%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : KRS114+1 : TPTP v9.3.1. Released v3.1.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n017.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 12:59:43 PM UTC 2026
% Result : Unsatisfiable 0.10s 5.39s
% Output : CNFRefutation 0.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 8
% Syntax : Number of formulae : 60 ( 16 unt; 0 def)
% Number of atoms : 212 ( 12 equ)
% Maximal formula atoms : 12 ( 3 avg)
% Number of connectives : 243 ( 91 ~; 86 |; 54 &)
% ( 10 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 13 ( 11 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 1 con; 0-1 aty)
% Number of variables : 117 ( 95 !; 22 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f25,axiom,
! [X] :
( cUnsatisfiable(X)
<=> ( ? [Y] :
( ca_Ax3(Y)
& rs(X,Y) )
& ? [Y] :
( ca_Ax4(Y)
& rr(X,Y) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f26,axiom,
! [X] :
( cp(X)
<=> ~ ? [Y] : ra_Px1(X,Y) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f27,axiom,
! [X] :
( cpxcomp(X)
<=> ? [Y0] : ra_Px1(X,Y0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f30,axiom,
! [X] :
( ca_Ax3(X)
<=> ( cpxcomp(X)
& cqxcomp(X) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f31,axiom,
! [X] :
( ca_Ax4(X)
<=> ( ? [Y] :
( ca_Vx5(Y)
& rinvR(X,Y) )
& ! [Y0,Y1] :
( ( rinvR(X,Y1)
& rinvR(X,Y0) )
=> Y0 = Y1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f32,axiom,
! [X] :
( ca_Vx5(X)
<=> ! [Y] :
( rs(X,Y)
=> cp(Y) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f33,axiom,
! [X,Y] :
( rinvR(X,Y)
<=> rr(Y,X) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f34,axiom,
cUnsatisfiable(i2003_11_14_17_21_262),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f108,plain,
! [X] :
( ( ! [Y] :
( ~ ca_Ax3(Y)
| ~ rs(X,Y) )
| ! [Y] :
( ~ ca_Ax4(Y)
| ~ rr(X,Y) )
| cUnsatisfiable(X) )
& ( ( ? [Y] :
( ca_Ax3(Y)
& rs(X,Y) )
& ? [Y] :
( ca_Ax4(Y)
& rr(X,Y) ) )
| ~ cUnsatisfiable(X) ) ),
inference(NNF_transformation,[status(thm)],[f25]) ).
fof(f109,plain,
( ! [X] :
( ! [Y] :
( ~ ca_Ax3(Y)
| ~ rs(X,Y) )
| ! [Y] :
( ~ ca_Ax4(Y)
| ~ rr(X,Y) )
| cUnsatisfiable(X) )
& ! [X] :
( ( ? [Y] :
( ca_Ax3(Y)
& rs(X,Y) )
& ? [Y] :
( ca_Ax4(Y)
& rr(X,Y) ) )
| ~ cUnsatisfiable(X) ) ),
inference(miniscoping,[status(thm)],[f108]) ).
fof(f110,plain,
( ! [X] :
( ! [Y] :
( ~ ca_Ax3(Y)
| ~ rs(X,Y) )
| ! [Y] :
( ~ ca_Ax4(Y)
| ~ rr(X,Y) )
| cUnsatisfiable(X) )
& ! [X] :
( ( ca_Ax3(sK1_skl(X))
& rs(X,sK1_skl(X))
& ca_Ax4(sK0_skl(X))
& rr(X,sK0_skl(X)) )
| ~ cUnsatisfiable(X) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl,sK1_skl]),skolemize(Y,sK0_skl(X)),skolemize(Y,sK1_skl(X))],[f109]) ).
fof(f111,plain,
! [X0] :
( rr(X0,sK0_skl(X0))
| ~ cUnsatisfiable(X0) ),
inference(cnf_transformation,[status(thm)],[f110]) ).
fof(f112,plain,
! [X0] :
( ca_Ax4(sK0_skl(X0))
| ~ cUnsatisfiable(X0) ),
inference(cnf_transformation,[status(thm)],[f110]) ).
fof(f113,plain,
! [X0] :
( rs(X0,sK1_skl(X0))
| ~ cUnsatisfiable(X0) ),
inference(cnf_transformation,[status(thm)],[f110]) ).
fof(f114,plain,
! [X0] :
( ca_Ax3(sK1_skl(X0))
| ~ cUnsatisfiable(X0) ),
inference(cnf_transformation,[status(thm)],[f110]) ).
