))
& reachable(sK0_skl(X),sK2_skl(X)) )
| sP0_prd(sK1_skl(X),sK0_skl(X)) )
& reachable(X,sK0_skl(X)) )
| ~ reachable(initial_world,X) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl,sK1_skl,sK2_skl,sK3_skl]),skolemize(Y,sK0_skl(X)),skolemize(Z,sK1_skl(X)),skolemize(W,sK2_skl(X)),skolemize(W,sK3_skl(X))],[f12]) ).
fof(f14,plain,
! [X0] :
( reachable(X0,sK0_skl(X0))
| ~ reachable(initial_world,X0) ),
inference(cnf_transformation,[status(thm)],[f13]) ).
fof(f15,plain,
! [X0] :
( reachable(sK0_skl(X0),sK3_skl(X0))
| reachable(sK0_skl(X0),sK2_skl(X0))
| sP0_prd(sK1_skl(X0),sK0_skl(X0))
| ~ reachable(initial_world,X0) ),
inference(cnf_transformation,[status(thm)],[f13]) ).
fof(f16,plain,
! [X0] :
( q(sK3_skl(X0))
| reachable(sK0_skl(X0),sK2_skl(X0))
| sP0_prd(sK1_skl(X0),sK0_skl(X0))
| ~ reachable(initial_world,X0) ),
inference(cnf_transformation,[status(thm)],[f13]) ).
fof(f17,plain,
! [X0] :
( reachable(sK0_skl(X0),sK3_skl(X0))
| p(sK2_skl(X0))
| sP0_prd(sK1_skl(X0),sK0_skl(X0))
| ~ reachable(initial_world,X0) ),
inference(cnf_transformation,[status(thm)],[f13]) ).
fof(f18,plain,
! [X0] :
( q(sK3_skl(X0))
| p(sK2_skl(X0))
| sP0_prd(sK1_skl(X0),sK0_skl(X0))
| ~ reachable(initial_world,X0) ),
inference(cnf_transformation,[status(thm)],[f13]) ).
fof(f19,plain,
! [X0,X1,X2] :
( ~ p(X2)
| ~ reachable(sK0_skl(X0),X2)
| ~ sP0_prd(X1,sK0_skl(X0))
| ~ reachable(initial_world,X0) ),
inference(cnf_transformation,[status(thm)],[f13]) ).
fof(f20,plain,
! [X0,X1,X2] :
( ~ q(X2)
| ~ reachable(sK0_skl(X0),X2)
| ~ sP0_prd(X1,sK0_skl(X0))
| ~ reachable(initial_world,X0) ),
inference(cnf_transformation,[status(thm)],[f13]) ).
fof(f21,plain,
! [Y,Z] :
( ( ( ! [V] :
( ~ q(V)
| ~ reachable(Z,V) )
& ~ p(Z) )
| ~ reachable(Y,Z)
| sP0_prd(Z,Y) )
& ( ( ( ? [V] :
( q(V)
& reachable(Z,V) )
| p(Z) )
& reachable(Y,Z) )
| ~ sP0_prd(Z,Y) ) ),
inference(NNF_transformation,[status(thm)],[f10]) ).
fof(f22,plain,
( ! [Y,Z] :
( ( ! [V] :
( ~ q(V)
| ~ reachable(Z,V) )
& ~ p(Z) )
| ~ reachable(Y,Z)
| sP0_prd(Z,Y) )
& ! [Y,Z] :
( ( ( ? [V] :
( q(V)
& reachable(Z,V) )
| p(Z) )
& reachable(Y,Z) )
| ~ sP0_prd(Z,Y) ) ),
inference(miniscoping,[status(thm)],[f21]) ).
fof(f23,plain,
( ! [Y,Z] :
( ( ! [V] :
( ~ q(V)
| ~ reachable(Z,V) )
& ~ p(Z) )
| ~ reachable(Y,Z)
| sP0_prd(Z,Y) )
& ! [Y,Z] :
( ( ( ( q(sK4_skl(Z,Y))
& reachable(Z,sK4_skl(Z,Y)) )
| p(Z) )
& reachable(Y,Z) )
| ~ sP0_prd(Z,Y) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4_skl]),skolemize(V,sK4_skl(Z,Y))],[f22]) ).
