%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : NUN059+2 : TPTP v9.3.1. Bugfixed v7.4.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n008.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 01:57:09 PM UTC 2026
% Result : Theorem 0.11s 0.40s
% Output : CNFRefutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 6
% Syntax : Number of formulae : 42 ( 18 unt; 2 def)
% Number of atoms : 103 ( 26 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 104 ( 43 ~; 32 |; 27 &)
% ( 2 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 5 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 2 prp; 0-3 aty)
% Number of functors : 6 ( 6 usr; 1 con; 0-1 aty)
% Number of variables : 90 ( 69 !; 21 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
? [Y24] :
! [X19] :
( ( X19 = Y24
& r1(X19) )
| ( X19 != Y24
& ~ r1(X19) ) ),
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(f9,axiom,
! [X5] :
? [Y8] :
( ? [Y18] :
( Y8 = Y18
& r1(Y18) )
& ? [Y17] :
( r4(X5,Y17,Y8)
& r1(Y17) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f12,conjecture,
? [Y1,Y3,Y2,Y4] :
( ? [Y6] :
( ? [Y7] :
( r3(Y7,Y6,Y4)
& r4(Y1,Y1,Y7) )
& r4(Y3,Y3,Y6) )
& ? [Y5] :
( Y4 = Y5
& r4(Y2,Y2,Y5) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f13,negated_conjecture,
~ ? [Y1,Y3,Y2,Y4] :
( ? [Y6] :
( ? [Y7] :
( r3(Y7,Y6,Y4)
& r4(Y1,Y1,Y7) )
& r4(Y3,Y3,Y6) )
& ? [Y5] :
( Y4 = Y5
& r4(Y2,Y2,Y5) ) ),
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(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(f51,plain,
! [X5] :
( sK14_skl(X5) = sK16_skl(X5)
& r1(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))],[f9]) ).
fof(f52,plain,
! [X0] : r1(sK15_skl(X0)),
inference(cnf_transformation,[status(thm)],[f51]) ).
fof(f53,plain,
! [X0] : r4(X0,sK15_skl(X0),sK14_skl(X0)),
inference(cnf_transformation,[status(thm)],[f51]) ).
fof(f54,plain,
! [X0] : r1(sK16_skl(X0)),
inference(cnf_transformation,[status(thm)],[f51]) ).
fof(f55,plain,
! [X0] : sK14_skl(X0) = sK16_skl(X0),
inference(cnf_transformation,[status(thm)],[f51]) ).
fof(f64,plain,
! [Y1,Y3,Y2,Y4] :
( ! [Y6] :
( ! [Y7] :
( ~ r3(Y7,Y6,Y4)
| ~ r4(Y1,Y1,Y7) )
| ~ r4(Y3,Y3,Y6) )
| ! [Y5] :
( Y4 != Y5
| ~ r4(Y2,Y2,Y5) ) ),
inference(pre_NNF_transformation,[status(thm)],[f13]) ).
fof(f65,plain,
! [Y4] :
( ! [Y6] :
( ! [Y7] :
( ~ r3(Y7,Y6,Y4)
| ! [Y1] : ~ r4(Y1,Y1,Y7) )
| ! [Y3] : ~ r4(Y3,Y3,Y6) )
| ! [Y5] :
( Y4 != Y5
| ! [Y2] : ~ r4(Y2,Y2,Y5) ) ),
inference(miniscoping,[status(thm)],[f64]) ).
fof(f66,plain,
! [X0,X1,X2,X3,X4,X5,X6] :
( ~ r3(X6,X4,X2)
| ~ r4(X5,X5,X6)
| ~ r4(X3,X3,X4)
| X2 != X1
| ~ r4(X0,X0,X1) ),
inference(cnf_transformation,[status(thm)],[f65]) ).
fof(f67,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(f68,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)],[f67]) ).
fof(f69,plain,
! [X0,X1] :
( ~ r1(X0)
| ~ sP0_prd(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f68]) ).
fof(f94,plain,
! [X0,X1,X2,X3,X4,X5] :
( ~ r3(X5,X3,X1)
| ~ r4(X4,X4,X5)
| ~ r4(X2,X2,X3)
| ~ r4(X0,X0,X1) ),
inference(destructive_equality_resolution,[status(thm)],[f66]) ).
fof(f100,plain,
! [X0,X1,X2,X3] :
( ~ r3(X3,X3,X1)
| ~ r4(X2,X2,X3)
| ~ r4(X0,X0,X1) ),
inference(factoring,[status(thm)],[f94]) ).
fof(f107,plain,
! [X0] :
( X0 = sK0_skl
| ~ r1(X0) ),
inference(resolution,[status(thm)],[f69,f18]) ).
fof(f109,plain,
! [X0] : sK16_skl(X0) = sK0_skl,
inference(resolution,[status(thm)],[f107,f54]) ).
fof(f110,plain,
! [X0] : sK15_skl(X0) = sK0_skl,
inference(resolution,[status(thm)],[f107,f52]) ).
fof(f112,plain,
! [X0] : sK13_skl(X0) = sK0_skl,
inference(resolution,[status(thm)],[f107,f48]) ).
fof(f113,plain,
! [X0] : sK14_skl(X0) = sK0_skl,
inference(backward_demodulation,[status(thm)],[f109,f55]) ).
fof(f137,plain,
! [X0] : r3(X0,sK0_skl,sK12_skl(X0)),
inference(forward_demodulation,[status(thm)],[f112,f49]) ).
fof(f138,plain,
! [X0] : r3(X0,sK0_skl,X0),
inference(forward_demodulation,[status(thm)],[f50,f137]) ).
fof(f140,plain,
! [X0,X1] :
( ~ r4(X1,X1,sK0_skl)
| ~ r4(X0,X0,sK0_skl) ),
inference(resolution,[status(thm)],[f138,f100]) ).
fof(f145,definition,
! [X2] :
( sQ1_spl
<=> ~ r4(X2,X2,sK0_skl) ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f146,plain,
! [X0] :
( ~ sQ1_spl
| ~ r4(X0,X0,sK0_skl) ),
inference(component_clause,[status(thm)],[f145]) ).
fof(f149,plain,
sQ1_spl,
inference(split_clause,[status(thm)],[f140,f145]) ).
fof(f154,plain,
! [X0] : r4(X0,sK0_skl,sK14_skl(X0)),
inference(forward_demodulation,[status(thm)],[f110,f53]) ).
fof(f155,plain,
! [X0] : r4(X0,sK0_skl,sK0_skl),
inference(forward_demodulation,[status(thm)],[f113,f154]) ).
fof(f156,plain,
( ~ sQ1_spl
| $false ),
inference(resolution,[status(thm)],[f155,f146]) ).
fof(f162,plain,
~ sQ1_spl,
inference(contradiction_clause,[status(thm)],[f156]) ).
fof(f163,plain,
$false,
inference(sat_refutation,[status(thm)],[f149,f162]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUN059+2 : TPTP v9.3.1. Bugfixed v7.4.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.11/0.37 % Computer : n008.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Mon Sep 21 03:24:24 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.39 % Drodi V4.1.1
% 0.11/0.40 % Refutation found
% 0.11/0.40 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.11/0.40 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.14/0.51 % Elapsed time: 0.129866 seconds
% 0.14/0.51 % CPU time: 0.110148 seconds
% 0.14/0.51 % Total memory used: 6.504 MB
% 0.14/0.51 % Net memory used: 6.501 MB
%------------------------------------------------------------------------------