%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SYN078+1 : TPTP v9.3.1. Released v2.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n014.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 03:15:10 PM UTC 2026
% Result : Theorem 0.13s 0.39s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 10
% Syntax : Number of formulae : 54 ( 1 unt; 9 def)
% Number of atoms : 162 ( 13 equ)
% Maximal formula atoms : 8 ( 3 avg)
% Number of connectives : 175 ( 67 ~; 76 |; 15 &)
% ( 11 <=>; 4 =>; 0 <=; 2 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 12 ( 10 usr; 9 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 2 con; 0-1 aty)
% Number of variables : 41 ( 35 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,conjecture,
( ! [X] :
( ? [Y] :
( X = f(Y)
& big_p(Y) )
=> big_p(X) )
<=> ! [U] :
( big_p(U)
=> big_p(f(U)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f2,negated_conjecture,
~ ( ! [X] :
( ? [Y] :
( X = f(Y)
& big_p(Y) )
=> big_p(X) )
<=> ! [U] :
( big_p(U)
=> big_p(f(U)) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
fof(f3,plain,
( ! [X] :
( big_p(X)
| ! [Y] :
( X != f(Y)
| ~ big_p(Y) ) )
<~> ! [U] :
( big_p(f(U))
| ~ big_p(U) ) ),
inference(pre_NNF_transformation,[status(thm)],[f2]) ).
fof(f4,definition,
! [X] :
( sP0_prd(X)
<=> ( big_p(X)
| ! [Y] :
( X != f(Y)
| ~ big_p(Y) ) ) ),
introduced(definition,[new_symbols(definition,[sP0_prd])],[]) ).
fof(f5,plain,
( ! [X] : sP0_prd(X)
<~> ! [U] :
( big_p(f(U))
| ~ big_p(U) ) ),
inference(formula_renaming,[status(thm)],[f3,f4]) ).
fof(f6,plain,
( ( ? [U] :
( ~ big_p(f(U))
& big_p(U) )
| ? [X] : ~ sP0_prd(X) )
& ( ! [U] :
( big_p(f(U))
| ~ big_p(U) )
| ! [X] : sP0_prd(X) ) ),
inference(NNF_transformation,[status(thm)],[f5]) ).
fof(f7,plain,
( ( ( ~ big_p(f(sK1_skl))
& big_p(sK1_skl) )
| ~ sP0_prd(sK0_skl) )
& ( ! [U] :
( big_p(f(U))
| ~ big_p(U) )
| ! [X] : sP0_prd(X) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl,sK1_skl]),skolemize(X,sK0_skl),skolemize(U,sK1_skl)],[f6]) ).
fof(f8,plain,
! [X0,X1] :
( big_p(f(X1))
| ~ big_p(X1)
| sP0_prd(X0) ),
inference(cnf_transformation,[status(thm)],[f7]) ).
fof(f9,plain,
( big_p(sK1_skl)
| ~ sP0_prd(sK0_skl) ),
inference(cnf_transformation,[status(thm)],[f7]) ).
fof(f10,plain,
( ~ big_p(f(sK1_skl))
| ~ sP0_prd(sK0_skl) ),
inference(cnf_transformation,[status(thm)],[f7]) ).
fof(f11,plain,
! [X] :
( ( ( ~ big_p(X)
& ? [Y] :
( X = f(Y)
& big_p(Y) ) )
| sP0_prd(X) )
& ( big_p(X)
| ! [Y] :
( X != f(Y)
| ~ big_p(Y) )
| ~ sP0_prd(X) ) ),
inference(NNF_transformation,[status(thm)],[f4]) ).
fof(f12,plain,
( ! [X] :
( ( ~ big_p(X)
& ? [Y] :
( X = f(Y)
& big_p(Y) ) )
| sP0_prd(X) )
& ! [X] :
( big_p(X)
| ! [Y] :
( X != f(Y)
| ~ big_p(Y) )
| ~ sP0_prd(X) ) ),
inference(miniscoping,[status(thm)],[f11]) ).
