%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : SYN414+1 : TPTP v9.3.1. Released v2.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n018.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 03:19:35 PM UTC 2026
% Result : CounterSatisfiable 0.15s 0.39s
% Output : Saturation 0.15s
% Verified :
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)
% Comments :
%------------------------------------------------------------------------------
fof(f1,conjecture,
( ! [X] :
( ? [Y] :
( f(Y)
& h(X,Y) )
=> ? [Z] :
( g(Z)
& h(X,Z) ) )
<=> ! [U,V,W] :
( ( f(V)
& h(U,V) )
=> ( g(W)
& h(U,W) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f2,negated_conjecture,
~ ( ! [X] :
( ? [Y] :
( f(Y)
& h(X,Y) )
=> ? [Z] :
( g(Z)
& h(X,Z) ) )
<=> ! [U,V,W] :
( ( f(V)
& h(U,V) )
=> ( g(W)
& h(U,W) ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
fof(f3,plain,
( ! [X] :
( ? [Z] :
( g(Z)
& h(X,Z) )
| ! [Y] :
( ~ f(Y)
| ~ h(X,Y) ) )
<~> ! [U,V,W] :
( ( g(W)
& h(U,W) )
| ~ f(V)
| ~ h(U,V) ) ),
inference(pre_NNF_transformation,[status(thm)],[f2]) ).
fof(f4,definition,
! [X] :
( sP0_prd(X)
<=> ( ? [Z] :
( g(Z)
& h(X,Z) )
| ! [Y] :
( ~ f(Y)
| ~ h(X,Y) ) ) ),
introduced(definition,[new_symbols(definition,[sP0_prd])],[]) ).
fof(f5,plain,
( ! [X] : sP0_prd(X)
<~> ! [U,V,W] :
( ( g(W)
& h(U,W) )
| ~ f(V)
| ~ h(U,V) ) ),
inference(formula_renaming,[status(thm)],[f3,f4]) ).
fof(f6,plain,
( ( ? [U,V,W] :
( ( ~ g(W)
| ~ h(U,W) )
& f(V)
& h(U,V) )
| ? [X] : ~ sP0_prd(X) )
& ( ! [U,V,W] :
( ( g(W)
& h(U,W) )
| ~ f(V)
| ~ h(U,V) )
| ! [X] : sP0_prd(X) ) ),
inference(NNF_transformation,[status(thm)],[f5]) ).
fof(f7,plain,
( ( ? [U] :
( ( ? [W] : ~ g(W)
| ? [W] : ~ h(U,W) )
& ? [V] :
( f(V)
& h(U,V) ) )
| ? [X] : ~ sP0_prd(X) )
& ( ! [U] :
( ( ! [W] : g(W)
& ! [W] : h(U,W) )
| ! [V] :
( ~ f(V)
| ~ h(U,V) ) )
| ! [X] : sP0_prd(X) ) ),
inference(miniscoping,[status(thm)],[f6]) ).
fof(f8,plain,
( ( ( ( ~ g(sK4_skl)
| ~ h(sK1_skl,sK3_skl) )
& f(sK2_skl)
& h(sK1_skl,sK2_skl) )
| ~ sP0_prd(sK0_skl) )
& ( ! [U] :
( ( ! [W] : g(W)
& ! [W] : h(U,W) )
| ! [V] :
( ~ f(V)
| ~ h(U,V) ) )
| ! [X] : sP0_prd(X) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl,sK1_skl,sK2_skl,sK3_skl,sK4_skl]),skolemize(X,sK0_skl),skolemize(U,sK1_skl),skolemize(V,sK2_skl),skolemize(W,sK3_skl),skolemize(W,sK4_skl)],[f7]) ).
fof(f9,plain,
! [X0,X1,X2,X3] :
( h(X1,X3)
| ~ f(X2)
| ~ h(X1,X2)
| sP0_prd(X0) ),
inference(cnf_transformation,[status(thm)],[f8]) ).
fof(f10,plain,
! [X0,X1,X2,X3] :
( g(X3)
| ~ f(X2)
| ~ h(X1,X2)
| sP0_prd(X0) ),
inference(cnf_transformation,[status(thm)],[f8]) ).
