%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : KRS106+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 3.40s 1.09s
% Output : Proof 3.40s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 8
% Syntax : Number of formulae : 51 ( 17 unt; 0 def)
% Number of atoms : 130 ( 12 equ)
% Maximal formula atoms : 14 ( 2 avg)
% Number of connectives : 132 ( 53 ~; 49 |; 23 &)
% ( 3 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 10 ( 8 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 1 con; 0-1 aty)
% Number of variables : 79 ( 3 sgn 47 !; 10 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f22,axiom,
! [X,Y,Z] :
( ( rf2(X,Z)
& rf2(X,Y) )
=> Y = Z ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_6) ).
fof(f22_nnf,plain,
! [X,Y,Z] :
( Y = Z
| ~ rf2(X,Z)
| ~ rf2(X,Y) ),
inference(nnf_transformation,[status(thm)],[f22]) ).
fof(f22_sk,plain,
! [X,Y,Z] :
( Y = Z
| ~ rf2(X,Z)
| ~ rf2(X,Y) ),
inference(skolemisation,[status(esa)],[f22_nnf]) ).
cnf(c32,plain,
( X1 = X2
| ~ rf2(X0,X2)
| ~ rf2(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f22_sk]) ).
fof(f18,axiom,
! [X] :
( cUnsatisfiable(X)
<=> ( ? [Y] :
( cp1xcomp(Y)
& rf2(X,Y) )
& ? [Y] :
( cp1(Y)
& rf1(X,Y) )
& ? [Y] :
( cp2(Y)
& rf3(X,Y) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_2) ).
fof(f18_nnf,plain,
! [X] :
( ( ! [Y] :
( ~ cp1xcomp(Y)
| ~ rf2(X,Y) )
| ! [Y] :
( ~ cp1(Y)
| ~ rf1(X,Y) )
| ! [Y] :
( ~ cp2(Y)
| ~ rf3(X,Y) )
| cUnsatisfiable(X) )
& ( ( ? [Y] :
( cp1xcomp(Y)
& rf2(X,Y) )
& ? [Y] :
( cp1(Y)
& rf1(X,Y) )
& ? [Y] :
( cp2(Y)
& rf3(X,Y) ) )
| ~ cUnsatisfiable(X) ) ),
inference(nnf_transformation,[status(thm)],[f18]) ).
fof(f18_sk,plain,
! [X,Y] :
( ( ~ cp1xcomp(Y)
| ~ rf2(X,Y)
| ~ cp1(Y)
| ~ rf1(X,Y)
| ~ cp2(Y)
| ~ rf3(X,Y)
| cUnsatisfiable(X) )
& ( ( cp1xcomp(sk2(X))
& rf2(X,sk2(X))
& cp1(sk1(X))
& rf1(X,sk1(X))
& cp2(sk0(X))
& rf3(X,sk0(X)) )
| ~ cUnsatisfiable(X) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk0,sk1,sk2])],[f18_nnf]) ).
cnf(c24,plain,
( rf2(X0,sk2(X0))
| ~ cUnsatisfiable(X0) ),
inference(cnf_transformation,[status(esa)],[f18_sk]) ).
fof(f24,axiom,
cUnsatisfiable(i2003_11_14_17_20_57644),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_8) ).
fof(f24_nnf,plain,
cUnsatisfiable(i2003_11_14_17_20_57644),
inference(nnf_transformation,[status(thm)],[f24]) ).
cnf(c34,plain,
cUnsatisfiable(i2003_11_14_17_20_57644),
inference(cnf_transformation,[status(esa)],[f24_nnf]) ).
cnf(p43,plain,
rf2(i2003_11_14_17_20_57644,sk2(i2003_11_14_17_20_57644)),
inference(resolution,[status(thm)],[c24,c34]) ).
cnf(p54,plain,
( sk2(i2003_11_14_17_20_57644) = X0
| ~ rf2(i2003_11_14_17_20_57644,X0) ),
inference(resolution,[status(thm)],[c32,p43]) ).
fof(f26,axiom,
! [X,Y] :
( rf3(X,Y)
=> rf2(X,Y) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_10) ).
fof(f26_nnf,plain,
! [X,Y] :
( rf2(X,Y)
| ~ rf3(X,Y) ),
inference(nnf_transformation,[status(thm)],[f26]) ).
fof(f26_sk,plain,
! [X,Y] :
( rf2(X,Y)
| ~ rf3(X,Y) ),
inference(skolemisation,[status(esa)],[f26_nnf]) ).
cnf(c36,plain,
( rf2(X0,X1)
| ~ rf3(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f26_sk]) ).
cnf(c20,plain,
( rf3(X0,sk0(X0))
| ~ cUnsatisfiable(X0) ),
inference(cnf_transformation,[status(esa)],[f18_sk]) ).
cnf(p41,plain,
rf3(i2003_11_14_17_20_57644,sk0(i2003_11_14_17_20_57644)),
inference(resolution,[status(thm)],[c20,c34]) ).
cnf(p48,plain,
rf2(i2003_11_14_17_20_57644,sk0(i2003_11_14_17_20_57644)),
inference(resolution,[status(thm)],[c36,p41]) ).
cnf(p56,plain,
sk2(i2003_11_14_17_20_57644) = sk0(i2003_11_14_17_20_57644),
inference(resolution,[status(thm)],[p54,p48]) ).
fof(f20,axiom,
! [X] :
( cp1xcomp(X)
<=> ? [Y0] : ra_Px1(X,Y0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_4) ).
fof(f20_nnf,plain,
! [X] :
( ( ! [Y0] : ~ ra_Px1(X,Y0)
| cp1xcomp(X) )
& ( ? [Y0] : ra_Px1(X,Y0)
| ~ cp1xcomp(X) ) ),
inference(nnf_transformation,[status(thm)],[f20]) ).
