%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : KRS105+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 0.56s 0.90s
% Output : Proof 0.56s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 8
% Syntax : Number of formulae : 42 ( 10 unt; 0 def)
% Number of atoms : 95 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 89 ( 36 ~; 36 |; 8 &)
% ( 3 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 8 ( 7 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 1 con; 0-1 aty)
% Number of variables : 48 ( 2 sgn 31 !; 5 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f7,axiom,
! [X] :
( ca_Ax2(X)
<=> ! [Y] :
( rr(X,Y)
=> cc(Y) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_7) ).
fof(f7_nnf,plain,
! [X] :
( ( ? [Y] :
( ~ cc(Y)
& rr(X,Y) )
| ca_Ax2(X) )
& ( ! [Y] :
( cc(Y)
| ~ rr(X,Y) )
| ~ ca_Ax2(X) ) ),
inference(nnf_transformation,[status(thm)],[f7]) ).
fof(f7_sk,plain,
! [X,Y] :
( ( ( ~ cc(sk2(X))
& rr(X,sk2(X)) )
| ca_Ax2(X) )
& ( cc(Y)
| ~ rr(X,Y)
| ~ ca_Ax2(X) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk2])],[f7_nnf]) ).
cnf(c12,plain,
( rr(X0,sk2(X0))
| ca_Ax2(X0) ),
inference(cnf_transformation,[status(esa)],[f7_sk]) ).
fof(f4,axiom,
! [X] :
( cc(X)
=> ! [Y] :
( rr(X,Y)
=> cc(Y) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_4) ).
fof(f4_nnf,plain,
! [X] :
( ! [Y] :
( cc(Y)
| ~ rr(X,Y) )
| ~ cc(X) ),
inference(nnf_transformation,[status(thm)],[f4]) ).
fof(f4_sk,plain,
! [X,Y] :
( cc(Y)
| ~ rr(X,Y)
| ~ cc(X) ),
inference(skolemisation,[status(esa)],[f4_nnf]) ).
cnf(c6,plain,
( cc(X1)
| ~ rr(X0,X1)
| ~ cc(X0) ),
inference(cnf_transformation,[status(esa)],[f4_sk]) ).
fof(f3,axiom,
! [X] :
( cUnsatisfiable(X)
=> cc(X) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_3) ).
fof(f3_nnf,plain,
! [X] :
( cc(X)
| ~ cUnsatisfiable(X) ),
inference(nnf_transformation,[status(thm)],[f3]) ).
fof(f3_sk,plain,
! [X] :
( cc(X)
| ~ cUnsatisfiable(X) ),
inference(skolemisation,[status(esa)],[f3_nnf]) ).
cnf(c5,plain,
( cc(X0)
| ~ cUnsatisfiable(X0) ),
inference(cnf_transformation,[status(esa)],[f3_sk]) ).
fof(f9,axiom,
cUnsatisfiable(i2003_11_14_17_20_53634),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_9) ).
fof(f9_nnf,plain,
cUnsatisfiable(i2003_11_14_17_20_53634),
inference(nnf_transformation,[status(thm)],[f9]) ).
cnf(c15,plain,
cUnsatisfiable(i2003_11_14_17_20_53634),
inference(cnf_transformation,[status(esa)],[f9_nnf]) ).
cnf(p17,plain,
cc(i2003_11_14_17_20_53634),
inference(resolution,[status(thm)],[c5,c15]) ).
cnf(p18,plain,
( cc(X0)
| ~ rr(i2003_11_14_17_20_53634,X0) ),
inference(resolution,[status(thm)],[c6,p17]) ).
cnf(p21,plain,
( cc(sk2(i2003_11_14_17_20_53634))
| ca_Ax2(i2003_11_14_17_20_53634) ),
inference(resolution,[status(thm)],[c12,p18]) ).
cnf(c13,plain,
( ~ cc(sk2(X0))
| ca_Ax2(X0) ),
inference(cnf_transformation,[status(esa)],[f7_sk]) ).
cnf(p23,plain,
( ca_Ax2(i2003_11_14_17_20_53634)
| ca_Ax2(i2003_11_14_17_20_53634) ),
inference(resolution,[status(thm)],[p21,c13]) ).
cnf(p24,plain,
ca_Ax2(i2003_11_14_17_20_53634),
inference(factoring,[status(thm)],[p23]) ).