fof(f11,plain,
( h(sK1_skl,sK2_skl)
| ~ sP0_prd(sK0_skl) ),
inference(cnf_transformation,[status(thm)],[f8]) ).
fof(f12,plain,
( f(sK2_skl)
| ~ sP0_prd(sK0_skl) ),
inference(cnf_transformation,[status(thm)],[f8]) ).
fof(f13,plain,
( ~ g(sK4_skl)
| ~ h(sK1_skl,sK3_skl)
| ~ sP0_prd(sK0_skl) ),
inference(cnf_transformation,[status(thm)],[f8]) ).
fof(f14,plain,
! [X] :
( ( ( ! [Z] :
( ~ g(Z)
| ~ h(X,Z) )
& ? [Y] :
( f(Y)
& h(X,Y) ) )
| sP0_prd(X) )
& ( ? [Z] :
( g(Z)
& h(X,Z) )
| ! [Y] :
( ~ f(Y)
| ~ h(X,Y) )
| ~ sP0_prd(X) ) ),
inference(NNF_transformation,[status(thm)],[f4]) ).
fof(f15,plain,
( ! [X] :
( ( ! [Z] :
( ~ g(Z)
| ~ h(X,Z) )
& ? [Y] :
( f(Y)
& h(X,Y) ) )
| sP0_prd(X) )
& ! [X] :
( ? [Z] :
( g(Z)
& h(X,Z) )
| ! [Y] :
( ~ f(Y)
| ~ h(X,Y) )
| ~ sP0_prd(X) ) ),
inference(miniscoping,[status(thm)],[f14]) ).
fof(f16,plain,
( ! [X] :
( ( ! [Z] :
( ~ g(Z)
| ~ h(X,Z) )
& f(sK6_skl(X))
& h(X,sK6_skl(X)) )
| sP0_prd(X) )
& ! [X] :
( ( g(sK5_skl(X))
& h(X,sK5_skl(X)) )
| ! [Y] :
( ~ f(Y)
| ~ h(X,Y) )
| ~ sP0_prd(X) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK5_skl,sK6_skl]),skolemize(Z,sK5_skl(X)),skolemize(Y,sK6_skl(X))],[f15]) ).
fof(f17,plain,
! [X0,X1] :
( h(X0,sK5_skl(X0))
| ~ f(X1)
| ~ h(X0,X1)
| ~ sP0_prd(X0) ),
inference(cnf_transformation,[status(thm)],[f16]) ).
fof(f18,plain,
! [X0,X1] :
( g(sK5_skl(X0))
| ~ f(X1)
| ~ h(X0,X1)
| ~ sP0_prd(X0) ),
inference(cnf_transformation,[status(thm)],[f16]) ).
fof(f19,plain,
! [X0] :
( h(X0,sK6_skl(X0))
| sP0_prd(X0) ),
inference(cnf_transformation,[status(thm)],[f16]) ).
fof(f20,plain,
! [X0] :
( f(sK6_skl(X0))
| sP0_prd(X0) ),
inference(cnf_transformation,[status(thm)],[f16]) ).
fof(f21,plain,
! [X0,X1] :
( ~ g(X1)
| ~ h(X0,X1)
| sP0_prd(X0) ),
inference(cnf_transformation,[status(thm)],[f16]) ).
fof(f22,definition,
! [X0] :
( sQ0_spl
<=> sP0_prd(X0) ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f23,plain,
! [X0] :
( ~ sQ0_spl
| sP0_prd(X0) ),
inference(component_clause,[status(thm)],[f22]) ).
fof(f25,definition,
! [X1,X2,X3] :
( sQ1_spl
<=> ( h(X1,X3)
| ~ f(X2)
| ~ h(X1,X2) ) ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f26,plain,
! [X0,X1,X2] :
( ~ sQ1_spl
| h(X0,X2)
| ~ f(X1)
| ~ h(X0,X1) ),
inference(component_clause,[status(thm)],[f25]) ).
fof(f28,plain,
( sQ1_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f9,f22,f25]) ).
fof(f29,definition,
! [X1,X2] :
( sQ2_spl
<=> ( ~ f(X2)
| ~ h(X1,X2) ) ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f30,plain,
! [X0,X1] :
( ~ sQ2_spl
| ~ f(X1)
| ~ h(X0,X1) ),
inference(component_clause,[status(thm)],[f29]) ).
