%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : NUN076+1 : TPTP v9.3.1. Released v7.3.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n015.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 01:57:13 PM UTC 2026
% Result : Theorem 1.45s 0.84s
% Output : CNFRefutation 1.45s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 10
% Syntax : Number of formulae : 65 ( 16 unt; 2 def)
% Number of atoms : 199 ( 0 equ)
% Maximal formula atoms : 7 ( 3 avg)
% Number of connectives : 237 ( 103 ~; 84 |; 48 &)
% ( 2 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 6 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 8 ( 7 usr; 1 prp; 0-3 aty)
% Number of functors : 11 ( 11 usr; 1 con; 0-2 aty)
% Number of variables : 169 ( 140 !; 29 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
? [Y24] :
! [X19] :
( ( ~ id(X19,Y24)
& ~ r1(X19) )
| ( r1(X19)
& id(X19,Y24) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f2,axiom,
! [X11] :
? [Y21] :
! [X12] :
( ( ~ id(X12,Y21)
& ~ r2(X11,X12) )
| ( r2(X11,X12)
& id(X12,Y21) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f6,axiom,
! [X21,X22] :
( id(X22,X21)
| ~ id(X21,X22) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f7,axiom,
! [X23,X24,X25] :
( ~ id(X24,X25)
| id(X23,X25)
| ~ id(X23,X24) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f12,axiom,
! [X1,X8] :
? [Y4] :
( ? [Y7] :
( r3(X1,X8,Y7)
& r2(Y7,Y4) )
& ? [Y5] :
( ? [Y15] :
( r3(X1,Y15,Y5)
& r2(X8,Y15) )
& id(Y5,Y4) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f15,axiom,
! [X4] :
? [Y9] :
( ? [Y16] :
( r3(X4,Y16,Y9)
& r1(Y16) )
& id(Y9,X4) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f16,axiom,
! [X5] :
? [Y8] :
( ? [Y18] :
( r1(Y18)
& id(Y8,Y18) )
& ? [Y17] :
( r4(X5,Y17,Y8)
& r1(Y17) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f19,conjecture,
? [Y1,Y2,Y3] :
( ? [Y5] :
( r3(Y2,Y3,Y5)
& id(Y5,Y1) )
& ? [Y4] :
( ? [Y6] :
( ? [Y7] :
( ? [Y8] :
( r2(Y8,Y7)
& r1(Y8) )
& r2(Y7,Y6) )
& r4(Y6,Y2,Y4) )
& id(Y4,Y1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f20,negated_conjecture,
~ ? [Y1,Y2,Y3] :
( ? [Y5] :
( r3(Y2,Y3,Y5)
& id(Y5,Y1) )
& ? [Y4] :
( ? [Y6] :
( ? [Y7] :
( ? [Y8] :
( r2(Y8,Y7)
& r1(Y8) )
& r2(Y7,Y6) )
& r4(Y6,Y2,Y4) )
& id(Y4,Y1) ) ),
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(f25,plain,
! [X0] :
( ~ id(X0,sK0_skl)
| sP0_prd(X0,sK0_skl) ),
inference(cnf_transformation,[status(thm)],[f23]) ).
fof(f26,definition,
! [X11,Y21,X12] :
( sP1_prd(X12,Y21,X11)
<=> ( r2(X11,X12)
& id(X12,Y21) ) ),
introduced(definition,[new_symbols(definition,[sP1_prd])],[]) ).
fof(f27,plain,
! [X11] :
? [Y21] :
! [X12] :
( ( ~ id(X12,Y21)
& ~ r2(X11,X12) )
| sP1_prd(X12,Y21,X11) ),
inference(formula_renaming,[status(thm)],[f2,f26]) ).
fof(f28,plain,
! [X11,X12] :
( ( ~ id(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))],[f27]) ).
fof(f30,plain,
! [X0,X1] :
( ~ id(X0,sK1_skl(X1))
| sP1_prd(X0,sK1_skl(X1),X1) ),
inference(cnf_transformation,[status(thm)],[f28]) ).
fof(f42,plain,
! [X0,X1] :
( id(X1,X0)
| ~ id(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f6]) ).
fof(f43,plain,
! [X24,X25] :
( ~ id(X24,X25)
| ! [X23] :
( id(X23,X25)
| ~ id(X23,X24) ) ),
inference(miniscoping,[status(thm)],[f7]) ).
fof(f44,plain,
! [X0,X1,X2] :
( ~ id(X1,X2)
| id(X0,X2)
| ~ id(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f43]) ).
fof(f61,plain,
! [X1,X8] :
( r3(X1,X8,sK7_skl(X8,X1))
& r2(sK7_skl(X8,X1),sK4_skl(X8,X1))
& r3(X1,sK6_skl(X8,X1),sK5_skl(X8,X1))
& r2(X8,sK6_skl(X8,X1))
& id(sK5_skl(X8,X1),sK4_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))],[f12]) ).
