%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : SYN551+2 : TPTP v9.3.1. Bugfixed v3.1.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n006.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 03:20:08 PM UTC 2026
% Result : CounterSatisfiable 0.13s 5.41s
% Output : Saturation 0.13s
% Verified :
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)
% Comments :
%------------------------------------------------------------------------------
fof(f1,conjecture,
( ? [X] :
! [Y] :
( Y = f(g(Y))
<=> X = Y )
<=> ? [X] :
! [Y] :
( Y = g(f(Y))
<=> X = Y ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f2,negated_conjecture,
~ ( ? [X] :
! [Y] :
( Y = f(g(Y))
<=> X = Y )
<=> ? [X] :
! [Y] :
( Y = g(f(Y))
<=> X = Y ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
fof(f3,plain,
( ? [X] :
! [Y] :
( Y = f(g(Y))
<=> X = Y )
<~> ? [X] :
! [Y] :
( Y = g(f(Y))
<=> X = Y ) ),
inference(pre_NNF_transformation,[status(thm)],[f2]) ).
fof(f4,definition,
! [X,Y] :
( sP0_prd(Y,X)
<=> ( Y = f(g(Y))
<=> X = Y ) ),
introduced(definition,[new_symbols(definition,[sP0_prd])],[]) ).
fof(f5,plain,
( ? [X] :
! [Y] : sP0_prd(Y,X)
<~> ? [X] :
! [Y] :
( Y = g(f(Y))
<=> X = Y ) ),
inference(formula_renaming,[status(thm)],[f3,f4]) ).
fof(f6,plain,
( ( ! [X] :
? [Y] :
( ( X = Y
| Y = g(f(Y)) )
& ( X != Y
| Y != g(f(Y)) ) )
| ! [X] :
? [Y] : ~ sP0_prd(Y,X) )
& ( ? [X] :
! [Y] :
( ( X != Y
| Y = g(f(Y)) )
& ( X = Y
| Y != g(f(Y)) ) )
| ? [X] :
! [Y] : sP0_prd(Y,X) ) ),
inference(NNF_transformation,[status(thm)],[f5]) ).
fof(f7,plain,
( ( ! [X] :
? [Y] :
( ( X = Y
| Y = g(f(Y)) )
& ( X != Y
| Y != g(f(Y)) ) )
| ! [X] :
? [Y] : ~ sP0_prd(Y,X) )
& ( ? [X] :
( ! [Y] :
( X != Y
| Y = g(f(Y)) )
& ! [Y] :
( X = Y
| Y != g(f(Y)) ) )
| ? [X] :
! [Y] : sP0_prd(Y,X) ) ),
inference(miniscoping,[status(thm)],[f6]) ).
fof(f8,plain,
( ( ! [X] :
( ( X = sK3_skl(X)
| sK3_skl(X) = g(f(sK3_skl(X))) )
& ( X != sK3_skl(X)
| sK3_skl(X) != g(f(sK3_skl(X))) ) )
| ! [X] : ~ sP0_prd(sK2_skl(X),X) )
& ( ( ! [Y] :
( sK1_skl != Y
| Y = g(f(Y)) )
& ! [Y] :
( sK1_skl = Y
| Y != g(f(Y)) ) )
| ! [Y] : sP0_prd(Y,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))],[f7]) ).
fof(f9,plain,
! [X0,X1] :
( sK1_skl = X1
| X1 != g(f(X1))
| sP0_prd(X0,sK0_skl) ),
inference(cnf_transformation,[status(thm)],[f8]) ).
fof(f10,plain,
! [X0,X1] :
( sK1_skl != X1
| X1 = g(f(X1))
| sP0_prd(X0,sK0_skl) ),
inference(cnf_transformation,[status(thm)],[f8]) ).
fof(f11,plain,
! [X0,X1] :
( X1 != sK3_skl(X1)
| sK3_skl(X1) != g(f(sK3_skl(X1)))
| ~ sP0_prd(sK2_skl(X0),X0) ),
inference(cnf_transformation,[status(thm)],[f8]) ).
fof(f12,plain,
! [X0,X1] :
( X1 = sK3_skl(X1)
| sK3_skl(X1) = g(f(sK3_skl(X1)))
| ~ sP0_prd(sK2_skl(X0),X0) ),
inference(cnf_transformation,[status(thm)],[f8]) ).