fof(f13,plain,
( ! [X] :
( ( ~ big_p(X)
& X = f(sK2_skl(X))
& big_p(sK2_skl(X)) )
| sP0_prd(X) )
& ! [X] :
( big_p(X)
| ! [Y] :
( X != f(Y)
| ~ big_p(Y) )
| ~ sP0_prd(X) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2_skl]),skolemize(Y,sK2_skl(X))],[f12]) ).
fof(f14,plain,
! [X0,X1] :
( big_p(X0)
| X0 != f(X1)
| ~ big_p(X1)
| ~ sP0_prd(X0) ),
inference(cnf_transformation,[status(thm)],[f13]) ).
fof(f15,plain,
! [X0] :
( big_p(sK2_skl(X0))
| sP0_prd(X0) ),
inference(cnf_transformation,[status(thm)],[f13]) ).
fof(f16,plain,
! [X0] :
( X0 = f(sK2_skl(X0))
| sP0_prd(X0) ),
inference(cnf_transformation,[status(thm)],[f13]) ).
fof(f17,plain,
! [X0] :
( ~ big_p(X0)
| sP0_prd(X0) ),
inference(cnf_transformation,[status(thm)],[f13]) ).
fof(f18,definition,
! [X0] :
( sQ0_spl
<=> sP0_prd(X0) ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f19,plain,
! [X0] :
( ~ sQ0_spl
| sP0_prd(X0) ),
inference(component_clause,[status(thm)],[f18]) ).
fof(f21,definition,
! [X1] :
( sQ1_spl
<=> ( big_p(f(X1))
| ~ big_p(X1) ) ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f22,plain,
! [X0] :
( ~ sQ1_spl
| big_p(f(X0))
| ~ big_p(X0) ),
inference(component_clause,[status(thm)],[f21]) ).
fof(f24,plain,
( sQ1_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f8,f18,f21]) ).
fof(f25,definition,
( sQ2_spl
<=> sP0_prd(sK0_skl) ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f27,plain,
( sQ2_spl
| ~ sP0_prd(sK0_skl) ),
inference(component_clause,[status(thm)],[f25]) ).
fof(f28,definition,
( sQ3_spl
<=> big_p(sK1_skl) ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f31,plain,
( sQ3_spl
| ~ sQ2_spl ),
inference(split_clause,[status(thm)],[f9,f25,f28]) ).
fof(f32,definition,
( sQ4_spl
<=> big_p(f(sK1_skl)) ),
introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition]) ).
fof(f34,plain,
( sQ4_spl
| ~ big_p(f(sK1_skl)) ),
inference(component_clause,[status(thm)],[f32]) ).
fof(f35,plain,
( ~ sQ4_spl
| ~ sQ2_spl ),
inference(split_clause,[status(thm)],[f10,f25,f32]) ).
fof(f36,plain,
! [X0] :
( big_p(f(X0))
| ~ big_p(X0)
| ~ sP0_prd(f(X0)) ),
inference(destructive_equality_resolution,[status(thm)],[f14]) ).
fof(f37,plain,
( sQ2_spl
| ~ sQ0_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f27,f19]) ).
fof(f38,plain,
( sQ2_spl
| ~ sQ0_spl ),
inference(contradiction_clause,[status(thm)],[f37]) ).
fof(f39,plain,
( sQ4_spl
| ~ big_p(sK1_skl)
| ~ sP0_prd(f(sK1_skl)) ),
inference(resolution,[status(thm)],[f34,f36]) ).
fof(f40,definition,
( sQ5_spl
<=> sP0_prd(f(sK1_skl)) ),
introduced(definition,[new_symbols(definition,[sQ5_spl])],[split_symbol_definition]) ).
