%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : NUN054+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 : n019.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 01:57:08 PM UTC 2026
% Result : Theorem 0.10s 0.39s
% Output : CNFRefutation 0.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 11
% Syntax : Number of formulae : 78 ( 26 unt; 5 def)
% Number of atoms : 214 ( 52 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 235 ( 99 ~; 80 |; 51 &)
% ( 5 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 10 ( 8 usr; 3 prp; 0-4 aty)
% Number of functors : 9 ( 9 usr; 1 con; 0-2 aty)
% Number of variables : 178 ( 154 !; 24 ?)
% 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(f3,axiom,
! [X13,X14] :
? [Y22] :
! [X15] :
( ( X15 = Y22
& r3(X13,X14,X15) )
| ( X15 != Y22
& ~ r3(X13,X14,X15) ) ),
file('/export/starexec/sandbox/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/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] :
( ? [Y3] :
( ? [Y6] :
( r2(Y6,Y3)
& r1(Y6) )
& Y1 = Y3 )
& ? [Y2] :
( ? [Y5] :
( r2(Y5,Y2)
& r1(Y5) )
& ? [Y4] :
( r3(Y4,Y2,Y1)
& r1(Y4) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f13,negated_conjecture,
~ ? [Y1] :
( ? [Y3] :
( ? [Y6] :
( r2(Y6,Y3)
& r1(Y6) )
& Y1 = Y3 )
& ? [Y2] :
( ? [Y5] :
( r2(Y5,Y2)
& r1(Y5) )
& ? [Y4] :
( r3(Y4,Y2,Y1)
& r1(Y4) ) ) ),
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(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(f64,plain,
! [Y1] :
( ! [Y3] :
( ! [Y6] :
( ~ r2(Y6,Y3)
| ~ r1(Y6) )
| Y1 != Y3 )
| ! [Y2] :
( ! [Y5] :
( ~ r2(Y5,Y2)
| ~ r1(Y5) )
| ! [Y4] :
( ~ r3(Y4,Y2,Y1)
| ~ r1(Y4) ) ) ),
inference(pre_NNF_transformation,[status(thm)],[f13]) ).
fof(f65,plain,
! [X0,X1,X2,X3,X4,X5] :
( ~ r2(X5,X4)
| ~ r1(X5)
| X2 != X4
| ~ r2(X3,X1)
| ~ r1(X3)
| ~ r3(X0,X1,X2)
| ~ 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(f71,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(f72,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)],[f71]) ).
fof(f73,plain,
! [X0,X1,X2] :
( ~ r2(X2,X0)
| ~ sP1_prd(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f72]) ).
fof(f74,plain,
! [X0,X1,X2] :
( X0 != X1
| ~ sP1_prd(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f72]) ).
fof(f76,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(f77,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)],[f76]) ).
fof(f78,plain,
! [X0,X1,X2,X3] :
( ~ r3(X3,X2,X0)
| ~ sP2_prd(X0,X1,X2,X3) ),
inference(cnf_transformation,[status(thm)],[f77]) ).
fof(f93,plain,
! [X0,X1,X2,X3,X4] :
( ~ r2(X4,X2)
| ~ r1(X4)
| ~ r2(X3,X1)
| ~ r1(X3)
| ~ r3(X0,X1,X2)
| ~ 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(f95,plain,
! [X0,X1] : ~ sP1_prd(X0,X0,X1),
inference(destructive_equality_resolution,[status(thm)],[f74]) ).
fof(f99,plain,
r1(sK0_skl),
inference(resolution,[status(thm)],[f17,f94]) ).
fof(f108,plain,
! [X0] :
( ~ r1(X0)
| X0 = sK0_skl ),
inference(resolution,[status(thm)],[f18,f68]) ).
fof(f112,plain,
! [X0] : sK13_skl(X0) = sK0_skl,
inference(resolution,[status(thm)],[f108,f48]) ).
fof(f119,plain,
! [X0] : r2(X0,sK1_skl(X0)),
inference(resolution,[status(thm)],[f22,f95]) ).
fof(f128,plain,
! [X0] : r3(X0,sK0_skl,sK12_skl(X0)),
inference(forward_demodulation,[status(thm)],[f112,f49]) ).
fof(f129,plain,
! [X0] : r3(X0,sK0_skl,X0),
inference(forward_demodulation,[status(thm)],[f50,f128]) ).
fof(f142,plain,
! [X0,X1] :
( X1 = sK1_skl(X0)
| ~ r2(X0,X1) ),
inference(resolution,[status(thm)],[f73,f23]) ).
fof(f146,plain,
! [X0,X1] : sK6_skl(X0,X1) = sK1_skl(X0),
inference(resolution,[status(thm)],[f142,f35]) ).
