%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SYN551+1 : TPTP v9.3.1. Bugfixed v3.1.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/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 0.11s 0.41s
% Output : CNFRefutation 0.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 42
% Syntax : Number of formulae : 195 ( 10 unt; 41 def)
% Number of atoms : 614 ( 240 equ)
% Maximal formula atoms : 10 ( 3 avg)
% Number of connectives : 743 ( 324 ~; 342 |; 28 &)
% ( 43 <=>; 4 =>; 0 <=; 2 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 3 ( 2 avg)
% Number of predicates : 43 ( 41 usr; 42 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 6 con; 0-1 aty)
% Number of variables : 87 ( 73 !; 14 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,conjecture,
( ( ! [Y,Z] :
( ( Z = f(g(Z))
& Y = f(g(Y)) )
=> Y = Z )
& ? [X] : X = f(g(X)) )
<=> ( ! [Y,Z] :
( ( Z = g(f(Z))
& Y = g(f(Y)) )
=> Y = Z )
& ? [X] : X = g(f(X)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f2,negated_conjecture,
~ ( ( ! [Y,Z] :
( ( Z = f(g(Z))
& Y = f(g(Y)) )
=> Y = Z )
& ? [X] : X = f(g(X)) )
<=> ( ! [Y,Z] :
( ( Z = g(f(Z))
& Y = g(f(Y)) )
=> Y = Z )
& ? [X] : X = g(f(X)) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
fof(f3,plain,
( ( ! [Y,Z] :
( Y = Z
| Z != f(g(Z))
| Y != f(g(Y)) )
& ? [X] : X = f(g(X)) )
<~> ( ! [Y,Z] :
( Y = Z
| Z != g(f(Z))
| Y != g(f(Y)) )
& ? [X] : X = g(f(X)) ) ),
inference(pre_NNF_transformation,[status(thm)],[f2]) ).
fof(f4,definition,
( sP0_prd
<=> ( ! [Y,Z] :
( Y = Z
| Z != f(g(Z))
| Y != f(g(Y)) )
& ? [X] : X = f(g(X)) ) ),
introduced(definition,[new_symbols(definition,[sP0_prd])],[]) ).
fof(f5,plain,
( sP0_prd
<~> ( ! [Y,Z] :
( Y = Z
| Z != g(f(Z))
| Y != g(f(Y)) )
& ? [X] : X = g(f(X)) ) ),
inference(formula_renaming,[status(thm)],[f3,f4]) ).
fof(f6,plain,
( ( ? [Y,Z] :
( Y != Z
& Z = g(f(Z))
& Y = g(f(Y)) )
| ! [X] : X != g(f(X))
| ~ sP0_prd )
& ( ( ! [Y,Z] :
( Y = Z
| Z != g(f(Z))
| Y != g(f(Y)) )
& ? [X] : X = g(f(X)) )
| sP0_prd ) ),
inference(NNF_transformation,[status(thm)],[f5]) ).
fof(f7,plain,
( ( ( sK1_skl != sK2_skl
& sK2_skl = g(f(sK2_skl))
& sK1_skl = g(f(sK1_skl)) )
| ! [X] : X != g(f(X))
| ~ sP0_prd )
& ( ( ! [Y,Z] :
( Y = Z
| Z != g(f(Z))
| Y != g(f(Y)) )
& sK0_skl = g(f(sK0_skl)) )
| sP0_prd ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl,sK1_skl,sK2_skl]),skolemize(X,sK0_skl),skolemize(Y,sK1_skl),skolemize(Z,sK2_skl)],[f6]) ).
fof(f8,plain,
( sK0_skl = g(f(sK0_skl))
| sP0_prd ),
inference(cnf_transformation,[status(thm)],[f7]) ).
fof(f9,plain,
! [X0,X1] :
( X0 = X1
| X1 != g(f(X1))
| X0 != g(f(X0))
| sP0_prd ),
inference(cnf_transformation,[status(thm)],[f7]) ).
fof(f10,plain,
! [X0] :
( sK1_skl = g(f(sK1_skl))
| X0 != g(f(X0))
| ~ sP0_prd ),
inference(cnf_transformation,[status(thm)],[f7]) ).
fof(f11,plain,
! [X0] :
( sK2_skl = g(f(sK2_skl))
| X0 != g(f(X0))
| ~ sP0_prd ),
inference(cnf_transformation,[status(thm)],[f7]) ).
fof(f12,plain,
! [X0] :
( sK1_skl != sK2_skl
| X0 != g(f(X0))
| ~ sP0_prd ),
inference(cnf_transformation,[status(thm)],[f7]) ).
fof(f13,plain,
( ( ? [Y,Z] :
( Y != Z
& Z = f(g(Z))
& Y = f(g(Y)) )
| ! [X] : X != f(g(X))
| sP0_prd )
& ( ( ! [Y,Z] :
( Y = Z
| Z != f(g(Z))
| Y != f(g(Y)) )
& ? [X] : X = f(g(X)) )
| ~ sP0_prd ) ),
inference(NNF_transformation,[status(thm)],[f4]) ).
