%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SYN063+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 : n016.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 03:15:05 PM UTC 2026
% Result : Theorem 0.08s 0.59s
% Output : CNFRefutation 0.08s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 13
% Syntax : Number of formulae : 69 ( 1 unt; 12 def)
% Number of atoms : 256 ( 0 equ)
% Maximal formula atoms : 10 ( 3 avg)
% Number of connectives : 305 ( 118 ~; 133 |; 34 &)
% ( 14 <=>; 4 =>; 0 <=; 2 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 14 ( 13 usr; 11 prp; 0-1 aty)
% Number of functors : 5 ( 5 usr; 5 con; 0-0 aty)
% Number of variables : 48 ( 44 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,conjecture,
( ! [X] :
( ( ( big_p(X)
=> big_p(b) )
& big_p(a) )
=> big_p(c) )
<=> ! [X1] :
( ( big_p(c)
| ~ big_p(b)
| ~ big_p(a) )
& ( big_p(c)
| big_p(X1)
| ~ big_p(a) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f2,negated_conjecture,
~ ( ! [X] :
( ( ( big_p(X)
=> big_p(b) )
& big_p(a) )
=> big_p(c) )
<=> ! [X1] :
( ( big_p(c)
| ~ big_p(b)
| ~ big_p(a) )
& ( big_p(c)
| big_p(X1)
| ~ big_p(a) ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
fof(f3,plain,
( ! [X] :
( big_p(c)
| ( ~ big_p(b)
& big_p(X) )
| ~ big_p(a) )
<~> ! [X1] :
( ( big_p(c)
| ~ big_p(b)
| ~ big_p(a) )
& ( big_p(c)
| big_p(X1)
| ~ big_p(a) ) ) ),
inference(pre_NNF_transformation,[status(thm)],[f2]) ).
fof(f4,definition,
! [X] :
( sP0_prd(X)
<=> ( big_p(c)
| ( ~ big_p(b)
& big_p(X) )
| ~ big_p(a) ) ),
introduced(definition,[new_symbols(definition,[sP0_prd])],[]) ).
fof(f5,definition,
! [X1] :
( sP1_prd(X1)
<=> ( big_p(c)
| big_p(X1)
| ~ big_p(a) ) ),
introduced(definition,[new_symbols(definition,[sP1_prd])],[]) ).
fof(f6,plain,
( ! [X] : sP0_prd(X)
<~> ! [X1] :
( ( big_p(c)
| ~ big_p(b)
| ~ big_p(a) )
& sP1_prd(X1) ) ),
inference(formula_renaming,[status(thm)],[f3,f5,f4]) ).
fof(f7,plain,
( ( ? [X1] :
( ( ~ big_p(c)
& big_p(b)
& big_p(a) )
| ~ sP1_prd(X1) )
| ? [X] : ~ sP0_prd(X) )
& ( ! [X1] :
( ( big_p(c)
| ~ big_p(b)
| ~ big_p(a) )
& sP1_prd(X1) )
| ! [X] : sP0_prd(X) ) ),
inference(NNF_transformation,[status(thm)],[f6]) ).
fof(f8,plain,
( ( ( ~ big_p(c)
& big_p(b)
& big_p(a) )
| ? [X1] : ~ sP1_prd(X1)
| ? [X] : ~ sP0_prd(X) )
& ( ( ( big_p(c)
| ~ big_p(b)
| ~ big_p(a) )
& ! [X1] : sP1_prd(X1) )
| ! [X] : sP0_prd(X) ) ),
inference(miniscoping,[status(thm)],[f7]) ).
fof(f9,plain,
( ( ( ~ big_p(c)
& big_p(b)
& big_p(a) )
| ~ sP1_prd(sK1_skl)
| ~ sP0_prd(sK0_skl) )
& ( ( ( big_p(c)
| ~ big_p(b)
| ~ big_p(a) )
& ! [X1] : sP1_prd(X1) )
| ! [X] : sP0_prd(X) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl,sK1_skl]),skolemize(X,sK0_skl),skolemize(X1,sK1_skl)],[f8]) ).
fof(f10,plain,
! [X0,X1] :
( sP1_prd(X1)
| sP0_prd(X0) ),
inference(cnf_transformation,[status(thm)],[f9]) ).
fof(f11,plain,
! [X0] :
( big_p(c)
| ~ big_p(b)
| ~ 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(b)
| ~ sP1_prd(sK1_skl)
| ~ sP0_prd(sK0_skl) ),
inference(cnf_transformation,[status(thm)],[f9]) ).
