%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : KRS121+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 : n003.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 4.60s 1.26s
% Output : Proof 4.60s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 8
% Syntax : Number of formulae : 47 ( 14 unt; 0 def)
% Number of atoms : 134 ( 0 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 142 ( 55 ~; 52 |; 27 &)
% ( 6 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 9 ( 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(f29,axiom,
! [X,Y,Z] :
( ( rr(Y,Z)
& rr(X,Y) )
=> rr(X,Z) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_10) ).
fof(f29_nnf,plain,
! [X,Y,Z] :
( rr(X,Z)
| ~ rr(Y,Z)
| ~ rr(X,Y) ),
inference(nnf_transformation,[status(thm)],[f29]) ).
fof(f29_sk,plain,
! [X,Y,Z] :
( rr(X,Z)
| ~ rr(Y,Z)
| ~ rr(X,Y) ),
inference(skolemisation,[status(esa)],[f29_nnf]) ).
cnf(c43,plain,
( rr(X0,X2)
| ~ rr(X1,X2)
| ~ rr(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f29_sk]) ).
fof(f21,axiom,
! [X] :
( cUnsatisfiable(X)
<=> ( cp1(X)
& ? [Y] :
( ca_Vx3(Y)
& rr(X,Y) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_2) ).
fof(f21_nnf,plain,
! [X] :
( ( ~ cp1(X)
| ! [Y] :
( ~ ca_Vx3(Y)
| ~ rr(X,Y) )
| cUnsatisfiable(X) )
& ( ( cp1(X)
& ? [Y] :
( ca_Vx3(Y)
& rr(X,Y) ) )
| ~ cUnsatisfiable(X) ) ),
inference(nnf_transformation,[status(thm)],[f21]) ).
fof(f21_sk,plain,
! [X,Y] :
( ( ~ cp1(X)
| ~ ca_Vx3(Y)
| ~ rr(X,Y)
| cUnsatisfiable(X) )
& ( ( cp1(X)
& ca_Vx3(sk0(X))
& rr(X,sk0(X)) )
| ~ cUnsatisfiable(X) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk0])],[f21_nnf]) ).
cnf(c23,plain,
( rr(X0,sk0(X0))
| ~ cUnsatisfiable(X0) ),
inference(cnf_transformation,[status(esa)],[f21_sk]) ).
fof(f30,axiom,
cUnsatisfiable(i2003_11_14_17_21_5199),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_11) ).
fof(f30_nnf,plain,
cUnsatisfiable(i2003_11_14_17_21_5199),
inference(nnf_transformation,[status(thm)],[f30]) ).
cnf(c44,plain,
cUnsatisfiable(i2003_11_14_17_21_5199),
inference(cnf_transformation,[status(esa)],[f30_nnf]) ).
cnf(p51,plain,
rr(i2003_11_14_17_21_5199,sk0(i2003_11_14_17_21_5199)),
inference(resolution,[status(thm)],[c23,c44]) ).
cnf(p68,plain,
( rr(i2003_11_14_17_21_5199,X0)
| ~ rr(sk0(i2003_11_14_17_21_5199),X0) ),
inference(resolution,[status(thm)],[c43,p51]) ).
fof(f25,axiom,
! [X] :
( ca_Vx3(X)
<=> ? [Y] :
( ca_Ax2(Y)
& rr(X,Y) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_6) ).
fof(f25_nnf,plain,
! [X] :
( ( ! [Y] :
( ~ ca_Ax2(Y)
| ~ rr(X,Y) )
| ca_Vx3(X) )
& ( ? [Y] :
( ca_Ax2(Y)
& rr(X,Y) )
| ~ ca_Vx3(X) ) ),
inference(nnf_transformation,[status(thm)],[f25]) ).
fof(f25_sk,plain,
! [X,Y] :
( ( ~ ca_Ax2(Y)
| ~ rr(X,Y)
| ca_Vx3(X) )
& ( ( ca_Ax2(sk4(X))
& rr(X,sk4(X)) )
| ~ ca_Vx3(X) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk4])],[f25_nnf]) ).
cnf(c35,plain,
( rr(X0,sk4(X0))
| ~ ca_Vx3(X0) ),
inference(cnf_transformation,[status(esa)],[f25_sk]) ).
cnf(c24,plain,
( ca_Vx3(sk0(X0))
| ~ cUnsatisfiable(X0) ),
inference(cnf_transformation,[status(esa)],[f21_sk]) ).
cnf(p46,plain,
ca_Vx3(sk0(i2003_11_14_17_21_5199)),
inference(resolution,[status(thm)],[c24,c44]) ).
cnf(p54,plain,
rr(sk0(i2003_11_14_17_21_5199),sk4(sk0(i2003_11_14_17_21_5199))),
inference(resolution,[status(thm)],[c35,p46]) ).
cnf(p71,plain,
rr(i2003_11_14_17_21_5199,sk4(sk0(i2003_11_14_17_21_5199))),
inference(resolution,[status(thm)],[p68,p54]) ).
