%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SYN551+3 : TPTP v9.3.1. Bugfixed v3.1.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n017.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 03:16:47 PM UTC 2026
% Result : Theorem 0.14s 0.61s
% Output : CNFRefutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 25
% Syntax : Number of formulae : 123 ( 8 unt; 24 def)
% Number of atoms : 365 ( 159 equ)
% Maximal formula atoms : 12 ( 2 avg)
% Number of connectives : 427 ( 185 ~; 195 |; 16 &)
% ( 26 <=>; 4 =>; 0 <=; 1 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 26 ( 24 usr; 25 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 2 con; 0-1 aty)
% Number of variables : 48 ( 38 !; 10 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,conjecture,
( ? [X] :
( ! [Y] :
( Y = f(g(Y))
=> Y = X )
& X = f(g(X)) )
<=> ? [X] :
( ! [Y] :
( Y = g(f(Y))
=> Y = X )
& X = g(f(X)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f2,negated_conjecture,
~ ( ? [X] :
( ! [Y] :
( Y = f(g(Y))
=> Y = X )
& X = f(g(X)) )
<=> ? [X] :
( ! [Y] :
( Y = g(f(Y))
=> Y = X )
& X = g(f(X)) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
fof(f3,plain,
( ? [X] :
( ! [Y] :
( Y = X
| Y != f(g(Y)) )
& X = f(g(X)) )
<~> ? [X] :
( ! [Y] :
( Y = X
| Y != g(f(Y)) )
& X = g(f(X)) ) ),
inference(pre_NNF_transformation,[status(thm)],[f2]) ).
fof(f4,plain,
( ( ! [X] :
( ? [Y] :
( Y != X
& Y = g(f(Y)) )
| X != g(f(X)) )
| ! [X] :
( ? [Y] :
( Y != X
& Y = f(g(Y)) )
| X != f(g(X)) ) )
& ( ? [X] :
( ! [Y] :
( Y = X
| Y != g(f(Y)) )
& X = g(f(X)) )
| ? [X] :
( ! [Y] :
( Y = X
| Y != f(g(Y)) )
& X = f(g(X)) ) ) ),
inference(NNF_transformation,[status(thm)],[f3]) ).
fof(f5,plain,
( ( ! [X] :
( ( sK3_skl(X) != X
& sK3_skl(X) = g(f(sK3_skl(X))) )
| X != g(f(X)) )
| ! [X] :
( ( sK2_skl(X) != X
& sK2_skl(X) = f(g(sK2_skl(X))) )
| X != f(g(X)) ) )
& ( ( ! [Y] :
( Y = sK1_skl
| Y != g(f(Y)) )
& sK1_skl = g(f(sK1_skl)) )
| ( ! [Y] :
( Y = sK0_skl
| Y != f(g(Y)) )
& sK0_skl = f(g(sK0_skl)) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl,sK1_skl,sK2_skl,sK3_skl]),skolemize(X,sK0_skl),skolemize(X,sK1_skl),skolemize(Y,sK2_skl(X)),skolemize(Y,sK3_skl(X))],[f4]) ).
fof(f6,plain,
( sK1_skl = g(f(sK1_skl))
| sK0_skl = f(g(sK0_skl)) ),
inference(cnf_transformation,[status(thm)],[f5]) ).
fof(f7,plain,
! [X0] :
( X0 = sK1_skl
| X0 != g(f(X0))
| sK0_skl = f(g(sK0_skl)) ),
inference(cnf_transformation,[status(thm)],[f5]) ).
fof(f8,plain,
! [X0] :
( sK1_skl = g(f(sK1_skl))
| X0 = sK0_skl
| X0 != f(g(X0)) ),
inference(cnf_transformation,[status(thm)],[f5]) ).
fof(f9,plain,
! [X0,X1] :
( X1 = sK1_skl
| X1 != g(f(X1))
| X0 = sK0_skl
| X0 != f(g(X0)) ),
inference(cnf_transformation,[status(thm)],[f5]) ).
