%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : NUN068+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 : n017.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 2.98s 1.03s
% Output : CNFRefutation 2.98s
% Verified :
% SZS Type : Refutation
% Derivation depth : 22
% Number of leaves : 9
% Syntax : Number of formulae : 84 ( 10 unt; 3 def)
% Number of atoms : 236 ( 99 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 233 ( 81 ~; 105 |; 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 : 169 ( 151 !; 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(f104,plain,
! [X0,X1,X2] :
( X0 = X2
| ~ r2(X2,X1)
| ~ r2(X0,X1) ),
inference(destructive_equality_resolution,[status(thm)],[f46]) ).
fof(f107,plain,
! [X0,X1] :
( ~ r2(X1,X0)
| ~ r1(X0) ),
inference(destructive_equality_resolution,[status(thm)],[f63]) ).
fof(f108,plain,
! [X0] : ~ sP0_prd(X0,X0),
inference(destructive_equality_resolution,[status(thm)],[f73]) ).
fof(f109,plain,
! [X0,X1] : ~ sP1_prd(X0,X0,X1),
inference(destructive_equality_resolution,[status(thm)],[f78]) ).
fof(f114,plain,
! [X0] :
( X0 = sK20_skl(X0)
| X0 = sK21_skl(X0) ),
inference(resolution,[status(thm)],[f69,f100]) ).
fof(f115,plain,
! [X0] :
( X0 = sK20_skl(X0)
| r1(sK21_skl(X0)) ),
inference(resolution,[status(thm)],[f68,f100]) ).
fof(f116,plain,
! [X0] :
( X0 = sK20_skl(X0)
| X0 = sK20_skl(X0)
| r1(X0) ),
inference(paramodulation,[status(thm)],[f114,f115]) ).
fof(f117,plain,
! [X0] :
( X0 = sK20_skl(X0)
| r1(X0) ),
inference(duplicate_literals_removal,[status(thm)],[f116]) ).
fof(f118,plain,
! [X0] :
( r1(sK21_skl(X0))
| r1(sK22_skl(sK20_skl(X0),X0)) ),
inference(resolution,[status(thm)],[f98,f68]) ).
fof(f119,plain,
! [X0] :
( X0 = sK21_skl(X0)
| r1(sK22_skl(sK20_skl(X0),X0)) ),
inference(resolution,[status(thm)],[f98,f69]) ).
fof(f120,plain,
r1(sK0_skl),
inference(resolution,[status(thm)],[f17,f108]) ).
fof(f122,plain,
! [X0] : r2(X0,sK1_skl(X0)),
inference(resolution,[status(thm)],[f22,f109]) ).
fof(f123,plain,
! [X0] :
( r1(sK21_skl(X0))
| r2(sK22_skl(sK20_skl(X0),X0),sK20_skl(X0)) ),
inference(resolution,[status(thm)],[f99,f68]) ).
fof(f124,plain,
! [X0] :
( X0 = sK21_skl(X0)
| r2(sK22_skl(sK20_skl(X0),X0),sK20_skl(X0)) ),
inference(resolution,[status(thm)],[f99,f69]) ).
fof(f140,plain,
! [X0,X1] :
( X1 = X0
| ~ r2(X0,sK1_skl(X1)) ),
inference(resolution,[status(thm)],[f122,f104]) ).
fof(f141,plain,
! [X0] : ~ r1(sK1_skl(X0)),
inference(resolution,[status(thm)],[f122,f107]) ).
fof(f216,plain,
! [X0] :
( X0 = sK0_skl
| ~ r1(X0) ),
inference(resolution,[status(thm)],[f72,f18]) ).
fof(f219,plain,
! [X0] :
( X0 = sK21_skl(X0)
| sK22_skl(sK20_skl(X0),X0) = sK0_skl ),
inference(resolution,[status(thm)],[f216,f119]) ).
fof(f220,plain,
! [X0] :
( r1(sK21_skl(X0))
| sK22_skl(sK20_skl(X0),X0) = sK0_skl ),
inference(resolution,[status(thm)],[f216,f118]) ).
fof(f225,plain,
! [X0] :
( X0 = sK20_skl(X0)
| X0 = sK0_skl ),
inference(resolution,[status(thm)],[f216,f117]) ).
fof(f345,plain,
! [X0] :
( X0 = sK21_skl(X0)
| X0 = sK21_skl(X0)
| r2(sK0_skl,sK20_skl(X0)) ),
inference(paramodulation,[status(thm)],[f219,f124]) ).
fof(f348,plain,
! [X0] :
( X0 = sK21_skl(X0)
| r2(sK0_skl,sK20_skl(X0)) ),
inference(duplicate_literals_removal,[status(thm)],[f345]) ).
