%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : KRS120+1 : TPTP v9.3.1. Released v3.1.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n013.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 : Sun Sep 27 07:46:05 AM UTC 2026
% Result : Unsatisfiable 0.08s 0.37s
% Output : CNFRefutation 0.08s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 10
% Syntax : Number of formulae : 52 ( 17 unt; 0 def)
% Number of atoms : 150 ( 10 equ)
% Maximal formula atoms : 10 ( 2 avg)
% Number of connectives : 165 ( 67 ~; 58 |; 31 &)
% ( 6 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 12 ( 10 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 1 con; 0-1 aty)
% Number of variables : 77 ( 3 sgn 45 !; 9 ?)
% Comments :
%------------------------------------------------------------------------------
fof(cp1xcomp_substitution_1,axiom,
! [A,B] :
( ( cp1xcomp(A)
& A = B )
=> cp1xcomp(B) ),
file('theBenchmark.p',cp1xcomp_substitution_1) ).
fof(axiom_0,axiom,
! [X] :
( ~ cowlNothing(X)
& cowlThing(X) ),
file('theBenchmark.p',axiom_0) ).
fof(axiom_2,axiom,
! [X] :
( cUnsatisfiable(X)
<=> ? [Y] :
( ca_Ax2(Y)
& rf(X,Y) ) ),
file('theBenchmark.p',axiom_2) ).
fof(axiom_3,axiom,
! [X] :
( cp1(X)
<=> ~ ? [Y] : ra_Px1(X,Y) ),
file('theBenchmark.p',axiom_3) ).
fof(axiom_4,axiom,
! [X] :
( cp1xcomp(X)
<=> ? [Y0] : ra_Px1(X,Y0) ),
file('theBenchmark.p',axiom_4) ).
fof(axiom_5,axiom,
! [X] :
( ca_Ax2(X)
<=> ( cp1(X)
& ? [Y] :
( ca_Vx3(Y)
& rinvF(X,Y) ) ) ),
file('theBenchmark.p',axiom_5) ).
fof(axiom_6,axiom,
! [X] :
( ca_Vx3(X)
<=> ? [Y] :
( cp1xcomp(Y)
& rf(X,Y) ) ),
file('theBenchmark.p',axiom_6) ).
fof(axiom_7,axiom,
! [X] :
( cowlThing(X)
=> ! [Y0,Y1] :
( ( rf(X,Y1)
& rf(X,Y0) )
=> Y0 = Y1 ) ),
file('theBenchmark.p',axiom_7) ).
fof(axiom_8,axiom,
! [X,Y] :
( rinvF(X,Y)
<=> rf(Y,X) ),
file('theBenchmark.p',axiom_8) ).
cnf(c_37,plain,
( cp1xcomp(A)
| ~ cp1xcomp(B)
| A != B ),
inference(clausify,[status(thm)],[cp1xcomp_substitution_1]) ).
cnf(c_50,plain,
cowlThing(A),
inference(clausify,[status(thm)],[axiom_0]) ).
fof(nnf_22,plain,
! [X] :
( ( ! [Y] :
( ~ ca_Ax2(Y)
| ~ rf(X,Y) )
| cUnsatisfiable(X) )
& ( ? [X0] :
( ca_Ax2(X0)
& rf(X,X0) )
| ~ cUnsatisfiable(X) ) ),
inference(fof_nnf,[status(thm)],[axiom_2]) ).
fof(sk_axiom_2_sk,plain,
! [X] :
( ( ! [Y] :
( ~ ca_Ax2(Y)
| ~ rf(X,Y) )
| cUnsatisfiable(X) )
& ( ( ca_Ax2(sK0(X))
& rf(X,sK0(X)) )
| ~ cUnsatisfiable(X) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X0,sK0(X))],[nnf_22]) ).
fof(sk_axiom_2,plain,
( ! [VAR_0,VAR_1] :
( ~ ca_Ax2(VAR_1)
| ~ rf(VAR_0,VAR_1)
| cUnsatisfiable(VAR_0) )
& ! [VAR_0] :
( ca_Ax2(sK0(VAR_0))
| ~ cUnsatisfiable(VAR_0) )
& ! [VAR_0] :
( rf(VAR_0,sK0(VAR_0))
| ~ cUnsatisfiable(VAR_0) ) ),
inference(cnf_transformation,[status(thm)],[sk_axiom_2_sk]) ).
cnf(c_55,plain,
( ca_Ax2(sK0(A))
| ~ cUnsatisfiable(A) ),
inference(split_conjunct,[status(thm)],[sk_axiom_2]) ).
cnf(c_57,plain,
( ~ ra_Px1(A,B)
| ~ cp1(A) ),
inference(clausify,[status(thm)],[axiom_3]) ).
fof(nnf_24,plain,
! [X] :
( ( ! [Y0] : ~ ra_Px1(X,Y0)
| cp1xcomp(X) )
& ( ? [X0] : ra_Px1(X,X0)
| ~ cp1xcomp(X) ) ),
inference(fof_nnf,[status(thm)],[axiom_4]) ).
