%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : NUN065+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 : 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 01:57:11 PM UTC 2026
% Result : Theorem 4.06s 1.05s
% Output : CNFRefutation 4.06s
% Verified :
% SZS Type : Refutation
% Derivation depth : 27
% Number of leaves : 9
% Syntax : Number of formulae : 88 ( 13 unt; 3 def)
% Number of atoms : 242 ( 101 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 235 ( 81 ~; 107 |; 44 &)
% ( 3 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 8 ( 6 usr; 1 prp; 0-3 aty)
% Number of functors : 9 ( 9 usr; 1 con; 0-2 aty)
% Number of variables : 184 ( 166 !; 18 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
? [Y24] :
! [X19] :
( ( X19 = Y24
& r1(X19) )
| ( X19 != Y24
& ~ r1(X19) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f2,axiom,
! [X11] :
? [Y21] :
! [X12] :
( ( X12 = Y21
& r2(X11,X12) )
| ( X12 != Y21
& ~ r2(X11,X12) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f5,axiom,
! [X1,X8] :
? [Y4] :
( ? [Y7] :
( r3(X1,X8,Y7)
& r2(Y7,Y4) )
& ? [Y5] :
( Y5 = Y4
& ? [Y15] :
( r3(X1,Y15,Y5)
& r2(X8,Y15) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f7,axiom,
! [X3,X10] :
( X3 = X10
| ! [Y12] :
( ~ r2(X10,Y12)
| ! [Y13] :
( Y13 != Y12
| ~ r2(X3,Y13) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f11,axiom,
! [X7,Y10] :
( ~ r2(X7,Y10)
| ! [Y20] :
( Y20 != Y10
| ~ r1(Y20) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f12,conjecture,
? [Y1] :
( ! [Y4] :
( Y1 != Y4
| ~ r1(Y4) )
& ! [Y2] :
( Y1 != Y2
| ! [Y3] :
( ~ r2(Y3,Y2)
| ~ r1(Y3) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f13,negated_conjecture,
~ ? [Y1] :
( ! [Y4] :
( Y1 != Y4
| ~ r1(Y4) )
& ! [Y2] :
( Y1 != Y2
| ! [Y3] :
( ~ r2(Y3,Y2)
| ~ r1(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(f23,plain,
! [X0,X1] :
( X0 = sK1_skl(X1)
| sP1_prd(X0,sK1_skl(X1),X1) ),
inference(cnf_transformation,[status(thm)],[f21]) ).
fof(f34,plain,
! [X1,X8] :
( r3(X1,X8,sK7_skl(X8,X1))
& r2(sK7_skl(X8,X1),sK4_skl(X8,X1))
& sK5_skl(X8,X1) = sK4_skl(X8,X1)
& r3(X1,sK6_skl(X8,X1),sK5_skl(X8,X1))
& r2(X8,sK6_skl(X8,X1)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4_skl,sK5_skl,sK6_skl,sK7_skl]),skolemize(Y4,sK4_skl(X8,X1)),skolemize(Y5,sK5_skl(X8,X1)),skolemize(Y15,sK6_skl(X8,X1)),skolemize(Y7,sK7_skl(X8,X1))],[f5]) ).
fof(f38,plain,
! [X0,X1] : r2(sK7_skl(X0,X1),sK4_skl(X0,X1)),
inference(cnf_transformation,[status(thm)],[f34]) ).
fof(f46,plain,
! [X0,X1,X2,X3] :
( X0 = X3
| ~ r2(X3,X2)
| X1 != X2
| ~ r2(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f7]) ).
fof(f62,plain,
! [Y10] :
( ! [X7] : ~ r2(X7,Y10)
| ! [Y20] :
( Y20 != Y10
| ~ r1(Y20) ) ),
inference(miniscoping,[status(thm)],[f11]) ).
fof(f63,plain,
! [X0,X1,X2] :
( ~ r2(X2,X1)
| X0 != X1
| ~ r1(X0) ),
inference(cnf_transformation,[status(thm)],[f62]) ).
fof(f64,plain,
! [Y1] :
( ? [Y4] :
( Y1 = Y4
& r1(Y4) )
| ? [Y2] :
( Y1 = Y2
& ? [Y3] :
( r2(Y3,Y2)
& r1(Y3) ) ) ),
inference(pre_NNF_transformation,[status(thm)],[f13]) ).
fof(f65,definition,
! [Y1,Y2] :
( sP5_prd(Y2,Y1)
<=> ( Y1 = Y2
& ? [Y3] :
( r2(Y3,Y2)
& r1(Y3) ) ) ),
introduced(definition,[new_symbols(definition,[sP5_prd])],[]) ).
