%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SYN084+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 : n005.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 03:15:11 PM UTC 2026
% Result : Theorem 0.16s 0.45s
% Output : CNFRefutation 0.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 14
% Syntax : Number of formulae : 78 ( 1 unt; 13 def)
% Number of atoms : 299 ( 0 equ)
% Maximal formula atoms : 10 ( 3 avg)
% Number of connectives : 362 ( 141 ~; 166 |; 34 &)
% ( 15 <=>; 4 =>; 0 <=; 2 <~>)
% Maximal formula depth : 8 ( 5 avg)
% Maximal term depth : 3 ( 2 avg)
% Number of predicates : 15 ( 14 usr; 12 prp; 0-1 aty)
% Number of functors : 5 ( 5 usr; 4 con; 0-1 aty)
% Number of variables : 63 ( 58 !; 5 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,conjecture,
( ! [X] :
( ( ( big_p(X)
=> big_p(f(X)) )
& big_p(a) )
=> big_p(f(f(X))) )
<=> ! [X1] :
( ( big_p(f(f(X1)))
| ~ big_p(f(X1))
| ~ big_p(a) )
& ( big_p(f(f(X1)))
| big_p(X1)
| ~ big_p(a) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f2,negated_conjecture,
~ ( ! [X] :
( ( ( big_p(X)
=> big_p(f(X)) )
& big_p(a) )
=> big_p(f(f(X))) )
<=> ! [X1] :
( ( big_p(f(f(X1)))
| ~ big_p(f(X1))
| ~ big_p(a) )
& ( big_p(f(f(X1)))
| big_p(X1)
| ~ big_p(a) ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
fof(f3,plain,
( ! [X] :
( big_p(f(f(X)))
| ( ~ big_p(f(X))
& big_p(X) )
| ~ big_p(a) )
<~> ! [X1] :
( ( big_p(f(f(X1)))
| ~ big_p(f(X1))
| ~ big_p(a) )
& ( big_p(f(f(X1)))
| big_p(X1)
| ~ big_p(a) ) ) ),
inference(pre_NNF_transformation,[status(thm)],[f2]) ).
fof(f4,definition,
! [X] :
( sP0_prd(X)
<=> ( big_p(f(f(X)))
| ( ~ big_p(f(X))
& big_p(X) )
| ~ big_p(a) ) ),
introduced(definition,[new_symbols(definition,[sP0_prd])],[]) ).
fof(f5,definition,
! [X1] :
( sP1_prd(X1)
<=> ( big_p(f(f(X1)))
| big_p(X1)
| ~ big_p(a) ) ),
introduced(definition,[new_symbols(definition,[sP1_prd])],[]) ).
fof(f6,plain,
( ! [X] : sP0_prd(X)
<~> ! [X1] :
( ( big_p(f(f(X1)))
| ~ big_p(f(X1))
| ~ big_p(a) )
& sP1_prd(X1) ) ),
inference(formula_renaming,[status(thm)],[f3,f5,f4]) ).
fof(f7,plain,
( ( ? [X1] :
( ( ~ big_p(f(f(X1)))
& big_p(f(X1))
& big_p(a) )
| ~ sP1_prd(X1) )
| ? [X] : ~ sP0_prd(X) )
& ( ! [X1] :
( ( big_p(f(f(X1)))
| ~ big_p(f(X1))
| ~ big_p(a) )
& sP1_prd(X1) )
| ! [X] : sP0_prd(X) ) ),
inference(NNF_transformation,[status(thm)],[f6]) ).
fof(f8,plain,
( ( ? [X1] :
( ~ big_p(f(f(X1)))
& big_p(f(X1))
& big_p(a) )
| ? [X1] : ~ sP1_prd(X1)
| ? [X] : ~ sP0_prd(X) )
& ( ( ! [X1] :
( big_p(f(f(X1)))
| ~ big_p(f(X1))
| ~ big_p(a) )
& ! [X1] : sP1_prd(X1) )
| ! [X] : sP0_prd(X) ) ),
inference(miniscoping,[status(thm)],[f7]) ).
fof(f9,plain,
( ( ( ~ big_p(f(f(sK2_skl)))
& big_p(f(sK2_skl))
& big_p(a) )
| ~ sP1_prd(sK1_skl)
| ~ sP0_prd(sK0_skl) )
& ( ( ! [X1] :
( big_p(f(f(X1)))
| ~ big_p(f(X1))
| ~ big_p(a) )
& ! [X1] : sP1_prd(X1) )
| ! [X] : sP0_prd(X) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl,sK1_skl,sK2_skl]),skolemize(X,sK0_skl),skolemize(X1,sK1_skl),skolemize(X1,sK2_skl)],[f8]) ).