fof(f13,plain,
! [X,Y] :
( ( ( ( X = Y
| Y = f(g(Y)) )
& ( X != Y
| Y != f(g(Y)) ) )
| sP0_prd(Y,X) )
& ( ( ( X != Y
| Y = f(g(Y)) )
& ( X = Y
| Y != f(g(Y)) ) )
| ~ sP0_prd(Y,X) ) ),
inference(NNF_transformation,[status(thm)],[f4]) ).
fof(f14,plain,
( ! [X,Y] :
( ( ( X = Y
| Y = f(g(Y)) )
& ( X != Y
| Y != f(g(Y)) ) )
| sP0_prd(Y,X) )
& ! [X,Y] :
( ( ( X != Y
| Y = f(g(Y)) )
& ( X = Y
| Y != f(g(Y)) ) )
| ~ sP0_prd(Y,X) ) ),
inference(miniscoping,[status(thm)],[f13]) ).
fof(f15,plain,
! [X0,X1] :
( X1 = X0
| X0 != f(g(X0))
| ~ sP0_prd(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f14]) ).
fof(f16,plain,
! [X0,X1] :
( X1 != X0
| X0 = f(g(X0))
| ~ sP0_prd(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f14]) ).
fof(f17,plain,
! [X0,X1] :
( X1 != X0
| X0 != f(g(X0))
| sP0_prd(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f14]) ).
fof(f18,plain,
! [X0,X1] :
( X1 = X0
| X0 = f(g(X0))
| sP0_prd(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f14]) ).
fof(f19,definition,
! [X0] :
( sQ0_spl
<=> sP0_prd(X0,sK0_skl) ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f20,plain,
! [X0] :
( ~ sQ0_spl
| sP0_prd(X0,sK0_skl) ),
inference(component_clause,[status(thm)],[f19]) ).
fof(f22,definition,
! [X1] :
( sQ1_spl
<=> ( sK1_skl = X1
| X1 != g(f(X1)) ) ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f23,plain,
! [X0] :
( ~ sQ1_spl
| sK1_skl = X0
| X0 != g(f(X0)) ),
inference(component_clause,[status(thm)],[f22]) ).
fof(f25,plain,
( sQ1_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f9,f19,f22]) ).
fof(f26,definition,
! [X1] :
( sQ2_spl
<=> ( sK1_skl != X1
| X1 = g(f(X1)) ) ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f27,plain,
! [X0] :
( ~ sQ2_spl
| sK1_skl != X0
| X0 = g(f(X0)) ),
inference(component_clause,[status(thm)],[f26]) ).
fof(f29,plain,
( sQ2_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f10,f19,f26]) ).
fof(f30,definition,
! [X0] :
( sQ3_spl
<=> ~ sP0_prd(sK2_skl(X0),X0) ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f31,plain,
! [X0] :
( ~ sQ3_spl
| ~ sP0_prd(sK2_skl(X0),X0) ),
inference(component_clause,[status(thm)],[f30]) ).
fof(f33,definition,
! [X1] :
( sQ4_spl
<=> ( X1 != sK3_skl(X1)
| sK3_skl(X1) != g(f(sK3_skl(X1))) ) ),
introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition]) ).
fof(f34,plain,
! [X0] :
( ~ sQ4_spl
| X0 != sK3_skl(X0)
| sK3_skl(X0) != g(f(sK3_skl(X0))) ),
inference(component_clause,[status(thm)],[f33]) ).
fof(f36,plain,
( sQ4_spl
| sQ3_spl ),
inference(split_clause,[status(thm)],[f11,f30,f33]) ).
fof(f37,definition,
! [X1] :
( sQ5_spl
<=> ( X1 = sK3_skl(X1)
| sK3_skl(X1) = g(f(sK3_skl(X1))) ) ),
introduced(definition,[new_symbols(definition,[sQ5_spl])],[split_symbol_definition]) ).
fof(f38,plain,
! [X0] :
( ~ sQ5_spl
| X0 = sK3_skl(X0)
| sK3_skl(X0) = g(f(sK3_skl(X0))) ),
inference(component_clause,[status(thm)],[f37]) ).
fof(f40,plain,
( sQ5_spl
| sQ3_spl ),
inference(split_clause,[status(thm)],[f12,f30,f37]) ).
fof(f41,plain,
! [X0] :
( X0 = f(g(X0))
| ~ sP0_prd(X0,X0) ),
inference(destructive_equality_resolution,[status(thm)],[f16]) ).