fof(f63,plain,
! [X0,X1] : r2(X0,sK6_skl(X0,X1)),
inference(cnf_transformation,[status(thm)],[f61]) ).
fof(f74,plain,
! [X4] :
( r3(X4,sK13_skl(X4),sK12_skl(X4))
& r1(sK13_skl(X4))
& id(sK12_skl(X4),X4) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK12_skl,sK13_skl]),skolemize(Y9,sK12_skl(X4)),skolemize(Y16,sK13_skl(X4))],[f15]) ).
fof(f75,plain,
! [X0] : id(sK12_skl(X0),X0),
inference(cnf_transformation,[status(thm)],[f74]) ).
fof(f77,plain,
! [X0] : r3(X0,sK13_skl(X0),sK12_skl(X0)),
inference(cnf_transformation,[status(thm)],[f74]) ).
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,Y2,Y3] :
( ! [Y5] :
( ~ r3(Y2,Y3,Y5)
| ~ id(Y5,Y1) )
| ! [Y4] :
( ! [Y6] :
( ! [Y7] :
( ! [Y8] :
( ~ r2(Y8,Y7)
| ~ r1(Y8) )
| ~ r2(Y7,Y6) )
| ~ r4(Y6,Y2,Y4) )
| ~ id(Y4,Y1) ) ),
inference(pre_NNF_transformation,[status(thm)],[f20]) ).
fof(f92,plain,
! [Y1,Y2] :
( ! [Y5] :
( ! [Y3] : ~ r3(Y2,Y3,Y5)
| ~ id(Y5,Y1) )
| ! [Y4] :
( ! [Y6] :
( ! [Y7] :
( ! [Y8] :
( ~ r2(Y8,Y7)
| ~ r1(Y8) )
| ~ r2(Y7,Y6) )
| ~ r4(Y6,Y2,Y4) )
| ~ id(Y4,Y1) ) ),
inference(miniscoping,[status(thm)],[f91]) ).
fof(f93,plain,
! [X0,X1,X2,X3,X4,X5,X6,X7] :
( ~ r3(X3,X7,X6)
| ~ id(X6,X1)
| ~ r2(X5,X4)
| ~ r1(X5)
| ~ r2(X4,X2)
| ~ r4(X2,X3,X0)
| ~ id(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f92]) ).
fof(f94,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(f95,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)],[f94]) ).
fof(f96,plain,
! [X0,X1] :
( id(X0,X1)
| ~ sP0_prd(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f95]) ).
fof(f97,plain,
! [X0,X1] :
( r1(X0)
| ~ sP0_prd(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f95]) ).
fof(f99,plain,
! [X11,Y21,X12] :
( ( ~ r2(X11,X12)
| ~ id(X12,Y21)
| sP1_prd(X12,Y21,X11) )
& ( ( r2(X11,X12)
& id(X12,Y21) )
| ~ sP1_prd(X12,Y21,X11) ) ),
inference(NNF_transformation,[status(thm)],[f26]) ).
fof(f100,plain,
( ! [X11,Y21,X12] :
( ~ r2(X11,X12)
| ~ id(X12,Y21)
| sP1_prd(X12,Y21,X11) )
& ! [X11,Y21,X12] :
( ( r2(X11,X12)
& id(X12,Y21) )
| ~ sP1_prd(X12,Y21,X11) ) ),
inference(miniscoping,[status(thm)],[f99]) ).
fof(f102,plain,
! [X0,X1,X2] :
( r2(X2,X0)
| ~ sP1_prd(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f100]) ).
fof(f142,plain,
! [X0] : id(X0,sK12_skl(X0)),
inference(resolution,[status(thm)],[f75,f42]) ).
fof(f146,plain,
! [X0,X1] :
( id(X0,sK12_skl(X1))
| ~ id(X0,X1) ),
inference(resolution,[status(thm)],[f142,f44]) ).
fof(f184,plain,
! [X0,X1] :
( id(sK12_skl(X1),X0)
| ~ id(X0,X1) ),
inference(resolution,[status(thm)],[f146,f42]) ).
fof(f196,plain,
! [X0] : id(sK16_skl(X0),sK14_skl(X0)),
inference(resolution,[status(thm)],[f81,f42]) ).
fof(f198,plain,
! [X0] :
( ~ r1(X0)
| id(X0,sK0_skl) ),
inference(resolution,[status(thm)],[f96,f24]) ).
fof(f201,plain,
! [X0,X1] :
( id(X0,sK14_skl(X1))
| ~ id(X0,sK16_skl(X1)) ),
inference(resolution,[status(thm)],[f196,f44]) ).
fof(f207,plain,
! [X0] :
( id(sK0_skl,X0)
| ~ r1(X0) ),
inference(resolution,[status(thm)],[f198,f42]) ).