fof(f14,plain,
( ~ big_p(c)
| ~ sP1_prd(sK1_skl)
| ~ sP0_prd(sK0_skl) ),
inference(cnf_transformation,[status(thm)],[f9]) ).
fof(f15,plain,
! [X] :
( ( ( ~ big_p(c)
& ( big_p(b)
| ~ big_p(X) )
& big_p(a) )
| sP0_prd(X) )
& ( big_p(c)
| ( ~ big_p(b)
& big_p(X) )
| ~ big_p(a)
| ~ sP0_prd(X) ) ),
inference(NNF_transformation,[status(thm)],[f4]) ).
fof(f16,plain,
( ! [X] :
( ( ~ big_p(c)
& ( big_p(b)
| ~ big_p(X) )
& big_p(a) )
| sP0_prd(X) )
& ! [X] :
( big_p(c)
| ( ~ big_p(b)
& big_p(X) )
| ~ big_p(a)
| ~ sP0_prd(X) ) ),
inference(miniscoping,[status(thm)],[f15]) ).
fof(f17,plain,
! [X0] :
( big_p(c)
| big_p(X0)
| ~ big_p(a)
| ~ sP0_prd(X0) ),
inference(cnf_transformation,[status(thm)],[f16]) ).
fof(f18,plain,
! [X0] :
( big_p(c)
| ~ big_p(b)
| ~ 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(f21,plain,
! [X0] :
( ~ big_p(c)
| sP0_prd(X0) ),
inference(cnf_transformation,[status(thm)],[f16]) ).
fof(f22,plain,
! [X1] :
( ( ( ~ big_p(c)
& ~ big_p(X1)
& big_p(a) )
| sP1_prd(X1) )
& ( big_p(c)
| big_p(X1)
| ~ big_p(a)
| ~ sP1_prd(X1) ) ),
inference(NNF_transformation,[status(thm)],[f5]) ).
fof(f23,plain,
( ! [X1] :
( ( ~ big_p(c)
& ~ big_p(X1)
& big_p(a) )
| sP1_prd(X1) )
& ! [X1] :
( big_p(c)
| big_p(X1)
| ~ big_p(a)
| ~ sP1_prd(X1) ) ),
inference(miniscoping,[status(thm)],[f22]) ).
fof(f24,plain,
! [X0] :
( big_p(c)
| 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(f27,plain,
! [X0] :
( ~ big_p(c)
| 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,
( sQ3_spl
<=> big_p(b) ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f40,plain,
( sQ3_spl
| ~ big_p(b) ),
inference(component_clause,[status(thm)],[f38]) ).
fof(f41,definition,
( sQ4_spl
<=> big_p(c) ),
introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition]) ).
fof(f43,plain,
( sQ4_spl
| ~ big_p(c) ),
inference(component_clause,[status(thm)],[f41]) ).
fof(f44,plain,
( sQ4_spl
| ~ sQ3_spl
| ~ sQ2_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f11,f28,f35,f38,f41]) ).
fof(f45,definition,
( sQ5_spl
<=> sP0_prd(sK0_skl) ),
introduced(definition,[new_symbols(definition,[sQ5_spl])],[split_symbol_definition]) ).
fof(f47,plain,
( sQ5_spl
| ~ sP0_prd(sK0_skl) ),
inference(component_clause,[status(thm)],[f45]) ).
fof(f48,definition,
( sQ6_spl
<=> sP1_prd(sK1_skl) ),
introduced(definition,[new_symbols(definition,[sQ6_spl])],[split_symbol_definition]) ).
fof(f50,plain,
( sQ6_spl
| ~ sP1_prd(sK1_skl) ),
inference(component_clause,[status(thm)],[f48]) ).
fof(f51,plain,
( sQ2_spl
| ~ sQ6_spl
| ~ sQ5_spl ),
inference(split_clause,[status(thm)],[f12,f45,f48,f35]) ).
fof(f52,plain,
( sQ3_spl
| ~ sQ6_spl
| ~ sQ5_spl ),
inference(split_clause,[status(thm)],[f13,f45,f48,f38]) ).
fof(f53,plain,
( ~ sQ4_spl
| ~ sQ6_spl
| ~ sQ5_spl ),
inference(split_clause,[status(thm)],[f14,f45,f48,f41]) ).
fof(f54,definition,
! [X0] :
( sQ7_spl
<=> ( big_p(X0)
| ~ sP0_prd(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ7_spl])],[split_symbol_definition]) ).
fof(f55,plain,
! [X0] :
( ~ sQ7_spl
| big_p(X0)
| ~ sP0_prd(X0) ),
inference(component_clause,[status(thm)],[f54]) ).