fof(f10,plain,
! [X0,X1] :
( sK3_skl(X1) = g(f(sK3_skl(X1)))
| X1 != g(f(X1))
| sK2_skl(X0) = f(g(sK2_skl(X0)))
| X0 != f(g(X0)) ),
inference(cnf_transformation,[status(thm)],[f5]) ).
fof(f11,plain,
! [X0,X1] :
( sK3_skl(X1) != X1
| X1 != g(f(X1))
| sK2_skl(X0) = f(g(sK2_skl(X0)))
| X0 != f(g(X0)) ),
inference(cnf_transformation,[status(thm)],[f5]) ).
fof(f12,plain,
! [X0,X1] :
( sK3_skl(X1) = g(f(sK3_skl(X1)))
| X1 != g(f(X1))
| sK2_skl(X0) != X0
| X0 != f(g(X0)) ),
inference(cnf_transformation,[status(thm)],[f5]) ).
fof(f13,plain,
! [X0,X1] :
( sK3_skl(X1) != X1
| X1 != g(f(X1))
| sK2_skl(X0) != X0
| X0 != f(g(X0)) ),
inference(cnf_transformation,[status(thm)],[f5]) ).
fof(f14,definition,
( sQ0_spl
<=> sK0_skl = f(g(sK0_skl)) ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f15,plain,
( ~ sQ0_spl
| sK0_skl = f(g(sK0_skl)) ),
inference(component_clause,[status(thm)],[f14]) ).
fof(f17,definition,
( sQ1_spl
<=> sK1_skl = g(f(sK1_skl)) ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f18,plain,
( ~ sQ1_spl
| sK1_skl = g(f(sK1_skl)) ),
inference(component_clause,[status(thm)],[f17]) ).
fof(f19,plain,
( sQ1_spl
| sK1_skl != g(f(sK1_skl)) ),
inference(component_clause,[status(thm)],[f17]) ).
fof(f20,plain,
( sQ1_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f6,f14,f17]) ).
fof(f21,definition,
! [X0] :
( sQ2_spl
<=> ( X0 = sK1_skl
| X0 != g(f(X0)) ) ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f22,plain,
! [X0] :
( ~ sQ2_spl
| X0 = sK1_skl
| X0 != g(f(X0)) ),
inference(component_clause,[status(thm)],[f21]) ).
fof(f24,plain,
( sQ2_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f7,f14,f21]) ).
fof(f25,definition,
! [X0] :
( sQ3_spl
<=> ( X0 = sK0_skl
| X0 != f(g(X0)) ) ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f26,plain,
! [X0] :
( ~ sQ3_spl
| X0 = sK0_skl
| X0 != f(g(X0)) ),
inference(component_clause,[status(thm)],[f25]) ).
fof(f28,plain,
( sQ1_spl
| sQ3_spl ),
inference(split_clause,[status(thm)],[f8,f25,f17]) ).
fof(f29,plain,
( sQ2_spl
| sQ3_spl ),
inference(split_clause,[status(thm)],[f9,f25,f21]) ).
fof(f30,definition,
! [X0] :
( sQ4_spl
<=> ( sK2_skl(X0) = f(g(sK2_skl(X0)))
| X0 != f(g(X0)) ) ),
introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition]) ).
fof(f31,plain,
! [X0] :
( ~ sQ4_spl
| sK2_skl(X0) = f(g(sK2_skl(X0)))
| X0 != f(g(X0)) ),
inference(component_clause,[status(thm)],[f30]) ).
fof(f33,definition,
! [X1] :
( sQ5_spl
<=> ( sK3_skl(X1) = g(f(sK3_skl(X1)))
| X1 != g(f(X1)) ) ),
introduced(definition,[new_symbols(definition,[sQ5_spl])],[split_symbol_definition]) ).