fof(f24,plain,
! [X0,X1] :
( reachable(X1,X0)
| ~ sP0_prd(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f23]) ).
fof(f25,plain,
! [X0,X1] :
( reachable(X0,sK4_skl(X0,X1))
| p(X0)
| ~ sP0_prd(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f23]) ).
fof(f26,plain,
! [X0,X1] :
( q(sK4_skl(X0,X1))
| p(X0)
| ~ sP0_prd(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f23]) ).
fof(f27,plain,
! [X0,X1] :
( ~ p(X0)
| ~ reachable(X1,X0)
| sP0_prd(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f23]) ).
fof(f28,plain,
! [X0,X1,X2] :
( ~ q(X2)
| ~ reachable(X0,X2)
| ~ reachable(X1,X0)
| sP0_prd(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f23]) ).
fof(f29,plain,
( reachable(sK0_skl(initial_world),sK3_skl(initial_world))
| reachable(sK0_skl(initial_world),sK2_skl(initial_world))
| sP0_prd(sK1_skl(initial_world),sK0_skl(initial_world)) ),
inference(resolution,[status(thm)],[f5,f15]) ).
fof(f30,plain,
reachable(initial_world,sK0_skl(initial_world)),
inference(resolution,[status(thm)],[f5,f14]) ).
fof(f31,definition,
( sQ0_spl
<=> sP0_prd(sK1_skl(initial_world),sK0_skl(initial_world)) ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f32,plain,
( ~ sQ0_spl
| sP0_prd(sK1_skl(initial_world),sK0_skl(initial_world)) ),
inference(component_clause,[status(thm)],[f31]) ).
fof(f33,plain,
( sQ0_spl
| ~ sP0_prd(sK1_skl(initial_world),sK0_skl(initial_world)) ),
inference(component_clause,[status(thm)],[f31]) ).
fof(f34,definition,
( sQ1_spl
<=> reachable(sK0_skl(initial_world),sK2_skl(initial_world)) ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f35,plain,
( ~ sQ1_spl
| reachable(sK0_skl(initial_world),sK2_skl(initial_world)) ),
inference(component_clause,[status(thm)],[f34]) ).
fof(f37,definition,
( sQ2_spl
<=> reachable(sK0_skl(initial_world),sK3_skl(initial_world)) ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f38,plain,
( ~ sQ2_spl
| reachable(sK0_skl(initial_world),sK3_skl(initial_world)) ),
inference(component_clause,[status(thm)],[f37]) ).
fof(f40,plain,
( sQ2_spl
| sQ1_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f29,f31,f34,f37]) ).
fof(f53,plain,
! [X0,X1] :
( reachable(sK0_skl(X1),sK3_skl(X1))
| reachable(sK0_skl(X1),sK2_skl(X1))
| sP0_prd(sK1_skl(X1),sK0_skl(X1))
| ~ reachable(X0,X1)
| ~ reachable(initial_world,X0) ),
inference(resolution,[status(thm)],[f8,f15]) ).
fof(f54,plain,
! [X0,X1] :
( reachable(X1,sK0_skl(X1))
| ~ reachable(X0,X1)
| ~ reachable(initial_world,X0) ),
inference(resolution,[status(thm)],[f8,f14]) ).
fof(f75,plain,
! [X0] :
( reachable(sK0_skl(initial_world),sK0_skl(sK0_skl(initial_world)))
| ~ reachable(X0,initial_world)
| ~ reachable(initial_world,X0) ),
inference(resolution,[status(thm)],[f54,f14]) ).
fof(f76,definition,
! [X0] :
( sQ9_spl
<=> ( ~ reachable(X0,initial_world)
| ~ reachable(initial_world,X0) ) ),
introduced(definition,[new_symbols(definition,[sQ9_spl])],[split_symbol_definition]) ).