fof(f42,plain,
! [X0] :
( X0 != f(g(X0))
| sP0_prd(X0,X0) ),
inference(destructive_equality_resolution,[status(thm)],[f17]) ).
fof(f43,plain,
( ~ sQ0_spl
| sK0_skl = f(g(sK0_skl)) ),
inference(resolution,[status(thm)],[f41,f20]) ).
fof(f44,plain,
( ~ sQ0_spl
| ~ sQ3_spl
| $false ),
inference(resolution,[status(thm)],[f31,f20]) ).
fof(f45,plain,
( ~ sQ0_spl
| ~ sQ3_spl ),
inference(contradiction_clause,[status(thm)],[f44]) ).
fof(f46,plain,
! [X0] :
( ~ sQ0_spl
| X0 = sK0_skl
| ~ sP0_prd(sK0_skl,X0) ),
inference(resolution,[status(thm)],[f43,f15]) ).
fof(f47,plain,
! [X0] :
( ~ sQ0_spl
| X0 = sK0_skl
| sK0_skl != sK0_skl
| ~ sP0_prd(sK0_skl,X0) ),
inference(paramodulation,[status(thm)],[f43,f15]) ).
fof(f48,definition,
! [X0] :
( sQ6_spl
<=> ( X0 = sK0_skl
| ~ sP0_prd(sK0_skl,X0) ) ),
introduced(definition,[new_symbols(definition,[sQ6_spl])],[split_symbol_definition]) ).
fof(f49,plain,
! [X0] :
( ~ sQ6_spl
| X0 = sK0_skl
| ~ sP0_prd(sK0_skl,X0) ),
inference(component_clause,[status(thm)],[f48]) ).
fof(f51,definition,
( sQ7_spl
<=> sK0_skl = sK0_skl ),
introduced(definition,[new_symbols(definition,[sQ7_spl])],[split_symbol_definition]) ).
fof(f53,plain,
( sQ7_spl
| sK0_skl != sK0_skl ),
inference(component_clause,[status(thm)],[f51]) ).
fof(f54,plain,
( ~ sQ0_spl
| ~ sQ7_spl
| sQ6_spl ),
inference(split_clause,[status(thm)],[f47,f48,f51,f19]) ).
fof(f55,plain,
( ~ sQ2_spl
| sK1_skl = g(f(sK1_skl)) ),
inference(destructive_equality_resolution,[status(thm)],[f27]) ).
fof(f59,plain,
( ~ sQ2_spl
| f(sK1_skl) != f(sK1_skl)
| sP0_prd(f(sK1_skl),f(sK1_skl)) ),
inference(paramodulation,[status(thm)],[f55,f42]) ).
fof(f60,plain,
! [X0] :
( ~ sQ2_spl
| X0 = f(sK1_skl)
| f(sK1_skl) != f(sK1_skl)
| ~ sP0_prd(f(sK1_skl),X0) ),
inference(paramodulation,[status(thm)],[f55,f15]) ).
fof(f65,definition,
( sQ9_spl
<=> sP0_prd(f(sK1_skl),f(sK1_skl)) ),
introduced(definition,[new_symbols(definition,[sQ9_spl])],[split_symbol_definition]) ).
fof(f66,plain,
( ~ sQ9_spl
| sP0_prd(f(sK1_skl),f(sK1_skl)) ),
inference(component_clause,[status(thm)],[f65]) ).
fof(f68,definition,
( sQ10_spl
<=> f(sK1_skl) = f(sK1_skl) ),
introduced(definition,[new_symbols(definition,[sQ10_spl])],[split_symbol_definition]) ).
fof(f70,plain,
( sQ10_spl
| f(sK1_skl) != f(sK1_skl) ),
inference(component_clause,[status(thm)],[f68]) ).
fof(f71,plain,
( ~ sQ2_spl
| ~ sQ10_spl
| sQ9_spl ),
inference(split_clause,[status(thm)],[f59,f65,f68,f26]) ).
fof(f72,definition,
! [X0] :
( sQ11_spl
<=> ( X0 = f(sK1_skl)
| ~ sP0_prd(f(sK1_skl),X0) ) ),
introduced(definition,[new_symbols(definition,[sQ11_spl])],[split_symbol_definition]) ).