fof(f66,plain,
! [Y1] :
( ? [Y4] :
( Y1 = Y4
& r1(Y4) )
| ? [Y2] : sP5_prd(Y2,Y1) ),
inference(formula_renaming,[status(thm)],[f64,f65]) ).
fof(f67,plain,
! [Y1] :
( ( Y1 = sK21_skl(Y1)
& r1(sK21_skl(Y1)) )
| sP5_prd(sK20_skl(Y1),Y1) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK20_skl,sK21_skl]),skolemize(Y2,sK20_skl(Y1)),skolemize(Y4,sK21_skl(Y1))],[f66]) ).
fof(f68,plain,
! [X0] :
( r1(sK21_skl(X0))
| sP5_prd(sK20_skl(X0),X0) ),
inference(cnf_transformation,[status(thm)],[f67]) ).
fof(f69,plain,
! [X0] :
( X0 = sK21_skl(X0)
| sP5_prd(sK20_skl(X0),X0) ),
inference(cnf_transformation,[status(thm)],[f67]) ).
fof(f70,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(f71,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)],[f70]) ).
fof(f72,plain,
! [X0,X1] :
( ~ r1(X0)
| ~ sP0_prd(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f71]) ).
fof(f73,plain,
! [X0,X1] :
( X0 != X1
| ~ sP0_prd(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f71]) ).
fof(f75,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(f76,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)],[f75]) ).
fof(f77,plain,
! [X0,X1,X2] :
( ~ r2(X2,X0)
| ~ sP1_prd(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f76]) ).
fof(f78,plain,
! [X0,X1,X2] :
( X0 != X1
| ~ sP1_prd(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f76]) ).
fof(f95,plain,
! [Y1,Y2] :
( ( Y1 != Y2
| ! [Y3] :
( ~ r2(Y3,Y2)
| ~ r1(Y3) )
| sP5_prd(Y2,Y1) )
& ( ( Y1 = Y2
& ? [Y3] :
( r2(Y3,Y2)
& r1(Y3) ) )
| ~ sP5_prd(Y2,Y1) ) ),
inference(NNF_transformation,[status(thm)],[f65]) ).
fof(f96,plain,
( ! [Y1,Y2] :
( Y1 != Y2
| ! [Y3] :
( ~ r2(Y3,Y2)
| ~ r1(Y3) )
| sP5_prd(Y2,Y1) )
& ! [Y1,Y2] :
( ( Y1 = Y2
& ? [Y3] :
( r2(Y3,Y2)
& r1(Y3) ) )
| ~ sP5_prd(Y2,Y1) ) ),
inference(miniscoping,[status(thm)],[f95]) ).
fof(f97,plain,
( ! [Y1,Y2] :
( Y1 != Y2
| ! [Y3] :
( ~ r2(Y3,Y2)
| ~ r1(Y3) )
| sP5_prd(Y2,Y1) )
& ! [Y1,Y2] :
( ( Y1 = Y2
& r2(sK22_skl(Y2,Y1),Y2)
& r1(sK22_skl(Y2,Y1)) )
| ~ sP5_prd(Y2,Y1) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK22_skl]),skolemize(Y3,sK22_skl(Y2,Y1))],[f96]) ).
fof(f98,plain,
! [X0,X1] :
( r1(sK22_skl(X0,X1))
| ~ sP5_prd(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f97]) ).
fof(f99,plain,
! [X0,X1] :
( r2(sK22_skl(X0,X1),X0)
| ~ sP5_prd(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f97]) ).
fof(f100,plain,
! [X0,X1] :
( X1 = X0
| ~ sP5_prd(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f97]) ).
fof(f102,plain,
! [X0,X1,X2] :
( X0 = X2
| ~ r2(X2,X1)
| ~ r2(X0,X1) ),
inference(destructive_equality_resolution,[status(thm)],[f46]) ).
fof(f103,plain,
! [X0,X1] :
( ~ r2(X1,X0)
| ~ r1(X0) ),
inference(destructive_equality_resolution,[status(thm)],[f63]) ).
fof(f104,plain,
! [X0] : ~ sP0_prd(X0,X0),
inference(destructive_equality_resolution,[status(thm)],[f73]) ).
fof(f105,plain,
! [X0,X1] : ~ sP1_prd(X0,X0,X1),
inference(destructive_equality_resolution,[status(thm)],[f78]) ).
fof(f110,plain,
! [X0] :
( X0 = sK20_skl(X0)
| X0 = sK21_skl(X0) ),
inference(resolution,[status(thm)],[f69,f100]) ).
fof(f111,plain,
! [X0] :
( X0 = sK20_skl(X0)
| r1(sK21_skl(X0)) ),
inference(resolution,[status(thm)],[f68,f100]) ).
