%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : KRS107+1 : TPTP v9.3.1. Released v3.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n009.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 : Fri Sep 25 01:53:04 PM UTC 2026
% Result : Unsatisfiable 2.54s 0.81s
% Output : Proof 2.54s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 9
% Syntax : Number of formulae : 56 ( 16 unt; 0 def)
% Number of atoms : 152 ( 6 equ)
% Maximal formula atoms : 12 ( 2 avg)
% Number of connectives : 158 ( 62 ~; 59 |; 29 &)
% ( 5 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 12 ( 10 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 1 con; 0-1 aty)
% Number of variables : 75 ( 2 sgn 45 !; 10 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f44,axiom,
cUnsatisfiable(i2003_11_14_17_21_01226),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_12) ).
fof(f44_nnf,plain,
cUnsatisfiable(i2003_11_14_17_21_01226),
inference(nnf_transformation,[status(thm)],[f44]) ).
cnf(c57,plain,
cUnsatisfiable(i2003_11_14_17_21_01226),
inference(cnf_transformation,[status(esa)],[f44_nnf]) ).
fof(f34,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',axiom_2) ).
fof(f34_nnf,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)],[f34]) ).
fof(f34_sk,plain,
! [X,Y] :
( ( ~ ca_Cx1(X)
| ~ cc2(Y)
| ~ rrx4(X,Y)
| ~ cc1(Y)
| ~ rrx3(X,Y)
| cUnsatisfiable(X) )
& ( ( ca_Cx1(X)
& cc2(sk1(X))
& rrx4(X,sk1(X))
& cc1(sk0(X))
& rrx3(X,sk0(X)) )
| ~ cUnsatisfiable(X) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk0,sk1])],[f34_nnf]) ).
cnf(c38,plain,
( rrx4(X0,sk1(X0))
| ~ cUnsatisfiable(X0) ),
inference(cnf_transformation,[status(esa)],[f34_sk]) ).
cnf(p69,plain,
rrx4(i2003_11_14_17_21_01226,sk1(i2003_11_14_17_21_01226)),
inference(resolution,[status(thm)],[c57,c38]) ).
fof(f49,axiom,
! [X,Y] :
( rrx4(X,Y)
=> rrx(X,Y) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_17) ).
fof(f49_nnf,plain,
! [X,Y] :
( rrx(X,Y)
| ~ rrx4(X,Y) ),
inference(nnf_transformation,[status(thm)],[f49]) ).
fof(f49_sk,plain,
! [X,Y] :
( rrx(X,Y)
| ~ rrx4(X,Y) ),
inference(skolemisation,[status(esa)],[f49_nnf]) ).
cnf(c62,plain,
( rrx(X0,X1)
| ~ rrx4(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f49_sk]) ).
cnf(p80,plain,
rrx(i2003_11_14_17_21_01226,sk1(i2003_11_14_17_21_01226)),
inference(resolution,[status(thm)],[p69,c62]) ).
fof(f39,axiom,
! [X,Y,Z] :
( ( rrx(X,Z)
& rrx(X,Y) )
=> Y = Z ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_7) ).
fof(f39_nnf,plain,
! [X,Y,Z] :
( Y = Z
| ~ rrx(X,Z)
| ~ rrx(X,Y) ),
inference(nnf_transformation,[status(thm)],[f39]) ).
fof(f39_sk,plain,
! [X,Y,Z] :
( Y = Z
| ~ rrx(X,Z)
| ~ rrx(X,Y) ),
inference(skolemisation,[status(esa)],[f39_nnf]) ).
cnf(c52,plain,
( X1 = X2
| ~ rrx(X0,X2)
| ~ rrx(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f39_sk]) ).
cnf(p89,plain,
( sk1(i2003_11_14_17_21_01226) = X0
| ~ rrx(i2003_11_14_17_21_01226,X0) ),
inference(resolution,[status(thm)],[p80,c52]) ).