fof(f73,plain,
! [X0] :
( ~ sQ11_spl
| X0 = f(sK1_skl)
| ~ sP0_prd(f(sK1_skl),X0) ),
inference(component_clause,[status(thm)],[f72]) ).
fof(f75,plain,
( ~ sQ2_spl
| ~ sQ10_spl
| sQ11_spl ),
inference(split_clause,[status(thm)],[f60,f72,f68,f26]) ).
fof(f76,plain,
( sQ10_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f70]) ).
fof(f77,plain,
sQ10_spl,
inference(contradiction_clause,[status(thm)],[f76]) ).
fof(f78,plain,
! [X0] :
( ~ sQ3_spl
| X0 = sK2_skl(X0)
| sK2_skl(X0) = f(g(sK2_skl(X0))) ),
inference(resolution,[status(thm)],[f31,f18]) ).
fof(f79,plain,
( ~ sQ9_spl
| f(sK1_skl) = f(g(f(sK1_skl))) ),
inference(resolution,[status(thm)],[f66,f41]) ).
fof(f81,plain,
! [X0] :
( ~ sQ11_spl
| X0 = f(sK1_skl)
| f(sK1_skl) = f(g(f(sK1_skl)))
| X0 = f(sK1_skl) ),
inference(resolution,[status(thm)],[f73,f18]) ).
fof(f82,definition,
! [X0] :
( sQ12_spl
<=> ( X0 = f(sK1_skl)
| X0 = f(sK1_skl) ) ),
introduced(definition,[new_symbols(definition,[sQ12_spl])],[split_symbol_definition]) ).
fof(f83,plain,
! [X0] :
( ~ sQ12_spl
| X0 = f(sK1_skl)
| X0 = f(sK1_skl) ),
inference(component_clause,[status(thm)],[f82]) ).
fof(f85,definition,
( sQ13_spl
<=> f(sK1_skl) = f(g(f(sK1_skl))) ),
introduced(definition,[new_symbols(definition,[sQ13_spl])],[split_symbol_definition]) ).
fof(f86,plain,
( ~ sQ13_spl
| f(sK1_skl) = f(g(f(sK1_skl))) ),
inference(component_clause,[status(thm)],[f85]) ).
fof(f88,plain,
( ~ sQ11_spl
| sQ13_spl
| sQ12_spl ),
inference(split_clause,[status(thm)],[f81,f82,f85,f72]) ).
fof(f91,plain,
! [X0] :
( ~ sQ5_spl
| X0 = sK3_skl(X0)
| f(sK3_skl(X0)) != f(sK3_skl(X0))
| sP0_prd(f(sK3_skl(X0)),f(sK3_skl(X0))) ),
inference(paramodulation,[status(thm)],[f38,f42]) ).
fof(f92,plain,
! [X0,X1] :
( ~ sQ5_spl
| X0 = sK3_skl(X0)
| X1 = f(sK3_skl(X0))
| f(sK3_skl(X0)) != f(sK3_skl(X0))
| ~ sP0_prd(f(sK3_skl(X0)),X1) ),
inference(paramodulation,[status(thm)],[f38,f15]) ).
fof(f93,plain,
! [X0] :
( ~ sQ5_spl
| X0 = sK3_skl(X0)
| sP0_prd(f(sK3_skl(X0)),f(sK3_skl(X0))) ),
inference(trivial_equality_resolution,[status(thm)],[f91]) ).
fof(f94,plain,
! [X0,X1] :
( ~ sQ5_spl
| X0 = sK3_skl(X0)
| X1 = f(sK3_skl(X0))
| ~ sP0_prd(f(sK3_skl(X0)),X1) ),
inference(trivial_equality_resolution,[status(thm)],[f92]) ).
fof(f97,plain,
! [X0] :
( ~ sQ0_spl
| X0 = sK0_skl
| ~ sP0_prd(sK0_skl,X0) ),
inference(resolution,[status(thm)],[f43,f15]) ).
fof(f98,plain,
( ~ sQ0_spl
| sK0_skl != sK0_skl
| sP0_prd(sK0_skl,sK0_skl) ),
inference(paramodulation,[status(thm)],[f43,f42]) ).
fof(f100,definition,
( sQ14_spl
<=> sP0_prd(sK0_skl,sK0_skl) ),
introduced(definition,[new_symbols(definition,[sQ14_spl])],[split_symbol_definition]) ).