fof(f77,plain,
! [X0] :
( ~ sQ9_spl
| ~ reachable(X0,initial_world)
| ~ reachable(initial_world,X0) ),
inference(component_clause,[status(thm)],[f76]) ).
fof(f80,definition,
( sQ10_spl
<=> reachable(sK0_skl(initial_world),sK0_skl(sK0_skl(initial_world))) ),
introduced(definition,[new_symbols(definition,[sQ10_spl])],[split_symbol_definition]) ).
fof(f83,plain,
( sQ10_spl
| sQ9_spl ),
inference(split_clause,[status(thm)],[f75,f76,f80]) ).
fof(f86,plain,
! [X0,X1,X2,X3] :
( p(X2)
| ~ sP0_prd(X2,X3)
| ~ reachable(sK0_skl(X0),sK4_skl(X2,X3))
| ~ sP0_prd(X1,sK0_skl(X0))
| ~ reachable(initial_world,X0) ),
inference(resolution,[status(thm)],[f20,f26]) ).
fof(f88,plain,
( ~ sQ9_spl
| ~ reachable(initial_world,initial_world) ),
inference(resolution,[status(thm)],[f77,f5]) ).
fof(f89,plain,
( ~ sQ9_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f88,f5]) ).
fof(f90,plain,
~ sQ9_spl,
inference(contradiction_clause,[status(thm)],[f89]) ).
fof(f99,plain,
! [X0,X1,X2] :
( p(sK0_skl(X0))
| ~ sP0_prd(sK0_skl(X0),X2)
| p(sK0_skl(X0))
| ~ sP0_prd(sK0_skl(X0),X2)
| ~ sP0_prd(X1,sK0_skl(X0))
| ~ reachable(initial_world,X0) ),
inference(resolution,[status(thm)],[f86,f25]) ).
fof(f100,plain,
! [X0,X1,X2,X3,X4] :
( ~ reachable(X4,sK4_skl(X2,X3))
| ~ reachable(sK0_skl(X0),X4)
| p(X2)
| ~ sP0_prd(X2,X3)
| ~ sP0_prd(X1,sK0_skl(X0))
| ~ reachable(initial_world,X0) ),
inference(resolution,[status(thm)],[f86,f8]) ).
fof(f101,plain,
! [X0,X1,X2] :
( p(sK0_skl(X0))
| ~ sP0_prd(sK0_skl(X0),X2)
| ~ sP0_prd(X1,sK0_skl(X0))
| ~ reachable(initial_world,X0) ),
inference(duplicate_literals_removal,[status(thm)],[f99]) ).
fof(f105,plain,
! [X0,X1,X2,X3] :
( p(X2)
| ~ sP0_prd(X2,X3)
| ~ reachable(sK0_skl(X0),X2)
| p(X2)
| ~ sP0_prd(X2,X3)
| ~ sP0_prd(X1,sK0_skl(X0))
| ~ reachable(initial_world,X0) ),
inference(resolution,[status(thm)],[f100,f25]) ).
fof(f108,plain,
! [X0,X1,X2,X3] :
( ~ reachable(sK0_skl(X0),X2)
| p(X2)
| ~ sP0_prd(X2,X3)
| ~ sP0_prd(X1,sK0_skl(X0))
| ~ reachable(initial_world,X0) ),
inference(duplicate_literals_removal,[status(thm)],[f105]) ).
fof(f109,plain,
! [X0,X1,X2,X3] :
( ~ reachable(sK0_skl(X0),X2)
| ~ sP0_prd(X2,X3)
| ~ sP0_prd(X1,sK0_skl(X0))
| ~ reachable(initial_world,X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f108,f19]) ).
fof(f114,plain,
! [X0,X1,X2] :
( ~ reachable(sK0_skl(initial_world),X1)
| ~ sP0_prd(X1,X2)
| ~ sP0_prd(X0,sK0_skl(initial_world)) ),
inference(resolution,[status(thm)],[f109,f5]) ).