fof(f34,plain,
! [X0] :
( ~ sQ5_spl
| sK3_skl(X0) = g(f(sK3_skl(X0)))
| X0 != g(f(X0)) ),
inference(component_clause,[status(thm)],[f33]) ).
fof(f36,plain,
( sQ5_spl
| sQ4_spl ),
inference(split_clause,[status(thm)],[f10,f30,f33]) ).
fof(f37,definition,
! [X1] :
( sQ6_spl
<=> ( sK3_skl(X1) != X1
| X1 != g(f(X1)) ) ),
introduced(definition,[new_symbols(definition,[sQ6_spl])],[split_symbol_definition]) ).
fof(f38,plain,
! [X0] :
( ~ sQ6_spl
| sK3_skl(X0) != X0
| X0 != g(f(X0)) ),
inference(component_clause,[status(thm)],[f37]) ).
fof(f40,plain,
( sQ6_spl
| sQ4_spl ),
inference(split_clause,[status(thm)],[f11,f30,f37]) ).
fof(f41,definition,
! [X0] :
( sQ7_spl
<=> ( sK2_skl(X0) != X0
| X0 != f(g(X0)) ) ),
introduced(definition,[new_symbols(definition,[sQ7_spl])],[split_symbol_definition]) ).
fof(f42,plain,
! [X0] :
( ~ sQ7_spl
| sK2_skl(X0) != X0
| X0 != f(g(X0)) ),
inference(component_clause,[status(thm)],[f41]) ).
fof(f44,plain,
( sQ5_spl
| sQ7_spl ),
inference(split_clause,[status(thm)],[f12,f41,f33]) ).
fof(f45,plain,
( sQ6_spl
| sQ7_spl ),
inference(split_clause,[status(thm)],[f13,f41,f37]) ).
fof(f47,plain,
( ~ sQ0_spl
| ~ sQ7_spl
| sK2_skl(sK0_skl) != sK0_skl
| sK0_skl != sK0_skl ),
inference(paramodulation,[status(thm)],[f15,f42]) ).
fof(f48,definition,
( sQ8_spl
<=> sK0_skl = sK0_skl ),
introduced(definition,[new_symbols(definition,[sQ8_spl])],[split_symbol_definition]) ).
fof(f50,plain,
( sQ8_spl
| sK0_skl != sK0_skl ),
inference(component_clause,[status(thm)],[f48]) ).
fof(f51,definition,
( sQ9_spl
<=> sK2_skl(sK0_skl) = sK0_skl ),
introduced(definition,[new_symbols(definition,[sQ9_spl])],[split_symbol_definition]) ).
fof(f53,plain,
( sQ9_spl
| sK2_skl(sK0_skl) != sK0_skl ),
inference(component_clause,[status(thm)],[f51]) ).
fof(f54,plain,
( ~ sQ0_spl
| ~ sQ7_spl
| ~ sQ9_spl
| ~ sQ8_spl ),
inference(split_clause,[status(thm)],[f47,f48,f51,f41,f14]) ).
fof(f55,plain,
( ~ sQ1_spl
| ~ sQ4_spl
| sK2_skl(f(sK1_skl)) = f(g(sK2_skl(f(sK1_skl))))
| f(sK1_skl) != f(sK1_skl) ),
inference(paramodulation,[status(thm)],[f18,f31]) ).
fof(f56,definition,
( sQ10_spl
<=> f(sK1_skl) = f(sK1_skl) ),
introduced(definition,[new_symbols(definition,[sQ10_spl])],[split_symbol_definition]) ).
fof(f58,plain,
( sQ10_spl
| f(sK1_skl) != f(sK1_skl) ),
inference(component_clause,[status(thm)],[f56]) ).
fof(f59,definition,
( sQ11_spl
<=> sK2_skl(f(sK1_skl)) = f(g(sK2_skl(f(sK1_skl)))) ),
introduced(definition,[new_symbols(definition,[sQ11_spl])],[split_symbol_definition]) ).