fof(f32,definition,
! [X3] :
( sQ3_spl
<=> g(X3) ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f33,plain,
! [X0] :
( ~ sQ3_spl
| g(X0) ),
inference(component_clause,[status(thm)],[f32]) ).
fof(f35,plain,
( sQ3_spl
| sQ2_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f10,f22,f29,f32]) ).
fof(f36,definition,
( sQ4_spl
<=> sP0_prd(sK0_skl) ),
introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition]) ).
fof(f37,plain,
( ~ sQ4_spl
| sP0_prd(sK0_skl) ),
inference(component_clause,[status(thm)],[f36]) ).
fof(f38,plain,
( sQ4_spl
| ~ sP0_prd(sK0_skl) ),
inference(component_clause,[status(thm)],[f36]) ).
fof(f39,definition,
( sQ5_spl
<=> h(sK1_skl,sK2_skl) ),
introduced(definition,[new_symbols(definition,[sQ5_spl])],[split_symbol_definition]) ).
fof(f40,plain,
( ~ sQ5_spl
| h(sK1_skl,sK2_skl) ),
inference(component_clause,[status(thm)],[f39]) ).
fof(f42,plain,
( sQ5_spl
| ~ sQ4_spl ),
inference(split_clause,[status(thm)],[f11,f36,f39]) ).
fof(f43,definition,
( sQ6_spl
<=> f(sK2_skl) ),
introduced(definition,[new_symbols(definition,[sQ6_spl])],[split_symbol_definition]) ).
fof(f44,plain,
( ~ sQ6_spl
| f(sK2_skl) ),
inference(component_clause,[status(thm)],[f43]) ).
fof(f46,plain,
( sQ6_spl
| ~ sQ4_spl ),
inference(split_clause,[status(thm)],[f12,f36,f43]) ).
fof(f47,definition,
( sQ7_spl
<=> h(sK1_skl,sK3_skl) ),
introduced(definition,[new_symbols(definition,[sQ7_spl])],[split_symbol_definition]) ).
fof(f49,plain,
( sQ7_spl
| ~ h(sK1_skl,sK3_skl) ),
inference(component_clause,[status(thm)],[f47]) ).
fof(f50,definition,
( sQ8_spl
<=> g(sK4_skl) ),
introduced(definition,[new_symbols(definition,[sQ8_spl])],[split_symbol_definition]) ).
fof(f52,plain,
( sQ8_spl
| ~ g(sK4_skl) ),
inference(component_clause,[status(thm)],[f50]) ).
fof(f53,plain,
( ~ sQ8_spl
| ~ sQ7_spl
| ~ sQ4_spl ),
inference(split_clause,[status(thm)],[f13,f36,f47,f50]) ).
fof(f54,plain,
( sQ4_spl
| ~ sQ0_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f38,f23]) ).
fof(f55,plain,
( sQ4_spl
| ~ sQ0_spl ),
inference(contradiction_clause,[status(thm)],[f54]) ).
fof(f56,plain,
! [X0,X1] :
( ~ sQ0_spl
| h(X0,sK5_skl(X0))
| ~ f(X1)
| ~ h(X0,X1) ),
inference(forward_subsumption_resolution,[status(thm)],[f17,f23]) ).
fof(f57,plain,
( ~ sQ0_spl
| ~ sQ5_spl
| h(sK1_skl,sK5_skl(sK1_skl))
| ~ f(sK2_skl) ),
inference(resolution,[status(thm)],[f40,f56]) ).
fof(f58,definition,
( sQ9_spl
<=> h(sK1_skl,sK5_skl(sK1_skl)) ),
introduced(definition,[new_symbols(definition,[sQ9_spl])],[split_symbol_definition]) ).
fof(f59,plain,
( ~ sQ9_spl
| h(sK1_skl,sK5_skl(sK1_skl)) ),
inference(component_clause,[status(thm)],[f58]) ).
fof(f61,plain,
( ~ sQ0_spl
| ~ sQ5_spl
| sQ9_spl
| ~ sQ6_spl ),
inference(split_clause,[status(thm)],[f57,f43,f58,f39,f22]) ).