fof(f116,plain,
! [X] :
( cp(X)
<=> ! [Y] : ~ ra_Px1(X,Y) ),
inference(pre_NNF_transformation,[status(thm)],[f26]) ).
fof(f117,plain,
! [X] :
( ( ? [Y] : ra_Px1(X,Y)
| cp(X) )
& ( ! [Y] : ~ ra_Px1(X,Y)
| ~ cp(X) ) ),
inference(NNF_transformation,[status(thm)],[f116]) ).
fof(f118,plain,
( ! [X] :
( ? [Y] : ra_Px1(X,Y)
| cp(X) )
& ! [X] :
( ! [Y] : ~ ra_Px1(X,Y)
| ~ cp(X) ) ),
inference(miniscoping,[status(thm)],[f117]) ).
fof(f119,plain,
( ! [X] :
( ra_Px1(X,sK2_skl(X))
| cp(X) )
& ! [X] :
( ! [Y] : ~ ra_Px1(X,Y)
| ~ cp(X) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2_skl]),skolemize(Y,sK2_skl(X))],[f118]) ).
fof(f120,plain,
! [X0,X1] :
( ~ ra_Px1(X0,X1)
| ~ cp(X0) ),
inference(cnf_transformation,[status(thm)],[f119]) ).
fof(f122,plain,
! [X] :
( ( ! [Y0] : ~ ra_Px1(X,Y0)
| cpxcomp(X) )
& ( ? [Y0] : ra_Px1(X,Y0)
| ~ cpxcomp(X) ) ),
inference(NNF_transformation,[status(thm)],[f27]) ).
fof(f123,plain,
( ! [X] :
( ! [Y0] : ~ ra_Px1(X,Y0)
| cpxcomp(X) )
& ! [X] :
( ? [Y0] : ra_Px1(X,Y0)
| ~ cpxcomp(X) ) ),
inference(miniscoping,[status(thm)],[f122]) ).
fof(f124,plain,
( ! [X] :
( ! [Y0] : ~ ra_Px1(X,Y0)
| cpxcomp(X) )
& ! [X] :
( ra_Px1(X,sK3_skl(X))
| ~ cpxcomp(X) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3_skl]),skolemize(Y0,sK3_skl(X))],[f123]) ).
fof(f125,plain,
! [X0] :
( ra_Px1(X0,sK3_skl(X0))
| ~ cpxcomp(X0) ),
inference(cnf_transformation,[status(thm)],[f124]) ).
fof(f138,plain,
! [X] :
( ( ~ cpxcomp(X)
| ~ cqxcomp(X)
| ca_Ax3(X) )
& ( ( cpxcomp(X)
& cqxcomp(X) )
| ~ ca_Ax3(X) ) ),
inference(NNF_transformation,[status(thm)],[f30]) ).
fof(f139,plain,
( ! [X] :
( ~ cpxcomp(X)
| ~ cqxcomp(X)
| ca_Ax3(X) )
& ! [X] :
( ( cpxcomp(X)
& cqxcomp(X) )
| ~ ca_Ax3(X) ) ),
inference(miniscoping,[status(thm)],[f138]) ).
fof(f141,plain,
! [X0] :
( cpxcomp(X0)
| ~ ca_Ax3(X0) ),
inference(cnf_transformation,[status(thm)],[f139]) ).
fof(f143,plain,
! [X] :
( ca_Ax4(X)
<=> ( ? [Y] :
( ca_Vx5(Y)
& rinvR(X,Y) )
& ! [Y0,Y1] :
( Y0 = Y1
| ~ rinvR(X,Y1)
| ~ rinvR(X,Y0) ) ) ),
inference(pre_NNF_transformation,[status(thm)],[f31]) ).
fof(f144,plain,
! [X] :
( ( ! [Y] :
( ~ ca_Vx5(Y)
| ~ rinvR(X,Y) )
| ? [Y0,Y1] :
( Y0 != Y1
& rinvR(X,Y1)
& rinvR(X,Y0) )
| ca_Ax4(X) )
& ( ( ? [Y] :
( ca_Vx5(Y)
& rinvR(X,Y) )
& ! [Y0,Y1] :
( Y0 = Y1
| ~ rinvR(X,Y1)
| ~ rinvR(X,Y0) ) )
| ~ ca_Ax4(X) ) ),
inference(NNF_transformation,[status(thm)],[f143]) ).