fof(f60,plain,
( ~ sQ11_spl
| sK2_skl(f(sK1_skl)) = f(g(sK2_skl(f(sK1_skl)))) ),
inference(component_clause,[status(thm)],[f59]) ).
fof(f62,plain,
( ~ sQ1_spl
| ~ sQ4_spl
| sQ11_spl
| ~ sQ10_spl ),
inference(split_clause,[status(thm)],[f55,f56,f59,f30,f17]) ).
fof(f63,plain,
( sQ10_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f58]) ).
fof(f64,plain,
sQ10_spl,
inference(contradiction_clause,[status(thm)],[f63]) ).
fof(f67,plain,
( ~ sQ0_spl
| ~ sQ2_spl
| g(sK0_skl) = sK1_skl
| g(sK0_skl) != g(sK0_skl) ),
inference(paramodulation,[status(thm)],[f15,f22]) ).
fof(f68,plain,
( ~ sQ0_spl
| ~ sQ6_spl
| sK3_skl(g(sK0_skl)) != g(sK0_skl)
| g(sK0_skl) != g(sK0_skl) ),
inference(paramodulation,[status(thm)],[f15,f38]) ).
fof(f69,plain,
( ~ sQ0_spl
| ~ sQ5_spl
| sK3_skl(g(sK0_skl)) = g(f(sK3_skl(g(sK0_skl))))
| g(sK0_skl) != g(sK0_skl) ),
inference(paramodulation,[status(thm)],[f15,f34]) ).
fof(f71,definition,
( sQ12_spl
<=> g(sK0_skl) = g(sK0_skl) ),
introduced(definition,[new_symbols(definition,[sQ12_spl])],[split_symbol_definition]) ).
fof(f73,plain,
( sQ12_spl
| g(sK0_skl) != g(sK0_skl) ),
inference(component_clause,[status(thm)],[f71]) ).
fof(f74,definition,
( sQ13_spl
<=> g(sK0_skl) = sK1_skl ),
introduced(definition,[new_symbols(definition,[sQ13_spl])],[split_symbol_definition]) ).
fof(f75,plain,
( ~ sQ13_spl
| g(sK0_skl) = sK1_skl ),
inference(component_clause,[status(thm)],[f74]) ).
fof(f77,plain,
( ~ sQ0_spl
| ~ sQ2_spl
| sQ13_spl
| ~ sQ12_spl ),
inference(split_clause,[status(thm)],[f67,f71,f74,f21,f14]) ).
fof(f78,definition,
( sQ14_spl
<=> sK3_skl(g(sK0_skl)) = g(sK0_skl) ),
introduced(definition,[new_symbols(definition,[sQ14_spl])],[split_symbol_definition]) ).
fof(f80,plain,
( sQ14_spl
| sK3_skl(g(sK0_skl)) != g(sK0_skl) ),
inference(component_clause,[status(thm)],[f78]) ).
fof(f81,plain,
( ~ sQ0_spl
| ~ sQ6_spl
| ~ sQ14_spl
| ~ sQ12_spl ),
inference(split_clause,[status(thm)],[f68,f71,f78,f37,f14]) ).
fof(f82,definition,
( sQ15_spl
<=> sK3_skl(g(sK0_skl)) = g(f(sK3_skl(g(sK0_skl)))) ),
introduced(definition,[new_symbols(definition,[sQ15_spl])],[split_symbol_definition]) ).
fof(f83,plain,
( ~ sQ15_spl
| sK3_skl(g(sK0_skl)) = g(f(sK3_skl(g(sK0_skl)))) ),
inference(component_clause,[status(thm)],[f82]) ).
fof(f85,plain,
( ~ sQ0_spl
| ~ sQ5_spl
| sQ15_spl
| ~ sQ12_spl ),
inference(split_clause,[status(thm)],[f69,f71,f82,f33,f14]) ).
fof(f86,plain,
( sQ12_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f73]) ).
fof(f87,plain,
sQ12_spl,
inference(contradiction_clause,[status(thm)],[f86]) ).
