%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : KRS113+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 : n008.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 01:53:05 PM UTC 2026
% Result : Unsatisfiable 3.62s 0.93s
% Output : Proof 3.62s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 7
% Syntax : Number of formulae : 46 ( 15 unt; 0 def)
% Number of atoms : 141 ( 9 equ)
% Maximal formula atoms : 18 ( 3 avg)
% Number of connectives : 153 ( 58 ~; 55 |; 32 &)
% ( 5 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 10 ( 8 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 1 con; 0-1 aty)
% Number of variables : 72 ( 2 sgn 40 !; 11 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f18,axiom,
! [X] :
( cUnsatisfiable(X)
<=> ( cpxcomp(X)
& ? [Y] :
( cp(Y)
& rs(X,Y) )
& ? [Y] :
( ca_Vx2(Y)
& rr(X,Y) )
& ! [Y0,Y1] :
( ( rr(X,Y1)
& rr(X,Y0) )
=> Y0 = Y1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_2) ).
fof(f18_nnf,plain,
! [X] :
( ( ~ cpxcomp(X)
| ! [Y] :
( ~ cp(Y)
| ~ rs(X,Y) )
| ! [Y] :
( ~ ca_Vx2(Y)
| ~ rr(X,Y) )
| ? [Y0,Y1] :
( Y0 != Y1
& rr(X,Y1)
& rr(X,Y0) )
| cUnsatisfiable(X) )
& ( ( cpxcomp(X)
& ? [Y] :
( cp(Y)
& rs(X,Y) )
& ? [Y] :
( ca_Vx2(Y)
& rr(X,Y) )
& ! [Y0,Y1] :
( Y0 = Y1
| ~ rr(X,Y1)
| ~ rr(X,Y0) ) )
| ~ cUnsatisfiable(X) ) ),
inference(nnf_transformation,[status(thm)],[f18]) ).
fof(f18_sk,plain,
! [X,Y0,Y1,Y] :
( ( ~ cpxcomp(X)
| ~ cp(Y)
| ~ rs(X,Y)
| ~ ca_Vx2(Y)
| ~ rr(X,Y)
| ( sk2(X) != sk3(X)
& rr(X,sk3(X))
& rr(X,sk2(X)) )
| cUnsatisfiable(X) )
& ( ( cpxcomp(X)
& cp(sk1(X))
& rs(X,sk1(X))
& ca_Vx2(sk0(X))
& rr(X,sk0(X))
& ( Y0 = Y1
| ~ rr(X,Y1)
| ~ rr(X,Y0) ) )
| ~ cUnsatisfiable(X) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk0,sk1,sk2,sk3])],[f18_nnf]) ).
cnf(c20,plain,
( X1 = X2
| ~ rr(X0,X2)
| ~ rr(X0,X1)
| ~ cUnsatisfiable(X0) ),
inference(cnf_transformation,[status(esa)],[f18_sk]) ).
fof(f23,axiom,
cUnsatisfiable(i2003_11_14_17_21_22376),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_7) ).
fof(f23_nnf,plain,
cUnsatisfiable(i2003_11_14_17_21_22376),
inference(nnf_transformation,[status(thm)],[f23]) ).
cnf(c38,plain,
cUnsatisfiable(i2003_11_14_17_21_22376),
inference(cnf_transformation,[status(esa)],[f23_nnf]) ).
cnf(p54,plain,
( X0 = X1
| ~ rr(i2003_11_14_17_21_22376,X1)
| ~ rr(i2003_11_14_17_21_22376,X0) ),
inference(resolution,[status(thm)],[c20,c38]) ).
cnf(c21,plain,
( rr(X0,sk0(X0))
| ~ cUnsatisfiable(X0) ),
inference(cnf_transformation,[status(esa)],[f18_sk]) ).
cnf(p44,plain,
rr(i2003_11_14_17_21_22376,sk0(i2003_11_14_17_21_22376)),
inference(resolution,[status(thm)],[c21,c38]) ).
cnf(p55,plain,
( sk0(i2003_11_14_17_21_22376) = X0
| ~ rr(i2003_11_14_17_21_22376,X0) ),
inference(resolution,[status(thm)],[p54,p44]) ).
fof(f24,axiom,
! [X,Y] :
( rs(X,Y)
=> rr(X,Y) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_8) ).
fof(f24_nnf,plain,
! [X,Y] :
( rr(X,Y)
| ~ rs(X,Y) ),
inference(nnf_transformation,[status(thm)],[f24]) ).
fof(f24_sk,plain,
! [X,Y] :
( rr(X,Y)
| ~ rs(X,Y) ),
inference(skolemisation,[status(esa)],[f24_nnf]) ).
cnf(c39,plain,
( rr(X0,X1)
| ~ rs(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f24_sk]) ).
cnf(c23,plain,
( rs(X0,sk1(X0))
| ~ cUnsatisfiable(X0) ),
inference(cnf_transformation,[status(esa)],[f18_sk]) ).
cnf(p45,plain,
rs(i2003_11_14_17_21_22376,sk1(i2003_11_14_17_21_22376)),
inference(resolution,[status(thm)],[c23,c38]) ).
cnf(p51,plain,
rr(i2003_11_14_17_21_22376,sk1(i2003_11_14_17_21_22376)),
inference(resolution,[status(thm)],[c39,p45]) ).
cnf(p57,plain,
sk0(i2003_11_14_17_21_22376) = sk1(i2003_11_14_17_21_22376),
inference(resolution,[status(thm)],[p55,p51]) ).
fof(f22,axiom,
! [X,Y] :
( rinvS(X,Y)
<=> rs(Y,X) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_6) ).