fof(f14,plain,
( ( ( sK4_skl != sK5_skl
& sK5_skl = f(g(sK5_skl))
& sK4_skl = f(g(sK4_skl)) )
| ! [X] : X != f(g(X))
| sP0_prd )
& ( ( ! [Y,Z] :
( Y = Z
| Z != f(g(Z))
| Y != f(g(Y)) )
& sK3_skl = f(g(sK3_skl)) )
| ~ sP0_prd ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3_skl,sK4_skl,sK5_skl]),skolemize(X,sK3_skl),skolemize(Y,sK4_skl),skolemize(Z,sK5_skl)],[f13]) ).
fof(f15,plain,
( sK3_skl = f(g(sK3_skl))
| ~ sP0_prd ),
inference(cnf_transformation,[status(thm)],[f14]) ).
fof(f16,plain,
! [X0,X1] :
( X0 = X1
| X1 != f(g(X1))
| X0 != f(g(X0))
| ~ sP0_prd ),
inference(cnf_transformation,[status(thm)],[f14]) ).
fof(f17,plain,
! [X0] :
( sK4_skl = f(g(sK4_skl))
| X0 != f(g(X0))
| sP0_prd ),
inference(cnf_transformation,[status(thm)],[f14]) ).
fof(f18,plain,
! [X0] :
( sK5_skl = f(g(sK5_skl))
| X0 != f(g(X0))
| sP0_prd ),
inference(cnf_transformation,[status(thm)],[f14]) ).
fof(f19,plain,
! [X0] :
( sK4_skl != sK5_skl
| X0 != f(g(X0))
| sP0_prd ),
inference(cnf_transformation,[status(thm)],[f14]) ).
fof(f20,definition,
( sQ0_spl
<=> sP0_prd ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f23,definition,
( sQ1_spl
<=> sK0_skl = g(f(sK0_skl)) ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f24,plain,
( ~ sQ1_spl
| sK0_skl = g(f(sK0_skl)) ),
inference(component_clause,[status(thm)],[f23]) ).
fof(f26,plain,
( sQ1_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f8,f20,f23]) ).
fof(f27,definition,
! [X0,X1] :
( sQ2_spl
<=> ( X0 = X1
| X1 != g(f(X1))
| X0 != g(f(X0)) ) ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f28,plain,
! [X0,X1] :
( ~ sQ2_spl
| X0 = X1
| X1 != g(f(X1))
| X0 != g(f(X0)) ),
inference(component_clause,[status(thm)],[f27]) ).
fof(f30,plain,
( sQ2_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f9,f20,f27]) ).
fof(f31,definition,
! [X0] :
( sQ3_spl
<=> X0 != g(f(X0)) ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f32,plain,
! [X0] :
( ~ sQ3_spl
| X0 != g(f(X0)) ),
inference(component_clause,[status(thm)],[f31]) ).
fof(f34,definition,
( sQ4_spl
<=> sK1_skl = g(f(sK1_skl)) ),
introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition]) ).
fof(f35,plain,
( ~ sQ4_spl
| sK1_skl = g(f(sK1_skl)) ),
inference(component_clause,[status(thm)],[f34]) ).
fof(f37,plain,
( sQ4_spl
| sQ3_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f10,f20,f31,f34]) ).
fof(f38,definition,
( sQ5_spl
<=> sK2_skl = g(f(sK2_skl)) ),
introduced(definition,[new_symbols(definition,[sQ5_spl])],[split_symbol_definition]) ).
fof(f39,plain,
( ~ sQ5_spl
| sK2_skl = g(f(sK2_skl)) ),
inference(component_clause,[status(thm)],[f38]) ).
fof(f41,plain,
( sQ5_spl
| sQ3_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f11,f20,f31,f38]) ).
fof(f42,definition,
( sQ6_spl
<=> sK1_skl = sK2_skl ),
introduced(definition,[new_symbols(definition,[sQ6_spl])],[split_symbol_definition]) ).
fof(f44,plain,
( sQ6_spl
| sK1_skl != sK2_skl ),
inference(component_clause,[status(thm)],[f42]) ).
fof(f45,plain,
( ~ sQ6_spl
| sQ3_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f12,f20,f31,f42]) ).
fof(f46,definition,
( sQ7_spl
<=> sK3_skl = f(g(sK3_skl)) ),
introduced(definition,[new_symbols(definition,[sQ7_spl])],[split_symbol_definition]) ).
fof(f47,plain,
( ~ sQ7_spl
| sK3_skl = f(g(sK3_skl)) ),
inference(component_clause,[status(thm)],[f46]) ).
fof(f49,plain,
( sQ7_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f15,f20,f46]) ).
fof(f50,definition,
! [X0,X1] :
( sQ8_spl
<=> ( X0 = X1
| X1 != f(g(X1))
| X0 != f(g(X0)) ) ),
introduced(definition,[new_symbols(definition,[sQ8_spl])],[split_symbol_definition]) ).