fof(f127,definition,
! [X0] :
( sQ14_spl
<=> ~ sP0_prd(X0,sK0_skl(initial_world)) ),
introduced(definition,[new_symbols(definition,[sQ14_spl])],[split_symbol_definition]) ).
fof(f128,plain,
! [X0] :
( ~ sQ14_spl
| ~ sP0_prd(X0,sK0_skl(initial_world)) ),
inference(component_clause,[status(thm)],[f127]) ).
fof(f130,definition,
! [X1,X2] :
( sQ15_spl
<=> ( ~ reachable(sK0_skl(initial_world),X1)
| ~ sP0_prd(X1,X2) ) ),
introduced(definition,[new_symbols(definition,[sQ15_spl])],[split_symbol_definition]) ).
fof(f131,plain,
! [X0,X1] :
( ~ sQ15_spl
| ~ reachable(sK0_skl(initial_world),X0)
| ~ sP0_prd(X0,X1) ),
inference(component_clause,[status(thm)],[f130]) ).
fof(f133,plain,
( sQ15_spl
| sQ14_spl ),
inference(split_clause,[status(thm)],[f114,f127,f130]) ).
fof(f137,plain,
! [X0] :
( ~ sQ14_spl
| reachable(sK0_skl(initial_world),sK3_skl(initial_world))
| reachable(sK0_skl(initial_world),sK2_skl(initial_world))
| ~ reachable(X0,initial_world)
| ~ reachable(initial_world,X0) ),
inference(resolution,[status(thm)],[f128,f53]) ).
fof(f138,plain,
( ~ sQ14_spl
| q(sK3_skl(initial_world))
| p(sK2_skl(initial_world))
| ~ reachable(initial_world,initial_world) ),
inference(resolution,[status(thm)],[f128,f18]) ).
fof(f139,plain,
( ~ sQ14_spl
| reachable(sK0_skl(initial_world),sK3_skl(initial_world))
| p(sK2_skl(initial_world))
| ~ reachable(initial_world,initial_world) ),
inference(resolution,[status(thm)],[f128,f17]) ).
fof(f140,plain,
( ~ sQ14_spl
| q(sK3_skl(initial_world))
| reachable(sK0_skl(initial_world),sK2_skl(initial_world))
| ~ reachable(initial_world,initial_world) ),
inference(resolution,[status(thm)],[f128,f16]) ).
fof(f142,plain,
( ~ sQ14_spl
| sQ2_spl
| sQ1_spl
| sQ9_spl ),
inference(split_clause,[status(thm)],[f137,f76,f34,f37,f127]) ).
fof(f143,definition,
( sQ16_spl
<=> reachable(initial_world,initial_world) ),
introduced(definition,[new_symbols(definition,[sQ16_spl])],[split_symbol_definition]) ).
fof(f145,plain,
( sQ16_spl
| ~ reachable(initial_world,initial_world) ),
inference(component_clause,[status(thm)],[f143]) ).
fof(f146,definition,
( sQ17_spl
<=> p(sK2_skl(initial_world)) ),
introduced(definition,[new_symbols(definition,[sQ17_spl])],[split_symbol_definition]) ).
fof(f147,plain,
( ~ sQ17_spl
| p(sK2_skl(initial_world)) ),
inference(component_clause,[status(thm)],[f146]) ).
fof(f149,definition,
( sQ18_spl
<=> q(sK3_skl(initial_world)) ),
introduced(definition,[new_symbols(definition,[sQ18_spl])],[split_symbol_definition]) ).
fof(f150,plain,
( ~ sQ18_spl
| q(sK3_skl(initial_world)) ),
inference(component_clause,[status(thm)],[f149]) ).
fof(f152,plain,
( ~ sQ14_spl
| sQ18_spl
| sQ17_spl
| ~ sQ16_spl ),
inference(split_clause,[status(thm)],[f138,f143,f146,f149,f127]) ).