fof(f112,plain,
! [X0] :
( X0 = sK20_skl(X0)
| X0 = sK20_skl(X0)
| r1(X0) ),
inference(paramodulation,[status(thm)],[f110,f111]) ).
fof(f113,plain,
! [X0] :
( X0 = sK20_skl(X0)
| r1(X0) ),
inference(duplicate_literals_removal,[status(thm)],[f112]) ).
fof(f114,plain,
! [X0] :
( r1(sK21_skl(X0))
| r1(sK22_skl(sK20_skl(X0),X0)) ),
inference(resolution,[status(thm)],[f98,f68]) ).
fof(f115,plain,
! [X0] :
( X0 = sK21_skl(X0)
| r1(sK22_skl(sK20_skl(X0),X0)) ),
inference(resolution,[status(thm)],[f98,f69]) ).
fof(f116,plain,
r1(sK0_skl),
inference(resolution,[status(thm)],[f17,f104]) ).
fof(f118,plain,
! [X0] : r2(X0,sK1_skl(X0)),
inference(resolution,[status(thm)],[f22,f105]) ).
fof(f119,plain,
! [X0] :
( r1(sK21_skl(X0))
| r2(sK22_skl(sK20_skl(X0),X0),sK20_skl(X0)) ),
inference(resolution,[status(thm)],[f99,f68]) ).
fof(f120,plain,
! [X0] :
( X0 = sK21_skl(X0)
| r2(sK22_skl(sK20_skl(X0),X0),sK20_skl(X0)) ),
inference(resolution,[status(thm)],[f99,f69]) ).
fof(f187,plain,
! [X0] : ~ r1(sK1_skl(X0)),
inference(resolution,[status(thm)],[f118,f103]) ).
fof(f394,plain,
! [X0] :
( X0 = sK0_skl
| ~ r1(X0) ),
inference(resolution,[status(thm)],[f72,f18]) ).
fof(f400,plain,
! [X0] :
( X0 = sK21_skl(X0)
| sK22_skl(sK20_skl(X0),X0) = sK0_skl ),
inference(resolution,[status(thm)],[f394,f115]) ).
fof(f401,plain,
! [X0] :
( r1(sK21_skl(X0))
| sK22_skl(sK20_skl(X0),X0) = sK0_skl ),
inference(resolution,[status(thm)],[f394,f114]) ).
fof(f406,plain,
! [X0] :
( X0 = sK20_skl(X0)
| X0 = sK0_skl ),
inference(resolution,[status(thm)],[f394,f113]) ).
fof(f602,plain,
! [X0,X1] :
( X1 = sK1_skl(X0)
| ~ r2(X0,X1) ),
inference(resolution,[status(thm)],[f77,f23]) ).
fof(f604,plain,
! [X0,X1] : sK4_skl(X0,X1) = sK1_skl(sK7_skl(X0,X1)),
inference(resolution,[status(thm)],[f602,f38]) ).
fof(f643,plain,
! [X0] :
( X0 = sK21_skl(X0)
| X0 = sK21_skl(X0)
| r2(sK0_skl,sK20_skl(X0)) ),
inference(paramodulation,[status(thm)],[f400,f120]) ).
fof(f648,plain,
! [X0] :
( X0 = sK21_skl(X0)
| r2(sK0_skl,sK20_skl(X0)) ),
inference(duplicate_literals_removal,[status(thm)],[f643]) ).
fof(f654,plain,
! [X0] :
( sK20_skl(X0) = sK1_skl(sK0_skl)
| X0 = sK21_skl(X0) ),
inference(resolution,[status(thm)],[f648,f602]) ).
fof(f849,plain,
! [X0,X1,X2] :
( r2(sK7_skl(X1,X2),X0)
| sP1_prd(X0,sK4_skl(X1,X2),sK7_skl(X1,X2)) ),
inference(paramodulation,[status(thm)],[f604,f22]) ).
fof(f1132,plain,
! [X0] :
( sK21_skl(X0) = sK0_skl
| sK22_skl(sK20_skl(X0),X0) = sK0_skl ),
inference(resolution,[status(thm)],[f401,f394]) ).
fof(f2400,plain,
! [X0] :
( sK21_skl(X0) = sK0_skl
| r1(sK21_skl(X0))
| r2(sK0_skl,sK20_skl(X0)) ),
inference(paramodulation,[status(thm)],[f1132,f119]) ).
fof(f2414,plain,
! [X0] :
( sK21_skl(X0) = sK0_skl
| r2(sK0_skl,sK20_skl(X0)) ),
inference(forward_subsumption_resolution,[status(thm)],[f2400,f394]) ).
