%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SYN058+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 03:15:04 PM UTC 2026
% Result : Theorem 0.08s 0.36s
% Output : CNFRefutation 0.08s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 11
% Syntax : Number of formulae : 49 ( 6 unt; 7 def)
% Number of atoms : 118 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 120 ( 51 ~; 40 |; 16 &)
% ( 7 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 4 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 14 ( 13 usr; 7 prp; 0-1 aty)
% Number of functors : 3 ( 3 usr; 3 con; 0-0 aty)
% Number of variables : 37 ( 30 !; 7 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X] :
( big_p(X)
=> ! [Z] : big_q(Z) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f2,axiom,
( ! [X] :
( big_r(X)
| big_q(X) )
=> ? [X1] :
( big_s(X1)
& big_q(X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f3,axiom,
( ? [X] : big_s(X)
=> ! [X1] :
( big_f(X1)
=> big_g(X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f4,conjecture,
! [X] :
( ( big_f(X)
& big_p(X) )
=> big_g(X) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f5,negated_conjecture,
~ ! [X] :
( ( big_f(X)
& big_p(X) )
=> big_g(X) ),
inference(negated_conjecture,[status(cth)],[f4]) ).
fof(f6,plain,
! [X] :
( ! [Z] : big_q(Z)
| ~ big_p(X) ),
inference(pre_NNF_transformation,[status(thm)],[f1]) ).
fof(f7,plain,
( ! [Z] : big_q(Z)
| ! [X] : ~ big_p(X) ),
inference(miniscoping,[status(thm)],[f6]) ).
fof(f8,plain,
! [X0,X1] :
( big_q(X1)
| ~ big_p(X0) ),
inference(cnf_transformation,[status(thm)],[f7]) ).
fof(f9,plain,
( ? [X1] :
( big_s(X1)
& big_q(X1) )
| ? [X] :
( ~ big_r(X)
& ~ big_q(X) ) ),
inference(pre_NNF_transformation,[status(thm)],[f2]) ).
fof(f10,definition,
! [X] :
( sP0_prd(X)
<=> ( ~ big_r(X)
& ~ big_q(X) ) ),
introduced(definition,[new_symbols(definition,[sP0_prd])],[]) ).
fof(f11,plain,
( ? [X1] :
( big_s(X1)
& big_q(X1) )
| ? [X] : sP0_prd(X) ),
inference(formula_renaming,[status(thm)],[f9,f10]) ).
fof(f12,plain,
( ( big_s(sK1_skl)
& big_q(sK1_skl) )
| sP0_prd(sK0_skl) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl,sK1_skl]),skolemize(X,sK0_skl),skolemize(X1,sK1_skl)],[f11]) ).
fof(f14,plain,
( big_s(sK1_skl)
| sP0_prd(sK0_skl) ),
inference(cnf_transformation,[status(thm)],[f12]) ).
fof(f15,plain,
( ! [X1] :
( big_g(X1)
| ~ big_f(X1) )
| ! [X] : ~ big_s(X) ),
inference(pre_NNF_transformation,[status(thm)],[f3]) ).
fof(f16,plain,
! [X0,X1] :
( big_g(X1)
| ~ big_f(X1)
| ~ big_s(X0) ),
inference(cnf_transformation,[status(thm)],[f15]) ).
fof(f17,plain,
? [X] :
( ~ big_g(X)
& big_f(X)
& big_p(X) ),
inference(pre_NNF_transformation,[status(thm)],[f5]) ).
fof(f18,plain,
( ~ big_g(sK2_skl)
& big_f(sK2_skl)
& big_p(sK2_skl) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2_skl]),skolemize(X,sK2_skl)],[f17]) ).
fof(f19,plain,
big_p(sK2_skl),
inference(cnf_transformation,[status(thm)],[f18]) ).
fof(f20,plain,
big_f(sK2_skl),
inference(cnf_transformation,[status(thm)],[f18]) ).
fof(f21,plain,
~ big_g(sK2_skl),
inference(cnf_transformation,[status(thm)],[f18]) ).
fof(f22,plain,
! [X] :
( ( big_r(X)
| big_q(X)
| sP0_prd(X) )
& ( ( ~ big_r(X)
& ~ big_q(X) )
| ~ sP0_prd(X) ) ),
inference(NNF_transformation,[status(thm)],[f10]) ).
fof(f23,plain,
( ! [X] :
( big_r(X)
| big_q(X)
| sP0_prd(X) )
& ! [X] :
( ( ~ big_r(X)
& ~ big_q(X) )
| ~ sP0_prd(X) ) ),
inference(miniscoping,[status(thm)],[f22]) ).
