%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SWV046+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 : n026.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 0.17s 0.52s
% Output : CNFRefutation 0.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 14
% Syntax : Number of formulae : 56 ( 23 unt; 7 def)
% Number of atoms : 141 ( 56 equ)
% Maximal formula atoms : 12 ( 2 avg)
% Number of connectives : 130 ( 45 ~; 41 |; 31 &)
% ( 7 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 3 avg)
% Maximal term depth : 8 ( 2 avg)
% Number of predicates : 11 ( 9 usr; 9 prp; 0-2 aty)
% Number of functors : 24 ( 24 usr; 15 con; 0-3 aty)
% Number of variables : 12 ( 12 !; 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(f48,axiom,
! [X,U,VAL] : a_select2(tptp_update2(X,U,VAL),U) = VAL,
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)
& pv80 = sum(n0,minus(n135300,n1),times(a_select3(q,pv81,pv35),a_select2(x,pv81)))
& pv78 = sum(n0,minus(n135300,n1),a_select3(q,pv79,pv35)) )
=> ( ( n0 = pv44
=> true )
& ( n0 != pv44
=> ( 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(minus(a_select2(x,pv83),a_select2(tptp_update2(mu,pv35,divide(pv80,pv44)),pv35)),times(minus(a_select2(x,pv83),a_select2(tptp_update2(mu,pv35,divide(pv80,pv44)),pv35)),a_select3(q,pv83,pv35)))) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f54,negated_conjecture,
~ ( ( leq(pv35,minus(n5,n1))
& leq(n0,pv35)
& pv80 = sum(n0,minus(n135300,n1),times(a_select3(q,pv81,pv35),a_select2(x,pv81)))
& pv78 = sum(n0,minus(n135300,n1),a_select3(q,pv79,pv35)) )
=> ( ( n0 = pv44
=> true )
& ( n0 != pv44
=> ( 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(minus(a_select2(x,pv83),a_select2(tptp_update2(mu,pv35,divide(pv80,pv44)),pv35)),times(minus(a_select2(x,pv83),a_select2(tptp_update2(mu,pv35,divide(pv80,pv44)),pv35)),a_select3(q,pv83,pv35)))) ) ) ) ),
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(f240,plain,
! [X0,X1,X2] : a_select2(tptp_update2(X0,X1,X2),X1) = X2,
inference(cnf_transformation,[status(thm)],[f48]) ).
fof(f249,plain,
true,
inference(cnf_transformation,[status(thm)],[f51]) ).
fof(f251,plain,
( ( ( ~ true
& n0 = pv44 )
| ( ( ~ 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(minus(a_select2(x,pv83),a_select2(tptp_update2(mu,pv35,divide(pv80,pv44)),pv35)),times(minus(a_select2(x,pv83),a_select2(tptp_update2(mu,pv35,divide(pv80,pv44)),pv35)),a_select3(q,pv83,pv35)))) )
& n0 != pv44 ) )
& leq(pv35,minus(n5,n1))
& leq(n0,pv35)
& pv80 = sum(n0,minus(n135300,n1),times(a_select3(q,pv81,pv35),a_select2(x,pv81)))
& 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(minus(a_select2(x,pv83),a_select2(tptp_update2(mu,pv35,divide(pv80,pv44)),pv35)),times(minus(a_select2(x,pv83),a_select2(tptp_update2(mu,pv35,divide(pv80,pv44)),pv35)),a_select3(q,pv83,pv35)))) )
& n0 != pv44 ) ),
introduced(definition,[new_symbols(definition,[sP3_prd])],[]) ).
fof(f253,plain,
( ( ( ~ true
& n0 = pv44 )
| sP3_prd )
& leq(pv35,minus(n5,n1))
& leq(n0,pv35)
& pv80 = sum(n0,minus(n135300,n1),times(a_select3(q,pv81,pv35),a_select2(x,pv81)))
& 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(f256,plain,
leq(n0,pv35),
inference(cnf_transformation,[status(thm)],[f253]) ).
fof(f257,plain,
leq(pv35,minus(n5,n1)),
inference(cnf_transformation,[status(thm)],[f253]) ).