fof(f10,plain,
! [X0,X1] :
( sP1_prd(X1)
| sP0_prd(X0) ),
inference(cnf_transformation,[status(thm)],[f9]) ).
fof(f11,plain,
! [X0,X1] :
( big_p(f(f(X1)))
| ~ big_p(f(X1))
| ~ big_p(a)
| sP0_prd(X0) ),
inference(cnf_transformation,[status(thm)],[f9]) ).
fof(f12,plain,
( big_p(a)
| ~ sP1_prd(sK1_skl)
| ~ sP0_prd(sK0_skl) ),
inference(cnf_transformation,[status(thm)],[f9]) ).
fof(f13,plain,
( big_p(f(sK2_skl))
| ~ sP1_prd(sK1_skl)
| ~ sP0_prd(sK0_skl) ),
inference(cnf_transformation,[status(thm)],[f9]) ).
fof(f14,plain,
( ~ big_p(f(f(sK2_skl)))
| ~ sP1_prd(sK1_skl)
| ~ sP0_prd(sK0_skl) ),
inference(cnf_transformation,[status(thm)],[f9]) ).
fof(f15,plain,
! [X] :
( ( ( ~ big_p(f(f(X)))
& ( big_p(f(X))
| ~ big_p(X) )
& big_p(a) )
| sP0_prd(X) )
& ( big_p(f(f(X)))
| ( ~ big_p(f(X))
& big_p(X) )
| ~ big_p(a)
| ~ sP0_prd(X) ) ),
inference(NNF_transformation,[status(thm)],[f4]) ).
fof(f16,plain,
( ! [X] :
( ( ~ big_p(f(f(X)))
& ( big_p(f(X))
| ~ big_p(X) )
& big_p(a) )
| sP0_prd(X) )
& ! [X] :
( big_p(f(f(X)))
| ( ~ big_p(f(X))
& big_p(X) )
| ~ big_p(a)
| ~ sP0_prd(X) ) ),
inference(miniscoping,[status(thm)],[f15]) ).
fof(f17,plain,
! [X0] :
( big_p(f(f(X0)))
| big_p(X0)
| ~ big_p(a)
| ~ sP0_prd(X0) ),
inference(cnf_transformation,[status(thm)],[f16]) ).
fof(f18,plain,
! [X0] :
( big_p(f(f(X0)))
| ~ big_p(f(X0))
| ~ big_p(a)
| ~ sP0_prd(X0) ),
inference(cnf_transformation,[status(thm)],[f16]) ).
fof(f19,plain,
! [X0] :
( big_p(a)
| sP0_prd(X0) ),
inference(cnf_transformation,[status(thm)],[f16]) ).
fof(f20,plain,
! [X0] :
( big_p(f(X0))
| ~ big_p(X0)
| sP0_prd(X0) ),
inference(cnf_transformation,[status(thm)],[f16]) ).
fof(f21,plain,
! [X0] :
( ~ big_p(f(f(X0)))
| sP0_prd(X0) ),
inference(cnf_transformation,[status(thm)],[f16]) ).
fof(f22,plain,
! [X1] :
( ( ( ~ big_p(f(f(X1)))
& ~ big_p(X1)
& big_p(a) )
| sP1_prd(X1) )
& ( big_p(f(f(X1)))
| big_p(X1)
| ~ big_p(a)
| ~ sP1_prd(X1) ) ),
inference(NNF_transformation,[status(thm)],[f5]) ).
fof(f23,plain,
( ! [X1] :
( ( ~ big_p(f(f(X1)))
& ~ big_p(X1)
& big_p(a) )
| sP1_prd(X1) )
& ! [X1] :
( big_p(f(f(X1)))
| big_p(X1)
| ~ big_p(a)
| ~ sP1_prd(X1) ) ),
inference(miniscoping,[status(thm)],[f22]) ).
fof(f24,plain,
! [X0] :
( big_p(f(f(X0)))
| big_p(X0)
| ~ big_p(a)
| ~ sP1_prd(X0) ),
inference(cnf_transformation,[status(thm)],[f23]) ).
fof(f25,plain,
! [X0] :
( big_p(a)
| sP1_prd(X0) ),
inference(cnf_transformation,[status(thm)],[f23]) ).
fof(f26,plain,
! [X0] :
( ~ big_p(X0)
| sP1_prd(X0) ),
inference(cnf_transformation,[status(thm)],[f23]) ).
fof(f27,plain,
! [X0] :
( ~ big_p(f(f(X0)))
| sP1_prd(X0) ),
inference(cnf_transformation,[status(thm)],[f23]) ).
fof(f28,definition,
! [X0] :
( sQ0_spl
<=> sP0_prd(X0) ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f29,plain,
! [X0] :
( ~ sQ0_spl
| sP0_prd(X0) ),
inference(component_clause,[status(thm)],[f28]) ).
