%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SYN920+1 : TPTP v9.3.1. Released v3.1.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n013.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 03:18:19 PM UTC 2026
% Result : Theorem 0.08s 0.37s
% Output : CNFRefutation 0.08s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 7
% Syntax : Number of formulae : 43 ( 1 unt; 6 def)
% Number of atoms : 178 ( 0 equ)
% Maximal formula atoms : 15 ( 4 avg)
% Number of connectives : 221 ( 86 ~; 81 |; 34 &)
% ( 6 <=>; 14 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 10 ( 9 usr; 6 prp; 0-1 aty)
% Number of functors : 2 ( 2 usr; 2 con; 0-0 aty)
% Number of variables : 46 ( 38 !; 8 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,conjecture,
( ( ( ! [Z] :
( f(Z)
=> h(Z) )
| ! [W] :
( f(W)
=> g(W) ) )
& ( ! [X] :
( ( g(X)
& f(X) )
=> h(X) )
=> ? [X] :
( ~ g(X)
& f(X) ) ) )
=> ( ! [R] :
( ( h(R)
& f(R) )
=> g(R) )
=> ? [V] :
( ~ h(V)
& g(V)
& f(V) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f2,negated_conjecture,
~ ( ( ( ! [Z] :
( f(Z)
=> h(Z) )
| ! [W] :
( f(W)
=> g(W) ) )
& ( ! [X] :
( ( g(X)
& f(X) )
=> h(X) )
=> ? [X] :
( ~ g(X)
& f(X) ) ) )
=> ( ! [R] :
( ( h(R)
& f(R) )
=> g(R) )
=> ? [V] :
( ~ h(V)
& g(V)
& f(V) ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
fof(f3,plain,
( ! [V] :
( h(V)
| ~ g(V)
| ~ f(V) )
& ! [R] :
( g(R)
| ~ h(R)
| ~ f(R) )
& ( ! [Z] :
( h(Z)
| ~ f(Z) )
| ! [W] :
( g(W)
| ~ f(W) ) )
& ( ? [X] :
( ~ g(X)
& f(X) )
| ? [X] :
( ~ h(X)
& g(X)
& f(X) ) ) ),
inference(pre_NNF_transformation,[status(thm)],[f2]) ).
fof(f4,definition,
! [X] :
( sP0_prd(X)
<=> ( ~ h(X)
& g(X)
& f(X) ) ),
introduced(definition,[new_symbols(definition,[sP0_prd])],[]) ).
fof(f5,plain,
( ! [V] :
( h(V)
| ~ g(V)
| ~ f(V) )
& ! [R] :
( g(R)
| ~ h(R)
| ~ f(R) )
& ( ! [Z] :
( h(Z)
| ~ f(Z) )
| ! [W] :
( g(W)
| ~ f(W) ) )
& ( ? [X] :
( ~ g(X)
& f(X) )
| ? [X] : sP0_prd(X) ) ),
inference(formula_renaming,[status(thm)],[f3,f4]) ).
fof(f6,plain,
( ! [V] :
( h(V)
| ~ g(V)
| ~ f(V) )
& ! [R] :
( g(R)
| ~ h(R)
| ~ f(R) )
& ( ! [Z] :
( h(Z)
| ~ f(Z) )
| ! [W] :
( g(W)
| ~ f(W) ) )
& ( ( ~ g(sK1_skl)
& f(sK1_skl) )
| sP0_prd(sK0_skl) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl,sK1_skl]),skolemize(X,sK0_skl),skolemize(X,sK1_skl)],[f5]) ).
fof(f7,plain,
( f(sK1_skl)
| sP0_prd(sK0_skl) ),
inference(cnf_transformation,[status(thm)],[f6]) ).
fof(f8,plain,
( ~ g(sK1_skl)
| sP0_prd(sK0_skl) ),
inference(cnf_transformation,[status(thm)],[f6]) ).
fof(f9,plain,
! [X0,X1] :
( h(X1)
| ~ f(X1)
| g(X0)
| ~ f(X0) ),
inference(cnf_transformation,[status(thm)],[f6]) ).
fof(f10,plain,
! [X0] :
( g(X0)
| ~ h(X0)
| ~ f(X0) ),
inference(cnf_transformation,[status(thm)],[f6]) ).
fof(f11,plain,
! [X0] :
( h(X0)
| ~ g(X0)
| ~ f(X0) ),
inference(cnf_transformation,[status(thm)],[f6]) ).
fof(f12,plain,
! [X] :
( ( h(X)
| ~ g(X)
| ~ f(X)
| sP0_prd(X) )
& ( ( ~ h(X)
& g(X)
& f(X) )
| ~ sP0_prd(X) ) ),
inference(NNF_transformation,[status(thm)],[f4]) ).
fof(f13,plain,
( ! [X] :
( h(X)
| ~ g(X)
| ~ f(X)
| sP0_prd(X) )
& ! [X] :
( ( ~ h(X)
& g(X)
& f(X) )
| ~ sP0_prd(X) ) ),
inference(miniscoping,[status(thm)],[f12]) ).
