%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : KRS107+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 : n026.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 12:59:42 PM UTC 2026
% Result : Unsatisfiable 0.09s 0.38s
% Output : CNFRefutation 0.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 13
% Syntax : Number of formulae : 69 ( 4 unt; 4 def)
% Number of atoms : 218 ( 11 equ)
% Maximal formula atoms : 12 ( 3 avg)
% Number of connectives : 253 ( 104 ~; 98 |; 38 &)
% ( 10 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 5 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 16 ( 14 usr; 5 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 1 con; 0-1 aty)
% Number of variables : 106 ( 91 !; 15 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f35,axiom,
! [X] :
( cUnsatisfiable(X)
<=> ( ca_Cx1(X)
& ? [Y] :
( cc2(Y)
& rrx4(X,Y) )
& ? [Y] :
( cc1(Y)
& rrx3(X,Y) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f36,axiom,
! [X] :
( ca_Ax2(X)
<=> ( cc1(X)
& cc2(X) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f37,axiom,
! [X] :
( ca_Cx1(X)
<=> ? [Y0] : ra_Px1(X,Y0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f38,axiom,
! [X] :
( ca_Cx1xcomp(X)
<=> ? [Y] :
( ca_Ax2(Y)
& rrx3(X,Y) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f39,axiom,
! [X] :
( ca_Cx1xcomp(X)
<=> ~ ? [Y] : ra_Px1(X,Y) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f40,axiom,
! [X,Y,Z] :
( ( rrx(X,Z)
& rrx(X,Y) )
=> Y = Z ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f45,axiom,
cUnsatisfiable(i2003_11_14_17_21_01226),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f50,axiom,
! [X,Y] :
( rrx4(X,Y)
=> rrx(X,Y) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f53,axiom,
! [X,Y] :
( rrx3(X,Y)
=> rrx(X,Y) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f157,plain,
! [X] :
( ( ~ ca_Cx1(X)
| ! [Y] :
( ~ cc2(Y)
| ~ rrx4(X,Y) )
| ! [Y] :
( ~ cc1(Y)
| ~ rrx3(X,Y) )
| cUnsatisfiable(X) )
& ( ( ca_Cx1(X)
& ? [Y] :
( cc2(Y)
& rrx4(X,Y) )
& ? [Y] :
( cc1(Y)
& rrx3(X,Y) ) )
| ~ cUnsatisfiable(X) ) ),
inference(NNF_transformation,[status(thm)],[f35]) ).
fof(f158,plain,
( ! [X] :
( ~ ca_Cx1(X)
| ! [Y] :
( ~ cc2(Y)
| ~ rrx4(X,Y) )
| ! [Y] :
( ~ cc1(Y)
| ~ rrx3(X,Y) )
| cUnsatisfiable(X) )
& ! [X] :
( ( ca_Cx1(X)
& ? [Y] :
( cc2(Y)
& rrx4(X,Y) )
& ? [Y] :
( cc1(Y)
& rrx3(X,Y) ) )
| ~ cUnsatisfiable(X) ) ),
inference(miniscoping,[status(thm)],[f157]) ).
fof(f159,plain,
( ! [X] :
( ~ ca_Cx1(X)
| ! [Y] :
( ~ cc2(Y)
| ~ rrx4(X,Y) )
| ! [Y] :
( ~ cc1(Y)
| ~ rrx3(X,Y) )
| cUnsatisfiable(X) )
& ! [X] :
( ( ca_Cx1(X)
& cc2(sK1_skl(X))
& rrx4(X,sK1_skl(X))
& cc1(sK0_skl(X))
& rrx3(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))],[f158]) ).
fof(f160,plain,
! [X0] :
( rrx3(X0,sK0_skl(X0))
| ~ cUnsatisfiable(X0) ),
inference(cnf_transformation,[status(thm)],[f159]) ).
fof(f161,plain,
! [X0] :
( cc1(sK0_skl(X0))
| ~ cUnsatisfiable(X0) ),
inference(cnf_transformation,[status(thm)],[f159]) ).
fof(f162,plain,
! [X0] :
( rrx4(X0,sK1_skl(X0))
| ~ cUnsatisfiable(X0) ),
inference(cnf_transformation,[status(thm)],[f159]) ).