fof(f31,definition,
! [X1] :
( sQ1_spl
<=> sP1_prd(X1) ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f32,plain,
! [X0] :
( ~ sQ1_spl
| sP1_prd(X0) ),
inference(component_clause,[status(thm)],[f31]) ).
fof(f34,plain,
( sQ1_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f10,f28,f31]) ).
fof(f35,definition,
( sQ2_spl
<=> big_p(a) ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f38,definition,
! [X1] :
( sQ3_spl
<=> ( big_p(f(f(X1)))
| ~ big_p(f(X1)) ) ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f39,plain,
! [X0] :
( ~ sQ3_spl
| big_p(f(f(X0)))
| ~ big_p(f(X0)) ),
inference(component_clause,[status(thm)],[f38]) ).
fof(f41,plain,
( sQ3_spl
| ~ sQ2_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f11,f28,f35,f38]) ).
fof(f42,definition,
( sQ4_spl
<=> sP0_prd(sK0_skl) ),
introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition]) ).
fof(f44,plain,
( sQ4_spl
| ~ sP0_prd(sK0_skl) ),
inference(component_clause,[status(thm)],[f42]) ).
fof(f45,definition,
( sQ5_spl
<=> sP1_prd(sK1_skl) ),
introduced(definition,[new_symbols(definition,[sQ5_spl])],[split_symbol_definition]) ).
fof(f47,plain,
( sQ5_spl
| ~ sP1_prd(sK1_skl) ),
inference(component_clause,[status(thm)],[f45]) ).
fof(f48,plain,
( sQ2_spl
| ~ sQ5_spl
| ~ sQ4_spl ),
inference(split_clause,[status(thm)],[f12,f42,f45,f35]) ).
fof(f49,definition,
( sQ6_spl
<=> big_p(f(sK2_skl)) ),
introduced(definition,[new_symbols(definition,[sQ6_spl])],[split_symbol_definition]) ).
fof(f50,plain,
( ~ sQ6_spl
| big_p(f(sK2_skl)) ),
inference(component_clause,[status(thm)],[f49]) ).
fof(f52,plain,
( sQ6_spl
| ~ sQ5_spl
| ~ sQ4_spl ),
inference(split_clause,[status(thm)],[f13,f42,f45,f49]) ).
fof(f53,definition,
( sQ7_spl
<=> big_p(f(f(sK2_skl))) ),
introduced(definition,[new_symbols(definition,[sQ7_spl])],[split_symbol_definition]) ).
fof(f55,plain,
( sQ7_spl
| ~ big_p(f(f(sK2_skl))) ),
inference(component_clause,[status(thm)],[f53]) ).
fof(f56,plain,
( ~ sQ7_spl
| ~ sQ5_spl
| ~ sQ4_spl ),
inference(split_clause,[status(thm)],[f14,f42,f45,f53]) ).
fof(f57,definition,
! [X0] :
( sQ8_spl
<=> ( big_p(f(f(X0)))
| big_p(X0)
| ~ sP0_prd(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ8_spl])],[split_symbol_definition]) ).
fof(f58,plain,
! [X0] :
( ~ sQ8_spl
| big_p(f(f(X0)))
| big_p(X0)
| ~ sP0_prd(X0) ),
inference(component_clause,[status(thm)],[f57]) ).
fof(f60,plain,
( ~ sQ2_spl
| sQ8_spl ),
inference(split_clause,[status(thm)],[f17,f57,f35]) ).
fof(f61,definition,
! [X0] :
( sQ9_spl
<=> ( big_p(f(f(X0)))
| ~ big_p(f(X0))
| ~ sP0_prd(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ9_spl])],[split_symbol_definition]) ).
fof(f62,plain,
! [X0] :
( ~ sQ9_spl
| big_p(f(f(X0)))
| ~ big_p(f(X0))
| ~ sP0_prd(X0) ),
inference(component_clause,[status(thm)],[f61]) ).
fof(f64,plain,
( ~ sQ2_spl
| sQ9_spl ),
inference(split_clause,[status(thm)],[f18,f61,f35]) ).
fof(f65,plain,
( sQ2_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f19,f28,f35]) ).
fof(f66,definition,
! [X0] :
( sQ10_spl
<=> ( big_p(f(f(X0)))
| big_p(X0)
| ~ sP1_prd(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ10_spl])],[split_symbol_definition]) ).
fof(f67,plain,
! [X0] :
( ~ sQ10_spl
| big_p(f(f(X0)))
| big_p(X0)
| ~ sP1_prd(X0) ),
inference(component_clause,[status(thm)],[f66]) ).
fof(f69,plain,
( ~ sQ2_spl
| sQ10_spl ),
inference(split_clause,[status(thm)],[f24,f66,f35]) ).