fof(f51,plain,
! [X0,X1] :
( ~ sQ8_spl
| X0 = X1
| X1 != f(g(X1))
| X0 != f(g(X0)) ),
inference(component_clause,[status(thm)],[f50]) ).
fof(f53,plain,
( sQ8_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f16,f20,f50]) ).
fof(f54,definition,
! [X0] :
( sQ9_spl
<=> X0 != f(g(X0)) ),
introduced(definition,[new_symbols(definition,[sQ9_spl])],[split_symbol_definition]) ).
fof(f55,plain,
! [X0] :
( ~ sQ9_spl
| X0 != f(g(X0)) ),
inference(component_clause,[status(thm)],[f54]) ).
fof(f57,definition,
( sQ10_spl
<=> sK4_skl = f(g(sK4_skl)) ),
introduced(definition,[new_symbols(definition,[sQ10_spl])],[split_symbol_definition]) ).
fof(f58,plain,
( ~ sQ10_spl
| sK4_skl = f(g(sK4_skl)) ),
inference(component_clause,[status(thm)],[f57]) ).
fof(f60,plain,
( sQ10_spl
| sQ9_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f17,f20,f54,f57]) ).
fof(f61,definition,
( sQ11_spl
<=> sK5_skl = f(g(sK5_skl)) ),
introduced(definition,[new_symbols(definition,[sQ11_spl])],[split_symbol_definition]) ).
fof(f62,plain,
( ~ sQ11_spl
| sK5_skl = f(g(sK5_skl)) ),
inference(component_clause,[status(thm)],[f61]) ).
fof(f64,plain,
( sQ11_spl
| sQ9_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f18,f20,f54,f61]) ).
fof(f65,definition,
( sQ12_spl
<=> sK4_skl = sK5_skl ),
introduced(definition,[new_symbols(definition,[sQ12_spl])],[split_symbol_definition]) ).
fof(f67,plain,
( sQ12_spl
| sK4_skl != sK5_skl ),
inference(component_clause,[status(thm)],[f65]) ).
fof(f68,plain,
( ~ sQ12_spl
| sQ9_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f19,f20,f54,f65]) ).
fof(f71,plain,
! [X0] :
( ~ sQ1_spl
| ~ sQ8_spl
| X0 = f(sK0_skl)
| f(sK0_skl) != f(sK0_skl)
| X0 != f(g(X0)) ),
inference(paramodulation,[status(thm)],[f24,f51]) ).
fof(f72,definition,
! [X0] :
( sQ13_spl
<=> ( X0 = f(sK0_skl)
| X0 != f(g(X0)) ) ),
introduced(definition,[new_symbols(definition,[sQ13_spl])],[split_symbol_definition]) ).
fof(f73,plain,
! [X0] :
( ~ sQ13_spl
| X0 = f(sK0_skl)
| X0 != f(g(X0)) ),
inference(component_clause,[status(thm)],[f72]) ).
fof(f75,definition,
( sQ14_spl
<=> f(sK0_skl) = f(sK0_skl) ),
introduced(definition,[new_symbols(definition,[sQ14_spl])],[split_symbol_definition]) ).
fof(f77,plain,
( sQ14_spl
| f(sK0_skl) != f(sK0_skl) ),
inference(component_clause,[status(thm)],[f75]) ).
fof(f78,plain,
( ~ sQ1_spl
| ~ sQ8_spl
| ~ sQ14_spl
| sQ13_spl ),
inference(split_clause,[status(thm)],[f71,f72,f75,f50,f23]) ).
fof(f79,plain,
( sQ14_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f77]) ).
fof(f80,plain,
sQ14_spl,
inference(contradiction_clause,[status(thm)],[f79]) ).
fof(f81,plain,
( ~ sQ10_spl
| ~ sQ3_spl
| g(sK4_skl) != g(sK4_skl) ),
inference(paramodulation,[status(thm)],[f58,f32]) ).
fof(f82,plain,
( ~ sQ10_spl
| ~ sQ3_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f81]) ).
fof(f83,plain,
( ~ sQ10_spl
| ~ sQ3_spl ),
inference(contradiction_clause,[status(thm)],[f82]) ).
fof(f85,plain,
( ~ sQ7_spl
| ~ sQ13_spl
| sK3_skl = f(sK0_skl)
| sK3_skl != sK3_skl ),
inference(paramodulation,[status(thm)],[f47,f73]) ).
fof(f87,plain,
( ~ sQ4_spl
| ~ sQ13_spl
| f(sK1_skl) = f(sK0_skl)
| f(sK1_skl) != f(sK1_skl) ),
inference(paramodulation,[status(thm)],[f35,f73]) ).
fof(f88,definition,
( sQ15_spl
<=> sK3_skl = sK3_skl ),
introduced(definition,[new_symbols(definition,[sQ15_spl])],[split_symbol_definition]) ).
fof(f90,plain,
( sQ15_spl
| sK3_skl != sK3_skl ),
inference(component_clause,[status(thm)],[f88]) ).