fof(f163,plain,
! [X0] :
( cc2(sK1_skl(X0))
| ~ cUnsatisfiable(X0) ),
inference(cnf_transformation,[status(thm)],[f159]) ).
fof(f164,plain,
! [X0] :
( ca_Cx1(X0)
| ~ cUnsatisfiable(X0) ),
inference(cnf_transformation,[status(thm)],[f159]) ).
fof(f166,plain,
! [X] :
( ( ~ cc1(X)
| ~ cc2(X)
| ca_Ax2(X) )
& ( ( cc1(X)
& cc2(X) )
| ~ ca_Ax2(X) ) ),
inference(NNF_transformation,[status(thm)],[f36]) ).
fof(f167,plain,
( ! [X] :
( ~ cc1(X)
| ~ cc2(X)
| ca_Ax2(X) )
& ! [X] :
( ( cc1(X)
& cc2(X) )
| ~ ca_Ax2(X) ) ),
inference(miniscoping,[status(thm)],[f166]) ).
fof(f170,plain,
! [X0] :
( ~ cc1(X0)
| ~ cc2(X0)
| ca_Ax2(X0) ),
inference(cnf_transformation,[status(thm)],[f167]) ).
fof(f171,plain,
! [X] :
( ( ! [Y0] : ~ ra_Px1(X,Y0)
| ca_Cx1(X) )
& ( ? [Y0] : ra_Px1(X,Y0)
| ~ ca_Cx1(X) ) ),
inference(NNF_transformation,[status(thm)],[f37]) ).
fof(f172,plain,
( ! [X] :
( ! [Y0] : ~ ra_Px1(X,Y0)
| ca_Cx1(X) )
& ! [X] :
( ? [Y0] : ra_Px1(X,Y0)
| ~ ca_Cx1(X) ) ),
inference(miniscoping,[status(thm)],[f171]) ).
fof(f173,plain,
( ! [X] :
( ! [Y0] : ~ ra_Px1(X,Y0)
| ca_Cx1(X) )
& ! [X] :
( ra_Px1(X,sK2_skl(X))
| ~ ca_Cx1(X) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2_skl]),skolemize(Y0,sK2_skl(X))],[f172]) ).
fof(f174,plain,
! [X0] :
( ra_Px1(X0,sK2_skl(X0))
| ~ ca_Cx1(X0) ),
inference(cnf_transformation,[status(thm)],[f173]) ).
fof(f176,plain,
! [X] :
( ( ! [Y] :
( ~ ca_Ax2(Y)
| ~ rrx3(X,Y) )
| ca_Cx1xcomp(X) )
& ( ? [Y] :
( ca_Ax2(Y)
& rrx3(X,Y) )
| ~ ca_Cx1xcomp(X) ) ),
inference(NNF_transformation,[status(thm)],[f38]) ).
fof(f177,plain,
( ! [X] :
( ! [Y] :
( ~ ca_Ax2(Y)
| ~ rrx3(X,Y) )
| ca_Cx1xcomp(X) )
& ! [X] :
( ? [Y] :
( ca_Ax2(Y)
& rrx3(X,Y) )
| ~ ca_Cx1xcomp(X) ) ),
inference(miniscoping,[status(thm)],[f176]) ).
fof(f178,plain,
( ! [X] :
( ! [Y] :
( ~ ca_Ax2(Y)
| ~ rrx3(X,Y) )
| ca_Cx1xcomp(X) )
& ! [X] :
( ( ca_Ax2(sK3_skl(X))
& rrx3(X,sK3_skl(X)) )
| ~ ca_Cx1xcomp(X) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3_skl]),skolemize(Y,sK3_skl(X))],[f177]) ).
fof(f181,plain,
! [X0,X1] :
( ~ ca_Ax2(X1)
| ~ rrx3(X0,X1)
| ca_Cx1xcomp(X0) ),
inference(cnf_transformation,[status(thm)],[f178]) ).
fof(f182,plain,
! [X] :
( ca_Cx1xcomp(X)
<=> ! [Y] : ~ ra_Px1(X,Y) ),
inference(pre_NNF_transformation,[status(thm)],[f39]) ).
fof(f183,plain,
! [X] :
( ( ? [Y] : ra_Px1(X,Y)
| ca_Cx1xcomp(X) )
& ( ! [Y] : ~ ra_Px1(X,Y)
| ~ ca_Cx1xcomp(X) ) ),
inference(NNF_transformation,[status(thm)],[f182]) ).