fof(sk_axiom_4_sk,plain,
! [X] :
( ( ! [Y0] : ~ ra_Px1(X,Y0)
| cp1xcomp(X) )
& ( ra_Px1(X,sK1(X))
| ~ cp1xcomp(X) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(X0,sK1(X))],[nnf_24]) ).
fof(sk_axiom_4,plain,
( ! [VAR_0,VAR_1] :
( ~ ra_Px1(VAR_0,VAR_1)
| cp1xcomp(VAR_0) )
& ! [VAR_0] :
( ra_Px1(VAR_0,sK1(VAR_0))
| ~ cp1xcomp(VAR_0) ) ),
inference(cnf_transformation,[status(thm)],[sk_axiom_4_sk]) ).
cnf(c_59,plain,
( ra_Px1(A,sK1(A))
| ~ cp1xcomp(A) ),
inference(split_conjunct,[status(thm)],[sk_axiom_4]) ).
fof(nnf_25,plain,
! [X] :
( ( ~ cp1(X)
| ! [Y] :
( ~ ca_Vx3(Y)
| ~ rinvF(X,Y) )
| ca_Ax2(X) )
& ( ( cp1(X)
& ? [X0] :
( ca_Vx3(X0)
& rinvF(X,X0) ) )
| ~ ca_Ax2(X) ) ),
inference(fof_nnf,[status(thm)],[axiom_5]) ).
fof(sk_axiom_5_sk,plain,
! [X] :
( ( ~ cp1(X)
| ! [Y] :
( ~ ca_Vx3(Y)
| ~ rinvF(X,Y) )
| ca_Ax2(X) )
& ( ( cp1(X)
& ca_Vx3(sK2(X))
& rinvF(X,sK2(X)) )
| ~ ca_Ax2(X) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2]),skolemize(X0,sK2(X))],[nnf_25]) ).
fof(sk_axiom_5,plain,
( ! [VAR_0,VAR_1] :
( ~ cp1(VAR_0)
| ~ ca_Vx3(VAR_1)
| ~ rinvF(VAR_0,VAR_1)
| ca_Ax2(VAR_0) )
& ! [VAR_0] :
( cp1(VAR_0)
| ~ ca_Ax2(VAR_0) )
& ! [VAR_0] :
( ca_Vx3(sK2(VAR_0))
| ~ ca_Ax2(VAR_0) )
& ! [VAR_0] :
( rinvF(VAR_0,sK2(VAR_0))
| ~ ca_Ax2(VAR_0) ) ),
inference(cnf_transformation,[status(thm)],[sk_axiom_5_sk]) ).
cnf(c_61,plain,
( rinvF(A,sK2(A))
| ~ ca_Ax2(A) ),
inference(split_conjunct,[status(thm)],[sk_axiom_5]) ).
cnf(c_62,plain,
( ca_Vx3(sK2(A))
| ~ ca_Ax2(A) ),
inference(split_conjunct,[status(thm)],[sk_axiom_5]) ).
cnf(c_63,plain,
( cp1(A)
| ~ ca_Ax2(A) ),
inference(split_conjunct,[status(thm)],[sk_axiom_5]) ).
fof(nnf_26,plain,
! [X] :
( ( ! [Y] :
( ~ cp1xcomp(Y)
| ~ rf(X,Y) )
| ca_Vx3(X) )
& ( ? [X0] :
( cp1xcomp(X0)
& rf(X,X0) )
| ~ ca_Vx3(X) ) ),
inference(fof_nnf,[status(thm)],[axiom_6]) ).
fof(sk_axiom_6_sk,plain,
! [X] :
( ( ! [Y] :
( ~ cp1xcomp(Y)
| ~ rf(X,Y) )
| ca_Vx3(X) )
& ( ( cp1xcomp(sK3(X))
& rf(X,sK3(X)) )
| ~ ca_Vx3(X) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3]),skolemize(X0,sK3(X))],[nnf_26]) ).
fof(sk_axiom_6,plain,
( ! [VAR_0,VAR_1] :
( ~ cp1xcomp(VAR_1)
| ~ rf(VAR_0,VAR_1)
| ca_Vx3(VAR_0) )
& ! [VAR_0] :
( cp1xcomp(sK3(VAR_0))
| ~ ca_Vx3(VAR_0) )
& ! [VAR_0] :
( rf(VAR_0,sK3(VAR_0))
| ~ ca_Vx3(VAR_0) ) ),
inference(cnf_transformation,[status(thm)],[sk_axiom_6_sk]) ).
cnf(c_65,plain,
( rf(A,sK3(A))
| ~ ca_Vx3(A) ),
inference(split_conjunct,[status(thm)],[sk_axiom_6]) ).
cnf(c_66,plain,
( cp1xcomp(sK3(A))
| ~ ca_Vx3(A) ),
inference(split_conjunct,[status(thm)],[sk_axiom_6]) ).
cnf(c_68,plain,
( C = B
| ~ rf(A,C)
| ~ rf(A,B)
| ~ cowlThing(A) ),
inference(clausify,[status(thm)],[axiom_7]) ).