fof(f101,plain,
( ~ sQ14_spl
| sP0_prd(sK0_skl,sK0_skl) ),
inference(component_clause,[status(thm)],[f100]) ).
fof(f103,plain,
( ~ sQ0_spl
| ~ sQ7_spl
| sQ14_spl ),
inference(split_clause,[status(thm)],[f98,f100,f51,f19]) ).
fof(f105,plain,
( sQ7_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f53]) ).
fof(f106,plain,
sQ7_spl,
inference(contradiction_clause,[status(thm)],[f105]) ).
fof(f107,plain,
! [X0] :
( ~ sQ5_spl
| f(sK3_skl(X0)) = f(g(f(sK3_skl(X0))))
| X0 = sK3_skl(X0) ),
inference(resolution,[status(thm)],[f93,f41]) ).
fof(f109,plain,
! [X0] :
( ~ sQ0_spl
| ~ sQ5_spl
| X0 = sK3_skl(X0)
| sK0_skl = f(sK3_skl(X0)) ),
inference(resolution,[status(thm)],[f94,f20]) ).
fof(f113,plain,
! [X0] :
( ~ sQ6_spl
| X0 = sK0_skl
| sK0_skl = f(g(sK0_skl))
| X0 = sK0_skl ),
inference(resolution,[status(thm)],[f49,f18]) ).
fof(f114,definition,
! [X0] :
( sQ15_spl
<=> ( X0 = sK0_skl
| X0 = sK0_skl ) ),
introduced(definition,[new_symbols(definition,[sQ15_spl])],[split_symbol_definition]) ).
fof(f115,plain,
! [X0] :
( ~ sQ15_spl
| X0 = sK0_skl
| X0 = sK0_skl ),
inference(component_clause,[status(thm)],[f114]) ).
fof(f117,definition,
( sQ16_spl
<=> sK0_skl = f(g(sK0_skl)) ),
introduced(definition,[new_symbols(definition,[sQ16_spl])],[split_symbol_definition]) ).
fof(f118,plain,
( ~ sQ16_spl
| sK0_skl = f(g(sK0_skl)) ),
inference(component_clause,[status(thm)],[f117]) ).
fof(f120,plain,
( ~ sQ6_spl
| sQ16_spl
| sQ15_spl ),
inference(split_clause,[status(thm)],[f113,f114,f117,f48]) ).
fof(f121,plain,
! [X0] :
( ~ sQ15_spl
| X0 = sK0_skl ),
inference(duplicate_literals_removal,[status(thm)],[f115]) ).
fof(f122,plain,
( ~ sQ13_spl
| sP0_prd(f(sK1_skl),f(sK1_skl)) ),
inference(resolution,[status(thm)],[f86,f42]) ).
fof(f123,plain,
! [X0] :
( ~ sQ13_spl
| X0 = f(sK1_skl)
| ~ sP0_prd(f(sK1_skl),X0) ),
inference(resolution,[status(thm)],[f86,f15]) ).
fof(f124,plain,
( ~ sQ13_spl
| f(sK1_skl) != f(sK1_skl)
| sP0_prd(f(sK1_skl),f(sK1_skl)) ),
inference(paramodulation,[status(thm)],[f86,f42]) ).
fof(f125,plain,
! [X0] :
( ~ sQ13_spl
| X0 = f(sK1_skl)
| f(sK1_skl) != f(sK1_skl)
| ~ sP0_prd(f(sK1_skl),X0) ),
inference(paramodulation,[status(thm)],[f86,f15]) ).
fof(f126,plain,
( ~ sQ13_spl
| ~ sQ10_spl
| sQ9_spl ),
inference(split_clause,[status(thm)],[f124,f65,f68,f85]) ).
fof(f127,plain,
( ~ sQ13_spl
| ~ sQ10_spl
| sQ11_spl ),
inference(split_clause,[status(thm)],[f125,f72,f68,f85]) ).
fof(f128,plain,
! [X0] :
( ~ sQ12_spl
| X0 = f(sK1_skl) ),
inference(duplicate_literals_removal,[status(thm)],[f83]) ).
fof(f129,plain,
! [X0] :
( ~ sQ5_spl
| ~ sQ1_spl
| X0 = sK3_skl(X0)
| sK1_skl = sK3_skl(X0) ),
inference(resolution,[status(thm)],[f23,f38]) ).
