%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : NUN062+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 : n011.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 01:57:10 PM UTC 2026
% Result : Theorem 0.04s 20.37s
% Output : CNFRefutation 0.04s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 6
% Syntax : Number of formulae : 39 ( 7 unt; 2 def)
% Number of atoms : 112 ( 39 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 131 ( 58 ~; 46 |; 25 &)
% ( 2 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 6 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 1 prp; 0-4 aty)
% Number of functors : 4 ( 4 usr; 1 con; 0-2 aty)
% Number of variables : 120 ( 106 !; 14 ?)
% Comments :
%------------------------------------------------------------------------------
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(f11,axiom,
! [X7,Y10] :
( ~ r2(X7,Y10)
| ! [Y20] :
( Y20 != Y10
| ~ r1(Y20) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f12,conjecture,
! [X1] :
? [Y2,Y1] :
( ? [Y3] :
( Y3 = Y2
& r3(X1,Y1,Y3) )
& ! [Y4] :
( Y1 != Y4
| ~ r1(Y4) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f13,negated_conjecture,
~ ! [X1] :
? [Y2,Y1] :
( ? [Y3] :
( Y3 = Y2
& r3(X1,Y1,Y3) )
& ! [Y4] :
( Y1 != Y4
| ~ r1(Y4) ) ),
inference(negated_conjecture,[status(cth)],[f12]) ).
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(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(f27,plain,
! [X0,X1,X2] :
( r3(X2,X1,X0)
| sP2_prd(X0,sK2_skl(X1,X2),X1,X2) ),
inference(cnf_transformation,[status(thm)],[f26]) ).
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,
? [X1] :
! [Y2,Y1] :
( ! [Y3] :
( Y3 != Y2
| ~ r3(X1,Y1,Y3) )
| ? [Y4] :
( Y1 = Y4
& r1(Y4) ) ),
inference(pre_NNF_transformation,[status(thm)],[f13]) ).
fof(f65,plain,
? [X1] :
! [Y1] :
( ! [Y3] :
( ! [Y2] : Y3 != Y2
| ~ r3(X1,Y1,Y3) )
| ? [Y4] :
( Y1 = Y4
& r1(Y4) ) ),
inference(miniscoping,[status(thm)],[f64]) ).
fof(f66,plain,
! [Y1] :
( ! [Y3] :
( ! [Y2] : Y3 != Y2
| ~ r3(sK20_skl,Y1,Y3) )
| ( Y1 = sK21_skl(Y1)
& r1(sK21_skl(Y1)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK20_skl,sK21_skl]),skolemize(X1,sK20_skl),skolemize(Y4,sK21_skl(Y1))],[f65]) ).
fof(f67,plain,
! [X0,X1,X2] :
( X1 != X2
| ~ r3(sK20_skl,X0,X1)
| r1(sK21_skl(X0)) ),
inference(cnf_transformation,[status(thm)],[f66]) ).
fof(f68,plain,
! [X0,X1,X2] :
( X1 != X2
| ~ r3(sK20_skl,X0,X1)
| X0 = sK21_skl(X0) ),
inference(cnf_transformation,[status(thm)],[f66]) ).
fof(f74,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(f75,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)],[f74]) ).
fof(f77,plain,
! [X0,X1,X2] :
( X0 != X1
| ~ sP1_prd(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f75]) ).
fof(f79,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(f80,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)],[f79]) ).
fof(f82,plain,
! [X0,X1,X2,X3] :
( X0 != X1
| ~ sP2_prd(X0,X1,X2,X3) ),
inference(cnf_transformation,[status(thm)],[f80]) ).
fof(f95,plain,
! [X0,X1] :
( ~ r2(X1,X0)
| ~ r1(X0) ),
inference(destructive_equality_resolution,[status(thm)],[f63]) ).
fof(f96,plain,
! [X0,X1] :
( ~ r3(sK20_skl,X0,X1)
| r1(sK21_skl(X0)) ),
inference(destructive_equality_resolution,[status(thm)],[f67]) ).
fof(f97,plain,
! [X0,X1] :
( ~ r3(sK20_skl,X0,X1)
| X0 = sK21_skl(X0) ),
inference(destructive_equality_resolution,[status(thm)],[f68]) ).
fof(f99,plain,
! [X0,X1] : ~ sP1_prd(X0,X0,X1),
inference(destructive_equality_resolution,[status(thm)],[f77]) ).
fof(f100,plain,
! [X0,X1,X2] : ~ sP2_prd(X0,X0,X1,X2),
inference(destructive_equality_resolution,[status(thm)],[f82]) ).
fof(f105,plain,
! [X0,X1] :
( ~ r1(X0)
| sP1_prd(X0,sK1_skl(X1),X1) ),
inference(resolution,[status(thm)],[f22,f95]) ).
fof(f107,plain,
! [X0,X1] :
( X1 = sK21_skl(X1)
| sP2_prd(X0,sK2_skl(X1,sK20_skl),X1,sK20_skl) ),
inference(resolution,[status(thm)],[f27,f97]) ).
fof(f108,plain,
! [X0] : X0 = sK21_skl(X0),
inference(resolution,[status(thm)],[f107,f100]) ).
fof(f110,plain,
! [X0,X1] :
( ~ r3(sK20_skl,X0,X1)
| r1(X0) ),
inference(backward_demodulation,[status(thm)],[f108,f96]) ).
fof(f112,plain,
! [X0] : ~ r1(sK1_skl(X0)),
inference(resolution,[status(thm)],[f105,f99]) ).
fof(f113,plain,
! [X0,X1] : ~ r3(sK20_skl,sK1_skl(X0),X1),
inference(resolution,[status(thm)],[f112,f110]) ).
fof(f115,plain,
! [X0,X1] : sP2_prd(X0,sK2_skl(sK1_skl(X1),sK20_skl),sK1_skl(X1),sK20_skl),
inference(resolution,[status(thm)],[f113,f27]) ).
fof(f116,plain,
$false,
inference(resolution,[status(thm)],[f115,f100]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : NUN062+2 : TPTP v9.3.1. Released v7.3.0.
% 0.00/0.02 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/0.34 % Computer : n011.cluster.edu
% 0.08/0.34 % Model : x86_64 x86_64
% 0.08/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.34 % Memory : 8046.5625MB
% 0.08/0.34 % OS : Linux 6.8.0-71-generic
% 0.04/20.35 % CPULimit : 300
% 0.04/20.35 % WCLimit : 300
% 0.04/20.35 % DateTime : Mon Sep 21 03:23:12 UTC 2026
% 0.04/20.35 % CPUTime :
% 0.04/20.36 % Drodi V4.1.1
% 0.04/20.37 % Refutation found
% 0.04/20.37 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.04/20.37 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.04/20.40 % Elapsed time: 0.042497 seconds
% 0.04/20.40 % CPU time: 0.115662 seconds
% 0.04/20.40 % Total memory used: 92.833 MB
% 0.04/20.40 % Net memory used: 92.750 MB
%------------------------------------------------------------------------------