cnf(c_69,plain,
( C = B
| ~ rf(A,C)
| ~ rf(A,B) ),
inference(resolve,[status(thm)],[c_50,c_68]) ).
cnf(c_70,plain,
( rf(B,A)
| ~ rinvF(A,B) ),
inference(clausify,[status(thm)],[axiom_8]) ).
fof(axiom_11,axiom,
cUnsatisfiable(i2003_11_14_17_21_48796),
file('theBenchmark.p',axiom_11) ).
cnf(c_75,plain,
cUnsatisfiable(i2003_11_14_17_21_48796),
inference(clausify,[status(thm)],[axiom_11]) ).
cnf(c_80,plain,
ca_Ax2(sK0(i2003_11_14_17_21_48796)),
inference(resolve,[status(thm)],[c_75,c_55]) ).
cnf(c_83,plain,
cp1(sK0(i2003_11_14_17_21_48796)),
inference(resolve,[status(thm)],[c_80,c_63]) ).
cnf(c_84,plain,
ca_Vx3(sK2(sK0(i2003_11_14_17_21_48796))),
inference(resolve,[status(thm)],[c_80,c_62]) ).
cnf(c_85,plain,
rinvF(sK0(i2003_11_14_17_21_48796),sK2(sK0(i2003_11_14_17_21_48796))),
inference(resolve,[status(thm)],[c_80,c_61]) ).
cnf(c_88,plain,
~ ra_Px1(sK0(i2003_11_14_17_21_48796),A),
inference(resolve,[status(thm)],[c_57,c_83]) ).
cnf(c_95,plain,
~ cp1xcomp(sK0(i2003_11_14_17_21_48796)),
inference(resolve,[status(thm)],[c_59,c_88]) ).
cnf(c_96,plain,
cp1xcomp(sK3(sK2(sK0(i2003_11_14_17_21_48796)))),
inference(resolve,[status(thm)],[c_84,c_66]) ).
cnf(c_97,plain,
rf(sK2(sK0(i2003_11_14_17_21_48796)),sK3(sK2(sK0(i2003_11_14_17_21_48796)))),
inference(resolve,[status(thm)],[c_84,c_65]) ).
cnf(c_114,plain,
( cp1xcomp(A)
| A != sK3(sK2(sK0(i2003_11_14_17_21_48796))) ),
inference(resolve,[status(thm)],[c_37,c_96]) ).
cnf(c_115,plain,
sK0(i2003_11_14_17_21_48796) != sK3(sK2(sK0(i2003_11_14_17_21_48796))),
inference(resolve,[status(thm)],[c_114,c_95]) ).
cnf(c_103,plain,
sK3(sK2(sK0(i2003_11_14_17_21_48796))) != sK0(i2003_11_14_17_21_48796),
inference(copy,[status(thm)],[c_115]) ).
cnf(c_106,plain,
rf(sK2(sK0(i2003_11_14_17_21_48796)),sK0(i2003_11_14_17_21_48796)),
inference(resolve,[status(thm)],[c_85,c_70]) ).
cnf(c_116,plain,
( sK0(i2003_11_14_17_21_48796) = A
| ~ rf(sK2(sK0(i2003_11_14_17_21_48796)),A) ),
inference(resolve,[status(thm)],[c_69,c_106]) ).
cnf(c_117,plain,
sK0(i2003_11_14_17_21_48796) != sK3(sK2(sK0(i2003_11_14_17_21_48796))),
inference(copy,[status(thm)],[c_103]) ).
cnf(c_118,plain,
~ rf(sK2(sK0(i2003_11_14_17_21_48796)),sK3(sK2(sK0(i2003_11_14_17_21_48796)))),
inference(resolve,[status(thm)],[c_116,c_117]) ).
cnf(c_113,plain,
$false,
inference(resolve,[status(thm)],[c_97,c_118]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : KRS120+1 : TPTP v9.3.1. Released v3.1.0.
% 0.00/0.03 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/0.34 % Computer : n013.cluster.edu
% 0.08/0.34 % Model : x86_64 x86_64
% 0.08/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.34 % Memory : 8046.5625MB
% 0.08/0.34 % OS : Linux 6.8.0-71-generic
% 0.08/0.34 % CPULimit : 300
% 0.08/0.34 % WCLimit : 300
% 0.08/0.34 % DateTime : Fri Sep 25 19:39:36 UTC 2026
% 0.08/0.34 % CPUTime :
% 0.08/0.35 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.08/0.35 % Process 1031961 was started by sandbox2 on n013,
% 0.08/0.35 % Fri Sep 25 19:39:36 2026
% 0.08/0.35 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.08/0.36
% 0.08/0.36 % From the command line: assign(max_seconds, 300).
% 0.08/0.37
% 0.08/0.37 % SZS status Unsatisfiable for theBenchmark
% 0.08/0.37
% 0.08/0.37 % Proof 1 at 0.00 (+ 0.00) seconds.
% 0.08/0.37 % Length of proof is 34.
% 0.08/0.37 % Level of proof is 7.
% 0.08/0.37 % Maximum clause weight is 9.000.
% 0.08/0.37 % Given clauses 62.
% 0.08/0.37
% 0.08/0.37 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------