fof(f145,plain,
( ! [X] :
( ! [Y] :
( ~ ca_Vx5(Y)
| ~ rinvR(X,Y) )
| ? [Y0,Y1] :
( Y0 != Y1
& rinvR(X,Y1)
& rinvR(X,Y0) )
| ca_Ax4(X) )
& ! [X] :
( ( ? [Y] :
( ca_Vx5(Y)
& rinvR(X,Y) )
& ! [Y0,Y1] :
( Y0 = Y1
| ~ rinvR(X,Y1)
| ~ rinvR(X,Y0) ) )
| ~ ca_Ax4(X) ) ),
inference(miniscoping,[status(thm)],[f144]) ).
fof(f146,plain,
( ! [X] :
( ! [Y] :
( ~ ca_Vx5(Y)
| ~ rinvR(X,Y) )
| ( sK7_skl(X) != sK8_skl(X)
& rinvR(X,sK8_skl(X))
& rinvR(X,sK7_skl(X)) )
| ca_Ax4(X) )
& ! [X] :
( ( ca_Vx5(sK6_skl(X))
& rinvR(X,sK6_skl(X))
& ! [Y0,Y1] :
( Y0 = Y1
| ~ rinvR(X,Y1)
| ~ rinvR(X,Y0) ) )
| ~ ca_Ax4(X) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK6_skl,sK7_skl,sK8_skl]),skolemize(Y,sK6_skl(X)),skolemize(Y0,sK7_skl(X)),skolemize(Y1,sK8_skl(X))],[f145]) ).
fof(f147,plain,
! [X0,X1,X2] :
( X1 = X2
| ~ rinvR(X0,X2)
| ~ rinvR(X0,X1)
| ~ ca_Ax4(X0) ),
inference(cnf_transformation,[status(thm)],[f146]) ).
fof(f148,plain,
! [X0] :
( rinvR(X0,sK6_skl(X0))
| ~ ca_Ax4(X0) ),
inference(cnf_transformation,[status(thm)],[f146]) ).
fof(f149,plain,
! [X0] :
( ca_Vx5(sK6_skl(X0))
| ~ ca_Ax4(X0) ),
inference(cnf_transformation,[status(thm)],[f146]) ).
fof(f153,plain,
! [X] :
( ca_Vx5(X)
<=> ! [Y] :
( cp(Y)
| ~ rs(X,Y) ) ),
inference(pre_NNF_transformation,[status(thm)],[f32]) ).
fof(f154,plain,
! [X] :
( ( ? [Y] :
( ~ cp(Y)
& rs(X,Y) )
| ca_Vx5(X) )
& ( ! [Y] :
( cp(Y)
| ~ rs(X,Y) )
| ~ ca_Vx5(X) ) ),
inference(NNF_transformation,[status(thm)],[f153]) ).
fof(f155,plain,
( ! [X] :
( ? [Y] :
( ~ cp(Y)
& rs(X,Y) )
| ca_Vx5(X) )
& ! [X] :
( ! [Y] :
( cp(Y)
| ~ rs(X,Y) )
| ~ ca_Vx5(X) ) ),
inference(miniscoping,[status(thm)],[f154]) ).
fof(f156,plain,
( ! [X] :
( ( ~ cp(sK9_skl(X))
& rs(X,sK9_skl(X)) )
| ca_Vx5(X) )
& ! [X] :
( ! [Y] :
( cp(Y)
| ~ rs(X,Y) )
| ~ ca_Vx5(X) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK9_skl]),skolemize(Y,sK9_skl(X))],[f155]) ).
fof(f157,plain,
! [X0,X1] :
( cp(X1)
| ~ rs(X0,X1)
| ~ ca_Vx5(X0) ),
inference(cnf_transformation,[status(thm)],[f156]) ).
fof(f160,plain,
! [X,Y] :
( ( ~ rr(Y,X)
| rinvR(X,Y) )
& ( rr(Y,X)
| ~ rinvR(X,Y) ) ),
inference(NNF_transformation,[status(thm)],[f33]) ).
fof(f161,plain,
( ! [X,Y] :
( ~ rr(Y,X)
| rinvR(X,Y) )
& ! [X,Y] :
( rr(Y,X)
| ~ rinvR(X,Y) ) ),
inference(miniscoping,[status(thm)],[f160]) ).
