%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : NUN085+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 : n010.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 0.16s 0.46s
% Output : CNFRefutation 0.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 10
% Syntax : Number of formulae : 85 ( 45 unt; 3 def)
% Number of atoms : 191 ( 68 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 172 ( 66 ~; 54 |; 49 &)
% ( 3 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 8 ( 6 usr; 1 prp; 0-4 aty)
% Number of functors : 14 ( 14 usr; 6 con; 0-2 aty)
% Number of variables : 153 ( 136 !; 17 ?)
% 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(f3,axiom,
! [X13,X14] :
? [Y22] :
! [X15] :
( ( X15 = Y22
& r3(X13,X14,X15) )
| ( X15 != Y22
& ~ r3(X13,X14,X15) ) ),
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(f8,axiom,
! [X4] :
? [Y9] :
( Y9 = X4
& ? [Y16] :
( r3(X4,Y16,Y9)
& r1(Y16) ) ),
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] :
( ! [Y5] :
( ~ r1(Y5)
| Y1 != Y5 )
| ! [Y2] :
( ! [Y4] :
( ~ r2(Y4,Y2)
| ~ r1(Y4) )
| ! [Y3] :
( ~ r3(Y3,Y2,Y1)
| ~ r1(Y3) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f13,negated_conjecture,
~ ! [Y1] :
( ! [Y5] :
( ~ r1(Y5)
| Y1 != Y5 )
| ! [Y2] :
( ! [Y4] :
( ~ r2(Y4,Y2)
| ~ r1(Y4) )
| ! [Y3] :
( ~ r3(Y3,Y2,Y1)
| ~ 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(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(f23,plain,
! [X0,X1] :
( X0 = sK1_skl(X1)
| sP1_prd(X0,sK1_skl(X1),X1) ),
inference(cnf_transformation,[status(thm)],[f21]) ).
fof(f24,definition,
! [X13,X14,Y22,X15] :
( sP2_prd(X15,Y22,X14,X13)
<=> ( X15 != Y22
& ~ r3(X13,X14,X15) ) ),
introduced(definition,[new_symbols(definition,[sP2_prd])],[]) ).
fof(f25,plain,
! [X13,X14] :
? [Y22] :
! [X15] :
( ( X15 = Y22
& r3(X13,X14,X15) )
| sP2_prd(X15,Y22,X14,X13) ),
inference(formula_renaming,[status(thm)],[f3,f24]) ).
fof(f26,plain,
! [X13,X14,X15] :
( ( X15 = sK2_skl(X14,X13)
& r3(X13,X14,X15) )
| sP2_prd(X15,sK2_skl(X14,X13),X14,X13) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2_skl]),skolemize(Y22,sK2_skl(X14,X13))],[f25]) ).
fof(f28,plain,
! [X0,X1,X2] :
( X0 = sK2_skl(X1,X2)
| sP2_prd(X0,sK2_skl(X1,X2),X1,X2) ),
inference(cnf_transformation,[status(thm)],[f26]) ).
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(f35,plain,
! [X0,X1] : r2(X0,sK6_skl(X0,X1)),
inference(cnf_transformation,[status(thm)],[f34]) ).
fof(f36,plain,
! [X0,X1] : r3(X0,sK6_skl(X1,X0),sK5_skl(X1,X0)),
inference(cnf_transformation,[status(thm)],[f34]) ).
fof(f37,plain,
! [X0,X1] : sK5_skl(X0,X1) = sK4_skl(X0,X1),
inference(cnf_transformation,[status(thm)],[f34]) ).
fof(f38,plain,
! [X0,X1] : r2(sK7_skl(X0,X1),sK4_skl(X0,X1)),
inference(cnf_transformation,[status(thm)],[f34]) ).
fof(f39,plain,
! [X0,X1] : r3(X0,X1,sK7_skl(X1,X0)),
inference(cnf_transformation,[status(thm)],[f34]) ).
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(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] :
( ? [Y5] :
( r1(Y5)
& Y1 = Y5 )
& ? [Y2] :
( ? [Y4] :
( r2(Y4,Y2)
& r1(Y4) )
& ? [Y3] :
( r3(Y3,Y2,Y1)
& r1(Y3) ) ) ),
inference(pre_NNF_transformation,[status(thm)],[f13]) ).
fof(f65,plain,
( r1(sK24_skl)
& sK20_skl = sK24_skl
& r2(sK23_skl,sK21_skl)
& r1(sK23_skl)
& r3(sK22_skl,sK21_skl,sK20_skl)
& r1(sK22_skl) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK20_skl,sK21_skl,sK22_skl,sK23_skl,sK24_skl]),skolemize(Y1,sK20_skl),skolemize(Y2,sK21_skl),skolemize(Y3,sK22_skl),skolemize(Y4,sK23_skl),skolemize(Y5,sK24_skl)],[f64]) ).
