%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : KRS118+1 : TPTP v9.3.1. Released v3.1.0.
% 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 12:59:43 PM UTC 2026
% Result : Unsatisfiable 0.10s 5.40s
% Output : CNFRefutation 0.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 10
% Syntax : Number of formulae : 68 ( 19 unt; 0 def)
% Number of atoms : 213 ( 6 equ)
% Maximal formula atoms : 12 ( 3 avg)
% Number of connectives : 232 ( 87 ~; 83 |; 50 &)
% ( 9 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 12 ( 10 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 1 con; 0-1 aty)
% Number of variables : 122 ( 104 !; 18 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f22,axiom,
! [X] :
( cUnsatisfiable(X)
<=> ( ccxcomp(X)
& ? [Y] :
( cd(Y)
& rinvF(X,Y) )
& ! [Y] :
( rinvR(X,Y)
=> ca_Vx3(Y) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f23,axiom,
! [X] :
( cc(X)
<=> ~ ? [Y] : ra_Px1(X,Y) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f24,axiom,
! [X] :
( ccxcomp(X)
<=> ? [Y0] : ra_Px1(X,Y0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f25,axiom,
! [X] :
( cd(X)
<=> ( cc(X)
& ? [Y] :
( ccxcomp(Y)
& rf(X,Y) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f26,axiom,
! [X] :
( ca_Vx3(X)
<=> ? [Y] :
( cd(Y)
& rinvF(X,Y) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f27,axiom,
! [X,Y,Z] :
( ( rf(X,Z)
& rf(X,Y) )
=> Y = Z ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f28,axiom,
! [X,Y] :
( rinvF(X,Y)
<=> rf(Y,X) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f29,axiom,
! [X,Y] :
( rinvR(X,Y)
<=> rr(Y,X) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f31,axiom,
cUnsatisfiable(i2003_11_14_17_21_4056),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f32,axiom,
! [X,Y] :
( rf(X,Y)
=> rr(X,Y) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f97,plain,
! [X] :
( cUnsatisfiable(X)
<=> ( ccxcomp(X)
& ? [Y] :
( cd(Y)
& rinvF(X,Y) )
& ! [Y] :
( ca_Vx3(Y)
| ~ rinvR(X,Y) ) ) ),
inference(pre_NNF_transformation,[status(thm)],[f22]) ).
fof(f98,plain,
! [X] :
( ( ~ ccxcomp(X)
| ! [Y] :
( ~ cd(Y)
| ~ rinvF(X,Y) )
| ? [Y] :
( ~ ca_Vx3(Y)
& rinvR(X,Y) )
| cUnsatisfiable(X) )
& ( ( ccxcomp(X)
& ? [Y] :
( cd(Y)
& rinvF(X,Y) )
& ! [Y] :
( ca_Vx3(Y)
| ~ rinvR(X,Y) ) )
| ~ cUnsatisfiable(X) ) ),
inference(NNF_transformation,[status(thm)],[f97]) ).
fof(f99,plain,
( ! [X] :
( ~ ccxcomp(X)
| ! [Y] :
( ~ cd(Y)
| ~ rinvF(X,Y) )
| ? [Y] :
( ~ ca_Vx3(Y)
& rinvR(X,Y) )
| cUnsatisfiable(X) )
& ! [X] :
( ( ccxcomp(X)
& ? [Y] :
( cd(Y)
& rinvF(X,Y) )
& ! [Y] :
( ca_Vx3(Y)
| ~ rinvR(X,Y) ) )
| ~ cUnsatisfiable(X) ) ),
inference(miniscoping,[status(thm)],[f98]) ).
fof(f100,plain,
( ! [X] :
( ~ ccxcomp(X)
| ! [Y] :
( ~ cd(Y)
| ~ rinvF(X,Y) )
| ( ~ ca_Vx3(sK1_skl(X))
& rinvR(X,sK1_skl(X)) )
| cUnsatisfiable(X) )
& ! [X] :
( ( ccxcomp(X)
& cd(sK0_skl(X))
& rinvF(X,sK0_skl(X))
& ! [Y] :
( ca_Vx3(Y)
| ~ rinvR(X,Y) ) )
| ~ cUnsatisfiable(X) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl,sK1_skl]),skolemize(Y,sK0_skl(X)),skolemize(Y,sK1_skl(X))],[f99]) ).