fof(f70,plain,
( sQ2_spl
| sQ1_spl ),
inference(split_clause,[status(thm)],[f25,f31,f35]) ).
fof(f71,plain,
( sQ5_spl
| ~ sQ1_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f47,f32]) ).
fof(f72,plain,
( sQ5_spl
| ~ sQ1_spl ),
inference(contradiction_clause,[status(thm)],[f71]) ).
fof(f73,plain,
( sQ4_spl
| ~ sQ0_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f44,f29]) ).
fof(f74,plain,
( sQ4_spl
| ~ sQ0_spl ),
inference(contradiction_clause,[status(thm)],[f73]) ).
fof(f76,plain,
! [X0] :
( ~ sQ3_spl
| sP0_prd(X0)
| ~ big_p(f(X0)) ),
inference(resolution,[status(thm)],[f39,f21]) ).
fof(f77,plain,
! [X0] :
( ~ sQ10_spl
| ~ sQ1_spl
| big_p(f(f(X0)))
| big_p(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f67,f32]) ).
fof(f78,plain,
! [X0] :
( ~ sQ10_spl
| ~ sQ1_spl
| sP0_prd(X0)
| big_p(X0) ),
inference(resolution,[status(thm)],[f77,f21]) ).
fof(f79,plain,
! [X0] :
( ~ sQ10_spl
| ~ sQ1_spl
| big_p(f(X0))
| sP0_prd(X0) ),
inference(backward_subsumption_resolution,[status(thm)],[f20,f78]) ).
fof(f86,plain,
! [X0] :
( ~ sQ10_spl
| ~ sQ1_spl
| ~ sQ3_spl
| sP0_prd(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f79,f76]) ).
fof(f89,plain,
! [X0] :
( ~ sQ8_spl
| ~ sQ0_spl
| big_p(f(f(X0)))
| big_p(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f58,f29]) ).
fof(f91,plain,
! [X0] :
( ~ sQ8_spl
| ~ sQ0_spl
| big_p(X0)
| sP1_prd(X0) ),
inference(resolution,[status(thm)],[f27,f89]) ).
fof(f92,plain,
! [X0] :
( ~ sQ8_spl
| ~ sQ0_spl
| sP1_prd(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f91,f26]) ).
fof(f93,plain,
( sQ5_spl
| ~ sQ8_spl
| ~ sQ0_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f47,f92]) ).
fof(f94,plain,
( sQ5_spl
| ~ sQ8_spl
| ~ sQ0_spl ),
inference(contradiction_clause,[status(thm)],[f93]) ).
fof(f96,plain,
! [X0] :
( ~ sQ9_spl
| ~ sQ0_spl
| big_p(f(f(X0)))
| ~ big_p(f(X0)) ),
inference(forward_subsumption_resolution,[status(thm)],[f62,f29]) ).
fof(f97,plain,
( sQ7_spl
| ~ sQ9_spl
| ~ sQ0_spl
| ~ big_p(f(sK2_skl)) ),
inference(resolution,[status(thm)],[f96,f55]) ).
fof(f98,plain,
( sQ7_spl
| ~ sQ9_spl
| ~ sQ0_spl
| ~ sQ6_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f97,f50]) ).
fof(f99,plain,
( sQ7_spl
| ~ sQ9_spl
| ~ sQ0_spl
| ~ sQ6_spl ),
inference(contradiction_clause,[status(thm)],[f98]) ).
fof(f100,plain,
( ~ sQ10_spl
| ~ sQ1_spl
| ~ sQ3_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f86,f28,f38,f31,f66]) ).
fof(f101,plain,
$false,
inference(sat_refutation,[status(thm)],[f34,f41,f48,f52,f56,f60,f64,f65,f69,f70,f72,f74,f94,f99,f100]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SYN084+1 : TPTP v9.3.1. Released v2.0.0.
% 0.00/0.06 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.16/0.43 % Computer : n005.cluster.edu
% 0.16/0.43 % Model : x86_64 x86_64
% 0.16/0.43 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.43 % Memory : 8046.5625MB
% 0.16/0.43 % OS : Linux 6.8.0-71-generic
% 0.16/0.43 % CPULimit : 300
% 0.16/0.43 % WCLimit : 300
% 0.16/0.43 % DateTime : Mon Sep 21 10:43:03 UTC 2026
% 0.16/0.43 % CPUTime :
% 0.16/0.44 % Drodi V4.1.1
% 0.16/0.45 % Refutation found
% 0.16/0.45 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.16/0.45 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.16/0.51 % Elapsed time: 0.062588 seconds
% 0.16/0.51 % CPU time: 0.077145 seconds
% 0.16/0.51 % Total memory used: 2.662 MB
% 0.16/0.51 % Net memory used: 2.641 MB
%------------------------------------------------------------------------------