cnf(c36,plain,
( rrx3(X0,sk0(X0))
| ~ cUnsatisfiable(X0) ),
inference(cnf_transformation,[status(esa)],[f34_sk]) ).
cnf(p67,plain,
rrx3(i2003_11_14_17_21_01226,sk0(i2003_11_14_17_21_01226)),
inference(resolution,[status(thm)],[c57,c36]) ).
fof(f52,axiom,
! [X,Y] :
( rrx3(X,Y)
=> rrx(X,Y) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_20) ).
fof(f52_nnf,plain,
! [X,Y] :
( rrx(X,Y)
| ~ rrx3(X,Y) ),
inference(nnf_transformation,[status(thm)],[f52]) ).
fof(f52_sk,plain,
! [X,Y] :
( rrx(X,Y)
| ~ rrx3(X,Y) ),
inference(skolemisation,[status(esa)],[f52_nnf]) ).
cnf(c65,plain,
( rrx(X0,X1)
| ~ rrx3(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f52_sk]) ).
cnf(p77,plain,
rrx(i2003_11_14_17_21_01226,sk0(i2003_11_14_17_21_01226)),
inference(resolution,[status(thm)],[p67,c65]) ).
cnf(p92,plain,
sk1(i2003_11_14_17_21_01226) = sk0(i2003_11_14_17_21_01226),
inference(resolution,[status(thm)],[p89,p77]) ).
cnf(c39,plain,
( cc2(sk1(X0))
| ~ cUnsatisfiable(X0) ),
inference(cnf_transformation,[status(esa)],[f34_sk]) ).
cnf(p70,plain,
cc2(sk1(i2003_11_14_17_21_01226)),
inference(resolution,[status(thm)],[c57,c39]) ).
fof(f35,axiom,
! [X] :
( ca_Ax2(X)
<=> ( cc1(X)
& cc2(X) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_3) ).
fof(f35_nnf,plain,
! [X] :
( ( ~ cc1(X)
| ~ cc2(X)
| ca_Ax2(X) )
& ( ( cc1(X)
& cc2(X) )
| ~ ca_Ax2(X) ) ),
inference(nnf_transformation,[status(thm)],[f35]) ).
fof(f35_sk,plain,
! [X] :
( ( ~ cc1(X)
| ~ cc2(X)
| ca_Ax2(X) )
& ( ( cc1(X)
& cc2(X) )
| ~ ca_Ax2(X) ) ),
inference(skolemisation,[status(esa)],[f35_nnf]) ).
cnf(c44,plain,
( ~ cc1(X0)
| ~ cc2(X0)
| ca_Ax2(X0) ),
inference(cnf_transformation,[status(esa)],[f35_sk]) ).
cnf(p81,plain,
( ~ cc1(sk1(i2003_11_14_17_21_01226))
| ca_Ax2(sk1(i2003_11_14_17_21_01226)) ),
inference(resolution,[status(thm)],[p70,c44]) ).
cnf(p97,plain,
( ~ cc1(sk0(i2003_11_14_17_21_01226))
| ca_Ax2(sk0(i2003_11_14_17_21_01226)) ),
inference(demodulation,[status(thm)],[p92,p81]) ).
cnf(c37,plain,
( cc1(sk0(X0))
| ~ cUnsatisfiable(X0) ),
inference(cnf_transformation,[status(esa)],[f34_sk]) ).
cnf(p68,plain,
cc1(sk0(i2003_11_14_17_21_01226)),
inference(resolution,[status(thm)],[c57,c37]) ).
cnf(p98,plain,
ca_Ax2(sk0(i2003_11_14_17_21_01226)),
inference(resolution,[status(thm)],[p97,p68]) ).
fof(f37,axiom,
! [X] :
( ca_Cx1xcomp(X)
<=> ? [Y] :
( ca_Ax2(Y)
& rrx3(X,Y) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_5) ).
fof(f37_nnf,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)],[f37]) ).