fof(f153,plain,
( ~ sQ14_spl
| sQ2_spl
| sQ17_spl
| ~ sQ16_spl ),
inference(split_clause,[status(thm)],[f139,f143,f146,f37,f127]) ).
fof(f154,plain,
( ~ sQ14_spl
| sQ18_spl
| sQ1_spl
| ~ sQ16_spl ),
inference(split_clause,[status(thm)],[f140,f143,f34,f149,f127]) ).
fof(f155,plain,
( sQ16_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f145,f5]) ).
fof(f156,plain,
sQ16_spl,
inference(contradiction_clause,[status(thm)],[f155]) ).
fof(f158,plain,
! [X0] :
( ~ sQ17_spl
| ~ reachable(X0,sK2_skl(initial_world))
| sP0_prd(sK2_skl(initial_world),X0) ),
inference(resolution,[status(thm)],[f147,f27]) ).
fof(f167,definition,
! [X0] :
( sQ19_spl
<=> ( ~ reachable(X0,sK0_skl(initial_world))
| ~ reachable(initial_world,X0) ) ),
introduced(definition,[new_symbols(definition,[sQ19_spl])],[split_symbol_definition]) ).
fof(f168,plain,
! [X0] :
( ~ sQ19_spl
| ~ reachable(X0,sK0_skl(initial_world))
| ~ reachable(initial_world,X0) ),
inference(component_clause,[status(thm)],[f167]) ).
fof(f171,definition,
( sQ20_spl
<=> reachable(initial_world,sK0_skl(initial_world)) ),
introduced(definition,[new_symbols(definition,[sQ20_spl])],[split_symbol_definition]) ).
fof(f173,plain,
( sQ20_spl
| ~ reachable(initial_world,sK0_skl(initial_world)) ),
inference(component_clause,[status(thm)],[f171]) ).
fof(f190,plain,
( sQ20_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f173,f30]) ).
fof(f191,plain,
sQ20_spl,
inference(contradiction_clause,[status(thm)],[f190]) ).
fof(f207,definition,
! [X0] :
( sQ26_spl
<=> ~ reachable(X0,initial_world) ),
introduced(definition,[new_symbols(definition,[sQ26_spl])],[split_symbol_definition]) ).
fof(f208,plain,
! [X0] :
( ~ sQ26_spl
| ~ reachable(X0,initial_world) ),
inference(component_clause,[status(thm)],[f207]) ).
fof(f212,plain,
( ~ sQ26_spl
| $false ),
inference(resolution,[status(thm)],[f208,f5]) ).
fof(f213,plain,
~ sQ26_spl,
inference(contradiction_clause,[status(thm)],[f212]) ).
fof(f231,plain,
( ~ sQ14_spl
| ~ sQ17_spl
| ~ reachable(sK0_skl(initial_world),sK2_skl(initial_world)) ),
inference(resolution,[status(thm)],[f158,f128]) ).
fof(f233,plain,
( ~ sQ14_spl
| ~ sQ17_spl
| ~ sQ1_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f231,f35]) ).
fof(f234,plain,
( ~ sQ14_spl
| ~ sQ17_spl
| ~ sQ1_spl ),
inference(contradiction_clause,[status(thm)],[f233]) ).
fof(f236,plain,
! [X0,X1] :
( ~ sQ18_spl
| ~ reachable(X0,sK3_skl(initial_world))
| ~ reachable(X1,X0)
| sP0_prd(X0,X1) ),
inference(resolution,[status(thm)],[f150,f28]) ).
fof(f251,plain,
! [X0] :
( ~ sQ2_spl
| ~ sQ18_spl
| ~ reachable(X0,sK0_skl(initial_world))
| sP0_prd(sK0_skl(initial_world),X0) ),
inference(resolution,[status(thm)],[f236,f38]) ).
fof(f254,plain,
! [X0,X1] :
( ~ sQ2_spl
| ~ sQ18_spl
| p(sK0_skl(initial_world))
| ~ sP0_prd(X1,sK0_skl(initial_world))
| ~ reachable(initial_world,initial_world)
| ~ reachable(X0,sK0_skl(initial_world)) ),
inference(resolution,[status(thm)],[f251,f101]) ).