fof(f14,plain,
! [X0] :
( f(X0)
| ~ sP0_prd(X0) ),
inference(cnf_transformation,[status(thm)],[f13]) ).
fof(f16,plain,
! [X0] :
( ~ h(X0)
| ~ sP0_prd(X0) ),
inference(cnf_transformation,[status(thm)],[f13]) ).
fof(f18,definition,
( sQ0_spl
<=> sP0_prd(sK0_skl) ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f19,plain,
( ~ sQ0_spl
| sP0_prd(sK0_skl) ),
inference(component_clause,[status(thm)],[f18]) ).
fof(f21,definition,
( sQ1_spl
<=> f(sK1_skl) ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f22,plain,
( ~ sQ1_spl
| f(sK1_skl) ),
inference(component_clause,[status(thm)],[f21]) ).
fof(f24,plain,
( sQ1_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f7,f18,f21]) ).
fof(f25,definition,
( sQ2_spl
<=> g(sK1_skl) ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f27,plain,
( sQ2_spl
| ~ g(sK1_skl) ),
inference(component_clause,[status(thm)],[f25]) ).
fof(f28,plain,
( ~ sQ2_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f8,f18,f25]) ).
fof(f29,definition,
! [X0] :
( sQ3_spl
<=> ( g(X0)
| ~ f(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f30,plain,
! [X0] :
( ~ sQ3_spl
| g(X0)
| ~ f(X0) ),
inference(component_clause,[status(thm)],[f29]) ).
fof(f32,definition,
! [X1] :
( sQ4_spl
<=> ( h(X1)
| ~ f(X1) ) ),
introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition]) ).
fof(f33,plain,
! [X0] :
( ~ sQ4_spl
| h(X0)
| ~ f(X0) ),
inference(component_clause,[status(thm)],[f32]) ).
fof(f35,plain,
( sQ4_spl
| sQ3_spl ),
inference(split_clause,[status(thm)],[f9,f29,f32]) ).
fof(f36,plain,
! [X0] :
( ~ sQ3_spl
| h(X0)
| ~ f(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f11,f30]) ).
fof(f37,plain,
! [X0] :
( ~ sQ3_spl
| ~ sP0_prd(X0)
| ~ f(X0) ),
inference(resolution,[status(thm)],[f36,f16]) ).
fof(f38,plain,
! [X0] :
( ~ sQ3_spl
| ~ sP0_prd(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f37,f14]) ).
fof(f39,plain,
( ~ sQ0_spl
| ~ sQ3_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f19,f38]) ).
fof(f40,plain,
( ~ sQ0_spl
| ~ sQ3_spl ),
inference(contradiction_clause,[status(thm)],[f39]) ).
fof(f41,plain,
! [X0] :
( ~ sQ4_spl
| g(X0)
| ~ f(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f10,f33]) ).
fof(f42,plain,
( sQ2_spl
| ~ sQ4_spl
| ~ f(sK1_skl) ),
inference(resolution,[status(thm)],[f41,f27]) ).
fof(f43,plain,
( sQ2_spl
| ~ sQ4_spl
| ~ sQ1_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f42,f22]) ).
fof(f44,plain,
( sQ2_spl
| ~ sQ4_spl
| ~ sQ1_spl ),
inference(contradiction_clause,[status(thm)],[f43]) ).
fof(f46,plain,
( ~ sQ0_spl
| ~ h(sK0_skl) ),
inference(resolution,[status(thm)],[f19,f16]) ).
fof(f48,plain,
( ~ sQ4_spl
| ~ sQ0_spl
| ~ f(sK0_skl) ),
inference(resolution,[status(thm)],[f46,f33]) ).
fof(f49,plain,
( ~ sQ4_spl
| ~ sQ0_spl
| ~ sP0_prd(sK0_skl) ),
inference(resolution,[status(thm)],[f48,f14]) ).
fof(f50,plain,
( ~ sQ4_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f49,f18,f32]) ).
fof(f51,plain,
( ~ sQ3_spl
| sQ4_spl ),
inference(split_clause,[status(thm)],[f36,f32,f29]) ).
fof(f52,plain,
$false,
inference(sat_refutation,[status(thm)],[f24,f28,f35,f40,f44,f50,f51]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYN920+1 : TPTP v9.3.1. Released v3.1.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/0.35 % Computer : n013.cluster.edu
% 0.08/0.35 % Model : x86_64 x86_64
% 0.08/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.35 % Memory : 8046.5625MB
% 0.08/0.35 % OS : Linux 6.8.0-71-generic
% 0.08/0.35 % CPULimit : 300
% 0.08/0.35 % WCLimit : 300
% 0.08/0.35 % DateTime : Mon Sep 21 11:29:21 UTC 2026
% 0.08/0.35 % CPUTime :
% 0.08/0.36 % Drodi V4.1.1
% 0.08/0.37 % Refutation found
% 0.08/0.37 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.08/0.37 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.13/0.40 % Elapsed time: 0.038086 seconds
% 0.13/0.40 % CPU time: 0.099298 seconds
% 0.13/0.40 % Total memory used: 13.530 MB
% 0.13/0.40 % Net memory used: 13.076 MB
%------------------------------------------------------------------------------