%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : KRS122+1 : TPTP v9.3.1. Released v3.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n014.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 01:53:06 PM UTC 2026
% Result : Unsatisfiable 2.93s 0.84s
% Output : Proof 2.93s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 8
% Syntax : Number of formulae : 48 ( 15 unt; 0 def)
% Number of atoms : 130 ( 6 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 135 ( 53 ~; 50 |; 24 &)
% ( 6 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 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 : 68 ( 2 sgn 41 !; 9 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f26,axiom,
! [X,Y,Z] :
( ( rf(X,Z)
& rf(X,Y) )
=> Y = Z ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_7) ).
fof(f26_nnf,plain,
! [X,Y,Z] :
( Y = Z
| ~ rf(X,Z)
| ~ rf(X,Y) ),
inference(nnf_transformation,[status(thm)],[f26]) ).
fof(f26_sk,plain,
! [X,Y,Z] :
( Y = Z
| ~ rf(X,Z)
| ~ rf(X,Y) ),
inference(skolemisation,[status(esa)],[f26_nnf]) ).
cnf(c37,plain,
( X1 = X2
| ~ rf(X0,X2)
| ~ rf(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f26_sk]) ).
fof(f21,axiom,
! [X] :
( cUnsatisfiable(X)
<=> ? [Y] :
( ca_Ax2(Y)
& rf(X,Y) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_2) ).
fof(f21_nnf,plain,
! [X] :
( ( ! [Y] :
( ~ ca_Ax2(Y)
| ~ rf(X,Y) )
| cUnsatisfiable(X) )
& ( ? [Y] :
( ca_Ax2(Y)
& rf(X,Y) )
| ~ cUnsatisfiable(X) ) ),
inference(nnf_transformation,[status(thm)],[f21]) ).
fof(f21_sk,plain,
! [X,Y] :
( ( ~ ca_Ax2(Y)
| ~ rf(X,Y)
| cUnsatisfiable(X) )
& ( ( ca_Ax2(sk0(X))
& rf(X,sk0(X)) )
| ~ cUnsatisfiable(X) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk0])],[f21_nnf]) ).
cnf(c23,plain,
( rf(X0,sk0(X0))
| ~ cUnsatisfiable(X0) ),
inference(cnf_transformation,[status(esa)],[f21_sk]) ).
fof(f30,axiom,
cUnsatisfiable(i2003_11_14_17_21_55116),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_11) ).
fof(f30_nnf,plain,
cUnsatisfiable(i2003_11_14_17_21_55116),
inference(nnf_transformation,[status(thm)],[f30]) ).
cnf(c43,plain,
cUnsatisfiable(i2003_11_14_17_21_55116),
inference(cnf_transformation,[status(esa)],[f30_nnf]) ).
cnf(p47,plain,
rf(i2003_11_14_17_21_55116,sk0(i2003_11_14_17_21_55116)),
inference(resolution,[status(thm)],[c23,c43]) ).
cnf(p57,plain,
( sk0(i2003_11_14_17_21_55116) = X0
| ~ rf(i2003_11_14_17_21_55116,X0) ),
inference(resolution,[status(thm)],[c37,p47]) ).
fof(f24,axiom,
! [X] :
( ca_Ax2(X)
<=> ( ! [Y] :
( rinvF(X,Y)
=> ca_Vx3(Y) )
& cp1(X) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_5) ).
fof(f24_nnf,plain,
! [X] :
( ( ? [Y] :
( ~ ca_Vx3(Y)
& rinvF(X,Y) )
| ~ cp1(X)
| ca_Ax2(X) )
& ( ( ! [Y] :
( ca_Vx3(Y)
| ~ rinvF(X,Y) )
& cp1(X) )
| ~ ca_Ax2(X) ) ),
inference(nnf_transformation,[status(thm)],[f24]) ).
fof(f24_sk,plain,
! [X,Y] :
( ( ( ~ ca_Vx3(sk3(X))
& rinvF(X,sk3(X)) )
| ~ cp1(X)
| ca_Ax2(X) )
& ( ( ( ca_Vx3(Y)
| ~ rinvF(X,Y) )
& cp1(X) )
| ~ ca_Ax2(X) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk3])],[f24_nnf]) ).
cnf(c31,plain,
( ca_Vx3(X1)
| ~ rinvF(X0,X1)
| ~ ca_Ax2(X0) ),
inference(cnf_transformation,[status(esa)],[f24_sk]) ).
cnf(c24,plain,
( ca_Ax2(sk0(X0))
| ~ cUnsatisfiable(X0) ),
inference(cnf_transformation,[status(esa)],[f21_sk]) ).
cnf(p44,plain,
ca_Ax2(sk0(i2003_11_14_17_21_55116)),
inference(resolution,[status(thm)],[c24,c43]) ).
cnf(p51,plain,
( ca_Vx3(X0)
| ~ rinvF(sk0(i2003_11_14_17_21_55116),X0) ),
inference(resolution,[status(thm)],[c31,p44]) ).
fof(f27,axiom,
! [X,Y] :
( rinvF(X,Y)
<=> rf(Y,X) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_8) ).
fof(f27_nnf,plain,
! [X,Y] :
( ( ~ rf(Y,X)
| rinvF(X,Y) )
& ( rf(Y,X)
| ~ rinvF(X,Y) ) ),
inference(nnf_transformation,[status(thm)],[f27]) ).