fof(f250,plain,
! [X0,X1,X2,X3,X4,X5] :
( ~ r3(sK15_skl(X0),X5,X4)
| ~ id(X4,X1)
| ~ r2(X3,X2)
| ~ r1(X3)
| ~ r2(X2,X0)
| ~ id(sK14_skl(X0),X1) ),
inference(resolution,[status(thm)],[f80,f93]) ).
fof(f253,plain,
! [X0,X1] :
( ~ id(X1,sK1_skl(X0))
| r2(X0,X1) ),
inference(resolution,[status(thm)],[f102,f30]) ).
fof(f301,plain,
! [X0,X1,X2,X3] :
( ~ id(sK12_skl(sK15_skl(X0)),X1)
| ~ r2(X3,X2)
| ~ r1(X3)
| ~ r2(X2,X0)
| ~ id(sK14_skl(X0),X1) ),
inference(resolution,[status(thm)],[f250,f77]) ).
fof(f477,plain,
! [X0] : r2(X0,sK12_skl(sK1_skl(X0))),
inference(resolution,[status(thm)],[f253,f75]) ).
fof(f684,plain,
! [X0,X1,X2,X3] :
( ~ id(X1,sK15_skl(X0))
| ~ r2(X3,X2)
| ~ r1(X3)
| ~ r2(X2,X0)
| ~ id(sK14_skl(X0),X1) ),
inference(resolution,[status(thm)],[f301,f184]) ).
fof(f785,plain,
! [X0,X1,X2] :
( ~ r1(sK14_skl(X1))
| ~ id(sK0_skl,sK15_skl(X1))
| ~ r2(X2,X0)
| ~ r1(X2)
| ~ r2(X0,X1) ),
inference(resolution,[status(thm)],[f684,f198]) ).
fof(f1637,plain,
! [X0,X1,X2] :
( ~ r1(sK15_skl(X1))
| ~ r1(sK14_skl(X1))
| ~ r2(X2,X0)
| ~ r1(X2)
| ~ r2(X0,X1) ),
inference(resolution,[status(thm)],[f785,f207]) ).
fof(f1638,plain,
! [X0,X1,X2] :
( ~ r1(sK14_skl(X1))
| ~ r2(X2,X0)
| ~ r1(X2)
| ~ r2(X0,X1) ),
inference(forward_subsumption_resolution,[status(thm)],[f1637,f79]) ).
fof(f1686,plain,
! [X0,X1,X2] :
( ~ r1(sK14_skl(X2))
| ~ r1(X0)
| ~ r2(sK6_skl(X0,X1),X2) ),
inference(resolution,[status(thm)],[f1638,f63]) ).
fof(f1776,plain,
! [X0,X1] :
( ~ r1(sK14_skl(sK12_skl(sK1_skl(sK6_skl(X0,X1)))))
| ~ r1(X0) ),
inference(resolution,[status(thm)],[f1686,f477]) ).
fof(f1888,plain,
! [X0] :
( ~ r1(sK16_skl(X0))
| id(sK0_skl,sK14_skl(X0)) ),
inference(resolution,[status(thm)],[f201,f207]) ).
fof(f1898,plain,
! [X0] : id(sK0_skl,sK14_skl(X0)),
inference(forward_subsumption_resolution,[status(thm)],[f1888,f82]) ).
fof(f1905,plain,
! [X0] : id(sK14_skl(X0),sK0_skl),
inference(resolution,[status(thm)],[f1898,f42]) ).
fof(f1929,plain,
! [X0] : sP0_prd(sK14_skl(X0),sK0_skl),
inference(resolution,[status(thm)],[f1905,f25]) ).
fof(f1965,plain,
! [X0] : r1(sK14_skl(X0)),
inference(resolution,[status(thm)],[f1929,f97]) ).
fof(f1971,plain,
! [X0] : ~ r1(X0),
inference(backward_subsumption_resolution,[status(thm)],[f1776,f1965]) ).
fof(f1996,plain,
$false,
inference(backward_subsumption_resolution,[status(thm)],[f1965,f1971]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUN076+1 : TPTP v9.3.1. Released v7.3.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.37 % Computer : n015.cluster.edu
% 0.09/0.37 % Model : x86_64 x86_64
% 0.09/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.37 % Memory : 8046.5625MB
% 0.09/0.37 % OS : Linux 6.8.0-71-generic
% 0.09/0.37 % CPULimit : 300
% 0.09/0.37 % WCLimit : 300
% 0.09/0.37 % DateTime : Mon Sep 21 03:27:52 UTC 2026
% 0.09/0.38 % CPUTime :
% 0.09/0.38 % Drodi V4.1.1
% 1.45/0.84 % Refutation found
% 1.45/0.84 % SZS status Theorem for theBenchmark: Theorem is valid
% 1.45/0.84 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 1.45/0.86 % Elapsed time: 0.481142 seconds
% 1.45/0.86 % CPU time: 3.567667 seconds
% 1.45/0.86 % Total memory used: 46.669 MB
% 1.45/0.86 % Net memory used: 40.302 MB
%------------------------------------------------------------------------------