fof(f88,plain,
( sQ8_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f50]) ).
fof(f89,plain,
sQ8_spl,
inference(contradiction_clause,[status(thm)],[f88]) ).
fof(f92,plain,
( ~ sQ1_spl
| ~ sQ7_spl
| sK2_skl(f(sK1_skl)) != f(sK1_skl)
| f(sK1_skl) != f(sK1_skl) ),
inference(paramodulation,[status(thm)],[f18,f42]) ).
fof(f93,definition,
( sQ16_spl
<=> sK2_skl(f(sK1_skl)) = f(sK1_skl) ),
introduced(definition,[new_symbols(definition,[sQ16_spl])],[split_symbol_definition]) ).
fof(f95,plain,
( sQ16_spl
| sK2_skl(f(sK1_skl)) != f(sK1_skl) ),
inference(component_clause,[status(thm)],[f93]) ).
fof(f96,plain,
( ~ sQ1_spl
| ~ sQ7_spl
| ~ sQ16_spl
| ~ sQ10_spl ),
inference(split_clause,[status(thm)],[f92,f56,f93,f41,f17]) ).
fof(f99,definition,
( sQ17_spl
<=> sK1_skl = sK1_skl ),
introduced(definition,[new_symbols(definition,[sQ17_spl])],[split_symbol_definition]) ).
fof(f101,plain,
( sQ17_spl
| sK1_skl != sK1_skl ),
inference(component_clause,[status(thm)],[f99]) ).
fof(f103,plain,
( ~ sQ1_spl
| ~ sQ5_spl
| sK3_skl(sK1_skl) = g(f(sK3_skl(sK1_skl))) ),
inference(resolution,[status(thm)],[f34,f18]) ).
fof(f118,plain,
( sQ1_spl
| ~ sQ0_spl
| ~ sQ13_spl
| sK1_skl != g(sK0_skl) ),
inference(backward_demodulation,[status(thm)],[f119,f19]) ).
fof(f119,plain,
( ~ sQ0_spl
| ~ sQ13_spl
| sK0_skl = f(sK1_skl) ),
inference(forward_demodulation,[status(thm)],[f75,f15]) ).
fof(f120,plain,
( sQ1_spl
| ~ sQ0_spl
| ~ sQ13_spl
| sK1_skl != sK1_skl ),
inference(forward_demodulation,[status(thm)],[f75,f118]) ).
fof(f121,plain,
( sQ1_spl
| ~ sQ0_spl
| ~ sQ13_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f120]) ).
fof(f122,plain,
( sQ1_spl
| ~ sQ0_spl
| ~ sQ13_spl ),
inference(contradiction_clause,[status(thm)],[f121]) ).
fof(f144,plain,
( ~ sQ4_spl
| ~ sQ0_spl
| sK2_skl(sK0_skl) = f(g(sK2_skl(sK0_skl))) ),
inference(resolution,[status(thm)],[f15,f31]) ).
fof(f152,plain,
( ~ sQ15_spl
| ~ sQ3_spl
| f(sK3_skl(g(sK0_skl))) = sK0_skl
| f(sK3_skl(g(sK0_skl))) != f(sK3_skl(g(sK0_skl))) ),
inference(paramodulation,[status(thm)],[f83,f26]) ).
fof(f154,definition,
( sQ21_spl
<=> f(sK3_skl(g(sK0_skl))) = f(sK3_skl(g(sK0_skl))) ),
introduced(definition,[new_symbols(definition,[sQ21_spl])],[split_symbol_definition]) ).
fof(f156,plain,
( sQ21_spl
| f(sK3_skl(g(sK0_skl))) != f(sK3_skl(g(sK0_skl))) ),
inference(component_clause,[status(thm)],[f154]) ).
fof(f161,definition,
( sQ23_spl
<=> f(sK3_skl(g(sK0_skl))) = sK0_skl ),
introduced(definition,[new_symbols(definition,[sQ23_spl])],[split_symbol_definition]) ).