fof(f8,axiom,
! [X] :
( ca_Ax2(X)
=> cd(X) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_8) ).
fof(f8_nnf,plain,
! [X] :
( cd(X)
| ~ ca_Ax2(X) ),
inference(nnf_transformation,[status(thm)],[f8]) ).
fof(f8_sk,plain,
! [X] :
( cd(X)
| ~ ca_Ax2(X) ),
inference(skolemisation,[status(esa)],[f8_nnf]) ).
cnf(c14,plain,
( cd(X0)
| ~ ca_Ax2(X0) ),
inference(cnf_transformation,[status(esa)],[f8_sk]) ).
cnf(p25,plain,
cd(i2003_11_14_17_20_53634),
inference(resolution,[status(thm)],[p24,c14]) ).
fof(f5,axiom,
! [X] :
( cd(X)
<=> ~ ? [Y] : ra_Px1(X,Y) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_5) ).
fof(f5_nnf,plain,
! [X] :
( ( ? [Y] : ra_Px1(X,Y)
| cd(X) )
& ( ! [Y] : ~ ra_Px1(X,Y)
| ~ cd(X) ) ),
inference(nnf_transformation,[status(thm)],[f5]) ).
fof(f5_sk,plain,
! [X,Y] :
( ( ra_Px1(X,sk0(X))
| cd(X) )
& ( ~ ra_Px1(X,Y)
| ~ cd(X) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk0])],[f5_nnf]) ).
cnf(c7,plain,
( ~ ra_Px1(X0,X1)
| ~ cd(X0) ),
inference(cnf_transformation,[status(esa)],[f5_sk]) ).
cnf(p26,plain,
~ ra_Px1(i2003_11_14_17_20_53634,X0),
inference(resolution,[status(thm)],[p25,c7]) ).
fof(f6,axiom,
! [X] :
( cdxcomp(X)
<=> ? [Y0] : ra_Px1(X,Y0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_6) ).
fof(f6_nnf,plain,
! [X] :
( ( ! [Y0] : ~ ra_Px1(X,Y0)
| cdxcomp(X) )
& ( ? [Y0] : ra_Px1(X,Y0)
| ~ cdxcomp(X) ) ),
inference(nnf_transformation,[status(thm)],[f6]) ).
fof(f6_sk,plain,
! [X,Y0] :
( ( ~ ra_Px1(X,Y0)
| cdxcomp(X) )
& ( ra_Px1(X,sk1(X))
| ~ cdxcomp(X) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk1])],[f6_nnf]) ).
cnf(c9,plain,
( ra_Px1(X0,sk1(X0))
| ~ cdxcomp(X0) ),
inference(cnf_transformation,[status(esa)],[f6_sk]) ).
fof(f2,axiom,
! [X] :
( cUnsatisfiable(X)
=> cdxcomp(X) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_2) ).
fof(f2_nnf,plain,
! [X] :
( cdxcomp(X)
| ~ cUnsatisfiable(X) ),
inference(nnf_transformation,[status(thm)],[f2]) ).
fof(f2_sk,plain,
! [X] :
( cdxcomp(X)
| ~ cUnsatisfiable(X) ),
inference(skolemisation,[status(esa)],[f2_nnf]) ).
cnf(c4,plain,
( cdxcomp(X0)
| ~ cUnsatisfiable(X0) ),
inference(cnf_transformation,[status(esa)],[f2_sk]) ).
cnf(p16,plain,
cdxcomp(i2003_11_14_17_20_53634),
inference(resolution,[status(thm)],[c4,c15]) ).
cnf(p20,plain,
ra_Px1(i2003_11_14_17_20_53634,sk1(i2003_11_14_17_20_53634)),
inference(resolution,[status(thm)],[c9,p16]) ).
cnf(p27,plain,
$false,
inference(resolution,[status(thm)],[p26,p20]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : KRS105+1 : TPTP v9.3.1. Released v3.1.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.11/0.36 % Computer : n009.cluster.edu
% 0.11/0.36 % Model : x86_64 x86_64
% 0.11/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.36 % Memory : 8046.5625MB
% 0.11/0.36 % OS : Linux 6.8.0-71-generic
% 0.11/0.36 % CPULimit : 300
% 0.11/0.36 % WCLimit : 300
% 0.11/0.36 % DateTime : Wed Sep 23 19:24:28 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.37 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.56/0.90 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.56/0.90 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------