%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : KRS109+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 : n017.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 4.32s 1.08s
% Output : Proof 4.32s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 10
% Syntax : Number of formulae : 59 ( 17 unt; 0 def)
% Number of atoms : 165 ( 6 equ)
% Maximal formula atoms : 10 ( 2 avg)
% Number of connectives : 173 ( 67 ~; 64 |; 31 &)
% ( 7 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 12 ( 10 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 1 con; 0-1 aty)
% Number of variables : 89 ( 2 sgn 55 !; 10 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f36,axiom,
cUnsatisfiable(i2003_11_14_17_21_08508),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_13) ).
fof(f36_nnf,plain,
cUnsatisfiable(i2003_11_14_17_21_08508),
inference(nnf_transformation,[status(thm)],[f36]) ).
cnf(c53,plain,
cUnsatisfiable(i2003_11_14_17_21_08508),
inference(cnf_transformation,[status(esa)],[f36_nnf]) ).
fof(f25,axiom,
! [X] :
( cUnsatisfiable(X)
<=> ( ? [Y] :
( ca_Ax2(Y)
& rf(X,Y) )
& cpxcomp(X) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_2) ).
fof(f25_nnf,plain,
! [X] :
( ( ! [Y] :
( ~ ca_Ax2(Y)
| ~ rf(X,Y) )
| ~ cpxcomp(X)
| cUnsatisfiable(X) )
& ( ( ? [Y] :
( ca_Ax2(Y)
& rf(X,Y) )
& cpxcomp(X) )
| ~ cUnsatisfiable(X) ) ),
inference(nnf_transformation,[status(thm)],[f25]) ).
fof(f25_sk,plain,
! [X,Y] :
( ( ~ ca_Ax2(Y)
| ~ rf(X,Y)
| ~ cpxcomp(X)
| cUnsatisfiable(X) )
& ( ( ca_Ax2(sk0(X))
& rf(X,sk0(X))
& cpxcomp(X) )
| ~ cUnsatisfiable(X) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk0])],[f25_nnf]) ).
cnf(c29,plain,
( ca_Ax2(sk0(X0))
| ~ cUnsatisfiable(X0) ),
inference(cnf_transformation,[status(esa)],[f25_sk]) ).
cnf(p60,plain,
ca_Ax2(sk0(i2003_11_14_17_21_08508)),
inference(resolution,[status(thm)],[c53,c29]) ).
fof(f28,axiom,
! [X] :
( ca_Ax2(X)
<=> ( ! [Y] :
( rinvF(X,Y)
=> ca_Vx3(Y) )
& ! [Y] :
( rinvS(X,Y)
=> cp(Y) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_5) ).
fof(f28_nnf,plain,
! [X] :
( ( ? [Y] :
( ~ ca_Vx3(Y)
& rinvF(X,Y) )
| ? [Y] :
( ~ cp(Y)
& rinvS(X,Y) )
| ca_Ax2(X) )
& ( ( ! [Y] :
( ca_Vx3(Y)
| ~ rinvF(X,Y) )
& ! [Y] :
( cp(Y)
| ~ rinvS(X,Y) ) )
| ~ ca_Ax2(X) ) ),
inference(nnf_transformation,[status(thm)],[f28]) ).
fof(f28_sk,plain,
! [X,Y] :
( ( ( ~ ca_Vx3(sk4(X))
& rinvF(X,sk4(X)) )
| ( ~ cp(sk3(X))
& rinvS(X,sk3(X)) )
| ca_Ax2(X) )
& ( ( ( ca_Vx3(Y)
| ~ rinvF(X,Y) )
& ( cp(Y)
| ~ rinvS(X,Y) ) )
| ~ ca_Ax2(X) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk3,sk4])],[f28_nnf]) ).
cnf(c36,plain,
( ca_Vx3(X1)
| ~ rinvF(X0,X1)
| ~ ca_Ax2(X0) ),
inference(cnf_transformation,[status(esa)],[f28_sk]) ).
cnf(p71,plain,
( ca_Vx3(X0)
| ~ rinvF(sk0(i2003_11_14_17_21_08508),X0) ),
inference(resolution,[status(thm)],[p60,c36]) ).
cnf(c28,plain,
( rf(X0,sk0(X0))
| ~ cUnsatisfiable(X0) ),
inference(cnf_transformation,[status(esa)],[f25_sk]) ).