fof(f153,plain,
! [X0,X1] : r2(sK7_skl(X0,X1),sK5_skl(X0,X1)),
inference(forward_demodulation,[status(thm)],[f37,f38]) ).
fof(f154,plain,
! [X0,X1] : sK5_skl(X0,X1) = sK1_skl(sK7_skl(X0,X1)),
inference(resolution,[status(thm)],[f153,f142]) ).
fof(f170,plain,
! [X0,X1] : r3(X0,sK1_skl(X1),sK5_skl(X1,X0)),
inference(forward_demodulation,[status(thm)],[f146,f36]) ).
fof(f171,plain,
! [X0,X1,X2,X3] :
( ~ r2(X3,sK5_skl(X2,X0))
| ~ r1(X3)
| ~ r2(X1,sK1_skl(X2))
| ~ r1(X1)
| ~ r1(X0) ),
inference(resolution,[status(thm)],[f170,f93]) ).
fof(f179,plain,
! [X0,X1,X2] :
( X2 = sK2_skl(X1,X0)
| ~ r3(X0,X1,X2) ),
inference(resolution,[status(thm)],[f78,f28]) ).
fof(f183,plain,
! [X0] : X0 = sK2_skl(sK0_skl,X0),
inference(resolution,[status(thm)],[f179,f129]) ).
fof(f185,plain,
! [X0,X1] : sK7_skl(X0,X1) = sK2_skl(X0,X1),
inference(resolution,[status(thm)],[f179,f39]) ).
fof(f192,plain,
! [X0] : X0 = sK7_skl(sK0_skl,X0),
inference(backward_demodulation,[status(thm)],[f185,f183]) ).
fof(f199,plain,
! [X0] : sK5_skl(sK0_skl,X0) = sK1_skl(X0),
inference(paramodulation,[status(thm)],[f192,f154]) ).
fof(f219,plain,
! [X0,X1,X2] :
( ~ r2(X2,sK1_skl(X0))
| ~ r1(X2)
| ~ r2(X1,sK1_skl(sK0_skl))
| ~ r1(X1)
| ~ r1(X0) ),
inference(paramodulation,[status(thm)],[f199,f171]) ).
fof(f220,definition,
! [X0,X2] :
( sQ2_spl
<=> ( ~ r2(X2,sK1_skl(X0))
| ~ r1(X2)
| ~ r1(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f221,plain,
! [X0,X1] :
( ~ sQ2_spl
| ~ r2(X1,sK1_skl(X0))
| ~ r1(X1)
| ~ r1(X0) ),
inference(component_clause,[status(thm)],[f220]) ).
fof(f223,definition,
! [X1] :
( sQ3_spl
<=> ( ~ r2(X1,sK1_skl(sK0_skl))
| ~ r1(X1) ) ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f224,plain,
! [X0] :
( ~ sQ3_spl
| ~ r2(X0,sK1_skl(sK0_skl))
| ~ r1(X0) ),
inference(component_clause,[status(thm)],[f223]) ).
fof(f226,plain,
( sQ3_spl
| sQ2_spl ),
inference(split_clause,[status(thm)],[f219,f220,f223]) ).
fof(f227,plain,
! [X0] :
( ~ sQ2_spl
| ~ r1(X0)
| ~ r1(X0) ),
inference(resolution,[status(thm)],[f221,f119]) ).
fof(f229,plain,
! [X0] :
( ~ sQ2_spl
| ~ r1(X0) ),
inference(duplicate_literals_removal,[status(thm)],[f227]) ).
fof(f234,plain,
( ~ sQ2_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f99,f229]) ).
fof(f235,plain,
~ sQ2_spl,
inference(contradiction_clause,[status(thm)],[f234]) ).
fof(f236,plain,
( ~ sQ3_spl
| ~ r1(sK0_skl) ),
inference(resolution,[status(thm)],[f224,f119]) ).
fof(f261,plain,
( ~ sQ3_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f99,f236]) ).
fof(f262,plain,
~ sQ3_spl,
inference(contradiction_clause,[status(thm)],[f261]) ).
fof(f263,plain,
$false,
inference(sat_refutation,[status(thm)],[f226,f235,f262]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUN054+2 : TPTP v9.3.1. Released v7.3.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.36 % Computer : n019.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Mon Sep 21 03:23:04 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 % Drodi V4.1.1
% 0.10/0.39 % Refutation found
% 0.10/0.39 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.10/0.39 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.10/0.43 % Elapsed time: 0.049934 seconds
% 0.10/0.43 % CPU time: 0.165903 seconds
% 0.10/0.43 % Total memory used: 103.186 MB
% 0.10/0.43 % Net memory used: 102.922 MB
%------------------------------------------------------------------------------