fof(f42,plain,
( sQ5_spl
| ~ sP0_prd(f(sK1_skl)) ),
inference(component_clause,[status(thm)],[f40]) ).
fof(f43,plain,
( sQ4_spl
| ~ sQ3_spl
| ~ sQ5_spl ),
inference(split_clause,[status(thm)],[f39,f40,f28,f32]) ).
fof(f44,plain,
( sQ2_spl
| ~ big_p(sK0_skl) ),
inference(resolution,[status(thm)],[f27,f17]) ).
fof(f45,plain,
( sQ5_spl
| ~ big_p(f(sK1_skl)) ),
inference(resolution,[status(thm)],[f42,f17]) ).
fof(f47,plain,
( sQ2_spl
| sK0_skl = f(sK2_skl(sK0_skl)) ),
inference(resolution,[status(thm)],[f16,f27]) ).
fof(f50,plain,
( sQ5_spl
| ~ sQ1_spl
| ~ big_p(sK1_skl) ),
inference(resolution,[status(thm)],[f22,f45]) ).
fof(f51,plain,
( sQ2_spl
| ~ sQ1_spl
| big_p(sK0_skl)
| ~ big_p(sK2_skl(sK0_skl)) ),
inference(paramodulation,[status(thm)],[f47,f22]) ).
fof(f52,definition,
( sQ6_spl
<=> big_p(sK2_skl(sK0_skl)) ),
introduced(definition,[new_symbols(definition,[sQ6_spl])],[split_symbol_definition]) ).
fof(f54,plain,
( sQ6_spl
| ~ big_p(sK2_skl(sK0_skl)) ),
inference(component_clause,[status(thm)],[f52]) ).
fof(f55,definition,
( sQ7_spl
<=> big_p(sK0_skl) ),
introduced(definition,[new_symbols(definition,[sQ7_spl])],[split_symbol_definition]) ).
fof(f56,plain,
( ~ sQ7_spl
| big_p(sK0_skl) ),
inference(component_clause,[status(thm)],[f55]) ).
fof(f58,plain,
( sQ2_spl
| ~ sQ1_spl
| sQ7_spl
| ~ sQ6_spl ),
inference(split_clause,[status(thm)],[f51,f52,f55,f21,f25]) ).
fof(f59,plain,
( ~ sQ7_spl
| sQ2_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f56,f44]) ).
fof(f60,plain,
( ~ sQ7_spl
| sQ2_spl ),
inference(contradiction_clause,[status(thm)],[f59]) ).
fof(f61,plain,
( sQ5_spl
| ~ sQ0_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f42,f19]) ).
fof(f62,plain,
( sQ5_spl
| ~ sQ0_spl ),
inference(contradiction_clause,[status(thm)],[f61]) ).
fof(f64,plain,
( sQ6_spl
| sP0_prd(sK0_skl) ),
inference(resolution,[status(thm)],[f54,f15]) ).
fof(f65,plain,
( sQ6_spl
| sQ2_spl ),
inference(split_clause,[status(thm)],[f64,f25,f52]) ).
fof(f66,plain,
( sQ5_spl
| ~ sQ1_spl
| ~ sQ3_spl ),
inference(split_clause,[status(thm)],[f50,f28,f21,f40]) ).
fof(f67,plain,
$false,
inference(sat_refutation,[status(thm)],[f24,f31,f35,f38,f43,f58,f60,f62,f65,f66]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SYN078+1 : TPTP v9.3.1. Released v2.0.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n014.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Mon Sep 21 10:41:51 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.37 % Drodi V4.1.1
% 0.13/0.39 % Refutation found
% 0.13/0.39 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.13/0.39 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.13/0.43 % Elapsed time: 0.052352 seconds
% 0.13/0.43 % CPU time: 0.153150 seconds
% 0.13/0.43 % Total memory used: 79.761 MB
% 0.13/0.43 % Net memory used: 79.213 MB
%------------------------------------------------------------------------------