%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SWV056+1 : TPTP v9.3.1. Bugfixed v3.3.0.
% 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 02:46:32 PM UTC 2026
% Result : Theorem 0.13s 0.39s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 8
% Syntax : Number of formulae : 32 ( 15 unt; 3 def)
% Number of atoms : 60 ( 18 equ)
% Maximal formula atoms : 5 ( 1 avg)
% Number of connectives : 44 ( 16 ~; 15 |; 8 &)
% ( 3 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 4 prp; 0-2 aty)
% Number of functors : 12 ( 12 usr; 7 con; 0-3 aty)
% Number of variables : 6 ( 6 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f26,axiom,
! [Body] : sum(n0,tptp_minus_1,Body) = n0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f28,axiom,
succ(tptp_minus_1) = n0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f39,axiom,
! [X] : minus(X,n1) = pred(X),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f40,axiom,
! [X] : pred(succ(X)) = X,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f53,conjecture,
( ( leq(pv25,minus(n5,n1))
& leq(n0,pv25) )
=> ( leq(pv25,minus(n5,n1))
& leq(n0,pv25)
& n0 = sum(n0,minus(n0,n1),a_select3(q,pv77,pv25)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f54,negated_conjecture,
~ ( ( leq(pv25,minus(n5,n1))
& leq(n0,pv25) )
=> ( leq(pv25,minus(n5,n1))
& leq(n0,pv25)
& n0 = sum(n0,minus(n0,n1),a_select3(q,pv77,pv25)) ) ),
inference(negated_conjecture,[status(cth)],[f53]) ).
fof(f197,plain,
! [X0] : sum(n0,tptp_minus_1,X0) = n0,
inference(cnf_transformation,[status(thm)],[f26]) ).
fof(f199,plain,
succ(tptp_minus_1) = n0,
inference(cnf_transformation,[status(thm)],[f28]) ).
fof(f210,plain,
! [X0] : minus(X0,n1) = pred(X0),
inference(cnf_transformation,[status(thm)],[f39]) ).
fof(f211,plain,
! [X0] : pred(succ(X0)) = X0,
inference(cnf_transformation,[status(thm)],[f40]) ).
fof(f244,plain,
( ( ~ leq(pv25,minus(n5,n1))
| ~ leq(n0,pv25)
| n0 != sum(n0,minus(n0,n1),a_select3(q,pv77,pv25)) )
& leq(pv25,minus(n5,n1))
& leq(n0,pv25) ),
inference(pre_NNF_transformation,[status(thm)],[f54]) ).
fof(f245,plain,
leq(n0,pv25),
inference(cnf_transformation,[status(thm)],[f244]) ).
fof(f246,plain,
leq(pv25,minus(n5,n1)),
inference(cnf_transformation,[status(thm)],[f244]) ).
fof(f247,plain,
( ~ leq(pv25,minus(n5,n1))
| ~ leq(n0,pv25)
| n0 != sum(n0,minus(n0,n1),a_select3(q,pv77,pv25)) ),
inference(cnf_transformation,[status(thm)],[f244]) ).
fof(f322,definition,
( sQ0_spl
<=> n0 = sum(n0,minus(n0,n1),a_select3(q,pv77,pv25)) ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f324,plain,
( sQ0_spl
| n0 != sum(n0,minus(n0,n1),a_select3(q,pv77,pv25)) ),
inference(component_clause,[status(thm)],[f322]) ).
fof(f325,definition,
( sQ1_spl
<=> leq(n0,pv25) ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f327,plain,
( sQ1_spl
| ~ leq(n0,pv25) ),
inference(component_clause,[status(thm)],[f325]) ).
fof(f328,definition,
( sQ2_spl
<=> leq(pv25,minus(n5,n1)) ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f330,plain,
( sQ2_spl
| ~ leq(pv25,minus(n5,n1)) ),
inference(component_clause,[status(thm)],[f328]) ).
fof(f331,plain,
( ~ sQ2_spl
| ~ sQ1_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f247,f322,f325,f328]) ).
fof(f334,plain,
( sQ2_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f330,f246]) ).
fof(f335,plain,
sQ2_spl,
inference(contradiction_clause,[status(thm)],[f334]) ).
fof(f336,plain,
( sQ0_spl
| n0 != sum(n0,pred(n0),a_select3(q,pv77,pv25)) ),
inference(backward_demodulation,[status(thm)],[f210,f324]) ).
fof(f340,plain,
pred(n0) = tptp_minus_1,
inference(paramodulation,[status(thm)],[f199,f211]) ).
fof(f464,plain,
( sQ0_spl
| n0 != sum(n0,tptp_minus_1,a_select3(q,pv77,pv25)) ),
inference(backward_demodulation,[status(thm)],[f340,f336]) ).
fof(f468,plain,
( sQ0_spl
| n0 != n0 ),
inference(forward_demodulation,[status(thm)],[f197,f464]) ).
fof(f469,plain,
( sQ0_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f468]) ).
fof(f470,plain,
sQ0_spl,
inference(contradiction_clause,[status(thm)],[f469]) ).
fof(f471,plain,
( sQ1_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f327,f245]) ).
fof(f472,plain,
sQ1_spl,
inference(contradiction_clause,[status(thm)],[f471]) ).
fof(f473,plain,
$false,
inference(sat_refutation,[status(thm)],[f331,f335,f470,f472]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SWV056+1 : TPTP v9.3.1. Bugfixed v3.3.0.
% 0.00/0.03 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.35 % Computer : n013.cluster.edu
% 0.09/0.35 % Model : x86_64 x86_64
% 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.35 % Memory : 8046.5625MB
% 0.09/0.35 % OS : Linux 6.8.0-71-generic
% 0.09/0.35 % CPULimit : 300
% 0.09/0.35 % WCLimit : 300
% 0.09/0.35 % DateTime : Mon Sep 21 08:28:36 UTC 2026
% 0.09/0.35 % CPUTime :
% 0.09/0.38 % 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
% 0.13/0.42 % Elapsed time: 0.058383 seconds
% 0.13/0.42 % CPU time: 0.131083 seconds
% 0.13/0.42 % Total memory used: 20.656 MB
% 0.13/0.42 % Net memory used: 20.592 MB
%------------------------------------------------------------------------------