fof(f184,plain,
( ! [X] :
( ? [Y] : ra_Px1(X,Y)
| ca_Cx1xcomp(X) )
& ! [X] :
( ! [Y] : ~ ra_Px1(X,Y)
| ~ ca_Cx1xcomp(X) ) ),
inference(miniscoping,[status(thm)],[f183]) ).
fof(f185,plain,
( ! [X] :
( ra_Px1(X,sK4_skl(X))
| ca_Cx1xcomp(X) )
& ! [X] :
( ! [Y] : ~ ra_Px1(X,Y)
| ~ ca_Cx1xcomp(X) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4_skl]),skolemize(Y,sK4_skl(X))],[f184]) ).
fof(f186,plain,
! [X0,X1] :
( ~ ra_Px1(X0,X1)
| ~ ca_Cx1xcomp(X0) ),
inference(cnf_transformation,[status(thm)],[f185]) ).
fof(f188,plain,
! [X,Y,Z] :
( Y = Z
| ~ rrx(X,Z)
| ~ rrx(X,Y) ),
inference(pre_NNF_transformation,[status(thm)],[f40]) ).
fof(f189,plain,
! [Y,Z] :
( Y = Z
| ! [X] :
( ~ rrx(X,Z)
| ~ rrx(X,Y) ) ),
inference(miniscoping,[status(thm)],[f188]) ).
fof(f190,plain,
! [X0,X1,X2] :
( X1 = X2
| ~ rrx(X0,X2)
| ~ rrx(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f189]) ).
fof(f203,plain,
cUnsatisfiable(i2003_11_14_17_21_01226),
inference(cnf_transformation,[status(thm)],[f45]) ).
fof(f212,plain,
! [X,Y] :
( rrx(X,Y)
| ~ rrx4(X,Y) ),
inference(pre_NNF_transformation,[status(thm)],[f50]) ).
fof(f213,plain,
! [X0,X1] :
( rrx(X0,X1)
| ~ rrx4(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f212]) ).
fof(f218,plain,
! [X,Y] :
( rrx(X,Y)
| ~ rrx3(X,Y) ),
inference(pre_NNF_transformation,[status(thm)],[f53]) ).
fof(f219,plain,
! [X0,X1] :
( rrx(X0,X1)
| ~ rrx3(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f218]) ).
fof(f220,plain,
! [X0] :
( ~ cUnsatisfiable(X0)
| ~ ca_Ax2(sK0_skl(X0))
| ca_Cx1xcomp(X0) ),
inference(resolution,[status(thm)],[f181,f160]) ).
fof(f221,plain,
! [X0,X1,X2] :
( ~ rrx3(X0,X2)
| X1 = X2
| ~ rrx(X0,X1) ),
inference(resolution,[status(thm)],[f190,f219]) ).
fof(f225,plain,
! [X0,X1] :
( ~ cUnsatisfiable(X0)
| X1 = sK0_skl(X0)
| ~ rrx(X0,X1) ),
inference(resolution,[status(thm)],[f221,f160]) ).
fof(f226,plain,
! [X0] :
( ~ cc1(sK0_skl(X0))
| ~ cc2(sK0_skl(X0))
| ~ cUnsatisfiable(X0)
| ca_Cx1xcomp(X0) ),
inference(resolution,[status(thm)],[f220,f170]) ).
fof(f227,plain,
! [X0] :
( ~ cc2(sK0_skl(X0))
| ~ cUnsatisfiable(X0)
| ca_Cx1xcomp(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f226,f161]) ).
fof(f231,plain,
! [X0] :
( X0 = sK0_skl(i2003_11_14_17_21_01226)
| ~ rrx(i2003_11_14_17_21_01226,X0) ),
inference(resolution,[status(thm)],[f225,f203]) ).
fof(f234,plain,
! [X0] :
( ~ rrx4(i2003_11_14_17_21_01226,X0)
| X0 = sK0_skl(i2003_11_14_17_21_01226) ),
inference(resolution,[status(thm)],[f231,f213]) ).
fof(f239,definition,
( sQ1_spl
<=> cUnsatisfiable(i2003_11_14_17_21_01226) ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f241,plain,
( sQ1_spl
| ~ cUnsatisfiable(i2003_11_14_17_21_01226) ),
inference(component_clause,[status(thm)],[f239]) ).
