%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : NUN087+1 : TPTP v9.3.1. Released v7.3.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n018.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 8.70s 1.61s
% Output : CNFRefutation 8.95s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 7
% Syntax : Number of formulae : 41 ( 8 unt; 2 def)
% Number of atoms : 134 ( 0 equ)
% Maximal formula atoms : 7 ( 3 avg)
% Number of connectives : 171 ( 78 ~; 62 |; 29 &)
% ( 2 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 6 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 6 ( 5 usr; 1 prp; 0-6 aty)
% Number of functors : 4 ( 4 usr; 1 con; 0-1 aty)
% Number of variables : 120 ( 109 !; 11 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
? [Y24] :
! [X19] :
( ( ~ id(X19,Y24)
& ~ r1(X19) )
| ( r1(X19)
& id(X19,Y24) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f5,axiom,
! [X20] : id(X20,X20),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f11,axiom,
! [X38,X39,X40,X41,X42,X43] :
( ( r4(X41,X42,X43)
& r4(X38,X39,X40) )
| ( ~ r4(X41,X42,X43)
& ~ r4(X38,X39,X40) )
| ~ id(X40,X43)
| ~ id(X39,X42)
| ~ id(X38,X41) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f16,axiom,
! [X5] :
? [Y8] :
( ? [Y18] :
( r1(Y18)
& id(Y8,Y18) )
& ? [Y17] :
( r4(X5,Y17,Y8)
& r1(Y17) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f19,conjecture,
? [Y1] :
( ? [Y3] :
( r1(Y3)
& id(Y1,Y3) )
& ? [Y2] :
( r4(Y2,Y2,Y1)
& r1(Y2) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f20,negated_conjecture,
~ ? [Y1] :
( ? [Y3] :
( r1(Y3)
& id(Y1,Y3) )
& ? [Y2] :
( r4(Y2,Y2,Y1)
& r1(Y2) ) ),
inference(negated_conjecture,[status(cth)],[f19]) ).
fof(f21,definition,
! [Y24,X19] :
( sP0_prd(X19,Y24)
<=> ( r1(X19)
& id(X19,Y24) ) ),
introduced(definition,[new_symbols(definition,[sP0_prd])],[]) ).
fof(f22,plain,
? [Y24] :
! [X19] :
( ( ~ id(X19,Y24)
& ~ r1(X19) )
| sP0_prd(X19,Y24) ),
inference(formula_renaming,[status(thm)],[f1,f21]) ).
fof(f23,plain,
! [X19] :
( ( ~ id(X19,sK0_skl)
& ~ r1(X19) )
| sP0_prd(X19,sK0_skl) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl]),skolemize(Y24,sK0_skl)],[f22]) ).
fof(f24,plain,
! [X0] :
( ~ r1(X0)
| sP0_prd(X0,sK0_skl) ),
inference(cnf_transformation,[status(thm)],[f23]) ).
fof(f41,plain,
! [X0] : id(X0,X0),
inference(cnf_transformation,[status(thm)],[f5]) ).
fof(f57,definition,
! [X38,X39,X40,X41,X42,X43] :
( sP7_prd(X43,X42,X41,X40,X39,X38)
<=> ( ~ r4(X41,X42,X43)
& ~ r4(X38,X39,X40) ) ),
introduced(definition,[new_symbols(definition,[sP7_prd])],[]) ).
fof(f58,plain,
! [X38,X39,X40,X41,X42,X43] :
( ( r4(X41,X42,X43)
& r4(X38,X39,X40) )
| sP7_prd(X43,X42,X41,X40,X39,X38)
| ~ id(X40,X43)
| ~ id(X39,X42)
| ~ id(X38,X41) ),
inference(formula_renaming,[status(thm)],[f11,f57]) ).
fof(f59,plain,
! [X0,X1,X2,X3,X4,X5] :
( r4(X0,X2,X4)
| sP7_prd(X5,X3,X1,X4,X2,X0)
| ~ id(X4,X5)
| ~ id(X2,X3)
| ~ id(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f58]) ).