fof(f91,definition,
( sQ16_spl
<=> sK3_skl = f(sK0_skl) ),
introduced(definition,[new_symbols(definition,[sQ16_spl])],[split_symbol_definition]) ).
fof(f94,plain,
( ~ sQ7_spl
| ~ sQ13_spl
| sQ16_spl
| ~ sQ15_spl ),
inference(split_clause,[status(thm)],[f85,f88,f91,f72,f46]) ).
fof(f95,definition,
( sQ17_spl
<=> f(sK2_skl) = f(sK2_skl) ),
introduced(definition,[new_symbols(definition,[sQ17_spl])],[split_symbol_definition]) ).
fof(f97,plain,
( sQ17_spl
| f(sK2_skl) != f(sK2_skl) ),
inference(component_clause,[status(thm)],[f95]) ).
fof(f102,definition,
( sQ19_spl
<=> f(sK1_skl) = f(sK1_skl) ),
introduced(definition,[new_symbols(definition,[sQ19_spl])],[split_symbol_definition]) ).
fof(f104,plain,
( sQ19_spl
| f(sK1_skl) != f(sK1_skl) ),
inference(component_clause,[status(thm)],[f102]) ).
fof(f105,definition,
( sQ20_spl
<=> f(sK1_skl) = f(sK0_skl) ),
introduced(definition,[new_symbols(definition,[sQ20_spl])],[split_symbol_definition]) ).
fof(f106,plain,
( ~ sQ20_spl
| f(sK1_skl) = f(sK0_skl) ),
inference(component_clause,[status(thm)],[f105]) ).
fof(f107,plain,
( sQ20_spl
| f(sK1_skl) != f(sK0_skl) ),
inference(component_clause,[status(thm)],[f105]) ).
fof(f108,plain,
( ~ sQ4_spl
| ~ sQ13_spl
| sQ20_spl
| ~ sQ19_spl ),
inference(split_clause,[status(thm)],[f87,f102,f105,f72,f34]) ).
fof(f109,plain,
( sQ19_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f104]) ).
fof(f110,plain,
sQ19_spl,
inference(contradiction_clause,[status(thm)],[f109]) ).
fof(f113,plain,
! [X0] :
( ~ sQ20_spl
| ~ sQ2_spl
| X0 = sK0_skl
| sK0_skl != g(f(sK1_skl))
| X0 != g(f(X0)) ),
inference(paramodulation,[status(thm)],[f106,f28]) ).
fof(f121,definition,
! [X0] :
( sQ23_spl
<=> ( X0 = sK0_skl
| X0 != g(f(X0)) ) ),
introduced(definition,[new_symbols(definition,[sQ23_spl])],[split_symbol_definition]) ).
fof(f122,plain,
! [X0] :
( ~ sQ23_spl
| X0 = sK0_skl
| X0 != g(f(X0)) ),
inference(component_clause,[status(thm)],[f121]) ).
fof(f124,definition,
( sQ24_spl
<=> sK0_skl = g(f(sK1_skl)) ),
introduced(definition,[new_symbols(definition,[sQ24_spl])],[split_symbol_definition]) ).
fof(f126,plain,
( sQ24_spl
| sK0_skl != g(f(sK1_skl)) ),
inference(component_clause,[status(thm)],[f124]) ).
fof(f127,plain,
( ~ sQ20_spl
| ~ sQ2_spl
| ~ sQ24_spl
| sQ23_spl ),
inference(split_clause,[status(thm)],[f113,f121,f124,f27,f105]) ).
fof(f128,plain,
( sQ17_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f97]) ).
fof(f129,plain,
sQ17_spl,
inference(contradiction_clause,[status(thm)],[f128]) ).
fof(f130,plain,
( ~ sQ1_spl
| ~ sQ20_spl
| sK0_skl = g(f(sK1_skl)) ),
inference(forward_demodulation,[status(thm)],[f106,f24]) ).
fof(f131,plain,
! [X0] :
( ~ sQ1_spl
| ~ sQ20_spl
| ~ sQ2_spl
| X0 = sK1_skl
| sK1_skl != sK0_skl
| X0 != g(f(X0)) ),
inference(paramodulation,[status(thm)],[f130,f28]) ).
fof(f133,definition,
! [X0] :
( sQ25_spl
<=> ( X0 = sK1_skl
| X0 != g(f(X0)) ) ),
introduced(definition,[new_symbols(definition,[sQ25_spl])],[split_symbol_definition]) ).
fof(f134,plain,
! [X0] :
( ~ sQ25_spl
| X0 = sK1_skl
| X0 != g(f(X0)) ),
inference(component_clause,[status(thm)],[f133]) ).
fof(f136,definition,
( sQ26_spl
<=> sK1_skl = sK0_skl ),
introduced(definition,[new_symbols(definition,[sQ26_spl])],[split_symbol_definition]) ).
fof(f137,plain,
( ~ sQ26_spl
| sK1_skl = sK0_skl ),
inference(component_clause,[status(thm)],[f136]) ).
fof(f138,plain,
( sQ26_spl
| sK1_skl != sK0_skl ),
inference(component_clause,[status(thm)],[f136]) ).