fof(f66,plain,
r1(sK22_skl),
inference(cnf_transformation,[status(thm)],[f65]) ).
fof(f67,plain,
r3(sK22_skl,sK21_skl,sK20_skl),
inference(cnf_transformation,[status(thm)],[f65]) ).
fof(f68,plain,
r1(sK23_skl),
inference(cnf_transformation,[status(thm)],[f65]) ).
fof(f69,plain,
r2(sK23_skl,sK21_skl),
inference(cnf_transformation,[status(thm)],[f65]) ).
fof(f70,plain,
sK20_skl = sK24_skl,
inference(cnf_transformation,[status(thm)],[f65]) ).
fof(f71,plain,
r1(sK24_skl),
inference(cnf_transformation,[status(thm)],[f65]) ).
fof(f72,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(f73,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)],[f72]) ).
fof(f74,plain,
! [X0,X1] :
( ~ r1(X0)
| ~ sP0_prd(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f73]) ).
fof(f77,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(f78,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)],[f77]) ).
fof(f79,plain,
! [X0,X1,X2] :
( ~ r2(X2,X0)
| ~ sP1_prd(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f78]) ).
fof(f82,plain,
! [X13,X14,Y22,X15] :
( ( X15 = Y22
| r3(X13,X14,X15)
| sP2_prd(X15,Y22,X14,X13) )
& ( ( X15 != Y22
& ~ r3(X13,X14,X15) )
| ~ sP2_prd(X15,Y22,X14,X13) ) ),
inference(NNF_transformation,[status(thm)],[f24]) ).
fof(f83,plain,
( ! [X13,X14,Y22,X15] :
( X15 = Y22
| r3(X13,X14,X15)
| sP2_prd(X15,Y22,X14,X13) )
& ! [X13,X14,Y22,X15] :
( ( X15 != Y22
& ~ r3(X13,X14,X15) )
| ~ sP2_prd(X15,Y22,X14,X13) ) ),
inference(miniscoping,[status(thm)],[f82]) ).
fof(f84,plain,
! [X0,X1,X2,X3] :
( ~ r3(X3,X2,X0)
| ~ sP2_prd(X0,X1,X2,X3) ),
inference(cnf_transformation,[status(thm)],[f83]) ).
fof(f98,plain,
! [X0,X1] :
( ~ r2(X1,X0)
| ~ r1(X0) ),
inference(destructive_equality_resolution,[status(thm)],[f63]) ).
fof(f104,plain,
r3(sK22_skl,sK21_skl,sK24_skl),
inference(forward_demodulation,[status(thm)],[f70,f67]) ).
fof(f105,plain,
~ r1(sK21_skl),
inference(resolution,[status(thm)],[f98,f69]) ).
fof(f114,plain,
! [X0] :
( X0 = sK0_skl
| ~ r1(X0) ),
inference(resolution,[status(thm)],[f74,f18]) ).
fof(f120,plain,
sK24_skl = sK0_skl,
inference(resolution,[status(thm)],[f114,f71]) ).
fof(f121,plain,
sK23_skl = sK0_skl,
inference(resolution,[status(thm)],[f114,f68]) ).
fof(f122,plain,
sK22_skl = sK0_skl,
inference(resolution,[status(thm)],[f114,f66]) ).
fof(f123,plain,
! [X0] :
( X0 = sK24_skl
| ~ r1(X0) ),
inference(backward_demodulation,[status(thm)],[f120,f114]) ).
fof(f129,plain,
r2(sK24_skl,sK21_skl),
inference(backward_demodulation,[status(thm)],[f131,f69]) ).
fof(f131,plain,
sK23_skl = sK24_skl,
inference(forward_demodulation,[status(thm)],[f120,f121]) ).
fof(f132,plain,
r3(sK24_skl,sK21_skl,sK24_skl),
inference(backward_demodulation,[status(thm)],[f134,f104]) ).
fof(f134,plain,
sK22_skl = sK24_skl,
inference(forward_demodulation,[status(thm)],[f120,f122]) ).
fof(f142,plain,
! [X0] : sK13_skl(X0) = sK24_skl,
inference(resolution,[status(thm)],[f123,f48]) ).
fof(f163,plain,
! [X0] : r3(X0,sK24_skl,sK12_skl(X0)),
inference(forward_demodulation,[status(thm)],[f142,f49]) ).
fof(f164,plain,
! [X0] : r3(X0,sK24_skl,X0),
inference(forward_demodulation,[status(thm)],[f50,f163]) ).