fof(f256,plain,
( ~ sQ14_spl
| ~ sQ2_spl
| ~ sQ18_spl
| ~ reachable(sK0_skl(initial_world),sK0_skl(initial_world)) ),
inference(resolution,[status(thm)],[f251,f128]) ).
fof(f258,definition,
! [X0] :
( sQ27_spl
<=> ~ reachable(X0,sK0_skl(initial_world)) ),
introduced(definition,[new_symbols(definition,[sQ27_spl])],[split_symbol_definition]) ).
fof(f259,plain,
! [X0] :
( ~ sQ27_spl
| ~ reachable(X0,sK0_skl(initial_world)) ),
inference(component_clause,[status(thm)],[f258]) ).
fof(f261,definition,
( sQ28_spl
<=> p(sK0_skl(initial_world)) ),
introduced(definition,[new_symbols(definition,[sQ28_spl])],[split_symbol_definition]) ).
fof(f262,plain,
( ~ sQ28_spl
| p(sK0_skl(initial_world)) ),
inference(component_clause,[status(thm)],[f261]) ).
fof(f264,plain,
( ~ sQ2_spl
| ~ sQ18_spl
| sQ28_spl
| sQ14_spl
| ~ sQ16_spl
| sQ27_spl ),
inference(split_clause,[status(thm)],[f254,f258,f143,f127,f261,f149,f37]) ).
fof(f265,plain,
( ~ sQ14_spl
| ~ sQ2_spl
| ~ sQ18_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f256,f5]) ).
fof(f266,plain,
( ~ sQ14_spl
| ~ sQ2_spl
| ~ sQ18_spl ),
inference(contradiction_clause,[status(thm)],[f265]) ).
fof(f267,plain,
( ~ sQ27_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f30,f259]) ).
fof(f268,plain,
~ sQ27_spl,
inference(contradiction_clause,[status(thm)],[f267]) ).
fof(f270,plain,
! [X0] :
( ~ sQ28_spl
| ~ reachable(X0,sK0_skl(initial_world))
| sP0_prd(sK0_skl(initial_world),X0) ),
inference(resolution,[status(thm)],[f262,f27]) ).
fof(f278,plain,
( ~ sQ0_spl
| reachable(sK0_skl(initial_world),sK1_skl(initial_world)) ),
inference(resolution,[status(thm)],[f32,f24]) ).
fof(f283,plain,
( ~ sQ0_spl
| ~ sQ15_spl
| ~ reachable(sK0_skl(initial_world),sK1_skl(initial_world)) ),
inference(resolution,[status(thm)],[f131,f32]) ).
fof(f293,plain,
( ~ sQ0_spl
| ~ sQ15_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f283,f278]) ).
fof(f294,plain,
( ~ sQ0_spl
| ~ sQ15_spl ),
inference(contradiction_clause,[status(thm)],[f293]) ).
fof(f297,plain,
( sQ0_spl
| q(sK3_skl(initial_world))
| p(sK2_skl(initial_world))
| ~ reachable(initial_world,initial_world) ),
inference(resolution,[status(thm)],[f33,f18]) ).
fof(f298,plain,
( sQ0_spl
| reachable(sK0_skl(initial_world),sK3_skl(initial_world))
| p(sK2_skl(initial_world))
| ~ reachable(initial_world,initial_world) ),
inference(resolution,[status(thm)],[f33,f17]) ).
fof(f299,plain,
( sQ0_spl
| q(sK3_skl(initial_world))
| reachable(sK0_skl(initial_world),sK2_skl(initial_world))
| ~ reachable(initial_world,initial_world) ),
inference(resolution,[status(thm)],[f33,f16]) ).
fof(f302,plain,
( sQ0_spl
| sQ18_spl
| sQ17_spl
| ~ sQ16_spl ),
inference(split_clause,[status(thm)],[f297,f143,f146,f149,f31]) ).
