%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SYN319+1 : TPTP v9.3.1. Released v2.0.0.
% 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 03:15:44 PM UTC 2026
% Result : Theorem 0.07s 0.37s
% Output : CNFRefutation 0.07s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 6
% Syntax : Number of formulae : 36 ( 1 unt; 5 def)
% Number of atoms : 141 ( 0 equ)
% Maximal formula atoms : 12 ( 3 avg)
% Number of connectives : 158 ( 53 ~; 52 |; 34 &)
% ( 5 <=>; 14 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 5 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 9 ( 8 usr; 5 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 3 con; 0-1 aty)
% Number of variables : 49 ( 37 !; 12 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,conjecture,
? [X,Y] :
! [Z1,Z2] :
( ( ( big_f(Y)
=> big_g(Z1) )
=> ( ~ big_f(Z1)
& big_g(X) ) )
=> ( ( ( big_g(X)
| big_f(X) )
=> big_h(X) )
=> ( ( big_h(Y)
=> ( ( big_g(Z2)
| big_f(Z2) )
=> big_h(Z2) ) )
& big_h(Z2) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f2,negated_conjecture,
~ ? [X,Y] :
! [Z1,Z2] :
( ( ( big_f(Y)
=> big_g(Z1) )
=> ( ~ big_f(Z1)
& big_g(X) ) )
=> ( ( ( big_g(X)
| big_f(X) )
=> big_h(X) )
=> ( ( big_h(Y)
=> ( ( big_g(Z2)
| big_f(Z2) )
=> big_h(Z2) ) )
& big_h(Z2) ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
fof(f3,plain,
! [X,Y] :
? [Z1,Z2] :
( ( ( ~ big_h(Z2)
& ( big_g(Z2)
| big_f(Z2) )
& big_h(Y) )
| ~ big_h(Z2) )
& ( big_h(X)
| ( ~ big_g(X)
& ~ big_f(X) ) )
& ( ( ~ big_f(Z1)
& big_g(X) )
| ( ~ big_g(Z1)
& big_f(Y) ) ) ),
inference(pre_NNF_transformation,[status(thm)],[f2]) ).
fof(f4,definition,
! [Y,Z1] :
( sP0_prd(Z1,Y)
<=> ( ~ big_g(Z1)
& big_f(Y) ) ),
introduced(definition,[new_symbols(definition,[sP0_prd])],[]) ).
fof(f5,plain,
! [X,Y] :
? [Z1,Z2] :
( ( ( ~ big_h(Z2)
& ( big_g(Z2)
| big_f(Z2) )
& big_h(Y) )
| ~ big_h(Z2) )
& ( big_h(X)
| ( ~ big_g(X)
& ~ big_f(X) ) )
& ( ( ~ big_f(Z1)
& big_g(X) )
| sP0_prd(Z1,Y) ) ),
inference(formula_renaming,[status(thm)],[f3,f4]) ).
fof(f6,plain,
( ( ( ? [Z2] :
( ~ big_h(Z2)
& ( big_g(Z2)
| big_f(Z2) ) )
& ! [Y] : big_h(Y) )
| ? [Z2] : ~ big_h(Z2) )
& ! [X] :
( big_h(X)
| ( ~ big_g(X)
& ~ big_f(X) ) )
& ( ( ? [Z1] : ~ big_f(Z1)
& ! [X] : big_g(X) )
| ! [Y] :
? [Z1] : sP0_prd(Z1,Y) ) ),
inference(miniscoping,[status(thm)],[f5]) ).
fof(f7,plain,
( ( ( ~ big_h(sK3_skl)
& ( big_g(sK3_skl)
| big_f(sK3_skl) )
& ! [Y] : big_h(Y) )
| ~ big_h(sK2_skl) )
& ! [X] :
( big_h(X)
| ( ~ big_g(X)
& ~ big_f(X) ) )
& ( ( ~ big_f(sK1_skl)
& ! [X] : big_g(X) )
| ! [Y] : sP0_prd(sK0_skl(Y),Y) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl,sK1_skl,sK2_skl,sK3_skl]),skolemize(Z1,sK0_skl(Y)),skolemize(Z1,sK1_skl),skolemize(Z2,sK2_skl),skolemize(Z2,sK3_skl)],[f6]) ).
fof(f8,plain,
! [X0,X1] :
( big_g(X1)
| sP0_prd(sK0_skl(X0),X0) ),
inference(cnf_transformation,[status(thm)],[f7]) ).
fof(f10,plain,
! [X0] :
( big_h(X0)
| ~ big_f(X0) ),
inference(cnf_transformation,[status(thm)],[f7]) ).
fof(f11,plain,
! [X0] :
( big_h(X0)
| ~ big_g(X0) ),
inference(cnf_transformation,[status(thm)],[f7]) ).
fof(f14,plain,
( ~ big_h(sK3_skl)
| ~ big_h(sK2_skl) ),
inference(cnf_transformation,[status(thm)],[f7]) ).