fof(f27_sk,plain,
! [X,Y] :
( ( ~ rf(Y,X)
| rinvF(X,Y) )
& ( rf(Y,X)
| ~ rinvF(X,Y) ) ),
inference(skolemisation,[status(esa)],[f27_nnf]) ).
cnf(c39,plain,
( ~ rf(X1,X0)
| rinvF(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f27_sk]) ).
cnf(p50,plain,
rinvF(sk0(i2003_11_14_17_21_55116),i2003_11_14_17_21_55116),
inference(resolution,[status(thm)],[c39,p47]) ).
cnf(p52,plain,
ca_Vx3(i2003_11_14_17_21_55116),
inference(resolution,[status(thm)],[p51,p50]) ).
fof(f25,axiom,
! [X] :
( ca_Vx3(X)
<=> ? [Y] :
( cp1xcomp(Y)
& rf(X,Y) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_6) ).
fof(f25_nnf,plain,
! [X] :
( ( ! [Y] :
( ~ cp1xcomp(Y)
| ~ rf(X,Y) )
| ca_Vx3(X) )
& ( ? [Y] :
( cp1xcomp(Y)
& rf(X,Y) )
| ~ ca_Vx3(X) ) ),
inference(nnf_transformation,[status(thm)],[f25]) ).
fof(f25_sk,plain,
! [X,Y] :
( ( ~ cp1xcomp(Y)
| ~ rf(X,Y)
| ca_Vx3(X) )
& ( ( cp1xcomp(sk4(X))
& rf(X,sk4(X)) )
| ~ ca_Vx3(X) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk4])],[f25_nnf]) ).
cnf(c34,plain,
( rf(X0,sk4(X0))
| ~ ca_Vx3(X0) ),
inference(cnf_transformation,[status(esa)],[f25_sk]) ).
cnf(p54,plain,
rf(i2003_11_14_17_21_55116,sk4(i2003_11_14_17_21_55116)),
inference(resolution,[status(thm)],[p52,c34]) ).
cnf(p59,plain,
sk0(i2003_11_14_17_21_55116) = sk4(i2003_11_14_17_21_55116),
inference(resolution,[status(thm)],[p57,p54]) ).
cnf(c35,plain,
( cp1xcomp(sk4(X0))
| ~ ca_Vx3(X0) ),
inference(cnf_transformation,[status(esa)],[f25_sk]) ).
cnf(p53,plain,
cp1xcomp(sk4(i2003_11_14_17_21_55116)),
inference(resolution,[status(thm)],[p52,c35]) ).
fof(f23,axiom,
! [X] :
( cp1xcomp(X)
<=> ? [Y0] : ra_Px1(X,Y0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_4) ).
fof(f23_nnf,plain,
! [X] :
( ( ! [Y0] : ~ ra_Px1(X,Y0)
| cp1xcomp(X) )
& ( ? [Y0] : ra_Px1(X,Y0)
| ~ cp1xcomp(X) ) ),
inference(nnf_transformation,[status(thm)],[f23]) ).
fof(f23_sk,plain,
! [X,Y0] :
( ( ~ ra_Px1(X,Y0)
| cp1xcomp(X) )
& ( ra_Px1(X,sk2(X))
| ~ cp1xcomp(X) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk2])],[f23_nnf]) ).
cnf(c28,plain,
( ra_Px1(X0,sk2(X0))
| ~ cp1xcomp(X0) ),
inference(cnf_transformation,[status(esa)],[f23_sk]) ).
cnf(p55,plain,
ra_Px1(sk4(i2003_11_14_17_21_55116),sk2(sk4(i2003_11_14_17_21_55116))),
inference(resolution,[status(thm)],[p53,c28]) ).
cnf(p67,plain,
ra_Px1(sk0(i2003_11_14_17_21_55116),sk2(sk4(i2003_11_14_17_21_55116))),
inference(superposition,[status(thm)],[p59,p55]) ).
fof(f22,axiom,
! [X] :
( cp1(X)
<=> ~ ? [Y] : ra_Px1(X,Y) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_3) ).
fof(f22_nnf,plain,
! [X] :
( ( ? [Y] : ra_Px1(X,Y)
| cp1(X) )
& ( ! [Y] : ~ ra_Px1(X,Y)
| ~ cp1(X) ) ),
inference(nnf_transformation,[status(thm)],[f22]) ).
fof(f22_sk,plain,
! [X,Y] :
( ( ra_Px1(X,sk1(X))
| cp1(X) )
& ( ~ ra_Px1(X,Y)
| ~ cp1(X) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk1])],[f22_nnf]) ).
cnf(c26,plain,
( ~ ra_Px1(X0,X1)
| ~ cp1(X0) ),
inference(cnf_transformation,[status(esa)],[f22_sk]) ).
cnf(c30,plain,
( cp1(X0)
| ~ ca_Ax2(X0) ),
inference(cnf_transformation,[status(esa)],[f24_sk]) ).
cnf(p45,plain,
cp1(sk0(i2003_11_14_17_21_55116)),
inference(resolution,[status(thm)],[p44,c30]) ).
cnf(p46,plain,
~ ra_Px1(sk0(i2003_11_14_17_21_55116),X0),
inference(resolution,[status(thm)],[c26,p45]) ).
cnf(p79,plain,
$false,
inference(resolution,[status(thm)],[p67,p46]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : KRS122+1 : TPTP v9.3.1. Released v3.1.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.11/0.37 % Computer : n014.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Wed Sep 23 19:26:18 UTC 2026
% 0.11/0.38 % CPUTime :
% 0.11/0.38 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 2.93/0.84 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 2.93/0.84 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------