fof(f78,plain,
! [X5] :
( r1(sK16_skl(X5))
& id(sK14_skl(X5),sK16_skl(X5))
& r4(X5,sK15_skl(X5),sK14_skl(X5))
& r1(sK15_skl(X5)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK14_skl,sK15_skl,sK16_skl]),skolemize(Y8,sK14_skl(X5)),skolemize(Y17,sK15_skl(X5)),skolemize(Y18,sK16_skl(X5))],[f16]) ).
fof(f79,plain,
! [X0] : r1(sK15_skl(X0)),
inference(cnf_transformation,[status(thm)],[f78]) ).
fof(f80,plain,
! [X0] : r4(X0,sK15_skl(X0),sK14_skl(X0)),
inference(cnf_transformation,[status(thm)],[f78]) ).
fof(f81,plain,
! [X0] : id(sK14_skl(X0),sK16_skl(X0)),
inference(cnf_transformation,[status(thm)],[f78]) ).
fof(f82,plain,
! [X0] : r1(sK16_skl(X0)),
inference(cnf_transformation,[status(thm)],[f78]) ).
fof(f91,plain,
! [Y1] :
( ! [Y3] :
( ~ r1(Y3)
| ~ id(Y1,Y3) )
| ! [Y2] :
( ~ r4(Y2,Y2,Y1)
| ~ r1(Y2) ) ),
inference(pre_NNF_transformation,[status(thm)],[f20]) ).
fof(f92,plain,
! [X0,X1,X2] :
( ~ r1(X2)
| ~ id(X1,X2)
| ~ r4(X0,X0,X1)
| ~ r1(X0) ),
inference(cnf_transformation,[status(thm)],[f91]) ).
fof(f93,plain,
! [Y24,X19] :
( ( ~ r1(X19)
| ~ id(X19,Y24)
| sP0_prd(X19,Y24) )
& ( ( r1(X19)
& id(X19,Y24) )
| ~ sP0_prd(X19,Y24) ) ),
inference(NNF_transformation,[status(thm)],[f21]) ).
fof(f94,plain,
( ! [Y24,X19] :
( ~ r1(X19)
| ~ id(X19,Y24)
| sP0_prd(X19,Y24) )
& ! [Y24,X19] :
( ( r1(X19)
& id(X19,Y24) )
| ~ sP0_prd(X19,Y24) ) ),
inference(miniscoping,[status(thm)],[f93]) ).
fof(f95,plain,
! [X0,X1] :
( id(X0,X1)
| ~ sP0_prd(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f94]) ).
fof(f96,plain,
! [X0,X1] :
( r1(X0)
| ~ sP0_prd(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f94]) ).
fof(f128,plain,
! [X38,X39,X40,X41,X42,X43] :
( ( r4(X41,X42,X43)
| r4(X38,X39,X40)
| sP7_prd(X43,X42,X41,X40,X39,X38) )
& ( ( ~ r4(X41,X42,X43)
& ~ r4(X38,X39,X40) )
| ~ sP7_prd(X43,X42,X41,X40,X39,X38) ) ),
inference(NNF_transformation,[status(thm)],[f57]) ).
fof(f129,plain,
( ! [X38,X39,X40,X41,X42,X43] :
( r4(X41,X42,X43)
| r4(X38,X39,X40)
| sP7_prd(X43,X42,X41,X40,X39,X38) )
& ! [X38,X39,X40,X41,X42,X43] :
( ( ~ r4(X41,X42,X43)
& ~ r4(X38,X39,X40) )
| ~ sP7_prd(X43,X42,X41,X40,X39,X38) ) ),
inference(miniscoping,[status(thm)],[f128]) ).
fof(f131,plain,
! [X0,X1,X2,X3,X4,X5] :
( ~ r4(X2,X1,X0)
| ~ sP7_prd(X0,X1,X2,X3,X4,X5) ),
inference(cnf_transformation,[status(thm)],[f129]) ).