fof(f101,plain,
! [X0,X1] :
( ca_Vx3(X1)
| ~ rinvR(X0,X1)
| ~ cUnsatisfiable(X0) ),
inference(cnf_transformation,[status(thm)],[f100]) ).
fof(f102,plain,
! [X0] :
( rinvF(X0,sK0_skl(X0))
| ~ cUnsatisfiable(X0) ),
inference(cnf_transformation,[status(thm)],[f100]) ).
fof(f103,plain,
! [X0] :
( cd(sK0_skl(X0))
| ~ cUnsatisfiable(X0) ),
inference(cnf_transformation,[status(thm)],[f100]) ).
fof(f107,plain,
! [X] :
( cc(X)
<=> ! [Y] : ~ ra_Px1(X,Y) ),
inference(pre_NNF_transformation,[status(thm)],[f23]) ).
fof(f108,plain,
! [X] :
( ( ? [Y] : ra_Px1(X,Y)
| cc(X) )
& ( ! [Y] : ~ ra_Px1(X,Y)
| ~ cc(X) ) ),
inference(NNF_transformation,[status(thm)],[f107]) ).
fof(f109,plain,
( ! [X] :
( ? [Y] : ra_Px1(X,Y)
| cc(X) )
& ! [X] :
( ! [Y] : ~ ra_Px1(X,Y)
| ~ cc(X) ) ),
inference(miniscoping,[status(thm)],[f108]) ).
fof(f110,plain,
( ! [X] :
( ra_Px1(X,sK2_skl(X))
| cc(X) )
& ! [X] :
( ! [Y] : ~ ra_Px1(X,Y)
| ~ cc(X) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2_skl]),skolemize(Y,sK2_skl(X))],[f109]) ).
fof(f111,plain,
! [X0,X1] :
( ~ ra_Px1(X0,X1)
| ~ cc(X0) ),
inference(cnf_transformation,[status(thm)],[f110]) ).
fof(f113,plain,
! [X] :
( ( ! [Y0] : ~ ra_Px1(X,Y0)
| ccxcomp(X) )
& ( ? [Y0] : ra_Px1(X,Y0)
| ~ ccxcomp(X) ) ),
inference(NNF_transformation,[status(thm)],[f24]) ).
fof(f114,plain,
( ! [X] :
( ! [Y0] : ~ ra_Px1(X,Y0)
| ccxcomp(X) )
& ! [X] :
( ? [Y0] : ra_Px1(X,Y0)
| ~ ccxcomp(X) ) ),
inference(miniscoping,[status(thm)],[f113]) ).
fof(f115,plain,
( ! [X] :
( ! [Y0] : ~ ra_Px1(X,Y0)
| ccxcomp(X) )
& ! [X] :
( ra_Px1(X,sK3_skl(X))
| ~ ccxcomp(X) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3_skl]),skolemize(Y0,sK3_skl(X))],[f114]) ).
fof(f116,plain,
! [X0] :
( ra_Px1(X0,sK3_skl(X0))
| ~ ccxcomp(X0) ),
inference(cnf_transformation,[status(thm)],[f115]) ).
fof(f118,plain,
! [X] :
( ( ~ cc(X)
| ! [Y] :
( ~ ccxcomp(Y)
| ~ rf(X,Y) )
| cd(X) )
& ( ( cc(X)
& ? [Y] :
( ccxcomp(Y)
& rf(X,Y) ) )
| ~ cd(X) ) ),
inference(NNF_transformation,[status(thm)],[f25]) ).
fof(f119,plain,
( ! [X] :
( ~ cc(X)
| ! [Y] :
( ~ ccxcomp(Y)
| ~ rf(X,Y) )
| cd(X) )
& ! [X] :
( ( cc(X)
& ? [Y] :
( ccxcomp(Y)
& rf(X,Y) ) )
| ~ cd(X) ) ),
inference(miniscoping,[status(thm)],[f118]) ).
fof(f120,plain,
( ! [X] :
( ~ cc(X)
| ! [Y] :
( ~ ccxcomp(Y)
| ~ rf(X,Y) )
| cd(X) )
& ! [X] :
( ( cc(X)
& ccxcomp(sK4_skl(X))
& rf(X,sK4_skl(X)) )
| ~ cd(X) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4_skl]),skolemize(Y,sK4_skl(X))],[f119]) ).