fof(f169,plain,
! [X0,X1] :
( X1 = sK1_skl(X0)
| ~ r2(X0,X1) ),
inference(resolution,[status(thm)],[f79,f23]) ).
fof(f171,plain,
sK21_skl = sK1_skl(sK24_skl),
inference(resolution,[status(thm)],[f169,f129]) ).
fof(f174,plain,
! [X0,X1] : sK6_skl(X0,X1) = sK1_skl(X0),
inference(resolution,[status(thm)],[f169,f35]) ).
fof(f189,plain,
! [X0,X1] : r3(X0,sK1_skl(X1),sK5_skl(X1,X0)),
inference(forward_demodulation,[status(thm)],[f174,f36]) ).
fof(f190,plain,
! [X0] : r3(X0,sK21_skl,sK5_skl(sK24_skl,X0)),
inference(paramodulation,[status(thm)],[f171,f189]) ).
fof(f197,plain,
! [X0,X1] : r2(sK7_skl(X0,X1),sK5_skl(X0,X1)),
inference(forward_demodulation,[status(thm)],[f37,f38]) ).
fof(f198,plain,
! [X0,X1] : sK5_skl(X0,X1) = sK1_skl(sK7_skl(X0,X1)),
inference(resolution,[status(thm)],[f197,f169]) ).
fof(f231,plain,
! [X0,X1,X2] :
( X2 = sK2_skl(X1,X0)
| ~ r3(X0,X1,X2) ),
inference(resolution,[status(thm)],[f84,f28]) ).
fof(f234,plain,
sK24_skl = sK2_skl(sK21_skl,sK24_skl),
inference(resolution,[status(thm)],[f231,f132]) ).
fof(f235,plain,
! [X0] : sK5_skl(sK24_skl,X0) = sK2_skl(sK21_skl,X0),
inference(resolution,[status(thm)],[f231,f190]) ).
fof(f237,plain,
! [X0] : X0 = sK2_skl(sK24_skl,X0),
inference(resolution,[status(thm)],[f231,f164]) ).
fof(f239,plain,
! [X0,X1] : sK7_skl(X0,X1) = sK2_skl(X0,X1),
inference(resolution,[status(thm)],[f231,f39]) ).
fof(f248,plain,
sK24_skl = sK7_skl(sK21_skl,sK24_skl),
inference(backward_demodulation,[status(thm)],[f239,f234]) ).
fof(f249,plain,
! [X0] : X0 = sK7_skl(sK24_skl,X0),
inference(backward_demodulation,[status(thm)],[f239,f237]) ).
fof(f255,plain,
! [X0] : sK5_skl(sK24_skl,X0) = sK1_skl(X0),
inference(paramodulation,[status(thm)],[f249,f198]) ).
fof(f290,plain,
! [X0] : sK1_skl(X0) = sK2_skl(sK21_skl,X0),
inference(forward_demodulation,[status(thm)],[f255,f235]) ).
fof(f291,plain,
sK24_skl = sK1_skl(sK24_skl),
inference(backward_demodulation,[status(thm)],[f292,f248]) ).
fof(f292,plain,
! [X0] : sK1_skl(X0) = sK7_skl(sK21_skl,X0),
inference(forward_demodulation,[status(thm)],[f239,f290]) ).
fof(f296,plain,
sK24_skl = sK21_skl,
inference(forward_demodulation,[status(thm)],[f171,f291]) ).
fof(f309,plain,
~ r1(sK24_skl),
inference(backward_demodulation,[status(thm)],[f296,f105]) ).
fof(f315,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f309,f71]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : NUN085+2 : TPTP v9.3.1. Released v7.3.0.
% 0.00/0.06 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.16/0.42 % Computer : n010.cluster.edu
% 0.16/0.42 % Model : x86_64 x86_64
% 0.16/0.42 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.42 % Memory : 8046.5625MB
% 0.16/0.42 % OS : Linux 6.8.0-71-generic
% 0.16/0.42 % CPULimit : 300
% 0.16/0.42 % WCLimit : 300
% 0.16/0.42 % DateTime : Mon Sep 21 03:25:54 UTC 2026
% 0.16/0.43 % CPUTime :
% 0.16/0.44 % Drodi V4.1.1
% 0.16/0.46 % Refutation found
% 0.16/0.46 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.16/0.46 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.16/0.49 % Elapsed time: 0.056140 seconds
% 0.16/0.49 % CPU time: 0.155455 seconds
% 0.16/0.49 % Total memory used: 54.812 MB
% 0.16/0.49 % Net memory used: 54.747 MB
%------------------------------------------------------------------------------