fof(f303,plain,
( sQ0_spl
| sQ2_spl
| sQ17_spl
| ~ sQ16_spl ),
inference(split_clause,[status(thm)],[f298,f143,f146,f37,f31]) ).
fof(f304,plain,
( sQ0_spl
| sQ18_spl
| sQ1_spl
| ~ sQ16_spl ),
inference(split_clause,[status(thm)],[f299,f143,f34,f149,f31]) ).
fof(f323,plain,
( ~ sQ19_spl
| ~ reachable(initial_world,initial_world) ),
inference(resolution,[status(thm)],[f168,f30]) ).
fof(f327,plain,
( ~ sQ19_spl
| ~ sQ16_spl ),
inference(split_clause,[status(thm)],[f323,f143,f167]) ).
fof(f335,plain,
! [X0] :
( ~ sQ15_spl
| ~ sQ28_spl
| ~ reachable(sK0_skl(initial_world),sK0_skl(initial_world))
| ~ reachable(X0,sK0_skl(initial_world)) ),
inference(resolution,[status(thm)],[f270,f131]) ).
fof(f338,definition,
( sQ32_spl
<=> reachable(sK0_skl(initial_world),sK0_skl(initial_world)) ),
introduced(definition,[new_symbols(definition,[sQ32_spl])],[split_symbol_definition]) ).
fof(f340,plain,
( sQ32_spl
| ~ reachable(sK0_skl(initial_world),sK0_skl(initial_world)) ),
inference(component_clause,[status(thm)],[f338]) ).
fof(f341,plain,
( ~ sQ15_spl
| ~ sQ28_spl
| ~ sQ32_spl
| sQ27_spl ),
inference(split_clause,[status(thm)],[f335,f258,f338,f261,f130]) ).
fof(f342,plain,
( sQ32_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f340,f5]) ).
fof(f343,plain,
sQ32_spl,
inference(contradiction_clause,[status(thm)],[f342]) ).
fof(f346,plain,
! [X0] :
( ~ sQ15_spl
| ~ sQ17_spl
| ~ reachable(sK0_skl(initial_world),sK2_skl(initial_world))
| ~ reachable(X0,sK2_skl(initial_world)) ),
inference(resolution,[status(thm)],[f158,f131]) ).
fof(f348,definition,
! [X0] :
( sQ33_spl
<=> ~ reachable(X0,sK2_skl(initial_world)) ),
introduced(definition,[new_symbols(definition,[sQ33_spl])],[split_symbol_definition]) ).
fof(f349,plain,
! [X0] :
( ~ sQ33_spl
| ~ reachable(X0,sK2_skl(initial_world)) ),
inference(component_clause,[status(thm)],[f348]) ).
fof(f351,plain,
( ~ sQ15_spl
| ~ sQ17_spl
| ~ sQ1_spl
| sQ33_spl ),
inference(split_clause,[status(thm)],[f346,f348,f34,f146,f130]) ).
fof(f352,plain,
( ~ sQ1_spl
| ~ sQ33_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f35,f349]) ).
fof(f353,plain,
( ~ sQ1_spl
| ~ sQ33_spl ),
inference(contradiction_clause,[status(thm)],[f352]) ).
fof(f354,plain,
$false,
inference(sat_refutation,[status(thm)],[f40,f83,f90,f133,f142,f152,f153,f154,f156,f191,f213,f234,f264,f266,f268,f294,f302,f303,f304,f327,f341,f343,f351,f353]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYN549+1 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n009.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Mon Sep 21 11:07:28 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.13/0.37 % Drodi V4.1.1
% 0.13/0.43 % Refutation found
% 0.13/0.43 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.13/0.43 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.13/0.44 % Elapsed time: 0.074948 seconds
% 0.13/0.44 % CPU time: 0.390115 seconds
% 0.13/0.44 % Total memory used: 21.634 MB
% 0.13/0.44 % Net memory used: 20.527 MB
%------------------------------------------------------------------------------