fof(f2419,plain,
! [X0] :
( sK20_skl(X0) = sK1_skl(sK0_skl)
| sK21_skl(X0) = sK0_skl ),
inference(resolution,[status(thm)],[f2414,f602]) ).
fof(f2480,plain,
! [X0] :
( sK20_skl(X0) = sK1_skl(sK0_skl)
| sK20_skl(X0) = sK1_skl(sK0_skl)
| X0 = sK0_skl ),
inference(paramodulation,[status(thm)],[f654,f2419]) ).
fof(f2510,plain,
! [X0] :
( sK20_skl(X0) = sK1_skl(sK0_skl)
| X0 = sK0_skl ),
inference(duplicate_literals_removal,[status(thm)],[f2480]) ).
fof(f2524,plain,
! [X0] :
( X0 = sK0_skl
| X0 = sK1_skl(sK0_skl)
| X0 = sK0_skl ),
inference(paramodulation,[status(thm)],[f406,f2510]) ).
fof(f2596,plain,
! [X0] :
( X0 = sK1_skl(sK0_skl)
| X0 = sK0_skl ),
inference(duplicate_literals_removal,[status(thm)],[f2524]) ).
fof(f2602,plain,
! [X0,X1] :
( X1 = sK0_skl
| X0 = X1
| X0 = sK0_skl ),
inference(paramodulation,[status(thm)],[f2596,f2596]) ).
fof(f2723,plain,
! [X0,X1] :
( X1 = sK0_skl
| X0 = X1
| r1(X0) ),
inference(paramodulation,[status(thm)],[f2602,f116]) ).
fof(f2755,plain,
! [X0,X1] :
( X1 = sK0_skl
| sK1_skl(X0) = X1 ),
inference(resolution,[status(thm)],[f2723,f187]) ).
fof(f2829,plain,
! [X0,X1] :
( X1 = sK0_skl
| r2(X0,X1) ),
inference(paramodulation,[status(thm)],[f2755,f118]) ).
fof(f2913,plain,
! [X0,X1,X2] :
( X2 = X1
| ~ r2(X1,X0)
| X0 = sK0_skl ),
inference(resolution,[status(thm)],[f2829,f102]) ).
fof(f2915,plain,
! [X0,X1,X2] :
( X1 = X2
| X0 = sK0_skl ),
inference(forward_subsumption_resolution,[status(thm)],[f2913,f2829]) ).
fof(f2963,plain,
! [X0,X1] :
( X1 = X0
| sK0_skl != X0 ),
inference(equality_factoring,[status(thm)],[f2915]) ).
fof(f2968,plain,
! [X0,X1] : X0 = X1,
inference(forward_subsumption_resolution,[status(thm)],[f2963,f2915]) ).
fof(f2973,plain,
! [X0,X1] : r2(sK7_skl(X0,X1),sK4_skl(X0,X1)),
inference(resolution,[status(thm)],[f849,f105]) ).
fof(f3002,plain,
! [X0,X1,X2] : r2(X0,sK4_skl(X1,X2)),
inference(paramodulation,[status(thm)],[f2968,f2973]) ).
fof(f3008,plain,
! [X0,X1] : r2(X0,X1),
inference(paramodulation,[status(thm)],[f2968,f3002]) ).
fof(f3012,plain,
! [X0] : ~ r1(X0),
inference(backward_subsumption_resolution,[status(thm)],[f103,f3008]) ).
fof(f3024,plain,
$false,
inference(backward_subsumption_resolution,[status(thm)],[f116,f3012]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : NUN065+2 : TPTP v9.3.1. Released v7.3.0.
% 0.00/0.06 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.19/0.44 % Computer : n026.cluster.edu
% 0.19/0.44 % Model : x86_64 x86_64
% 0.19/0.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.19/0.44 % Memory : 8046.5625MB
% 0.19/0.44 % OS : Linux 6.8.0-71-generic
% 0.19/0.44 % CPULimit : 300
% 0.19/0.44 % WCLimit : 300
% 0.19/0.44 % DateTime : Mon Sep 21 03:26:52 UTC 2026
% 0.19/0.45 % CPUTime :
% 0.19/0.46 % Drodi V4.1.1
% 4.06/1.05 % Refutation found
% 4.06/1.05 % SZS status Theorem for theBenchmark: Theorem is valid
% 4.06/1.05 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 4.06/1.08 % Elapsed time: 0.610718 seconds
% 4.06/1.08 % CPU time: 4.393709 seconds
% 4.06/1.08 % Total memory used: 154.869 MB
% 4.06/1.08 % Net memory used: 146.129 MB
%------------------------------------------------------------------------------