%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : NUN081+2 : TPTP v9.3.1. Released v7.3.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/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 01:57:14 PM UTC 2026
% Result : Theorem 0.16s 0.48s
% Output : CNFRefutation 0.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 6
% Syntax : Number of formulae : 42 ( 12 unt; 2 def)
% Number of atoms : 126 ( 31 equ)
% Maximal formula atoms : 6 ( 3 avg)
% Number of connectives : 147 ( 63 ~; 50 |; 32 &)
% ( 2 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 6 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 1 prp; 0-3 aty)
% Number of functors : 4 ( 4 usr; 1 con; 0-1 aty)
% Number of variables : 110 ( 90 !; 20 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
? [Y24] :
! [X19] :
( ( X19 = Y24
& r1(X19) )
| ( X19 != Y24
& ~ r1(X19) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f2,axiom,
! [X11] :
? [Y21] :
! [X12] :
( ( X12 = Y21
& r2(X11,X12) )
| ( X12 != Y21
& ~ r2(X11,X12) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f8,axiom,
! [X4] :
? [Y9] :
( Y9 = X4
& ? [Y16] :
( r3(X4,Y16,Y9)
& r1(Y16) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f12,conjecture,
? [Y1,Y2,Y3] :
( ? [Y4] :
( ? [Y5] :
( ? [Y6] :
( ? [Y7] :
( r2(Y7,Y6)
& r1(Y7) )
& r2(Y6,Y5) )
& r2(Y5,Y4) )
& Y3 = Y4 )
& r3(Y1,Y2,Y3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f13,negated_conjecture,
~ ? [Y1,Y2,Y3] :
( ? [Y4] :
( ? [Y5] :
( ? [Y6] :
( ? [Y7] :
( r2(Y7,Y6)
& r1(Y7) )
& r2(Y6,Y5) )
& r2(Y5,Y4) )
& Y3 = Y4 )
& r3(Y1,Y2,Y3) ),
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(f19,definition,
! [X11,Y21,X12] :
( sP1_prd(X12,Y21,X11)
<=> ( X12 != Y21
& ~ r2(X11,X12) ) ),
introduced(definition,[new_symbols(definition,[sP1_prd])],[]) ).
fof(f20,plain,
! [X11] :
? [Y21] :
! [X12] :
( ( X12 = Y21
& r2(X11,X12) )
| sP1_prd(X12,Y21,X11) ),
inference(formula_renaming,[status(thm)],[f2,f19]) ).
fof(f21,plain,
! [X11,X12] :
( ( X12 = sK1_skl(X11)
& r2(X11,X12) )
| sP1_prd(X12,sK1_skl(X11),X11) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1_skl]),skolemize(Y21,sK1_skl(X11))],[f20]) ).
fof(f22,plain,
! [X0,X1] :
( r2(X1,X0)
| sP1_prd(X0,sK1_skl(X1),X1) ),
inference(cnf_transformation,[status(thm)],[f21]) ).
fof(f47,plain,
! [X4] :
( sK12_skl(X4) = X4
& r3(X4,sK13_skl(X4),sK12_skl(X4))
& r1(sK13_skl(X4)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK12_skl,sK13_skl]),skolemize(Y9,sK12_skl(X4)),skolemize(Y16,sK13_skl(X4))],[f8]) ).
fof(f48,plain,
! [X0] : r1(sK13_skl(X0)),
inference(cnf_transformation,[status(thm)],[f47]) ).
fof(f49,plain,
! [X0] : r3(X0,sK13_skl(X0),sK12_skl(X0)),
inference(cnf_transformation,[status(thm)],[f47]) ).
fof(f50,plain,
! [X0] : sK12_skl(X0) = X0,
inference(cnf_transformation,[status(thm)],[f47]) ).
fof(f64,plain,
! [Y1,Y2,Y3] :
( ! [Y4] :
( ! [Y5] :
( ! [Y6] :
( ! [Y7] :
( ~ r2(Y7,Y6)
| ~ r1(Y7) )
| ~ r2(Y6,Y5) )
| ~ r2(Y5,Y4) )
| Y3 != Y4 )
| ~ r3(Y1,Y2,Y3) ),
inference(pre_NNF_transformation,[status(thm)],[f13]) ).
fof(f65,plain,
! [Y3] :
( ! [Y4] :
( ! [Y5] :
( ! [Y6] :
( ! [Y7] :
( ~ r2(Y7,Y6)
| ~ r1(Y7) )
| ~ r2(Y6,Y5) )
| ~ r2(Y5,Y4) )
| Y3 != Y4 )
| ! [Y1,Y2] : ~ r3(Y1,Y2,Y3) ),
inference(miniscoping,[status(thm)],[f64]) ).
fof(f66,plain,
! [X0,X1,X2,X3,X4,X5,X6] :
( ~ r2(X6,X5)
| ~ r1(X6)
| ~ r2(X5,X4)
| ~ r2(X4,X3)
| X2 != X3
| ~ r3(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f65]) ).