fof(f121,plain,
! [X0] :
( rf(X0,sK4_skl(X0))
| ~ cd(X0) ),
inference(cnf_transformation,[status(thm)],[f120]) ).
fof(f122,plain,
! [X0] :
( ccxcomp(sK4_skl(X0))
| ~ cd(X0) ),
inference(cnf_transformation,[status(thm)],[f120]) ).
fof(f123,plain,
! [X0] :
( cc(X0)
| ~ cd(X0) ),
inference(cnf_transformation,[status(thm)],[f120]) ).
fof(f125,plain,
! [X] :
( ( ! [Y] :
( ~ cd(Y)
| ~ rinvF(X,Y) )
| ca_Vx3(X) )
& ( ? [Y] :
( cd(Y)
& rinvF(X,Y) )
| ~ ca_Vx3(X) ) ),
inference(NNF_transformation,[status(thm)],[f26]) ).
fof(f126,plain,
( ! [X] :
( ! [Y] :
( ~ cd(Y)
| ~ rinvF(X,Y) )
| ca_Vx3(X) )
& ! [X] :
( ? [Y] :
( cd(Y)
& rinvF(X,Y) )
| ~ ca_Vx3(X) ) ),
inference(miniscoping,[status(thm)],[f125]) ).
fof(f127,plain,
( ! [X] :
( ! [Y] :
( ~ cd(Y)
| ~ rinvF(X,Y) )
| ca_Vx3(X) )
& ! [X] :
( ( cd(sK5_skl(X))
& rinvF(X,sK5_skl(X)) )
| ~ ca_Vx3(X) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK5_skl]),skolemize(Y,sK5_skl(X))],[f126]) ).
fof(f128,plain,
! [X0] :
( rinvF(X0,sK5_skl(X0))
| ~ ca_Vx3(X0) ),
inference(cnf_transformation,[status(thm)],[f127]) ).
fof(f129,plain,
! [X0] :
( cd(sK5_skl(X0))
| ~ ca_Vx3(X0) ),
inference(cnf_transformation,[status(thm)],[f127]) ).
fof(f131,plain,
! [X,Y,Z] :
( Y = Z
| ~ rf(X,Z)
| ~ rf(X,Y) ),
inference(pre_NNF_transformation,[status(thm)],[f27]) ).
fof(f132,plain,
! [Y,Z] :
( Y = Z
| ! [X] :
( ~ rf(X,Z)
| ~ rf(X,Y) ) ),
inference(miniscoping,[status(thm)],[f131]) ).
fof(f133,plain,
! [X0,X1,X2] :
( X1 = X2
| ~ rf(X0,X2)
| ~ rf(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f132]) ).
fof(f134,plain,
! [X,Y] :
( ( ~ rf(Y,X)
| rinvF(X,Y) )
& ( rf(Y,X)
| ~ rinvF(X,Y) ) ),
inference(NNF_transformation,[status(thm)],[f28]) ).
fof(f135,plain,
( ! [X,Y] :
( ~ rf(Y,X)
| rinvF(X,Y) )
& ! [X,Y] :
( rf(Y,X)
| ~ rinvF(X,Y) ) ),
inference(miniscoping,[status(thm)],[f134]) ).
fof(f136,plain,
! [X0,X1] :
( rf(X1,X0)
| ~ rinvF(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f135]) ).
fof(f138,plain,
! [X,Y] :
( ( ~ rr(Y,X)
| rinvR(X,Y) )
& ( rr(Y,X)
| ~ rinvR(X,Y) ) ),
inference(NNF_transformation,[status(thm)],[f29]) ).
fof(f139,plain,
( ! [X,Y] :
( ~ rr(Y,X)
| rinvR(X,Y) )
& ! [X,Y] :
( rr(Y,X)
| ~ rinvR(X,Y) ) ),
inference(miniscoping,[status(thm)],[f138]) ).
fof(f141,plain,
! [X0,X1] :
( ~ rr(X1,X0)
| rinvR(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f139]) ).
fof(f145,plain,
cUnsatisfiable(i2003_11_14_17_21_4056),
inference(cnf_transformation,[status(thm)],[f31]) ).
fof(f146,plain,
! [X,Y] :
( rr(X,Y)
| ~ rf(X,Y) ),
inference(pre_NNF_transformation,[status(thm)],[f32]) ).
fof(f147,plain,
! [X0,X1] :
( rr(X0,X1)
| ~ rf(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f146]) ).
