%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SWV048+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 : n011.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 02:46:31 PM UTC 2026
% Result : Theorem 0.14s 0.40s
% Output : CNFRefutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 13
% Syntax : Number of formulae : 52 ( 21 unt; 7 def)
% Number of atoms : 131 ( 48 equ)
% Maximal formula atoms : 12 ( 2 avg)
% Number of connectives : 122 ( 43 ~; 39 |; 27 &)
% ( 7 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 3 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 11 ( 9 usr; 9 prp; 0-2 aty)
% Number of functors : 18 ( 18 usr; 11 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(f51,axiom,
true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f53,conjecture,
( ( leq(pv35,minus(n5,n1))
& leq(n0,pv35)
& pv78 = sum(n0,minus(n135300,n1),a_select3(q,pv79,pv35)) )
=> ( ( n0 = pv78
=> true )
& ( n0 != pv78
=> ( leq(pv35,minus(n5,n1))
& leq(n0,pv35)
& pv78 = sum(n0,minus(n135300,n1),a_select3(q,pv79,pv35))
& n0 = sum(n0,minus(n0,n1),times(a_select3(q,pv81,pv35),a_select2(x,pv81))) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f54,negated_conjecture,
~ ( ( leq(pv35,minus(n5,n1))
& leq(n0,pv35)
& pv78 = sum(n0,minus(n135300,n1),a_select3(q,pv79,pv35)) )
=> ( ( n0 = pv78
=> true )
& ( n0 != pv78
=> ( leq(pv35,minus(n5,n1))
& leq(n0,pv35)
& pv78 = sum(n0,minus(n135300,n1),a_select3(q,pv79,pv35))
& n0 = sum(n0,minus(n0,n1),times(a_select3(q,pv81,pv35),a_select2(x,pv81))) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f53]) ).
fof(f204,plain,
! [X0] : sum(n0,tptp_minus_1,X0) = n0,
inference(cnf_transformation,[status(thm)],[f26]) ).
fof(f206,plain,
succ(tptp_minus_1) = n0,
inference(cnf_transformation,[status(thm)],[f28]) ).
fof(f217,plain,
! [X0] : minus(X0,n1) = pred(X0),
inference(cnf_transformation,[status(thm)],[f39]) ).
fof(f218,plain,
! [X0] : pred(succ(X0)) = X0,
inference(cnf_transformation,[status(thm)],[f40]) ).
fof(f249,plain,
true,
inference(cnf_transformation,[status(thm)],[f51]) ).
fof(f251,plain,
( ( ( ~ true
& n0 = pv78 )
| ( ( ~ leq(pv35,minus(n5,n1))
| ~ leq(n0,pv35)
| pv78 != sum(n0,minus(n135300,n1),a_select3(q,pv79,pv35))
| n0 != sum(n0,minus(n0,n1),times(a_select3(q,pv81,pv35),a_select2(x,pv81))) )
& n0 != pv78 ) )
& leq(pv35,minus(n5,n1))
& leq(n0,pv35)
& pv78 = sum(n0,minus(n135300,n1),a_select3(q,pv79,pv35)) ),
inference(pre_NNF_transformation,[status(thm)],[f54]) ).
fof(f252,definition,
( sP3_prd
<=> ( ( ~ leq(pv35,minus(n5,n1))
| ~ leq(n0,pv35)
| pv78 != sum(n0,minus(n135300,n1),a_select3(q,pv79,pv35))
| n0 != sum(n0,minus(n0,n1),times(a_select3(q,pv81,pv35),a_select2(x,pv81))) )
& n0 != pv78 ) ),
introduced(definition,[new_symbols(definition,[sP3_prd])],[]) ).
fof(f253,plain,
( ( ( ~ true
& n0 = pv78 )
| sP3_prd )
& leq(pv35,minus(n5,n1))
& leq(n0,pv35)
& pv78 = sum(n0,minus(n135300,n1),a_select3(q,pv79,pv35)) ),
inference(formula_renaming,[status(thm)],[f251,f252]) ).
fof(f254,plain,
pv78 = sum(n0,minus(n135300,n1),a_select3(q,pv79,pv35)),
inference(cnf_transformation,[status(thm)],[f253]) ).
fof(f255,plain,
leq(n0,pv35),
inference(cnf_transformation,[status(thm)],[f253]) ).
fof(f256,plain,
leq(pv35,minus(n5,n1)),
inference(cnf_transformation,[status(thm)],[f253]) ).
fof(f258,plain,
( ~ true
| sP3_prd ),
inference(cnf_transformation,[status(thm)],[f253]) ).
fof(f332,plain,
( ( ( leq(pv35,minus(n5,n1))
& leq(n0,pv35)
& pv78 = sum(n0,minus(n135300,n1),a_select3(q,pv79,pv35))
& n0 = sum(n0,minus(n0,n1),times(a_select3(q,pv81,pv35),a_select2(x,pv81))) )
| n0 = pv78
| sP3_prd )
& ( ( ( ~ leq(pv35,minus(n5,n1))
| ~ leq(n0,pv35)
| pv78 != sum(n0,minus(n135300,n1),a_select3(q,pv79,pv35))
| n0 != sum(n0,minus(n0,n1),times(a_select3(q,pv81,pv35),a_select2(x,pv81))) )
& n0 != pv78 )
| ~ sP3_prd ) ),
inference(NNF_transformation,[status(thm)],[f252]) ).