fof(f20_sk,plain,
! [X,Y0] :
( ( ~ ra_Px1(X,Y0)
| cp1xcomp(X) )
& ( ra_Px1(X,sk4(X))
| ~ cp1xcomp(X) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk4])],[f20_nnf]) ).
cnf(c29,plain,
( ra_Px1(X0,sk4(X0))
| ~ cp1xcomp(X0) ),
inference(cnf_transformation,[status(esa)],[f20_sk]) ).
cnf(c25,plain,
( cp1xcomp(sk2(X0))
| ~ cUnsatisfiable(X0) ),
inference(cnf_transformation,[status(esa)],[f18_sk]) ).
cnf(p39,plain,
cp1xcomp(sk2(i2003_11_14_17_20_57644)),
inference(resolution,[status(thm)],[c25,c34]) ).
cnf(p45,plain,
ra_Px1(sk2(i2003_11_14_17_20_57644),sk4(sk2(i2003_11_14_17_20_57644))),
inference(resolution,[status(thm)],[c29,p39]) ).
cnf(p58,plain,
ra_Px1(sk0(i2003_11_14_17_20_57644),sk4(sk0(i2003_11_14_17_20_57644))),
inference(demodulation,[status(thm)],[p56,p45]) ).
fof(f21,axiom,
! [X,Y,Z] :
( ( rf1(X,Z)
& rf1(X,Y) )
=> Y = Z ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_5) ).
fof(f21_nnf,plain,
! [X,Y,Z] :
( Y = Z
| ~ rf1(X,Z)
| ~ rf1(X,Y) ),
inference(nnf_transformation,[status(thm)],[f21]) ).
fof(f21_sk,plain,
! [X,Y,Z] :
( Y = Z
| ~ rf1(X,Z)
| ~ rf1(X,Y) ),
inference(skolemisation,[status(esa)],[f21_nnf]) ).
cnf(c31,plain,
( X1 = X2
| ~ rf1(X0,X2)
| ~ rf1(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f21_sk]) ).
cnf(c22,plain,
( rf1(X0,sk1(X0))
| ~ cUnsatisfiable(X0) ),
inference(cnf_transformation,[status(esa)],[f18_sk]) ).
cnf(p42,plain,
rf1(i2003_11_14_17_20_57644,sk1(i2003_11_14_17_20_57644)),
inference(resolution,[status(thm)],[c22,c34]) ).
cnf(p49,plain,
( sk1(i2003_11_14_17_20_57644) = X0
| ~ rf1(i2003_11_14_17_20_57644,X0) ),
inference(resolution,[status(thm)],[c31,p42]) ).
fof(f25,axiom,
! [X,Y] :
( rf3(X,Y)
=> rf1(X,Y) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_9) ).
fof(f25_nnf,plain,
! [X,Y] :
( rf1(X,Y)
| ~ rf3(X,Y) ),
inference(nnf_transformation,[status(thm)],[f25]) ).
fof(f25_sk,plain,
! [X,Y] :
( rf1(X,Y)
| ~ rf3(X,Y) ),
inference(skolemisation,[status(esa)],[f25_nnf]) ).
cnf(c35,plain,
( rf1(X0,X1)
| ~ rf3(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f25_sk]) ).
cnf(p47,plain,
rf1(i2003_11_14_17_20_57644,sk0(i2003_11_14_17_20_57644)),
inference(resolution,[status(thm)],[c35,p41]) ).
cnf(p51,plain,
sk1(i2003_11_14_17_20_57644) = sk0(i2003_11_14_17_20_57644),
inference(resolution,[status(thm)],[p49,p47]) ).
fof(f19,axiom,
! [X] :
( cp1(X)
<=> ~ ? [Y] : ra_Px1(X,Y) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_3) ).
fof(f19_nnf,plain,
! [X] :
( ( ? [Y] : ra_Px1(X,Y)
| cp1(X) )
& ( ! [Y] : ~ ra_Px1(X,Y)
| ~ cp1(X) ) ),
inference(nnf_transformation,[status(thm)],[f19]) ).
fof(f19_sk,plain,
! [X,Y] :
( ( ra_Px1(X,sk3(X))
| cp1(X) )
& ( ~ ra_Px1(X,Y)
| ~ cp1(X) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk3])],[f19_nnf]) ).
cnf(c27,plain,
( ~ ra_Px1(X0,X1)
| ~ cp1(X0) ),
inference(cnf_transformation,[status(esa)],[f19_sk]) ).
cnf(c23,plain,
( cp1(sk1(X0))
| ~ cUnsatisfiable(X0) ),
inference(cnf_transformation,[status(esa)],[f18_sk]) ).
cnf(p38,plain,
cp1(sk1(i2003_11_14_17_20_57644)),
inference(resolution,[status(thm)],[c23,c34]) ).
cnf(p40,plain,
~ ra_Px1(sk1(i2003_11_14_17_20_57644),X0),
inference(resolution,[status(thm)],[c27,p38]) ).
cnf(p53,plain,
~ ra_Px1(sk0(i2003_11_14_17_20_57644),X0),
inference(demodulation,[status(thm)],[p51,p40]) ).
cnf(p60,plain,
$false,
inference(resolution,[status(thm)],[p58,p53]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : KRS106+1 : TPTP v9.3.1. Released v3.1.0.
% 0.00/0.03 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.08/0.36 % Computer : n009.cluster.edu
% 0.08/0.36 % Model : x86_64 x86_64
% 0.08/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.36 % Memory : 8046.5625MB
% 0.08/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Wed Sep 23 19:24:13 UTC 2026
% 0.10/0.36 % CPUTime :
% 0.10/0.36 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 3.40/1.09 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 3.40/1.09 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------