fof(f141,plain,
! [X0,X1,X2,X3] :
( ~ id(X3,X0)
| ~ r4(X2,X2,X3)
| ~ r1(X2)
| ~ sP0_prd(X0,X1) ),
inference(resolution,[status(thm)],[f96,f92]) ).
fof(f556,plain,
! [X0,X1,X2,X3,X4,X5] :
( r4(X3,X4,X5)
| ~ id(X5,X2)
| ~ id(X4,X1)
| ~ id(X3,X0)
| ~ r4(X0,X1,X2) ),
inference(resolution,[status(thm)],[f131,f59]) ).
fof(f1030,plain,
! [X0,X1,X2,X3] :
( r4(X0,X2,X3)
| ~ id(X3,sK14_skl(X1))
| ~ id(X2,sK15_skl(X1))
| ~ id(X0,X1) ),
inference(resolution,[status(thm)],[f556,f80]) ).
fof(f3088,plain,
! [X0,X1,X2] :
( r4(X0,sK15_skl(X1),X2)
| ~ id(X2,sK14_skl(X1))
| ~ id(X0,X1) ),
inference(resolution,[status(thm)],[f1030,f41]) ).
fof(f4280,plain,
! [X0,X1] :
( r4(X0,sK15_skl(X1),sK14_skl(X1))
| ~ id(X0,X1) ),
inference(resolution,[status(thm)],[f3088,f41]) ).
fof(f4289,plain,
! [X0,X1,X2] :
( ~ id(sK14_skl(X0),X1)
| ~ r1(sK15_skl(X0))
| ~ sP0_prd(X1,X2)
| ~ id(sK15_skl(X0),X0) ),
inference(resolution,[status(thm)],[f4280,f141]) ).
fof(f4299,plain,
! [X0,X1,X2] :
( ~ id(sK14_skl(X0),X1)
| ~ sP0_prd(X1,X2)
| ~ id(sK15_skl(X0),X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f4289,f79]) ).
fof(f4398,plain,
! [X0,X1] :
( ~ r1(X1)
| ~ id(sK14_skl(X0),X1)
| ~ id(sK15_skl(X0),X0) ),
inference(resolution,[status(thm)],[f4299,f24]) ).
fof(f4403,plain,
! [X0,X1] :
( ~ sP0_prd(sK15_skl(X0),X0)
| ~ r1(X1)
| ~ id(sK14_skl(X0),X1) ),
inference(resolution,[status(thm)],[f4398,f95]) ).
fof(f4407,plain,
! [X0] :
( ~ r1(sK15_skl(sK0_skl))
| ~ r1(X0)
| ~ id(sK14_skl(sK0_skl),X0) ),
inference(resolution,[status(thm)],[f4403,f24]) ).
fof(f4409,plain,
! [X0] :
( ~ r1(X0)
| ~ id(sK14_skl(sK0_skl),X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f4407,f79]) ).
fof(f4412,plain,
~ r1(sK16_skl(sK0_skl)),
inference(resolution,[status(thm)],[f4409,f81]) ).
fof(f4421,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f4412,f82]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : NUN087+1 : TPTP v9.3.1. Released v7.3.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.35 % Computer : n018.cluster.edu
% 0.08/0.35 % Model : x86_64 x86_64
% 0.08/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.35 % Memory : 8046.5625MB
% 0.08/0.35 % OS : Linux 6.8.0-71-generic
% 0.08/0.35 % CPULimit : 300
% 0.08/0.35 % WCLimit : 300
% 0.08/0.35 % DateTime : Mon Sep 21 03:27:28 UTC 2026
% 0.08/0.36 % CPUTime :
% 0.08/0.36 % Drodi V4.1.1
% 8.70/1.61 % Refutation found
% 8.70/1.61 % SZS status Theorem for theBenchmark: Theorem is valid
% 8.70/1.61 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 8.95/1.64 % Elapsed time: 1.270764 seconds
% 8.95/1.64 % CPU time: 9.742030 seconds
% 8.95/1.64 % Total memory used: 95.125 MB
% 8.95/1.64 % Net memory used: 76.288 MB
%------------------------------------------------------------------------------