fof(f139,plain,
( ~ sQ1_spl
| ~ sQ20_spl
| ~ sQ2_spl
| ~ sQ26_spl
| sQ25_spl ),
inference(split_clause,[status(thm)],[f131,f133,f136,f27,f105,f23]) ).
fof(f143,plain,
( sQ24_spl
| ~ sQ1_spl
| ~ sQ20_spl
| sK0_skl != sK0_skl ),
inference(forward_demodulation,[status(thm)],[f130,f126]) ).
fof(f144,plain,
( sQ24_spl
| ~ sQ1_spl
| ~ sQ20_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f143]) ).
fof(f145,plain,
( sQ24_spl
| ~ sQ1_spl
| ~ sQ20_spl ),
inference(contradiction_clause,[status(thm)],[f144]) ).
fof(f154,plain,
( sQ15_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f90]) ).
fof(f155,plain,
sQ15_spl,
inference(contradiction_clause,[status(thm)],[f154]) ).
fof(f158,plain,
! [X0] :
( ~ sQ11_spl
| ~ sQ2_spl
| X0 = g(sK5_skl)
| g(sK5_skl) != g(sK5_skl)
| X0 != g(f(X0)) ),
inference(paramodulation,[status(thm)],[f62,f28]) ).
fof(f159,definition,
! [X0] :
( sQ28_spl
<=> ( X0 = g(sK5_skl)
| X0 != g(f(X0)) ) ),
introduced(definition,[new_symbols(definition,[sQ28_spl])],[split_symbol_definition]) ).
fof(f160,plain,
! [X0] :
( ~ sQ28_spl
| X0 = g(sK5_skl)
| X0 != g(f(X0)) ),
inference(component_clause,[status(thm)],[f159]) ).
fof(f162,definition,
( sQ29_spl
<=> g(sK5_skl) = g(sK5_skl) ),
introduced(definition,[new_symbols(definition,[sQ29_spl])],[split_symbol_definition]) ).
fof(f164,plain,
( sQ29_spl
| g(sK5_skl) != g(sK5_skl) ),
inference(component_clause,[status(thm)],[f162]) ).
fof(f165,plain,
( ~ sQ11_spl
| ~ sQ2_spl
| ~ sQ29_spl
| sQ28_spl ),
inference(split_clause,[status(thm)],[f158,f159,f162,f27,f61]) ).
fof(f166,plain,
! [X0] :
( ~ sQ10_spl
| ~ sQ2_spl
| X0 = g(sK4_skl)
| g(sK4_skl) != g(sK4_skl)
| X0 != g(f(X0)) ),
inference(paramodulation,[status(thm)],[f58,f28]) ).
fof(f167,definition,
! [X0] :
( sQ30_spl
<=> ( X0 = g(sK4_skl)
| X0 != g(f(X0)) ) ),
introduced(definition,[new_symbols(definition,[sQ30_spl])],[split_symbol_definition]) ).
fof(f170,definition,
( sQ31_spl
<=> g(sK4_skl) = g(sK4_skl) ),
introduced(definition,[new_symbols(definition,[sQ31_spl])],[split_symbol_definition]) ).
fof(f172,plain,
( sQ31_spl
| g(sK4_skl) != g(sK4_skl) ),
inference(component_clause,[status(thm)],[f170]) ).
fof(f173,plain,
( ~ sQ10_spl
| ~ sQ2_spl
| ~ sQ31_spl
| sQ30_spl ),
inference(split_clause,[status(thm)],[f166,f167,f170,f27,f57]) ).
fof(f178,plain,
( ~ sQ10_spl
| ~ sQ23_spl
| g(sK4_skl) = sK0_skl
| g(sK4_skl) != g(sK4_skl) ),
inference(paramodulation,[status(thm)],[f58,f122]) ).
fof(f179,plain,
( ~ sQ11_spl
| ~ sQ23_spl
| g(sK5_skl) = sK0_skl
| g(sK5_skl) != g(sK5_skl) ),
inference(paramodulation,[status(thm)],[f62,f122]) ).
fof(f182,definition,
( sQ32_spl
<=> sK0_skl = sK0_skl ),
introduced(definition,[new_symbols(definition,[sQ32_spl])],[split_symbol_definition]) ).
fof(f184,plain,
( sQ32_spl
| sK0_skl != sK0_skl ),
inference(component_clause,[status(thm)],[f182]) ).
fof(f186,definition,
( sQ33_spl
<=> g(sK4_skl) = sK0_skl ),
introduced(definition,[new_symbols(definition,[sQ33_spl])],[split_symbol_definition]) ).
fof(f187,plain,
( ~ sQ33_spl
| g(sK4_skl) = sK0_skl ),
inference(component_clause,[status(thm)],[f186]) ).
fof(f189,plain,
( ~ sQ10_spl
| ~ sQ23_spl
| sQ33_spl
| ~ sQ31_spl ),
inference(split_clause,[status(thm)],[f178,f170,f186,f121,f57]) ).