fof(f57,plain,
( sQ4_spl
| ~ sQ2_spl
| sQ7_spl ),
inference(split_clause,[status(thm)],[f17,f54,f35,f41]) ).
fof(f58,definition,
! [X0] :
( sQ8_spl
<=> ~ sP0_prd(X0) ),
introduced(definition,[new_symbols(definition,[sQ8_spl])],[split_symbol_definition]) ).
fof(f59,plain,
! [X0] :
( ~ sQ8_spl
| ~ sP0_prd(X0) ),
inference(component_clause,[status(thm)],[f58]) ).
fof(f61,plain,
( sQ4_spl
| ~ sQ3_spl
| ~ sQ2_spl
| sQ8_spl ),
inference(split_clause,[status(thm)],[f18,f58,f35,f38,f41]) ).
fof(f62,plain,
( sQ2_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f19,f28,f35]) ).
fof(f67,plain,
( ~ sQ4_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f21,f28,f41]) ).
fof(f68,definition,
! [X0] :
( sQ10_spl
<=> ( big_p(X0)
| ~ sP1_prd(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ10_spl])],[split_symbol_definition]) ).
fof(f69,plain,
! [X0] :
( ~ sQ10_spl
| big_p(X0)
| ~ sP1_prd(X0) ),
inference(component_clause,[status(thm)],[f68]) ).
fof(f71,plain,
( sQ4_spl
| ~ sQ2_spl
| sQ10_spl ),
inference(split_clause,[status(thm)],[f24,f68,f35,f41]) ).
fof(f72,plain,
( sQ2_spl
| sQ1_spl ),
inference(split_clause,[status(thm)],[f25,f31,f35]) ).
fof(f73,plain,
( ~ sQ4_spl
| sQ1_spl ),
inference(split_clause,[status(thm)],[f27,f31,f41]) ).
fof(f74,plain,
( ~ sQ8_spl
| ~ sQ0_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f59,f29]) ).
fof(f75,plain,
( ~ sQ8_spl
| ~ sQ0_spl ),
inference(contradiction_clause,[status(thm)],[f74]) ).
fof(f77,plain,
( sQ3_spl
| ~ sQ10_spl
| ~ sQ1_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f40,f80]) ).
fof(f80,plain,
! [X0] :
( ~ sQ10_spl
| ~ sQ1_spl
| big_p(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f69,f32]) ).
fof(f81,plain,
( sQ3_spl
| ~ sQ10_spl
| ~ sQ1_spl ),
inference(contradiction_clause,[status(thm)],[f77]) ).
fof(f82,plain,
( sQ5_spl
| ~ sQ0_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f47,f29]) ).
fof(f83,plain,
( sQ5_spl
| ~ sQ0_spl ),
inference(contradiction_clause,[status(thm)],[f82]) ).
fof(f84,plain,
( sQ6_spl
| ~ sQ1_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f50,f32]) ).
fof(f85,plain,
( sQ6_spl
| ~ sQ1_spl ),
inference(contradiction_clause,[status(thm)],[f84]) ).
fof(f86,plain,
! [X0] :
( ~ sQ7_spl
| ~ sQ0_spl
| big_p(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f55,f29]) ).
fof(f87,plain,
( sQ4_spl
| ~ sQ7_spl
| ~ sQ0_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f43,f86]) ).
fof(f88,plain,
( sQ4_spl
| ~ sQ7_spl
| ~ sQ0_spl ),
inference(contradiction_clause,[status(thm)],[f87]) ).
fof(f89,plain,
$false,
inference(sat_refutation,[status(thm)],[f34,f44,f51,f52,f53,f57,f61,f62,f67,f71,f72,f73,f75,f81,f83,f85,f88]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYN063+1 : TPTP v9.3.1. Released v2.0.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/0.56 % Computer : n016.cluster.edu
% 0.08/0.56 % Model : x86_64 x86_64
% 0.08/0.56 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.56 % Memory : 8046.5625MB
% 0.08/0.56 % OS : Linux 6.8.0-71-generic
% 0.08/0.56 % CPULimit : 300
% 0.08/0.56 % WCLimit : 300
% 0.08/0.56 % DateTime : Mon Sep 21 10:46:24 UTC 2026
% 0.08/0.56 % CPUTime :
% 0.08/0.57 % Drodi V4.1.1
% 0.08/0.59 % Refutation found
% 0.08/0.59 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.08/0.59 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.08/0.62 % Elapsed time: 0.044122 seconds
% 0.08/0.62 % CPU time: 0.113912 seconds
% 0.08/0.62 % Total memory used: 16.770 MB
% 0.08/0.62 % Net memory used: 16.328 MB
%------------------------------------------------------------------------------