fof(f162,plain,
( ~ sQ23_spl
| f(sK3_skl(g(sK0_skl))) = sK0_skl ),
inference(component_clause,[status(thm)],[f161]) ).
fof(f164,plain,
( ~ sQ15_spl
| ~ sQ3_spl
| sQ23_spl
| ~ sQ21_spl ),
inference(split_clause,[status(thm)],[f152,f154,f161,f25,f82]) ).
fof(f169,plain,
( sQ21_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f156]) ).
fof(f170,plain,
sQ21_spl,
inference(contradiction_clause,[status(thm)],[f169]) ).
fof(f172,plain,
( ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ0_spl
| sK2_skl(sK0_skl) = sK0_skl ),
inference(resolution,[status(thm)],[f144,f26]) ).
fof(f177,plain,
( ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ0_spl
| sQ9_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f172,f53]) ).
fof(f178,plain,
( ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ0_spl
| sQ9_spl ),
inference(contradiction_clause,[status(thm)],[f177]) ).
fof(f189,plain,
( ~ sQ15_spl
| ~ sQ23_spl
| sK3_skl(g(sK0_skl)) = g(sK0_skl) ),
inference(forward_demodulation,[status(thm)],[f162,f83]) ).
fof(f190,plain,
( ~ sQ15_spl
| ~ sQ23_spl
| sQ14_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f189,f80]) ).
fof(f191,plain,
( ~ sQ15_spl
| ~ sQ23_spl
| sQ14_spl ),
inference(contradiction_clause,[status(thm)],[f190]) ).
fof(f192,plain,
( sQ17_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f101]) ).
fof(f193,plain,
sQ17_spl,
inference(contradiction_clause,[status(thm)],[f192]) ).
fof(f194,plain,
( ~ sQ6_spl
| ~ sQ1_spl
| sK3_skl(sK1_skl) != sK1_skl ),
inference(resolution,[status(thm)],[f18,f38]) ).
fof(f209,plain,
( ~ sQ11_spl
| ~ sQ4_spl
| sK2_skl(sK2_skl(f(sK1_skl))) = f(g(sK2_skl(sK2_skl(f(sK1_skl)))))
| sK2_skl(f(sK1_skl)) != sK2_skl(f(sK1_skl)) ),
inference(paramodulation,[status(thm)],[f60,f31]) ).
fof(f210,plain,
( ~ sQ11_spl
| ~ sQ2_spl
| g(sK2_skl(f(sK1_skl))) = sK1_skl
| g(sK2_skl(f(sK1_skl))) != g(sK2_skl(f(sK1_skl))) ),
inference(paramodulation,[status(thm)],[f60,f22]) ).
fof(f213,definition,
( sQ28_spl
<=> sK2_skl(f(sK1_skl)) = sK2_skl(f(sK1_skl)) ),
introduced(definition,[new_symbols(definition,[sQ28_spl])],[split_symbol_definition]) ).
fof(f215,plain,
( sQ28_spl
| sK2_skl(f(sK1_skl)) != sK2_skl(f(sK1_skl)) ),
inference(component_clause,[status(thm)],[f213]) ).
fof(f216,definition,
( sQ29_spl
<=> sK2_skl(sK2_skl(f(sK1_skl))) = f(g(sK2_skl(sK2_skl(f(sK1_skl))))) ),
introduced(definition,[new_symbols(definition,[sQ29_spl])],[split_symbol_definition]) ).
fof(f219,plain,
( ~ sQ11_spl
| ~ sQ4_spl
| sQ29_spl
| ~ sQ28_spl ),
inference(split_clause,[status(thm)],[f209,f213,f216,f30,f59]) ).
fof(f220,definition,
( sQ30_spl
<=> g(sK2_skl(f(sK1_skl))) = g(sK2_skl(f(sK1_skl))) ),
introduced(definition,[new_symbols(definition,[sQ30_spl])],[split_symbol_definition]) ).