fof(f190,definition,
( sQ34_spl
<=> g(sK5_skl) = sK0_skl ),
introduced(definition,[new_symbols(definition,[sQ34_spl])],[split_symbol_definition]) ).
fof(f191,plain,
( ~ sQ34_spl
| g(sK5_skl) = sK0_skl ),
inference(component_clause,[status(thm)],[f190]) ).
fof(f193,plain,
( ~ sQ11_spl
| ~ sQ23_spl
| sQ34_spl
| ~ sQ29_spl ),
inference(split_clause,[status(thm)],[f179,f162,f190,f121,f61]) ).
fof(f198,plain,
( sQ31_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f172]) ).
fof(f199,plain,
sQ31_spl,
inference(contradiction_clause,[status(thm)],[f198]) ).
fof(f200,plain,
( sQ29_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f164]) ).
fof(f201,plain,
sQ29_spl,
inference(contradiction_clause,[status(thm)],[f200]) ).
fof(f212,definition,
( sQ36_spl
<=> sK2_skl = sK2_skl ),
introduced(definition,[new_symbols(definition,[sQ36_spl])],[split_symbol_definition]) ).
fof(f214,plain,
( sQ36_spl
| sK2_skl != sK2_skl ),
inference(component_clause,[status(thm)],[f212]) ).
fof(f217,plain,
( sQ36_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f214]) ).
fof(f218,plain,
sQ36_spl,
inference(contradiction_clause,[status(thm)],[f217]) ).
fof(f220,plain,
! [X0] :
( ~ sQ1_spl
| ~ sQ2_spl
| X0 = sK0_skl
| sK0_skl != sK0_skl
| X0 != g(f(X0)) ),
inference(paramodulation,[status(thm)],[f24,f28]) ).
fof(f221,plain,
( ~ sQ1_spl
| ~ sQ9_spl
| f(sK0_skl) != f(sK0_skl) ),
inference(paramodulation,[status(thm)],[f24,f55]) ).
fof(f222,plain,
( ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ32_spl
| sQ23_spl ),
inference(split_clause,[status(thm)],[f220,f121,f182,f27,f23]) ).
fof(f223,plain,
( ~ sQ1_spl
| ~ sQ9_spl
| ~ sQ14_spl ),
inference(split_clause,[status(thm)],[f221,f75,f54,f23]) ).
fof(f224,plain,
( ~ sQ7_spl
| ~ sQ3_spl
| g(sK3_skl) != g(sK3_skl) ),
inference(paramodulation,[status(thm)],[f47,f32]) ).
fof(f225,plain,
( ~ sQ7_spl
| ~ sQ3_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f224]) ).
fof(f226,plain,
( ~ sQ7_spl
| ~ sQ3_spl ),
inference(contradiction_clause,[status(thm)],[f225]) ).
fof(f228,plain,
( ~ sQ5_spl
| ~ sQ25_spl
| sK2_skl = sK1_skl ),
inference(resolution,[status(thm)],[f134,f39]) ).
fof(f233,plain,
( ~ sQ5_spl
| ~ sQ25_spl
| sQ6_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f228,f44]) ).
fof(f234,plain,
( ~ sQ5_spl
| ~ sQ25_spl
| sQ6_spl ),
inference(contradiction_clause,[status(thm)],[f233]) ).
fof(f242,plain,
! [X0] :
( ~ sQ28_spl
| ~ sQ34_spl
| X0 = sK0_skl
| X0 != g(f(X0)) ),
inference(forward_demodulation,[status(thm)],[f191,f160]) ).
fof(f244,plain,
( ~ sQ4_spl
| ~ sQ28_spl
| ~ sQ34_spl
| sK1_skl = sK0_skl ),
inference(resolution,[status(thm)],[f242,f35]) ).
fof(f248,plain,
( ~ sQ4_spl
| ~ sQ28_spl
| ~ sQ34_spl
| sQ26_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f244,f138]) ).
fof(f249,plain,
( ~ sQ4_spl
| ~ sQ28_spl
| ~ sQ34_spl
| sQ26_spl ),
inference(contradiction_clause,[status(thm)],[f248]) ).
fof(f252,plain,
! [X0] :
( ~ sQ7_spl
| ~ sQ8_spl
| X0 = sK3_skl
| X0 != f(g(X0)) ),
inference(resolution,[status(thm)],[f51,f47]) ).
fof(f253,plain,
! [X0] :
( ~ sQ7_spl
| ~ sQ8_spl
| X0 = sK3_skl
| sK3_skl != sK3_skl
| X0 != f(g(X0)) ),
inference(paramodulation,[status(thm)],[f47,f51]) ).
fof(f255,plain,
! [X0] :
( ~ sQ4_spl
| ~ sQ8_spl
| X0 = f(sK1_skl)
| f(sK1_skl) != f(sK1_skl)
| X0 != f(g(X0)) ),
inference(paramodulation,[status(thm)],[f35,f51]) ).
