%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : NUN087+2 : TPTP v9.3.1. Released v7.3.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n009.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 01:57:15 PM UTC 2026
% Result : Theorem 0.13s 0.38s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 5
% Syntax : Number of formulae : 36 ( 14 unt; 2 def)
% Number of atoms : 84 ( 22 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 80 ( 32 ~; 25 |; 21 &)
% ( 2 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 2 prp; 0-3 aty)
% Number of functors : 4 ( 4 usr; 1 con; 0-1 aty)
% Number of variables : 49 ( 38 !; 11 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
? [Y24] :
! [X19] :
( ( X19 = Y24
& r1(X19) )
| ( X19 != Y24
& ~ r1(X19) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f9,axiom,
! [X5] :
? [Y8] :
( ? [Y18] :
( Y8 = Y18
& r1(Y18) )
& ? [Y17] :
( r4(X5,Y17,Y8)
& r1(Y17) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f12,conjecture,
? [Y1] :
( ? [Y3] :
( Y1 = Y3
& r1(Y3) )
& ? [Y2] :
( r4(Y2,Y2,Y1)
& r1(Y2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f13,negated_conjecture,
~ ? [Y1] :
( ? [Y3] :
( Y1 = Y3
& r1(Y3) )
& ? [Y2] :
( r4(Y2,Y2,Y1)
& r1(Y2) ) ),
inference(negated_conjecture,[status(cth)],[f12]) ).
fof(f14,definition,
! [Y24,X19] :
( sP0_prd(X19,Y24)
<=> ( X19 != Y24
& ~ r1(X19) ) ),
introduced(definition,[new_symbols(definition,[sP0_prd])],[]) ).
fof(f15,plain,
? [Y24] :
! [X19] :
( ( X19 = Y24
& r1(X19) )
| sP0_prd(X19,Y24) ),
inference(formula_renaming,[status(thm)],[f1,f14]) ).
fof(f16,plain,
! [X19] :
( ( X19 = sK0_skl
& r1(X19) )
| sP0_prd(X19,sK0_skl) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl]),skolemize(Y24,sK0_skl)],[f15]) ).
fof(f17,plain,
! [X0] :
( r1(X0)
| sP0_prd(X0,sK0_skl) ),
inference(cnf_transformation,[status(thm)],[f16]) ).
fof(f18,plain,
! [X0] :
( X0 = sK0_skl
| sP0_prd(X0,sK0_skl) ),
inference(cnf_transformation,[status(thm)],[f16]) ).
fof(f51,plain,
! [X5] :
( sK14_skl(X5) = sK16_skl(X5)
& r1(sK16_skl(X5))
& r4(X5,sK15_skl(X5),sK14_skl(X5))
& r1(sK15_skl(X5)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK14_skl,sK15_skl,sK16_skl]),skolemize(Y8,sK14_skl(X5)),skolemize(Y17,sK15_skl(X5)),skolemize(Y18,sK16_skl(X5))],[f9]) ).
fof(f52,plain,
! [X0] : r1(sK15_skl(X0)),
inference(cnf_transformation,[status(thm)],[f51]) ).
fof(f53,plain,
! [X0] : r4(X0,sK15_skl(X0),sK14_skl(X0)),
inference(cnf_transformation,[status(thm)],[f51]) ).
fof(f54,plain,
! [X0] : r1(sK16_skl(X0)),
inference(cnf_transformation,[status(thm)],[f51]) ).
fof(f55,plain,
! [X0] : sK14_skl(X0) = sK16_skl(X0),
inference(cnf_transformation,[status(thm)],[f51]) ).
fof(f64,plain,
! [Y1] :
( ! [Y3] :
( Y1 != Y3
| ~ r1(Y3) )
| ! [Y2] :
( ~ r4(Y2,Y2,Y1)
| ~ r1(Y2) ) ),
inference(pre_NNF_transformation,[status(thm)],[f13]) ).