fof(f24,plain,
! [X0] :
( ~ big_q(X0)
| ~ sP0_prd(X0) ),
inference(cnf_transformation,[status(thm)],[f23]) ).
fof(f27,definition,
! [X0] :
( sQ0_spl
<=> ~ big_p(X0) ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f28,plain,
! [X0] :
( ~ sQ0_spl
| ~ big_p(X0) ),
inference(component_clause,[status(thm)],[f27]) ).
fof(f30,definition,
! [X1] :
( sQ1_spl
<=> big_q(X1) ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f31,plain,
! [X0] :
( ~ sQ1_spl
| big_q(X0) ),
inference(component_clause,[status(thm)],[f30]) ).
fof(f33,plain,
( sQ1_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f8,f27,f30]) ).
fof(f34,definition,
( sQ2_spl
<=> sP0_prd(sK0_skl) ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f35,plain,
( ~ sQ2_spl
| sP0_prd(sK0_skl) ),
inference(component_clause,[status(thm)],[f34]) ).
fof(f41,definition,
( sQ4_spl
<=> big_s(sK1_skl) ),
introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition]) ).
fof(f42,plain,
( ~ sQ4_spl
| big_s(sK1_skl) ),
inference(component_clause,[status(thm)],[f41]) ).
fof(f44,plain,
( sQ4_spl
| sQ2_spl ),
inference(split_clause,[status(thm)],[f14,f34,f41]) ).
fof(f45,definition,
! [X0] :
( sQ5_spl
<=> ~ big_s(X0) ),
introduced(definition,[new_symbols(definition,[sQ5_spl])],[split_symbol_definition]) ).
fof(f46,plain,
! [X0] :
( ~ sQ5_spl
| ~ big_s(X0) ),
inference(component_clause,[status(thm)],[f45]) ).
fof(f48,definition,
! [X1] :
( sQ6_spl
<=> ( big_g(X1)
| ~ big_f(X1) ) ),
introduced(definition,[new_symbols(definition,[sQ6_spl])],[split_symbol_definition]) ).
fof(f49,plain,
! [X0] :
( ~ sQ6_spl
| big_g(X0)
| ~ big_f(X0) ),
inference(component_clause,[status(thm)],[f48]) ).
fof(f51,plain,
( sQ6_spl
| sQ5_spl ),
inference(split_clause,[status(thm)],[f16,f45,f48]) ).
fof(f52,plain,
( ~ sQ0_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f19,f28]) ).
fof(f53,plain,
~ sQ0_spl,
inference(contradiction_clause,[status(thm)],[f52]) ).
fof(f54,plain,
! [X0] :
( ~ sQ1_spl
| ~ sP0_prd(X0) ),
inference(backward_subsumption_resolution,[status(thm)],[f24,f31]) ).
fof(f55,plain,
( ~ sQ2_spl
| ~ sQ1_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f35,f54]) ).
fof(f56,plain,
( ~ sQ2_spl
| ~ sQ1_spl ),
inference(contradiction_clause,[status(thm)],[f55]) ).
fof(f57,plain,
( ~ sQ4_spl
| ~ sQ5_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f42,f46]) ).
fof(f58,plain,
( ~ sQ4_spl
| ~ sQ5_spl ),
inference(contradiction_clause,[status(thm)],[f57]) ).
fof(f59,plain,
( ~ sQ6_spl
| ~ big_f(sK2_skl) ),
inference(resolution,[status(thm)],[f49,f21]) ).
fof(f60,plain,
( ~ sQ6_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f59,f20]) ).
fof(f61,plain,
~ sQ6_spl,
inference(contradiction_clause,[status(thm)],[f60]) ).
fof(f62,plain,
$false,
inference(sat_refutation,[status(thm)],[f33,f44,f51,f53,f56,f58,f61]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYN058+1 : TPTP v9.3.1. Released v2.0.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/0.35 % Computer : n005.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 10:41:03 UTC 2026
% 0.08/0.35 % CPUTime :
% 0.08/0.36 % Drodi V4.1.1
% 0.08/0.36 % Refutation found
% 0.08/0.36 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.08/0.36 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.13/0.38 % Elapsed time: 0.022990 seconds
% 0.13/0.38 % CPU time: 0.032708 seconds
% 0.13/0.38 % Total memory used: 1.559 MB
% 0.13/0.38 % Net memory used: 1.518 MB
%------------------------------------------------------------------------------