fof(f256,plain,
! [X0] :
( ~ sQ33_spl
| ~ sQ8_spl
| X0 = sK4_skl
| sK4_skl != f(sK0_skl)
| X0 != f(g(X0)) ),
inference(paramodulation,[status(thm)],[f187,f51]) ).
fof(f257,definition,
! [X0] :
( sQ37_spl
<=> ( X0 = sK3_skl
| X0 != f(g(X0)) ) ),
introduced(definition,[new_symbols(definition,[sQ37_spl])],[split_symbol_definition]) ).
fof(f260,plain,
( ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ15_spl
| sQ37_spl ),
inference(split_clause,[status(thm)],[f253,f257,f88,f50,f46]) ).
fof(f265,definition,
! [X0] :
( sQ39_spl
<=> ( X0 = f(sK1_skl)
| X0 != f(g(X0)) ) ),
introduced(definition,[new_symbols(definition,[sQ39_spl])],[split_symbol_definition]) ).
fof(f268,plain,
( ~ sQ4_spl
| ~ sQ8_spl
| ~ sQ19_spl
| sQ39_spl ),
inference(split_clause,[status(thm)],[f255,f265,f102,f50,f34]) ).
fof(f269,definition,
! [X0] :
( sQ40_spl
<=> ( X0 = sK4_skl
| X0 != f(g(X0)) ) ),
introduced(definition,[new_symbols(definition,[sQ40_spl])],[split_symbol_definition]) ).
fof(f272,definition,
( sQ41_spl
<=> sK4_skl = f(sK0_skl) ),
introduced(definition,[new_symbols(definition,[sQ41_spl])],[split_symbol_definition]) ).
fof(f274,plain,
( sQ41_spl
| sK4_skl != f(sK0_skl) ),
inference(component_clause,[status(thm)],[f272]) ).
fof(f275,plain,
( ~ sQ33_spl
| ~ sQ8_spl
| ~ sQ41_spl
| sQ40_spl ),
inference(split_clause,[status(thm)],[f256,f269,f272,f50,f186]) ).
fof(f280,plain,
( ~ sQ5_spl
| ~ sQ7_spl
| ~ sQ8_spl
| f(sK2_skl) = sK3_skl
| f(sK2_skl) != f(sK2_skl) ),
inference(paramodulation,[status(thm)],[f39,f252]) ).
fof(f281,plain,
( ~ sQ4_spl
| ~ sQ7_spl
| ~ sQ8_spl
| f(sK1_skl) = sK3_skl
| f(sK1_skl) != f(sK1_skl) ),
inference(paramodulation,[status(thm)],[f35,f252]) ).
fof(f283,definition,
( sQ42_spl
<=> f(sK2_skl) = sK3_skl ),
introduced(definition,[new_symbols(definition,[sQ42_spl])],[split_symbol_definition]) ).
fof(f284,plain,
( ~ sQ42_spl
| f(sK2_skl) = sK3_skl ),
inference(component_clause,[status(thm)],[f283]) ).
fof(f286,plain,
( ~ sQ5_spl
| ~ sQ7_spl
| ~ sQ8_spl
| sQ42_spl
| ~ sQ17_spl ),
inference(split_clause,[status(thm)],[f280,f95,f283,f50,f46,f38]) ).
fof(f287,definition,
( sQ43_spl
<=> f(sK1_skl) = sK3_skl ),
introduced(definition,[new_symbols(definition,[sQ43_spl])],[split_symbol_definition]) ).
fof(f288,plain,
( ~ sQ43_spl
| f(sK1_skl) = sK3_skl ),
inference(component_clause,[status(thm)],[f287]) ).
fof(f290,plain,
( ~ sQ4_spl
| ~ sQ7_spl
| ~ sQ8_spl
| sQ43_spl
| ~ sQ19_spl ),
inference(split_clause,[status(thm)],[f281,f102,f287,f50,f46,f34]) ).
fof(f291,plain,
( ~ sQ5_spl
| ~ sQ42_spl
| sK2_skl = g(sK3_skl) ),
inference(backward_demodulation,[status(thm)],[f284,f39]) ).
fof(f292,plain,
( ~ sQ4_spl
| ~ sQ43_spl
| sK1_skl = g(sK3_skl) ),
inference(backward_demodulation,[status(thm)],[f288,f35]) ).
fof(f299,plain,
( ~ sQ5_spl
| ~ sQ42_spl
| ~ sQ4_spl
| ~ sQ43_spl
| sK2_skl = sK1_skl ),
inference(backward_demodulation,[status(thm)],[f292,f291]) ).
fof(f302,plain,
( ~ sQ5_spl
| ~ sQ42_spl
| ~ sQ4_spl
| ~ sQ43_spl
| sQ6_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f299,f44]) ).
fof(f303,plain,
( ~ sQ5_spl
| ~ sQ42_spl
| ~ sQ4_spl
| ~ sQ43_spl
| sQ6_spl ),
inference(contradiction_clause,[status(thm)],[f302]) ).
fof(f305,definition,
( sQ44_spl
<=> sK1_skl = sK1_skl ),
introduced(definition,[new_symbols(definition,[sQ44_spl])],[split_symbol_definition]) ).