fof(f133,plain,
( ~ sQ15_spl
| sP0_prd(sK0_skl,sK0_skl) ),
inference(resolution,[status(thm)],[f121,f42]) ).
fof(f135,plain,
! [X0,X1] :
( ~ sQ15_spl
| X0 = X1 ),
inference(paramodulation,[status(thm)],[f121,f121]) ).
fof(f136,plain,
! [X0] :
( ~ sQ4_spl
| ~ sQ15_spl
| sK3_skl(X0) != g(f(sK3_skl(X0))) ),
inference(backward_subsumption_resolution,[status(thm)],[f34,f135]) ).
fof(f137,plain,
! [X0] :
( ~ sQ15_spl
| sP0_prd(X0,X0) ),
inference(backward_subsumption_resolution,[status(thm)],[f42,f135]) ).
fof(f138,plain,
( ~ sQ4_spl
| ~ sQ15_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f136,f135]) ).
fof(f139,plain,
( ~ sQ4_spl
| ~ sQ15_spl ),
inference(contradiction_clause,[status(thm)],[f138]) ).
fof(f140,plain,
! [X0,X1] :
( ~ sQ12_spl
| X0 = X1 ),
inference(paramodulation,[status(thm)],[f128,f128]) ).
fof(f141,plain,
! [X0] :
( ~ sQ12_spl
| ~ sQ9_spl
| sP0_prd(f(sK1_skl),X0) ),
inference(paramodulation,[status(thm)],[f128,f66]) ).
fof(f143,plain,
! [X0] :
( ~ sQ12_spl
| sP0_prd(X0,X0) ),
inference(backward_subsumption_resolution,[status(thm)],[f42,f140]) ).
fof(f144,plain,
! [X0,X1] :
( ~ sQ12_spl
| ~ sQ9_spl
| sP0_prd(X0,X1) ),
inference(paramodulation,[status(thm)],[f140,f141]) ).
fof(f148,plain,
( ~ sQ3_spl
| ~ sQ12_spl
| ~ sQ9_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f31,f144]) ).
fof(f149,plain,
( ~ sQ3_spl
| ~ sQ12_spl
| ~ sQ9_spl ),
inference(contradiction_clause,[status(thm)],[f148]) ).
fof(f153,plain,
( ~ sQ16_spl
| ~ sQ1_spl
| sK1_skl = g(sK0_skl)
| g(sK0_skl) != g(sK0_skl) ),
inference(paramodulation,[status(thm)],[f118,f23]) ).
fof(f155,definition,
( sQ17_spl
<=> g(sK0_skl) = g(sK0_skl) ),
introduced(definition,[new_symbols(definition,[sQ17_spl])],[split_symbol_definition]) ).
fof(f157,plain,
( sQ17_spl
| g(sK0_skl) != g(sK0_skl) ),
inference(component_clause,[status(thm)],[f155]) ).
fof(f158,definition,
( sQ18_spl
<=> sK1_skl = g(sK0_skl) ),
introduced(definition,[new_symbols(definition,[sQ18_spl])],[split_symbol_definition]) ).
fof(f159,plain,
( ~ sQ18_spl
| sK1_skl = g(sK0_skl) ),
inference(component_clause,[status(thm)],[f158]) ).
fof(f161,plain,
( ~ sQ16_spl
| ~ sQ1_spl
| sQ18_spl
| ~ sQ17_spl ),
inference(split_clause,[status(thm)],[f153,f155,f158,f22,f117]) ).
fof(f162,plain,
( sQ17_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f157]) ).
fof(f163,plain,
sQ17_spl,
inference(contradiction_clause,[status(thm)],[f162]) ).
fof(f164,plain,
( ~ sQ16_spl
| ~ sQ18_spl
| sK0_skl = f(sK1_skl) ),
inference(backward_demodulation,[status(thm)],[f159,f118]) ).
fof(f166,plain,
( ~ sQ9_spl
| ~ sQ16_spl
| ~ sQ18_spl
| sP0_prd(f(sK1_skl),sK0_skl) ),
inference(backward_demodulation,[status(thm)],[f164,f66]) ).
fof(f167,plain,
! [X0] :
( ~ sQ13_spl
| ~ sQ16_spl
| ~ sQ18_spl
| X0 = sK0_skl
| ~ sP0_prd(f(sK1_skl),X0) ),
inference(backward_demodulation,[status(thm)],[f164,f123]) ).