fof(f357,plain,
! [X0,X1] : ~ r1(sK4_skl(X0,X1)),
inference(resolution,[status(thm)],[f38,f107]) ).
fof(f414,plain,
! [X0] :
( sK21_skl(X0) = sK0_skl
| sK22_skl(sK20_skl(X0),X0) = sK0_skl ),
inference(resolution,[status(thm)],[f220,f216]) ).
fof(f545,plain,
! [X0,X1] :
( X1 = sK1_skl(X0)
| ~ r2(X0,X1) ),
inference(resolution,[status(thm)],[f77,f23]) ).
fof(f548,plain,
! [X0] :
( X0 = sK21_skl(X0)
| sK20_skl(X0) = sK1_skl(sK0_skl) ),
inference(resolution,[status(thm)],[f545,f348]) ).
fof(f1617,plain,
! [X0] :
( sK21_skl(X0) = sK0_skl
| r1(sK21_skl(X0))
| r2(sK0_skl,sK20_skl(X0)) ),
inference(paramodulation,[status(thm)],[f414,f123]) ).
fof(f1625,plain,
! [X0] :
( sK21_skl(X0) = sK0_skl
| r2(sK0_skl,sK20_skl(X0)) ),
inference(forward_subsumption_resolution,[status(thm)],[f1617,f216]) ).
fof(f1755,plain,
! [X0] :
( sK20_skl(X0) = sK1_skl(sK0_skl)
| sK21_skl(X0) = sK0_skl ),
inference(resolution,[status(thm)],[f1625,f545]) ).
fof(f1927,plain,
! [X0] :
( sK20_skl(X0) = sK1_skl(sK0_skl)
| sK20_skl(X0) = sK1_skl(sK0_skl)
| X0 = sK0_skl ),
inference(paramodulation,[status(thm)],[f548,f1755]) ).
fof(f1956,plain,
! [X0] :
( sK20_skl(X0) = sK1_skl(sK0_skl)
| X0 = sK0_skl ),
inference(duplicate_literals_removal,[status(thm)],[f1927]) ).
fof(f1969,plain,
! [X0] :
( X0 = sK0_skl
| X0 = sK1_skl(sK0_skl)
| X0 = sK0_skl ),
inference(paramodulation,[status(thm)],[f225,f1956]) ).
fof(f2025,plain,
! [X0] :
( X0 = sK1_skl(sK0_skl)
| X0 = sK0_skl ),
inference(duplicate_literals_removal,[status(thm)],[f1969]) ).
fof(f2074,plain,
! [X0,X1] :
( X1 = sK0_skl
| X0 = X1
| X0 = sK0_skl ),
inference(paramodulation,[status(thm)],[f2025,f2025]) ).
fof(f2091,plain,
! [X0] :
( X0 = sK0_skl
| r2(sK0_skl,X0) ),
inference(paramodulation,[status(thm)],[f2025,f122]) ).
fof(f2129,plain,
! [X0,X1] :
( X1 = sK0_skl
| X0 = X1
| r1(X0) ),
inference(paramodulation,[status(thm)],[f2074,f120]) ).
fof(f2141,plain,
! [X0] :
( X0 = sK0_skl
| sK1_skl(X0) = sK0_skl ),
inference(resolution,[status(thm)],[f2091,f140]) ).
fof(f2159,plain,
! [X0,X1] :
( X1 = sK0_skl
| sK1_skl(X0) = X1 ),
inference(resolution,[status(thm)],[f2129,f141]) ).
fof(f2207,plain,
! [X0,X1] :
( X1 = sK0_skl
| sK1_skl(X0) != sK0_skl ),
inference(equality_factoring,[status(thm)],[f2159]) ).
fof(f2211,plain,
! [X0] : X0 = sK0_skl,
inference(backward_subsumption_resolution,[status(thm)],[f2141,f2207]) ).
fof(f2290,plain,
! [X0] : r1(X0),
inference(paramodulation,[status(thm)],[f2211,f120]) ).
fof(f2299,plain,
$false,
inference(backward_subsumption_resolution,[status(thm)],[f357,f2290]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUN068+2 : TPTP v9.3.1. Released v7.3.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n017.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Mon Sep 21 03:19:12 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.38 % Drodi V4.1.1
% 2.98/1.03 % Refutation found
% 2.98/1.03 % SZS status Theorem for theBenchmark: Theorem is valid
% 2.98/1.03 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 2.98/1.06 % Elapsed time: 0.671278 seconds
% 2.98/1.06 % CPU time: 4.988311 seconds
% 2.98/1.06 % Total memory used: 154.986 MB
% 2.98/1.06 % Net memory used: 146.015 MB
%------------------------------------------------------------------------------