fof(f222,plain,
( sQ30_spl
| g(sK2_skl(f(sK1_skl))) != g(sK2_skl(f(sK1_skl))) ),
inference(component_clause,[status(thm)],[f220]) ).
fof(f223,definition,
( sQ31_spl
<=> g(sK2_skl(f(sK1_skl))) = sK1_skl ),
introduced(definition,[new_symbols(definition,[sQ31_spl])],[split_symbol_definition]) ).
fof(f224,plain,
( ~ sQ31_spl
| g(sK2_skl(f(sK1_skl))) = sK1_skl ),
inference(component_clause,[status(thm)],[f223]) ).
fof(f226,plain,
( ~ sQ11_spl
| ~ sQ2_spl
| sQ31_spl
| ~ sQ30_spl ),
inference(split_clause,[status(thm)],[f210,f220,f223,f21,f59]) ).
fof(f235,plain,
( sQ30_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f222]) ).
fof(f236,plain,
sQ30_spl,
inference(contradiction_clause,[status(thm)],[f235]) ).
fof(f237,plain,
( sQ28_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f215]) ).
fof(f238,plain,
sQ28_spl,
inference(contradiction_clause,[status(thm)],[f237]) ).
fof(f239,plain,
( ~ sQ11_spl
| ~ sQ31_spl
| sK2_skl(f(sK1_skl)) = f(sK1_skl) ),
inference(backward_demodulation,[status(thm)],[f224,f60]) ).
fof(f249,plain,
( ~ sQ2_spl
| ~ sQ1_spl
| ~ sQ5_spl
| sK3_skl(sK1_skl) = sK1_skl ),
inference(resolution,[status(thm)],[f103,f22]) ).
fof(f256,plain,
( ~ sQ2_spl
| ~ sQ1_spl
| ~ sQ5_spl
| ~ sQ6_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f249,f194]) ).
fof(f257,plain,
( ~ sQ2_spl
| ~ sQ1_spl
| ~ sQ5_spl
| ~ sQ6_spl ),
inference(contradiction_clause,[status(thm)],[f256]) ).
fof(f258,plain,
( sQ16_spl
| ~ sQ11_spl
| ~ sQ31_spl
| f(sK1_skl) != f(sK1_skl) ),
inference(forward_demodulation,[status(thm)],[f239,f95]) ).
fof(f259,plain,
( sQ16_spl
| ~ sQ11_spl
| ~ sQ31_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f258]) ).
fof(f260,plain,
( sQ16_spl
| ~ sQ11_spl
| ~ sQ31_spl ),
inference(contradiction_clause,[status(thm)],[f259]) ).
fof(f261,plain,
$false,
inference(sat_refutation,[status(thm)],[f20,f24,f28,f29,f36,f40,f44,f45,f54,f62,f64,f77,f81,f85,f87,f89,f96,f122,f164,f170,f178,f191,f193,f219,f226,f236,f238,f257,f260]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYN551+3 : TPTP v9.3.1. Bugfixed v3.1.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.57 % Computer : n017.cluster.edu
% 0.09/0.57 % Model : x86_64 x86_64
% 0.09/0.57 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.57 % Memory : 8046.5625MB
% 0.09/0.57 % OS : Linux 6.8.0-71-generic
% 0.09/0.57 % CPULimit : 300
% 0.09/0.57 % WCLimit : 300
% 0.09/0.57 % DateTime : Mon Sep 21 11:03:42 UTC 2026
% 0.09/0.58 % CPUTime :
% 0.14/0.59 % Drodi V4.1.1
% 0.14/0.61 % Refutation found
% 0.14/0.61 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.14/0.61 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.14/0.63 % Elapsed time: 0.049373 seconds
% 0.14/0.63 % CPU time: 0.173610 seconds
% 0.14/0.63 % Total memory used: 61.119 MB
% 0.14/0.63 % Net memory used: 60.739 MB
%------------------------------------------------------------------------------