fof(f37_sk,plain,
! [X,Y] :
( ( ~ ca_Ax2(Y)
| ~ rrx3(X,Y)
| ca_Cx1xcomp(X) )
& ( ( ca_Ax2(sk3(X))
& rrx3(X,sk3(X)) )
| ~ ca_Cx1xcomp(X) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk3])],[f37_nnf]) ).
cnf(c49,plain,
( ~ ca_Ax2(X1)
| ~ rrx3(X0,X1)
| ca_Cx1xcomp(X0) ),
inference(cnf_transformation,[status(esa)],[f37_sk]) ).
cnf(p74,plain,
( ~ ca_Ax2(sk0(i2003_11_14_17_21_01226))
| ca_Cx1xcomp(i2003_11_14_17_21_01226) ),
inference(resolution,[status(thm)],[p67,c49]) ).
cnf(p99,plain,
ca_Cx1xcomp(i2003_11_14_17_21_01226),
inference(resolution,[status(thm)],[p98,p74]) ).
fof(f38,axiom,
! [X] :
( ca_Cx1xcomp(X)
<=> ~ ? [Y] : ra_Px1(X,Y) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_6) ).
fof(f38_nnf,plain,
! [X] :
( ( ? [Y] : ra_Px1(X,Y)
| ca_Cx1xcomp(X) )
& ( ! [Y] : ~ ra_Px1(X,Y)
| ~ ca_Cx1xcomp(X) ) ),
inference(nnf_transformation,[status(thm)],[f38]) ).
fof(f38_sk,plain,
! [X,Y] :
( ( ra_Px1(X,sk4(X))
| ca_Cx1xcomp(X) )
& ( ~ ra_Px1(X,Y)
| ~ ca_Cx1xcomp(X) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk4])],[f38_nnf]) ).
cnf(c50,plain,
( ~ ra_Px1(X0,X1)
| ~ ca_Cx1xcomp(X0) ),
inference(cnf_transformation,[status(esa)],[f38_sk]) ).
cnf(p102,plain,
~ ra_Px1(i2003_11_14_17_21_01226,X0),
inference(resolution,[status(thm)],[p99,c50]) ).
cnf(c40,plain,
( ca_Cx1(X0)
| ~ cUnsatisfiable(X0) ),
inference(cnf_transformation,[status(esa)],[f34_sk]) ).
cnf(p71,plain,
ca_Cx1(i2003_11_14_17_21_01226),
inference(resolution,[status(thm)],[c57,c40]) ).
fof(f36,axiom,
! [X] :
( ca_Cx1(X)
<=> ? [Y0] : ra_Px1(X,Y0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_4) ).
fof(f36_nnf,plain,
! [X] :
( ( ! [Y0] : ~ ra_Px1(X,Y0)
| ca_Cx1(X) )
& ( ? [Y0] : ra_Px1(X,Y0)
| ~ ca_Cx1(X) ) ),
inference(nnf_transformation,[status(thm)],[f36]) ).
fof(f36_sk,plain,
! [X,Y0] :
( ( ~ ra_Px1(X,Y0)
| ca_Cx1(X) )
& ( ra_Px1(X,sk2(X))
| ~ ca_Cx1(X) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk2])],[f36_nnf]) ).
cnf(c45,plain,
( ra_Px1(X0,sk2(X0))
| ~ ca_Cx1(X0) ),
inference(cnf_transformation,[status(esa)],[f36_sk]) ).
cnf(p82,plain,
ra_Px1(i2003_11_14_17_21_01226,sk2(i2003_11_14_17_21_01226)),
inference(resolution,[status(thm)],[p71,c45]) ).
cnf(p109,plain,
$false,
inference(resolution,[status(thm)],[p102,p82]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : KRS107+1 : TPTP v9.3.1. Released v3.1.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.10/0.37 % Computer : n009.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Wed Sep 23 19:24:44 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.38 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 2.54/0.81 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 2.54/0.81 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------