fof(f67,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(f68,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)],[f67]) ).
fof(f69,plain,
! [X0,X1] :
( ~ r1(X0)
| ~ sP0_prd(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f68]) ).
fof(f70,plain,
! [X0,X1] :
( X0 != X1
| ~ sP0_prd(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f68]) ).
fof(f72,plain,
! [X11,Y21,X12] :
( ( X12 = Y21
| r2(X11,X12)
| sP1_prd(X12,Y21,X11) )
& ( ( X12 != Y21
& ~ r2(X11,X12) )
| ~ sP1_prd(X12,Y21,X11) ) ),
inference(NNF_transformation,[status(thm)],[f19]) ).
fof(f73,plain,
( ! [X11,Y21,X12] :
( X12 = Y21
| r2(X11,X12)
| sP1_prd(X12,Y21,X11) )
& ! [X11,Y21,X12] :
( ( X12 != Y21
& ~ r2(X11,X12) )
| ~ sP1_prd(X12,Y21,X11) ) ),
inference(miniscoping,[status(thm)],[f72]) ).
fof(f75,plain,
! [X0,X1,X2] :
( X0 != X1
| ~ sP1_prd(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f73]) ).
fof(f94,plain,
! [X0,X1,X2,X3,X4,X5] :
( ~ r2(X5,X4)
| ~ r1(X5)
| ~ r2(X4,X3)
| ~ r2(X3,X2)
| ~ r3(X0,X1,X2) ),
inference(destructive_equality_resolution,[status(thm)],[f66]) ).
fof(f95,plain,
! [X0] : ~ sP0_prd(X0,X0),
inference(destructive_equality_resolution,[status(thm)],[f70]) ).
fof(f96,plain,
! [X0,X1] : ~ sP1_prd(X0,X0,X1),
inference(destructive_equality_resolution,[status(thm)],[f75]) ).
fof(f100,plain,
r1(sK0_skl),
inference(resolution,[status(thm)],[f17,f95]) ).
fof(f109,plain,
! [X0] :
( ~ r1(X0)
| X0 = sK0_skl ),
inference(resolution,[status(thm)],[f18,f69]) ).
fof(f113,plain,
! [X0] : sK13_skl(X0) = sK0_skl,
inference(resolution,[status(thm)],[f109,f48]) ).
fof(f120,plain,
! [X0] : r2(X0,sK1_skl(X0)),
inference(resolution,[status(thm)],[f22,f96]) ).
fof(f129,plain,
! [X0] : r3(X0,sK0_skl,sK12_skl(X0)),
inference(forward_demodulation,[status(thm)],[f113,f49]) ).
fof(f130,plain,
! [X0] : r3(X0,sK0_skl,X0),
inference(forward_demodulation,[status(thm)],[f50,f129]) ).
fof(f131,plain,
! [X0,X1,X2,X3] :
( ~ r2(X3,X2)
| ~ r1(X3)
| ~ r2(X2,X0)
| ~ r2(X0,X1) ),
inference(resolution,[status(thm)],[f130,f94]) ).
fof(f132,plain,
! [X0,X1,X2] :
( ~ r2(X2,X0)
| ~ r1(X2)
| ~ r2(sK1_skl(X0),X1) ),
inference(resolution,[status(thm)],[f131,f120]) ).
fof(f139,plain,
! [X0,X1] :
( ~ r2(X0,X1)
| ~ r1(X0) ),
inference(resolution,[status(thm)],[f132,f120]) ).
fof(f142,plain,
! [X0] : ~ r1(X0),
inference(resolution,[status(thm)],[f139,f120]) ).
fof(f148,plain,
$false,
inference(backward_subsumption_resolution,[status(thm)],[f100,f142]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUN081+2 : TPTP v9.3.1. Released v7.3.0.
% 0.00/0.05 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.16/0.44 % Computer : n009.cluster.edu
% 0.16/0.44 % Model : x86_64 x86_64
% 0.16/0.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.44 % Memory : 8046.5625MB
% 0.16/0.44 % OS : Linux 6.8.0-71-generic
% 0.16/0.44 % CPULimit : 300
% 0.16/0.44 % WCLimit : 300
% 0.16/0.44 % DateTime : Mon Sep 21 03:25:12 UTC 2026
% 0.16/0.45 % CPUTime :
% 0.16/0.48 % Drodi V4.1.1
% 0.16/0.48 % Refutation found
% 0.16/0.48 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.16/0.48 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.16/0.55 % Elapsed time: 0.084626 seconds
% 0.16/0.55 % CPU time: 0.096242 seconds
% 0.16/0.55 % Total memory used: 6.478 MB
% 0.16/0.55 % Net memory used: 6.466 MB
%------------------------------------------------------------------------------