fof(f307,plain,
( sQ44_spl
| sK1_skl != sK1_skl ),
inference(component_clause,[status(thm)],[f305]) ).
fof(f311,plain,
( sQ44_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f307]) ).
fof(f312,plain,
sQ44_spl,
inference(contradiction_clause,[status(thm)],[f311]) ).
fof(f313,plain,
( sQ41_spl
| ~ sQ26_spl
| sK4_skl != f(sK1_skl) ),
inference(backward_demodulation,[status(thm)],[f137,f274]) ).
fof(f327,plain,
( ~ sQ33_spl
| ~ sQ26_spl
| g(sK4_skl) = sK1_skl ),
inference(forward_demodulation,[status(thm)],[f137,f187]) ).
fof(f329,plain,
( ~ sQ10_spl
| ~ sQ33_spl
| ~ sQ26_spl
| sK4_skl = f(sK1_skl) ),
inference(forward_demodulation,[status(thm)],[f327,f58]) ).
fof(f330,plain,
( ~ sQ10_spl
| ~ sQ33_spl
| ~ sQ26_spl
| sQ41_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f329,f313]) ).
fof(f331,plain,
( ~ sQ10_spl
| ~ sQ33_spl
| ~ sQ26_spl
| sQ41_spl ),
inference(contradiction_clause,[status(thm)],[f330]) ).
fof(f335,definition,
( sQ45_spl
<=> sK1_skl = g(sK4_skl) ),
introduced(definition,[new_symbols(definition,[sQ45_spl])],[split_symbol_definition]) ).
fof(f337,plain,
( sQ45_spl
| sK1_skl != g(sK4_skl) ),
inference(component_clause,[status(thm)],[f335]) ).
fof(f339,plain,
( sQ45_spl
| ~ sQ33_spl
| ~ sQ26_spl
| sK1_skl != sK1_skl ),
inference(forward_demodulation,[status(thm)],[f327,f337]) ).
fof(f340,plain,
( sQ45_spl
| ~ sQ33_spl
| ~ sQ26_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f339]) ).
fof(f341,plain,
( sQ45_spl
| ~ sQ33_spl
| ~ sQ26_spl ),
inference(contradiction_clause,[status(thm)],[f340]) ).
fof(f346,plain,
( sQ20_spl
| ~ sQ26_spl
| f(sK1_skl) != f(sK1_skl) ),
inference(forward_demodulation,[status(thm)],[f137,f107]) ).
fof(f347,plain,
( sQ20_spl
| ~ sQ26_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f346]) ).
fof(f348,plain,
( sQ20_spl
| ~ sQ26_spl ),
inference(contradiction_clause,[status(thm)],[f347]) ).
fof(f349,plain,
( sQ32_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f184]) ).
fof(f350,plain,
sQ32_spl,
inference(contradiction_clause,[status(thm)],[f349]) ).
fof(f351,plain,
( ~ sQ10_spl
| ~ sQ33_spl
| sK4_skl = f(sK0_skl) ),
inference(forward_demodulation,[status(thm)],[f187,f58]) ).
fof(f354,plain,
( ~ sQ11_spl
| ~ sQ34_spl
| sK5_skl = f(sK0_skl) ),
inference(forward_demodulation,[status(thm)],[f191,f62]) ).
fof(f355,plain,
( ~ sQ11_spl
| ~ sQ34_spl
| ~ sQ10_spl
| ~ sQ33_spl
| sK5_skl = sK4_skl ),
inference(forward_demodulation,[status(thm)],[f351,f354]) ).
fof(f356,plain,
( ~ sQ11_spl
| ~ sQ34_spl
| ~ sQ10_spl
| ~ sQ33_spl
| sQ12_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f355,f67]) ).
fof(f357,plain,
( ~ sQ11_spl
| ~ sQ34_spl
| ~ sQ10_spl
| ~ sQ33_spl
| sQ12_spl ),
inference(contradiction_clause,[status(thm)],[f356]) ).
fof(f358,plain,
$false,
inference(sat_refutation,[status(thm)],[f26,f30,f37,f41,f45,f49,f53,f60,f64,f68,f78,f80,f83,f94,f108,f110,f127,f129,f139,f145,f155,f165,f173,f189,f193,f199,f201,f218,f222,f223,f226,f234,f249,f260,f268,f275,f286,f290,f303,f312,f331,f341,f348,f350,f357]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYN551+1 : TPTP v9.3.1. Bugfixed v3.1.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.11/0.37 % Computer : n009.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Mon Sep 21 11:08:28 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.38 % Drodi V4.1.1
% 0.11/0.41 % Refutation found
% 0.11/0.41 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.11/0.41 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.11/0.44 % Elapsed time: 0.059111 seconds
% 0.11/0.44 % CPU time: 0.165143 seconds
% 0.11/0.44 % Total memory used: 80.382 MB
% 0.11/0.44 % Net memory used: 79.921 MB
%------------------------------------------------------------------------------