fof(f259,plain,
( ~ true
| sP3_prd ),
inference(cnf_transformation,[status(thm)],[f253]) ).
fof(f333,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(minus(a_select2(x,pv83),a_select2(tptp_update2(mu,pv35,divide(pv80,pv44)),pv35)),times(minus(a_select2(x,pv83),a_select2(tptp_update2(mu,pv35,divide(pv80,pv44)),pv35)),a_select3(q,pv83,pv35)))) )
| n0 = pv44
| 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(minus(a_select2(x,pv83),a_select2(tptp_update2(mu,pv35,divide(pv80,pv44)),pv35)),times(minus(a_select2(x,pv83),a_select2(tptp_update2(mu,pv35,divide(pv80,pv44)),pv35)),a_select3(q,pv83,pv35)))) )
& n0 != pv44 )
| ~ sP3_prd ) ),
inference(NNF_transformation,[status(thm)],[f252]) ).
fof(f335,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(minus(a_select2(x,pv83),a_select2(tptp_update2(mu,pv35,divide(pv80,pv44)),pv35)),times(minus(a_select2(x,pv83),a_select2(tptp_update2(mu,pv35,divide(pv80,pv44)),pv35)),a_select3(q,pv83,pv35))))
| ~ sP3_prd ),
inference(cnf_transformation,[status(thm)],[f333]) ).
fof(f348,definition,
( sQ0_spl
<=> sP3_prd ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f355,definition,
( sQ2_spl
<=> true ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f357,plain,
( sQ2_spl
| ~ true ),
inference(component_clause,[status(thm)],[f355]) ).
fof(f358,plain,
( ~ sQ2_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f259,f348,f355]) ).
fof(f360,definition,
( sQ3_spl
<=> n0 = sum(n0,minus(n0,n1),times(minus(a_select2(x,pv83),a_select2(tptp_update2(mu,pv35,divide(pv80,pv44)),pv35)),times(minus(a_select2(x,pv83),a_select2(tptp_update2(mu,pv35,divide(pv80,pv44)),pv35)),a_select3(q,pv83,pv35)))) ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f362,plain,
( sQ3_spl
| n0 != sum(n0,minus(n0,n1),times(minus(a_select2(x,pv83),a_select2(tptp_update2(mu,pv35,divide(pv80,pv44)),pv35)),times(minus(a_select2(x,pv83),a_select2(tptp_update2(mu,pv35,divide(pv80,pv44)),pv35)),a_select3(q,pv83,pv35)))) ),
inference(component_clause,[status(thm)],[f360]) ).
fof(f363,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(f365,plain,
( sQ4_spl
| pv78 != sum(n0,minus(n135300,n1),a_select3(q,pv79,pv35)) ),
inference(component_clause,[status(thm)],[f363]) ).
fof(f366,definition,
( sQ5_spl
<=> leq(n0,pv35) ),
introduced(definition,[new_symbols(definition,[sQ5_spl])],[split_symbol_definition]) ).
fof(f368,plain,
( sQ5_spl
| ~ leq(n0,pv35) ),
inference(component_clause,[status(thm)],[f366]) ).
fof(f369,definition,
( sQ6_spl
<=> leq(pv35,minus(n5,n1)) ),
introduced(definition,[new_symbols(definition,[sQ6_spl])],[split_symbol_definition]) ).
fof(f371,plain,
( sQ6_spl
| ~ leq(pv35,minus(n5,n1)) ),
inference(component_clause,[status(thm)],[f369]) ).
fof(f372,plain,
( ~ sQ6_spl
| ~ sQ5_spl
| ~ sQ4_spl
| ~ sQ3_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f335,f348,f360,f363,f366,f369]) ).
fof(f381,plain,
( sQ2_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f249,f357]) ).
fof(f382,plain,
sQ2_spl,
inference(contradiction_clause,[status(thm)],[f381]) ).
fof(f384,plain,
pred(n0) = tptp_minus_1,
inference(paramodulation,[status(thm)],[f206,f218]) ).