cnf(p59,plain,
rf(i2003_11_14_17_21_08508,sk0(i2003_11_14_17_21_08508)),
inference(resolution,[status(thm)],[c53,c28]) ).
fof(f32,axiom,
! [X,Y] :
( rinvF(X,Y)
<=> rf(Y,X) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_9) ).
fof(f32_nnf,plain,
! [X,Y] :
( ( ~ rf(Y,X)
| rinvF(X,Y) )
& ( rf(Y,X)
| ~ rinvF(X,Y) ) ),
inference(nnf_transformation,[status(thm)],[f32]) ).
fof(f32_sk,plain,
! [X,Y] :
( ( ~ rf(Y,X)
| rinvF(X,Y) )
& ( rf(Y,X)
| ~ rinvF(X,Y) ) ),
inference(skolemisation,[status(esa)],[f32_nnf]) ).
cnf(c47,plain,
( ~ rf(X1,X0)
| rinvF(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f32_sk]) ).
cnf(p69,plain,
rinvF(sk0(i2003_11_14_17_21_08508),i2003_11_14_17_21_08508),
inference(resolution,[status(thm)],[p59,c47]) ).
cnf(p74,plain,
ca_Vx3(i2003_11_14_17_21_08508),
inference(resolution,[status(thm)],[p71,p69]) ).
fof(f29,axiom,
! [X] :
( ca_Vx3(X)
<=> ? [Y] :
( cp(Y)
& rs(X,Y) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_6) ).
fof(f29_nnf,plain,
! [X] :
( ( ! [Y] :
( ~ cp(Y)
| ~ rs(X,Y) )
| ca_Vx3(X) )
& ( ? [Y] :
( cp(Y)
& rs(X,Y) )
| ~ ca_Vx3(X) ) ),
inference(nnf_transformation,[status(thm)],[f29]) ).
fof(f29_sk,plain,
! [X,Y] :
( ( ~ cp(Y)
| ~ rs(X,Y)
| ca_Vx3(X) )
& ( ( cp(sk5(X))
& rs(X,sk5(X)) )
| ~ ca_Vx3(X) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk5])],[f29_nnf]) ).
cnf(c41,plain,
( rs(X0,sk5(X0))
| ~ ca_Vx3(X0) ),
inference(cnf_transformation,[status(esa)],[f29_sk]) ).
cnf(p78,plain,
rs(i2003_11_14_17_21_08508,sk5(i2003_11_14_17_21_08508)),
inference(resolution,[status(thm)],[p74,c41]) ).
fof(f37,axiom,
! [X,Y] :
( rs(X,Y)
=> rf(X,Y) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_14) ).
fof(f37_nnf,plain,
! [X,Y] :
( rf(X,Y)
| ~ rs(X,Y) ),
inference(nnf_transformation,[status(thm)],[f37]) ).
fof(f37_sk,plain,
! [X,Y] :
( rf(X,Y)
| ~ rs(X,Y) ),
inference(skolemisation,[status(esa)],[f37_nnf]) ).
cnf(c54,plain,
( rf(X0,X1)
| ~ rs(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f37_sk]) ).
cnf(p82,plain,
rf(i2003_11_14_17_21_08508,sk5(i2003_11_14_17_21_08508)),
inference(resolution,[status(thm)],[p78,c54]) ).
fof(f30,axiom,
! [X,Y,Z] :
( ( rf(X,Z)
& rf(X,Y) )
=> Y = Z ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_7) ).
fof(f30_nnf,plain,
! [X,Y,Z] :
( Y = Z
| ~ rf(X,Z)
| ~ rf(X,Y) ),
inference(nnf_transformation,[status(thm)],[f30]) ).
fof(f30_sk,plain,
! [X,Y,Z] :
( Y = Z
| ~ rf(X,Z)
| ~ rf(X,Y) ),
inference(skolemisation,[status(esa)],[f30_nnf]) ).
cnf(c44,plain,
( X1 = X2
| ~ rf(X0,X2)
| ~ rf(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f30_sk]) ).
cnf(p86,plain,
( sk5(i2003_11_14_17_21_08508) = X0
| ~ rf(i2003_11_14_17_21_08508,X0) ),
inference(resolution,[status(thm)],[p82,c44]) ).
cnf(p92,plain,
sk5(i2003_11_14_17_21_08508) = sk0(i2003_11_14_17_21_08508),
inference(resolution,[status(thm)],[p86,p59]) ).
fof(f34,axiom,
! [X,Y] :
( rinvS(X,Y)
<=> rs(Y,X) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_11) ).