fof(f28,axiom,
! [X,Y] :
( rinvR(X,Y)
<=> rr(Y,X) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_9) ).
fof(f28_nnf,plain,
! [X,Y] :
( ( ~ rr(Y,X)
| rinvR(X,Y) )
& ( rr(Y,X)
| ~ rinvR(X,Y) ) ),
inference(nnf_transformation,[status(thm)],[f28]) ).
fof(f28_sk,plain,
! [X,Y] :
( ( ~ rr(Y,X)
| rinvR(X,Y) )
& ( rr(Y,X)
| ~ rinvR(X,Y) ) ),
inference(skolemisation,[status(esa)],[f28_nnf]) ).
cnf(c42,plain,
( ~ rr(X1,X0)
| rinvR(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f28_sk]) ).
cnf(p72,plain,
rinvR(sk4(sk0(i2003_11_14_17_21_5199)),i2003_11_14_17_21_5199),
inference(resolution,[status(thm)],[p71,c42]) ).
fof(f24,axiom,
! [X] :
( ca_Ax2(X)
<=> ( ! [Y] :
( rinvR(X,Y)
=> cp1xcomp(Y) )
& cp1(X) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_5) ).
fof(f24_nnf,plain,
! [X] :
( ( ? [Y] :
( ~ cp1xcomp(Y)
& rinvR(X,Y) )
| ~ cp1(X)
| ca_Ax2(X) )
& ( ( ! [Y] :
( cp1xcomp(Y)
| ~ rinvR(X,Y) )
& cp1(X) )
| ~ ca_Ax2(X) ) ),
inference(nnf_transformation,[status(thm)],[f24]) ).
fof(f24_sk,plain,
! [X,Y] :
( ( ( ~ cp1xcomp(sk3(X))
& rinvR(X,sk3(X)) )
| ~ cp1(X)
| ca_Ax2(X) )
& ( ( ( cp1xcomp(Y)
| ~ rinvR(X,Y) )
& cp1(X) )
| ~ ca_Ax2(X) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk3])],[f24_nnf]) ).
cnf(c32,plain,
( cp1xcomp(X1)
| ~ rinvR(X0,X1)
| ~ ca_Ax2(X0) ),
inference(cnf_transformation,[status(esa)],[f24_sk]) ).
cnf(c36,plain,
( ca_Ax2(sk4(X0))
| ~ ca_Vx3(X0) ),
inference(cnf_transformation,[status(esa)],[f25_sk]) ).
cnf(p48,plain,
ca_Ax2(sk4(sk0(i2003_11_14_17_21_5199))),
inference(resolution,[status(thm)],[c36,p46]) ).
cnf(p57,plain,
( cp1xcomp(X0)
| ~ rinvR(sk4(sk0(i2003_11_14_17_21_5199)),X0) ),
inference(resolution,[status(thm)],[c32,p48]) ).
cnf(p75,plain,
cp1xcomp(i2003_11_14_17_21_5199),
inference(resolution,[status(thm)],[p72,p57]) ).
fof(f23,axiom,
! [X] :
( cp1xcomp(X)
<=> ? [Y0] : ra_Px1(X,Y0) ),
file('/export/starexec/sandbox/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(c29,plain,
( ra_Px1(X0,sk2(X0))
| ~ cp1xcomp(X0) ),
inference(cnf_transformation,[status(esa)],[f23_sk]) ).
cnf(p76,plain,
ra_Px1(i2003_11_14_17_21_5199,sk2(i2003_11_14_17_21_5199)),
inference(resolution,[status(thm)],[p75,c29]) ).
fof(f22,axiom,
! [X] :
( cp1(X)
<=> ~ ? [Y] : ra_Px1(X,Y) ),
file('/export/starexec/sandbox/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(c27,plain,
( ~ ra_Px1(X0,X1)
| ~ cp1(X0) ),
inference(cnf_transformation,[status(esa)],[f22_sk]) ).
cnf(c25,plain,
( cp1(X0)
| ~ cUnsatisfiable(X0) ),
inference(cnf_transformation,[status(esa)],[f21_sk]) ).
cnf(p45,plain,
cp1(i2003_11_14_17_21_5199),
inference(resolution,[status(thm)],[c25,c44]) ).
cnf(p47,plain,
~ ra_Px1(i2003_11_14_17_21_5199,X0),
inference(resolution,[status(thm)],[c27,p45]) ).
cnf(p77,plain,
$false,
inference(resolution,[status(thm)],[p76,p47]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : KRS121+1 : TPTP v9.3.1. Released v3.1.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.10/0.58 % Computer : n003.cluster.edu
% 0.10/0.58 % Model : x86_64 x86_64
% 0.10/0.58 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.58 % Memory : 8046.5625MB
% 0.10/0.58 % OS : Linux 6.8.0-71-generic
% 0.10/0.58 % CPULimit : 300
% 0.10/0.58 % WCLimit : 300
% 0.10/0.58 % DateTime : Wed Sep 23 19:28:05 UTC 2026
% 0.12/0.58 % CPUTime :
% 0.12/0.58 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 4.60/1.26 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 4.60/1.26 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------