fof(f22_nnf,plain,
! [X,Y] :
( ( ~ rs(Y,X)
| rinvS(X,Y) )
& ( rs(Y,X)
| ~ rinvS(X,Y) ) ),
inference(nnf_transformation,[status(thm)],[f22]) ).
fof(f22_sk,plain,
! [X,Y] :
( ( ~ rs(Y,X)
| rinvS(X,Y) )
& ( rs(Y,X)
| ~ rinvS(X,Y) ) ),
inference(skolemisation,[status(esa)],[f22_nnf]) ).
cnf(c37,plain,
( ~ rs(X1,X0)
| rinvS(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f22_sk]) ).
cnf(p50,plain,
rinvS(sk1(i2003_11_14_17_21_22376),i2003_11_14_17_21_22376),
inference(resolution,[status(thm)],[c37,p45]) ).
cnf(p64,plain,
rinvS(sk0(i2003_11_14_17_21_22376),i2003_11_14_17_21_22376),
inference(superposition,[status(thm)],[p57,p50]) ).
fof(f21,axiom,
! [X] :
( ca_Vx2(X)
<=> ! [Y] :
( rinvS(X,Y)
=> cp(Y) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_5) ).
fof(f21_nnf,plain,
! [X] :
( ( ? [Y] :
( ~ cp(Y)
& rinvS(X,Y) )
| ca_Vx2(X) )
& ( ! [Y] :
( cp(Y)
| ~ rinvS(X,Y) )
| ~ ca_Vx2(X) ) ),
inference(nnf_transformation,[status(thm)],[f21]) ).
fof(f21_sk,plain,
! [X,Y] :
( ( ( ~ cp(sk6(X))
& rinvS(X,sk6(X)) )
| ca_Vx2(X) )
& ( cp(Y)
| ~ rinvS(X,Y)
| ~ ca_Vx2(X) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk6])],[f21_nnf]) ).
cnf(c33,plain,
( cp(X1)
| ~ rinvS(X0,X1)
| ~ ca_Vx2(X0) ),
inference(cnf_transformation,[status(esa)],[f21_sk]) ).
cnf(c22,plain,
( ca_Vx2(sk0(X0))
| ~ cUnsatisfiable(X0) ),
inference(cnf_transformation,[status(esa)],[f18_sk]) ).
cnf(p41,plain,
ca_Vx2(sk0(i2003_11_14_17_21_22376)),
inference(resolution,[status(thm)],[c22,c38]) ).
cnf(p53,plain,
( cp(X0)
| ~ rinvS(sk0(i2003_11_14_17_21_22376),X0) ),
inference(resolution,[status(thm)],[c33,p41]) ).
cnf(p74,plain,
cp(i2003_11_14_17_21_22376),
inference(resolution,[status(thm)],[p64,p53]) ).
fof(f19,axiom,
! [X] :
( cp(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)
| cp(X) )
& ( ! [Y] : ~ ra_Px1(X,Y)
| ~ cp(X) ) ),
inference(nnf_transformation,[status(thm)],[f19]) ).
fof(f19_sk,plain,
! [X,Y] :
( ( ra_Px1(X,sk4(X))
| cp(X) )
& ( ~ ra_Px1(X,Y)
| ~ cp(X) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk4])],[f19_nnf]) ).
cnf(c29,plain,
( ~ ra_Px1(X0,X1)
| ~ cp(X0) ),
inference(cnf_transformation,[status(esa)],[f19_sk]) ).
cnf(p75,plain,
~ ra_Px1(i2003_11_14_17_21_22376,X0),
inference(resolution,[status(thm)],[p74,c29]) ).
fof(f20,axiom,
! [X] :
( cpxcomp(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)
| cpxcomp(X) )
& ( ? [Y0] : ra_Px1(X,Y0)
| ~ cpxcomp(X) ) ),
inference(nnf_transformation,[status(thm)],[f20]) ).
fof(f20_sk,plain,
! [X,Y0] :
( ( ~ ra_Px1(X,Y0)
| cpxcomp(X) )
& ( ra_Px1(X,sk5(X))
| ~ cpxcomp(X) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk5])],[f20_nnf]) ).
cnf(c31,plain,
( ra_Px1(X0,sk5(X0))
| ~ cpxcomp(X0) ),
inference(cnf_transformation,[status(esa)],[f20_sk]) ).
cnf(c25,plain,
( cpxcomp(X0)
| ~ cUnsatisfiable(X0) ),
inference(cnf_transformation,[status(esa)],[f18_sk]) ).
cnf(p40,plain,
cpxcomp(i2003_11_14_17_21_22376),
inference(resolution,[status(thm)],[c25,c38]) ).
cnf(p47,plain,
ra_Px1(i2003_11_14_17_21_22376,sk5(i2003_11_14_17_21_22376)),
inference(resolution,[status(thm)],[c31,p40]) ).
cnf(p76,plain,
$false,
inference(resolution,[status(thm)],[p75,p47]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : KRS113+1 : TPTP v9.3.1. Released v3.1.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.08/0.35 % Computer : n008.cluster.edu
% 0.08/0.35 % Model : x86_64 x86_64
% 0.08/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.35 % Memory : 8046.5625MB
% 0.08/0.35 % OS : Linux 6.8.0-71-generic
% 0.08/0.35 % CPULimit : 300
% 0.08/0.35 % WCLimit : 300
% 0.08/0.35 % DateTime : Wed Sep 23 19:26:24 UTC 2026
% 0.08/0.35 % CPUTime :
% 0.08/0.35 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 3.62/0.93 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 3.62/0.93 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------