fof(f390,plain,
( sQ6_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f371,f257]) ).
fof(f391,plain,
sQ6_spl,
inference(contradiction_clause,[status(thm)],[f390]) ).
fof(f392,plain,
( sQ5_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f368,f256]) ).
fof(f393,plain,
sQ5_spl,
inference(contradiction_clause,[status(thm)],[f392]) ).
fof(f395,plain,
( sQ3_spl
| n0 != sum(n0,minus(n0,n1),times(minus(a_select2(x,pv83),divide(pv80,pv44)),times(minus(a_select2(x,pv83),a_select2(tptp_update2(mu,pv35,divide(pv80,pv44)),pv35)),a_select3(q,pv83,pv35)))) ),
inference(forward_demodulation,[status(thm)],[f240,f362]) ).
fof(f396,plain,
( sQ3_spl
| n0 != sum(n0,minus(n0,n1),times(minus(a_select2(x,pv83),divide(pv80,pv44)),times(minus(a_select2(x,pv83),divide(pv80,pv44)),a_select3(q,pv83,pv35)))) ),
inference(forward_demodulation,[status(thm)],[f240,f395]) ).
fof(f474,plain,
( sQ3_spl
| n0 != sum(n0,pred(n0),times(minus(a_select2(x,pv83),divide(pv80,pv44)),times(minus(a_select2(x,pv83),divide(pv80,pv44)),a_select3(q,pv83,pv35)))) ),
inference(backward_demodulation,[status(thm)],[f217,f396]) ).
fof(f476,plain,
pv78 = sum(n0,pred(n135300),a_select3(q,pv79,pv35)),
inference(backward_demodulation,[status(thm)],[f217,f254]) ).
fof(f478,plain,
( sQ3_spl
| n0 != sum(n0,tptp_minus_1,times(minus(a_select2(x,pv83),divide(pv80,pv44)),times(minus(a_select2(x,pv83),divide(pv80,pv44)),a_select3(q,pv83,pv35)))) ),
inference(forward_demodulation,[status(thm)],[f384,f474]) ).
fof(f479,plain,
( sQ3_spl
| n0 != n0 ),
inference(forward_demodulation,[status(thm)],[f204,f478]) ).
fof(f480,plain,
( sQ3_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f479]) ).
fof(f481,plain,
sQ3_spl,
inference(contradiction_clause,[status(thm)],[f480]) ).
fof(f482,plain,
( sQ4_spl
| pv78 != sum(n0,pred(n135300),a_select3(q,pv79,pv35)) ),
inference(forward_demodulation,[status(thm)],[f217,f365]) ).
fof(f553,plain,
( sQ4_spl
| pv78 != pv78 ),
inference(forward_demodulation,[status(thm)],[f476,f482]) ).
fof(f554,plain,
( sQ4_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f553]) ).
fof(f555,plain,
sQ4_spl,
inference(contradiction_clause,[status(thm)],[f554]) ).
fof(f556,plain,
$false,
inference(sat_refutation,[status(thm)],[f358,f372,f382,f391,f393,f481,f555]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : SWV046+1 : TPTP v9.3.1. Bugfixed v3.3.0.
% 0.00/0.06 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.17/0.44 % Computer : n026.cluster.edu
% 0.17/0.44 % Model : x86_64 x86_64
% 0.17/0.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.44 % Memory : 8046.5625MB
% 0.17/0.44 % OS : Linux 6.8.0-71-generic
% 0.17/0.44 % CPULimit : 300
% 0.17/0.44 % WCLimit : 300
% 0.17/0.44 % DateTime : Mon Sep 21 08:31:22 UTC 2026
% 0.17/0.45 % CPUTime :
% 0.17/0.47 % Drodi V4.1.1
% 0.17/0.52 % Refutation found
% 0.17/0.52 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.17/0.52 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.17/0.55 % Elapsed time: 0.091545 seconds
% 0.17/0.55 % CPU time: 0.332218 seconds
% 0.17/0.55 % Total memory used: 56.837 MB
% 0.17/0.55 % Net memory used: 56.508 MB
%------------------------------------------------------------------------------