fof(f150,plain,
cd(sK0_skl(i2003_11_14_17_21_4056)),
inference(resolution,[status(thm)],[f103,f145]) ).
fof(f151,plain,
cc(sK0_skl(i2003_11_14_17_21_4056)),
inference(resolution,[status(thm)],[f150,f123]) ).
fof(f152,plain,
rinvF(i2003_11_14_17_21_4056,sK0_skl(i2003_11_14_17_21_4056)),
inference(resolution,[status(thm)],[f102,f145]) ).
fof(f155,plain,
rf(sK0_skl(i2003_11_14_17_21_4056),i2003_11_14_17_21_4056),
inference(resolution,[status(thm)],[f152,f136]) ).
fof(f156,plain,
rr(sK0_skl(i2003_11_14_17_21_4056),i2003_11_14_17_21_4056),
inference(resolution,[status(thm)],[f155,f147]) ).
fof(f158,plain,
rinvR(i2003_11_14_17_21_4056,sK0_skl(i2003_11_14_17_21_4056)),
inference(resolution,[status(thm)],[f156,f141]) ).
fof(f160,plain,
( ca_Vx3(sK0_skl(i2003_11_14_17_21_4056))
| ~ cUnsatisfiable(i2003_11_14_17_21_4056) ),
inference(resolution,[status(thm)],[f158,f101]) ).
fof(f161,plain,
ca_Vx3(sK0_skl(i2003_11_14_17_21_4056)),
inference(forward_subsumption_resolution,[status(thm)],[f160,f145]) ).
fof(f162,plain,
cd(sK5_skl(sK0_skl(i2003_11_14_17_21_4056))),
inference(resolution,[status(thm)],[f161,f129]) ).
fof(f163,plain,
ccxcomp(sK4_skl(sK5_skl(sK0_skl(i2003_11_14_17_21_4056)))),
inference(resolution,[status(thm)],[f162,f122]) ).
fof(f172,plain,
rf(sK5_skl(sK0_skl(i2003_11_14_17_21_4056)),sK4_skl(sK5_skl(sK0_skl(i2003_11_14_17_21_4056)))),
inference(resolution,[status(thm)],[f121,f162]) ).
fof(f174,plain,
rinvF(sK0_skl(i2003_11_14_17_21_4056),sK5_skl(sK0_skl(i2003_11_14_17_21_4056))),
inference(resolution,[status(thm)],[f128,f161]) ).
fof(f216,plain,
rf(sK5_skl(sK0_skl(i2003_11_14_17_21_4056)),sK0_skl(i2003_11_14_17_21_4056)),
inference(resolution,[status(thm)],[f174,f136]) ).
fof(f234,plain,
! [X0] :
( sK0_skl(i2003_11_14_17_21_4056) = X0
| ~ rf(sK5_skl(sK0_skl(i2003_11_14_17_21_4056)),X0) ),
inference(resolution,[status(thm)],[f216,f133]) ).
fof(f257,plain,
sK0_skl(i2003_11_14_17_21_4056) = sK4_skl(sK5_skl(sK0_skl(i2003_11_14_17_21_4056))),
inference(resolution,[status(thm)],[f172,f234]) ).
fof(f263,plain,
ccxcomp(sK0_skl(i2003_11_14_17_21_4056)),
inference(backward_demodulation,[status(thm)],[f257,f163]) ).
fof(f264,plain,
ra_Px1(sK0_skl(i2003_11_14_17_21_4056),sK3_skl(sK0_skl(i2003_11_14_17_21_4056))),
inference(resolution,[status(thm)],[f263,f116]) ).
fof(f266,plain,
~ cc(sK0_skl(i2003_11_14_17_21_4056)),
inference(resolution,[status(thm)],[f264,f111]) ).
fof(f267,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f266,f151]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : KRS118+1 : TPTP v9.3.1. Released v3.1.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/5.37 % Computer : n018.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 22:56:18 UTC 2026
% 0.10/5.38 % CPUTime :
% 0.10/5.38 % Drodi V4.1.1
% 0.10/5.40 % Refutation found
% 0.10/5.40 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.10/5.40 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.15/5.41 % Elapsed time: 0.030806 seconds
% 0.15/5.41 % CPU time: 0.093091 seconds
% 0.15/5.41 % Total memory used: 3.510 MB
% 0.15/5.41 % Net memory used: 3.379 MB
%------------------------------------------------------------------------------