fof(f34_nnf,plain,
! [X,Y] :
( ( ~ rs(Y,X)
| rinvS(X,Y) )
& ( rs(Y,X)
| ~ rinvS(X,Y) ) ),
inference(nnf_transformation,[status(thm)],[f34]) ).
fof(f34_sk,plain,
! [X,Y] :
( ( ~ rs(Y,X)
| rinvS(X,Y) )
& ( rs(Y,X)
| ~ rinvS(X,Y) ) ),
inference(skolemisation,[status(esa)],[f34_nnf]) ).
cnf(c51,plain,
( ~ rs(X1,X0)
| rinvS(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f34_sk]) ).
cnf(p80,plain,
rinvS(sk5(i2003_11_14_17_21_08508),i2003_11_14_17_21_08508),
inference(resolution,[status(thm)],[p78,c51]) ).
cnf(p95,plain,
rinvS(sk0(i2003_11_14_17_21_08508),i2003_11_14_17_21_08508),
inference(demodulation,[status(thm)],[p92,p80]) ).
cnf(c35,plain,
( cp(X1)
| ~ rinvS(X0,X1)
| ~ ca_Ax2(X0) ),
inference(cnf_transformation,[status(esa)],[f28_sk]) ).
cnf(p70,plain,
( cp(X0)
| ~ rinvS(sk0(i2003_11_14_17_21_08508),X0) ),
inference(resolution,[status(thm)],[p60,c35]) ).
cnf(p101,plain,
cp(i2003_11_14_17_21_08508),
inference(resolution,[status(thm)],[p95,p70]) ).
fof(f26,axiom,
! [X] :
( cp(X)
<=> ~ ? [Y] : ra_Px1(X,Y) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_3) ).
fof(f26_nnf,plain,
! [X] :
( ( ? [Y] : ra_Px1(X,Y)
| cp(X) )
& ( ! [Y] : ~ ra_Px1(X,Y)
| ~ cp(X) ) ),
inference(nnf_transformation,[status(thm)],[f26]) ).
fof(f26_sk,plain,
! [X,Y] :
( ( ra_Px1(X,sk1(X))
| cp(X) )
& ( ~ ra_Px1(X,Y)
| ~ cp(X) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk1])],[f26_nnf]) ).
cnf(c31,plain,
( ~ ra_Px1(X0,X1)
| ~ cp(X0) ),
inference(cnf_transformation,[status(esa)],[f26_sk]) ).
cnf(p102,plain,
~ ra_Px1(i2003_11_14_17_21_08508,X0),
inference(resolution,[status(thm)],[p101,c31]) ).
cnf(c27,plain,
( cpxcomp(X0)
| ~ cUnsatisfiable(X0) ),
inference(cnf_transformation,[status(esa)],[f25_sk]) ).
cnf(p58,plain,
cpxcomp(i2003_11_14_17_21_08508),
inference(resolution,[status(thm)],[c53,c27]) ).
fof(f27,axiom,
! [X] :
( cpxcomp(X)
<=> ? [Y0] : ra_Px1(X,Y0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_4) ).
fof(f27_nnf,plain,
! [X] :
( ( ! [Y0] : ~ ra_Px1(X,Y0)
| cpxcomp(X) )
& ( ? [Y0] : ra_Px1(X,Y0)
| ~ cpxcomp(X) ) ),
inference(nnf_transformation,[status(thm)],[f27]) ).
fof(f27_sk,plain,
! [X,Y0] :
( ( ~ ra_Px1(X,Y0)
| cpxcomp(X) )
& ( ra_Px1(X,sk2(X))
| ~ cpxcomp(X) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk2])],[f27_nnf]) ).
cnf(c33,plain,
( ra_Px1(X0,sk2(X0))
| ~ cpxcomp(X0) ),
inference(cnf_transformation,[status(esa)],[f27_sk]) ).
cnf(p67,plain,
ra_Px1(i2003_11_14_17_21_08508,sk2(i2003_11_14_17_21_08508)),
inference(resolution,[status(thm)],[p58,c33]) ).
cnf(p104,plain,
$false,
inference(resolution,[status(thm)],[p102,p67]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : KRS109+1 : TPTP v9.3.1. Released v3.1.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.10/0.36 % Computer : n017.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % 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 19:20:30 UTC 2026
% 0.10/0.36 % CPUTime :
% 0.10/0.36 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 4.32/1.08 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 4.32/1.08 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------