fof(f163,plain,
! [X0,X1] :
( ~ rr(X1,X0)
| rinvR(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f161]) ).
fof(f164,plain,
cUnsatisfiable(i2003_11_14_17_21_262),
inference(cnf_transformation,[status(thm)],[f34]) ).
fof(f166,plain,
rr(i2003_11_14_17_21_262,sK0_skl(i2003_11_14_17_21_262)),
inference(resolution,[status(thm)],[f111,f164]) ).
fof(f167,plain,
ca_Ax4(sK0_skl(i2003_11_14_17_21_262)),
inference(resolution,[status(thm)],[f112,f164]) ).
fof(f168,plain,
rs(i2003_11_14_17_21_262,sK1_skl(i2003_11_14_17_21_262)),
inference(resolution,[status(thm)],[f113,f164]) ).
fof(f169,plain,
ca_Ax3(sK1_skl(i2003_11_14_17_21_262)),
inference(resolution,[status(thm)],[f114,f164]) ).
fof(f170,plain,
cpxcomp(sK1_skl(i2003_11_14_17_21_262)),
inference(resolution,[status(thm)],[f169,f141]) ).
fof(f172,plain,
ca_Vx5(sK6_skl(sK0_skl(i2003_11_14_17_21_262))),
inference(resolution,[status(thm)],[f149,f167]) ).
fof(f173,plain,
rinvR(sK0_skl(i2003_11_14_17_21_262),i2003_11_14_17_21_262),
inference(resolution,[status(thm)],[f166,f163]) ).
fof(f180,plain,
ra_Px1(sK1_skl(i2003_11_14_17_21_262),sK3_skl(sK1_skl(i2003_11_14_17_21_262))),
inference(resolution,[status(thm)],[f125,f170]) ).
fof(f186,plain,
rinvR(sK0_skl(i2003_11_14_17_21_262),sK6_skl(sK0_skl(i2003_11_14_17_21_262))),
inference(resolution,[status(thm)],[f148,f167]) ).
fof(f189,plain,
( cp(sK1_skl(i2003_11_14_17_21_262))
| ~ ca_Vx5(i2003_11_14_17_21_262) ),
inference(resolution,[status(thm)],[f157,f168]) ).
fof(f191,plain,
! [X0] :
( i2003_11_14_17_21_262 = X0
| ~ rinvR(sK0_skl(i2003_11_14_17_21_262),X0)
| ~ ca_Ax4(sK0_skl(i2003_11_14_17_21_262)) ),
inference(resolution,[status(thm)],[f147,f173]) ).
fof(f192,plain,
! [X0] :
( i2003_11_14_17_21_262 = X0
| ~ rinvR(sK0_skl(i2003_11_14_17_21_262),X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f191,f167]) ).
fof(f195,plain,
~ cp(sK1_skl(i2003_11_14_17_21_262)),
inference(resolution,[status(thm)],[f180,f120]) ).
fof(f196,plain,
~ ca_Vx5(i2003_11_14_17_21_262),
inference(backward_subsumption_resolution,[status(thm)],[f189,f195]) ).
fof(f198,plain,
i2003_11_14_17_21_262 = sK6_skl(sK0_skl(i2003_11_14_17_21_262)),
inference(resolution,[status(thm)],[f186,f192]) ).
fof(f203,plain,
ca_Vx5(i2003_11_14_17_21_262),
inference(backward_demodulation,[status(thm)],[f198,f172]) ).
fof(f204,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f203,f196]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : KRS114+1 : TPTP v9.3.1. Released v3.1.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/5.37 % Computer : n017.cluster.edu
% 0.10/5.37 % Model : x86_64 x86_64
% 0.10/5.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/5.37 % Memory : 8046.5625MB
% 0.10/5.37 % OS : Linux 6.8.0-71-generic
% 0.10/5.37 % CPULimit : 300
% 0.10/5.37 % WCLimit : 300
% 0.10/5.37 % DateTime : Sun Sep 20 22:49:03 UTC 2026
% 0.10/5.37 % CPUTime :
% 0.10/5.38 % Drodi V4.1.1
% 0.10/5.39 % Refutation found
% 0.10/5.39 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.10/5.39 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.15/5.41 % Elapsed time: 0.029053 seconds
% 0.15/5.41 % CPU time: 0.089242 seconds
% 0.15/5.41 % Total memory used: 3.500 MB
% 0.15/5.41 % Net memory used: 3.372 MB
%------------------------------------------------------------------------------