fof(f65,plain,
! [X0,X1,X2] :
( X1 != X2
| ~ r1(X2)
| ~ r4(X0,X0,X1)
| ~ r1(X0) ),
inference(cnf_transformation,[status(thm)],[f64]) ).
fof(f66,plain,
! [Y24,X19] :
( ( X19 = Y24
| r1(X19)
| sP0_prd(X19,Y24) )
& ( ( X19 != Y24
& ~ r1(X19) )
| ~ sP0_prd(X19,Y24) ) ),
inference(NNF_transformation,[status(thm)],[f14]) ).
fof(f67,plain,
( ! [Y24,X19] :
( X19 = Y24
| r1(X19)
| sP0_prd(X19,Y24) )
& ! [Y24,X19] :
( ( X19 != Y24
& ~ r1(X19) )
| ~ sP0_prd(X19,Y24) ) ),
inference(miniscoping,[status(thm)],[f66]) ).
fof(f68,plain,
! [X0,X1] :
( ~ r1(X0)
| ~ sP0_prd(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f67]) ).
fof(f69,plain,
! [X0,X1] :
( X0 != X1
| ~ sP0_prd(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f67]) ).
fof(f93,plain,
! [X0,X1] :
( ~ r1(X1)
| ~ r4(X0,X0,X1)
| ~ r1(X0) ),
inference(destructive_equality_resolution,[status(thm)],[f65]) ).
fof(f94,plain,
! [X0] : ~ sP0_prd(X0,X0),
inference(destructive_equality_resolution,[status(thm)],[f69]) ).
fof(f99,plain,
r1(sK0_skl),
inference(resolution,[status(thm)],[f17,f94]) ).
fof(f105,plain,
! [X0] :
( X0 = sK0_skl
| ~ r1(X0) ),
inference(resolution,[status(thm)],[f68,f18]) ).
fof(f107,plain,
! [X0] : sK16_skl(X0) = sK0_skl,
inference(resolution,[status(thm)],[f105,f54]) ).
fof(f109,plain,
! [X0] : sK15_skl(X0) = sK0_skl,
inference(resolution,[status(thm)],[f105,f52]) ).
fof(f111,plain,
! [X0] : sK14_skl(X0) = sK0_skl,
inference(backward_demodulation,[status(thm)],[f107,f55]) ).
fof(f123,plain,
! [X0] : r4(X0,sK0_skl,sK14_skl(X0)),
inference(forward_demodulation,[status(thm)],[f109,f53]) ).
fof(f124,plain,
! [X0] : r4(X0,sK0_skl,sK0_skl),
inference(forward_demodulation,[status(thm)],[f111,f123]) ).
fof(f125,plain,
( ~ r1(sK0_skl)
| ~ r1(sK0_skl) ),
inference(resolution,[status(thm)],[f124,f93]) ).
fof(f126,definition,
( sQ0_spl
<=> r1(sK0_skl) ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f128,plain,
( sQ0_spl
| ~ r1(sK0_skl) ),
inference(component_clause,[status(thm)],[f126]) ).
fof(f129,plain,
~ sQ0_spl,
inference(split_clause,[status(thm)],[f125,f126]) ).
fof(f130,plain,
( sQ0_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f128,f99]) ).
fof(f131,plain,
sQ0_spl,
inference(contradiction_clause,[status(thm)],[f130]) ).
fof(f132,plain,
$false,
inference(sat_refutation,[status(thm)],[f129,f131]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUN087+2 : TPTP v9.3.1. Released v7.3.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/0.35 % Computer : n009.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 03:25:27 UTC 2026
% 0.08/0.35 % CPUTime :
% 0.08/0.36 % Drodi V4.1.1
% 0.13/0.38 % Refutation found
% 0.13/0.38 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.13/0.38 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.13/0.41 % Elapsed time: 0.046663 seconds
% 0.13/0.41 % CPU time: 0.134725 seconds
% 0.13/0.41 % Total memory used: 67.298 MB
% 0.13/0.41 % Net memory used: 67.225 MB
%------------------------------------------------------------------------------