fof(f334,plain,
( ~ leq(pv35,minus(n5,n1))
| ~ leq(n0,pv35)
| pv78 != sum(n0,minus(n135300,n1),a_select3(q,pv79,pv35))
| n0 != sum(n0,minus(n0,n1),times(a_select3(q,pv81,pv35),a_select2(x,pv81)))
| ~ sP3_prd ),
inference(cnf_transformation,[status(thm)],[f332]) ).
fof(f347,definition,
( sQ0_spl
<=> sP3_prd ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f354,definition,
( sQ2_spl
<=> true ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f356,plain,
( sQ2_spl
| ~ true ),
inference(component_clause,[status(thm)],[f354]) ).
fof(f357,plain,
( ~ sQ2_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f258,f347,f354]) ).
fof(f359,definition,
( sQ3_spl
<=> n0 = sum(n0,minus(n0,n1),times(a_select3(q,pv81,pv35),a_select2(x,pv81))) ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f361,plain,
( sQ3_spl
| n0 != sum(n0,minus(n0,n1),times(a_select3(q,pv81,pv35),a_select2(x,pv81))) ),
inference(component_clause,[status(thm)],[f359]) ).
fof(f362,definition,
( sQ4_spl
<=> pv78 = sum(n0,minus(n135300,n1),a_select3(q,pv79,pv35)) ),
introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition]) ).
fof(f364,plain,
( sQ4_spl
| pv78 != sum(n0,minus(n135300,n1),a_select3(q,pv79,pv35)) ),
inference(component_clause,[status(thm)],[f362]) ).
fof(f365,definition,
( sQ5_spl
<=> leq(n0,pv35) ),
introduced(definition,[new_symbols(definition,[sQ5_spl])],[split_symbol_definition]) ).
fof(f367,plain,
( sQ5_spl
| ~ leq(n0,pv35) ),
inference(component_clause,[status(thm)],[f365]) ).
fof(f368,definition,
( sQ6_spl
<=> leq(pv35,minus(n5,n1)) ),
introduced(definition,[new_symbols(definition,[sQ6_spl])],[split_symbol_definition]) ).
fof(f370,plain,
( sQ6_spl
| ~ leq(pv35,minus(n5,n1)) ),
inference(component_clause,[status(thm)],[f368]) ).
fof(f371,plain,
( ~ sQ6_spl
| ~ sQ5_spl
| ~ sQ4_spl
| ~ sQ3_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f334,f347,f359,f362,f365,f368]) ).
fof(f380,plain,
( sQ2_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f249,f356]) ).
fof(f381,plain,
sQ2_spl,
inference(contradiction_clause,[status(thm)],[f380]) ).
fof(f383,plain,
pred(n0) = tptp_minus_1,
inference(paramodulation,[status(thm)],[f206,f218]) ).
fof(f389,plain,
( sQ6_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f370,f256]) ).
fof(f390,plain,
sQ6_spl,
inference(contradiction_clause,[status(thm)],[f389]) ).
fof(f391,plain,
( sQ5_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f367,f255]) ).
fof(f392,plain,
sQ5_spl,
inference(contradiction_clause,[status(thm)],[f391]) ).
fof(f482,plain,
( sQ3_spl
| n0 != sum(n0,pred(n0),times(a_select3(q,pv81,pv35),a_select2(x,pv81))) ),
inference(backward_demodulation,[status(thm)],[f217,f361]) ).
fof(f483,plain,
pv78 = sum(n0,pred(n135300),a_select3(q,pv79,pv35)),
inference(backward_demodulation,[status(thm)],[f217,f254]) ).
fof(f486,plain,
( sQ3_spl
| n0 != sum(n0,tptp_minus_1,times(a_select3(q,pv81,pv35),a_select2(x,pv81))) ),
inference(forward_demodulation,[status(thm)],[f383,f482]) ).
fof(f487,plain,
( sQ3_spl
| n0 != n0 ),
inference(forward_demodulation,[status(thm)],[f204,f486]) ).
fof(f488,plain,
( sQ3_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f487]) ).
fof(f489,plain,
sQ3_spl,
inference(contradiction_clause,[status(thm)],[f488]) ).
fof(f490,plain,
( sQ4_spl
| pv78 != sum(n0,pred(n135300),a_select3(q,pv79,pv35)) ),
inference(forward_demodulation,[status(thm)],[f217,f364]) ).
fof(f568,plain,
( sQ4_spl
| pv78 != pv78 ),
inference(forward_demodulation,[status(thm)],[f483,f490]) ).
fof(f569,plain,
( sQ4_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f568]) ).
fof(f570,plain,
sQ4_spl,
inference(contradiction_clause,[status(thm)],[f569]) ).
fof(f571,plain,
$false,
inference(sat_refutation,[status(thm)],[f357,f371,f381,f390,f392,f489,f570]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWV048+1 : TPTP v9.3.1. Bugfixed v3.3.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.35 % Computer : n011.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 08:28:40 UTC 2026
% 0.09/0.35 % CPUTime :
% 0.09/0.37 % Drodi V4.1.1
% 0.14/0.40 % Refutation found
% 0.14/0.40 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.14/0.40 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.14/0.43 % Elapsed time: 0.070740 seconds
% 0.14/0.43 % CPU time: 0.220846 seconds
% 0.14/0.43 % Total memory used: 110.643 MB
% 0.14/0.43 % Net memory used: 110.278 MB
%------------------------------------------------------------------------------