fof(f15,plain,
! [Y,Z1] :
( ( big_g(Z1)
| ~ big_f(Y)
| sP0_prd(Z1,Y) )
& ( ( ~ big_g(Z1)
& big_f(Y) )
| ~ sP0_prd(Z1,Y) ) ),
inference(NNF_transformation,[status(thm)],[f4]) ).
fof(f16,plain,
( ! [Y,Z1] :
( big_g(Z1)
| ~ big_f(Y)
| sP0_prd(Z1,Y) )
& ! [Y,Z1] :
( ( ~ big_g(Z1)
& big_f(Y) )
| ~ sP0_prd(Z1,Y) ) ),
inference(miniscoping,[status(thm)],[f15]) ).
fof(f17,plain,
! [X0,X1] :
( big_f(X1)
| ~ sP0_prd(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f16]) ).
fof(f20,definition,
! [X0] :
( sQ0_spl
<=> sP0_prd(sK0_skl(X0),X0) ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f21,plain,
! [X0] :
( ~ sQ0_spl
| sP0_prd(sK0_skl(X0),X0) ),
inference(component_clause,[status(thm)],[f20]) ).
fof(f23,definition,
! [X1] :
( sQ1_spl
<=> big_g(X1) ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f24,plain,
! [X0] :
( ~ sQ1_spl
| big_g(X0) ),
inference(component_clause,[status(thm)],[f23]) ).
fof(f26,plain,
( sQ1_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f8,f20,f23]) ).
fof(f31,definition,
( sQ3_spl
<=> big_h(sK2_skl) ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f33,plain,
( sQ3_spl
| ~ big_h(sK2_skl) ),
inference(component_clause,[status(thm)],[f31]) ).
fof(f45,definition,
( sQ7_spl
<=> big_h(sK3_skl) ),
introduced(definition,[new_symbols(definition,[sQ7_spl])],[split_symbol_definition]) ).
fof(f47,plain,
( sQ7_spl
| ~ big_h(sK3_skl) ),
inference(component_clause,[status(thm)],[f45]) ).
fof(f48,plain,
( ~ sQ7_spl
| ~ sQ3_spl ),
inference(split_clause,[status(thm)],[f14,f31,f45]) ).
fof(f49,plain,
! [X0] :
( ~ sQ0_spl
| big_f(X0) ),
inference(resolution,[status(thm)],[f21,f17]) ).
fof(f50,plain,
! [X0] :
( ~ sQ0_spl
| big_h(X0) ),
inference(backward_subsumption_resolution,[status(thm)],[f10,f49]) ).
fof(f51,plain,
( sQ3_spl
| ~ sQ0_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f33,f50]) ).
fof(f52,plain,
( sQ3_spl
| ~ sQ0_spl ),
inference(contradiction_clause,[status(thm)],[f51]) ).
fof(f53,plain,
( sQ7_spl
| ~ sQ0_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f47,f50]) ).
fof(f54,plain,
( sQ7_spl
| ~ sQ0_spl ),
inference(contradiction_clause,[status(thm)],[f53]) ).
fof(f56,plain,
( sQ3_spl
| ~ sQ1_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f33,f57]) ).
fof(f57,plain,
! [X0] :
( ~ sQ1_spl
| big_h(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f11,f24]) ).
fof(f58,plain,
( sQ3_spl
| ~ sQ1_spl ),
inference(contradiction_clause,[status(thm)],[f56]) ).
fof(f59,plain,
( sQ7_spl
| ~ sQ1_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f47,f57]) ).
fof(f60,plain,
( sQ7_spl
| ~ sQ1_spl ),
inference(contradiction_clause,[status(thm)],[f59]) ).
fof(f61,plain,
$false,
inference(sat_refutation,[status(thm)],[f26,f48,f52,f54,f58,f60]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SYN319+1 : TPTP v9.3.1. Released v2.0.0.
% 0.00/0.03 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.07/0.34 % Computer : n013.cluster.edu
% 0.07/0.34 % Model : x86_64 x86_64
% 0.07/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.34 % Memory : 8046.5625MB
% 0.07/0.34 % OS : Linux 6.8.0-71-generic
% 0.07/0.34 % CPULimit : 300
% 0.07/0.34 % WCLimit : 300
% 0.07/0.34 % DateTime : Mon Sep 21 10:48:36 UTC 2026
% 0.07/0.34 % CPUTime :
% 0.07/0.35 % Drodi V4.1.1
% 0.07/0.37 % Refutation found
% 0.07/0.37 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.07/0.37 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.13/0.39 % Elapsed time: 0.042023 seconds
% 0.13/0.39 % CPU time: 0.102363 seconds
% 0.13/0.39 % Total memory used: 16.720 MB
% 0.13/0.39 % Net memory used: 16.206 MB
%------------------------------------------------------------------------------