fof(f62,plain,
! [X0] :
( ~ g(sK6_skl(X0))
| sP0_prd(X0)
| sP0_prd(X0) ),
inference(resolution,[status(thm)],[f19,f21]) ).
fof(f63,plain,
! [X0] :
( ~ sQ2_spl
| ~ f(sK6_skl(X0))
| sP0_prd(X0) ),
inference(resolution,[status(thm)],[f19,f30]) ).
fof(f64,plain,
! [X0] :
( ~ g(sK6_skl(X0))
| sP0_prd(X0) ),
inference(duplicate_literals_removal,[status(thm)],[f62]) ).
fof(f65,plain,
! [X0] :
( ~ sQ2_spl
| sP0_prd(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f63,f20]) ).
fof(f66,plain,
( sQ4_spl
| ~ sQ2_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f38,f65]) ).
fof(f67,plain,
( sQ4_spl
| ~ sQ2_spl ),
inference(contradiction_clause,[status(thm)],[f66]) ).
fof(f68,plain,
( sQ8_spl
| ~ sQ3_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f52,f33]) ).
fof(f69,plain,
( sQ8_spl
| ~ sQ3_spl ),
inference(contradiction_clause,[status(thm)],[f68]) ).
fof(f70,plain,
! [X0,X1] :
( ~ sQ0_spl
| h(X0,sK5_skl(X0))
| ~ f(X1)
| ~ h(X0,X1) ),
inference(forward_subsumption_resolution,[status(thm)],[f17,f23]) ).
fof(f73,definition,
( sQ10_spl
<=> f(sK5_skl(sK1_skl)) ),
introduced(definition,[new_symbols(definition,[sQ10_spl])],[split_symbol_definition]) ).
fof(f78,plain,
! [X0,X1] :
( ~ sQ0_spl
| g(sK5_skl(X0))
| ~ f(X1)
| ~ h(X0,X1) ),
inference(forward_subsumption_resolution,[status(thm)],[f18,f23]) ).
fof(f79,plain,
( ~ sQ9_spl
| ~ sQ0_spl
| g(sK5_skl(sK1_skl))
| ~ f(sK5_skl(sK1_skl)) ),
inference(resolution,[status(thm)],[f78,f59]) ).
fof(f80,plain,
( ~ sQ5_spl
| ~ sQ0_spl
| g(sK5_skl(sK1_skl))
| ~ f(sK2_skl) ),
inference(resolution,[status(thm)],[f78,f40]) ).
fof(f81,definition,
( sQ11_spl
<=> g(sK5_skl(sK1_skl)) ),
introduced(definition,[new_symbols(definition,[sQ11_spl])],[split_symbol_definition]) ).
fof(f82,plain,
( ~ sQ11_spl
| g(sK5_skl(sK1_skl)) ),
inference(component_clause,[status(thm)],[f81]) ).
fof(f84,plain,
( ~ sQ9_spl
| ~ sQ0_spl
| sQ11_spl
| ~ sQ10_spl ),
inference(split_clause,[status(thm)],[f79,f73,f81,f22,f58]) ).
fof(f85,plain,
( ~ sQ5_spl
| ~ sQ0_spl
| sQ11_spl
| ~ sQ6_spl ),
inference(split_clause,[status(thm)],[f80,f43,f81,f22,f39]) ).
fof(model,axiom,
( sQ0_spl
| ~ sQ3_spl
| sQ4_spl
| sQ5_spl
| sQ6_spl
| ~ sQ7_spl
| sQ9_spl
| sQ11_spl ) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYN414+1 : TPTP v9.3.1. Released v2.0.0.
% 0.00/0.04 % Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.36 % Computer : n018.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Mon Sep 21 10:55:28 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.15/0.37 % Drodi V4.1.1
% 0.15/0.39 % SZS status CounterSatisfiable for theBenchmark: Theorem is counter-satisfiable, conjecture is false
% 0.15/0.39 % SZS output start Saturation for theBenchmark
% See solution above
% 0.15/0.41 % Elapsed time: 0.041443 seconds
% 0.15/0.41 % CPU time: 0.107378 seconds
% 0.15/0.41 % Total memory used: 16.726 MB
% 0.15/0.41 % Net memory used: 16.284 MB
%------------------------------------------------------------------------------