fof(f168,plain,
( ~ sQ9_spl
| ~ sQ16_spl
| ~ sQ18_spl
| sP0_prd(sK0_skl,sK0_skl) ),
inference(forward_demodulation,[status(thm)],[f164,f166]) ).
fof(f169,plain,
! [X0] :
( ~ sQ13_spl
| ~ sQ16_spl
| ~ sQ18_spl
| X0 = sK0_skl
| ~ sP0_prd(sK0_skl,X0) ),
inference(forward_demodulation,[status(thm)],[f164,f167]) ).
fof(f172,plain,
! [X0] :
( ~ sQ3_spl
| sP0_prd(sK2_skl(X0),sK2_skl(X0))
| X0 = sK2_skl(X0) ),
inference(resolution,[status(thm)],[f78,f42]) ).
fof(f173,plain,
! [X0,X1] :
( ~ sQ3_spl
| X1 = sK2_skl(X0)
| ~ sP0_prd(sK2_skl(X0),X1)
| X0 = sK2_skl(X0) ),
inference(resolution,[status(thm)],[f78,f15]) ).
fof(f176,plain,
! [X0] :
( ~ sQ3_spl
| ~ sQ1_spl
| X0 = sK2_skl(X0)
| sK1_skl = g(sK2_skl(X0))
| g(sK2_skl(X0)) != g(sK2_skl(X0)) ),
inference(paramodulation,[status(thm)],[f78,f23]) ).
fof(f179,plain,
! [X0] :
( ~ sQ3_spl
| ~ sQ1_spl
| X0 = sK2_skl(X0)
| sK1_skl = g(sK2_skl(X0)) ),
inference(trivial_equality_resolution,[status(thm)],[f176]) ).
fof(f180,plain,
( ~ sQ18_spl
| sK0_skl != f(sK1_skl)
| sP0_prd(sK0_skl,sK0_skl) ),
inference(paramodulation,[status(thm)],[f159,f42]) ).
fof(f181,plain,
! [X0] :
( ~ sQ18_spl
| X0 = sK0_skl
| sK0_skl != f(sK1_skl)
| ~ sP0_prd(sK0_skl,X0) ),
inference(paramodulation,[status(thm)],[f159,f15]) ).
fof(f182,definition,
( sQ19_spl
<=> sK0_skl = f(sK1_skl) ),
introduced(definition,[new_symbols(definition,[sQ19_spl])],[split_symbol_definition]) ).
fof(f185,plain,
( ~ sQ18_spl
| ~ sQ19_spl
| sQ14_spl ),
inference(split_clause,[status(thm)],[f180,f100,f182,f158]) ).
fof(f186,plain,
( ~ sQ18_spl
| ~ sQ19_spl
| sQ6_spl ),
inference(split_clause,[status(thm)],[f181,f48,f182,f158]) ).
fof(model,axiom,
( ~ sQ0_spl
| sQ1_spl
| sQ2_spl
| sQ3_spl
| ~ sQ4_spl
| sQ6_spl
| sQ7_spl
| sQ9_spl
| sQ10_spl
| sQ11_spl
| ~ sQ12_spl
| sQ13_spl
| sQ14_spl
| sQ15_spl
| sQ17_spl
| sQ18_spl ) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYN551+2 : TPTP v9.3.1. Bugfixed v3.1.0.
% 0.00/0.04 % Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/5.37 % Computer : n006.cluster.edu
% 0.10/5.37 % Model : x86_64 x86_64
% 0.10/5.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/5.37 % Memory : 8046.5625MB
% 0.10/5.37 % OS : Linux 6.8.0-71-generic
% 0.10/5.37 % CPULimit : 300
% 0.10/5.37 % WCLimit : 300
% 0.10/5.37 % DateTime : Mon Sep 21 11:08:19 UTC 2026
% 0.10/5.37 % CPUTime :
% 0.10/5.38 % Drodi V4.1.1
% 0.13/5.41 % SZS status CounterSatisfiable for theBenchmark: Theorem is counter-satisfiable, conjecture is false
% 0.13/5.41 % SZS output start Saturation for theBenchmark
% See solution above
% 0.13/5.43 % Elapsed time: 0.053733 seconds
% 0.13/5.43 % CPU time: 0.163872 seconds
% 0.13/5.43 % Total memory used: 80.516 MB
% 0.13/5.43 % Net memory used: 79.970 MB
%------------------------------------------------------------------------------