fof(f243,plain,
( ~ cUnsatisfiable(i2003_11_14_17_21_01226)
| sK1_skl(i2003_11_14_17_21_01226) = sK0_skl(i2003_11_14_17_21_01226) ),
inference(resolution,[status(thm)],[f234,f162]) ).
fof(f244,definition,
( sQ2_spl
<=> sK1_skl(i2003_11_14_17_21_01226) = sK0_skl(i2003_11_14_17_21_01226) ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f245,plain,
( ~ sQ2_spl
| sK1_skl(i2003_11_14_17_21_01226) = sK0_skl(i2003_11_14_17_21_01226) ),
inference(component_clause,[status(thm)],[f244]) ).
fof(f247,plain,
( ~ sQ1_spl
| sQ2_spl ),
inference(split_clause,[status(thm)],[f243,f244,f239]) ).
fof(f248,plain,
( sQ1_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f241,f203]) ).
fof(f249,plain,
sQ1_spl,
inference(contradiction_clause,[status(thm)],[f248]) ).
fof(f252,plain,
( ~ sQ2_spl
| cc2(sK0_skl(i2003_11_14_17_21_01226))
| ~ cUnsatisfiable(i2003_11_14_17_21_01226) ),
inference(paramodulation,[status(thm)],[f245,f163]) ).
fof(f257,definition,
( sQ4_spl
<=> cc2(sK0_skl(i2003_11_14_17_21_01226)) ),
introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition]) ).
fof(f258,plain,
( ~ sQ4_spl
| cc2(sK0_skl(i2003_11_14_17_21_01226)) ),
inference(component_clause,[status(thm)],[f257]) ).
fof(f260,plain,
( ~ sQ2_spl
| sQ4_spl
| ~ sQ1_spl ),
inference(split_clause,[status(thm)],[f252,f239,f257,f244]) ).
fof(f261,plain,
( ~ sQ4_spl
| ~ cUnsatisfiable(i2003_11_14_17_21_01226)
| ca_Cx1xcomp(i2003_11_14_17_21_01226) ),
inference(resolution,[status(thm)],[f258,f227]) ).
fof(f262,definition,
( sQ5_spl
<=> ca_Cx1xcomp(i2003_11_14_17_21_01226) ),
introduced(definition,[new_symbols(definition,[sQ5_spl])],[split_symbol_definition]) ).
fof(f263,plain,
( ~ sQ5_spl
| ca_Cx1xcomp(i2003_11_14_17_21_01226) ),
inference(component_clause,[status(thm)],[f262]) ).
fof(f265,plain,
( ~ sQ4_spl
| ~ sQ1_spl
| sQ5_spl ),
inference(split_clause,[status(thm)],[f261,f262,f239,f257]) ).
fof(f267,plain,
! [X0] :
( ~ sQ5_spl
| ~ ra_Px1(i2003_11_14_17_21_01226,X0) ),
inference(resolution,[status(thm)],[f263,f186]) ).
fof(f272,plain,
( ~ sQ5_spl
| ~ ca_Cx1(i2003_11_14_17_21_01226) ),
inference(resolution,[status(thm)],[f267,f174]) ).
fof(f274,plain,
( ~ sQ5_spl
| ~ cUnsatisfiable(i2003_11_14_17_21_01226) ),
inference(resolution,[status(thm)],[f272,f164]) ).
fof(f275,plain,
( ~ sQ5_spl
| ~ sQ1_spl ),
inference(split_clause,[status(thm)],[f274,f239,f262]) ).
fof(f276,plain,
$false,
inference(sat_refutation,[status(thm)],[f247,f249,f260,f265,f275]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : KRS107+1 : TPTP v9.3.1. Released v3.1.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n026.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Sun Sep 20 22:56:39 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.36 % Drodi V4.1.1
% 0.09/0.38 % Refutation found
% 0.09/0.38 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.09/0.38 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.09/0.40 % Elapsed time: 0.036074 seconds
% 0.09/0.40 % CPU time: 0.082448 seconds
% 0.09/0.40 % Total memory used: 3.736 MB
% 0.09/0.40 % Net memory used: 3.539 MB
%------------------------------------------------------------------------------