%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : KRS089+1 : TPTP v9.3.1. Released v3.1.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 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 : Sun Sep 27 07:46:00 AM UTC 2026
% Result : Unsatisfiable 0.13s 0.39s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 6
% Syntax : Number of formulae : 39 ( 14 unt; 0 def)
% Number of atoms : 108 ( 49 equ)
% Maximal formula atoms : 12 ( 2 avg)
% Number of connectives : 114 ( 45 ~; 38 |; 27 &)
% ( 1 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 8 ( 6 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 2 con; 0-1 aty)
% Number of variables : 56 ( 4 sgn 20 !; 8 ?)
% Comments :
%------------------------------------------------------------------------------
fof(axiom_0,axiom,
! [X] :
( ~ cowlNothing(X)
& cowlThing(X) ),
file('theBenchmark.p',axiom_0) ).
fof(axiom_2,axiom,
! [X] :
( cUnsatisfiable(X)
=> ? [Y0,Y1,Y2] :
( Y1 != Y2
& Y0 != Y2
& Y0 != Y1
& rr(X,Y2)
& rr(X,Y1)
& rr(X,Y0) ) ),
file('theBenchmark.p',axiom_2) ).
fof(axiom_3,axiom,
! [X] :
( cowlThing(X)
=> ? [Y] :
( Y = ispy
& rp(X,Y) ) ),
file('theBenchmark.p',axiom_3) ).
fof(axiom_4,axiom,
! [X,Y] :
( rp(X,Y)
<=> rinvP(Y,X) ),
file('theBenchmark.p',axiom_4) ).
fof(axiom_5,axiom,
! [X0,X1,X2] :
( ( rinvP(ispy,X2)
& rinvP(ispy,X1)
& rinvP(ispy,X0) )
=> ( X1 = X2
| X0 = X2
| X0 = X1 ) ),
file('theBenchmark.p',axiom_5) ).
cnf(c_29,plain,
cowlThing(A),
inference(clausify,[status(thm)],[axiom_0]) ).
fof(nnf_14,plain,
! [X] :
( ? [Y0,Y1,Y2] :
( Y2 != Y1
& Y2 != Y0
& Y1 != Y0
& rr(X,Y2)
& rr(X,Y1)
& rr(X,Y0) )
| ~ cUnsatisfiable(X) ),
inference(fof_nnf,[status(thm)],[axiom_2]) ).
fof(sk_axiom_2_sk,plain,
! [X] :
( ( sK2(X) != sK0(X)
& sK2(X) != sK1(X)
& sK0(X) != sK1(X)
& rr(X,sK2(X))
& rr(X,sK0(X))
& rr(X,sK1(X)) )
| ~ cUnsatisfiable(X) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1,sK0,sK2]),skolemize(Y0,sK1(X)),skolemize(Y1,sK0(X)),skolemize(Y2,sK2(X))],[nnf_14]) ).
fof(sk_axiom_2,plain,
( ! [VAR_0] :
( sK2(VAR_0) != sK0(VAR_0)
| ~ cUnsatisfiable(VAR_0) )
& ! [VAR_0] :
( sK2(VAR_0) != sK1(VAR_0)
| ~ cUnsatisfiable(VAR_0) )
& ! [VAR_0] :
( sK0(VAR_0) != sK1(VAR_0)
| ~ cUnsatisfiable(VAR_0) )
& ! [VAR_0] :
( rr(VAR_0,sK2(VAR_0))
| ~ cUnsatisfiable(VAR_0) )
& ! [VAR_0] :
( rr(VAR_0,sK0(VAR_0))
| ~ cUnsatisfiable(VAR_0) )
& ! [VAR_0] :
( rr(VAR_0,sK1(VAR_0))
| ~ cUnsatisfiable(VAR_0) ) ),
inference(cnf_transformation,[status(thm)],[sk_axiom_2_sk]) ).
cnf(c_36,plain,
( sK0(A) != sK1(A)
| ~ cUnsatisfiable(A) ),
inference(split_conjunct,[status(thm)],[sk_axiom_2]) ).
cnf(c_37,plain,
( sK2(A) != sK1(A)
| ~ cUnsatisfiable(A) ),
inference(split_conjunct,[status(thm)],[sk_axiom_2]) ).
cnf(c_38,plain,
( sK2(A) != sK0(A)
| ~ cUnsatisfiable(A) ),
inference(split_conjunct,[status(thm)],[sk_axiom_2]) ).
fof(nnf_15,plain,
! [X] :
( ? [Y] :
( ispy = Y
& rp(X,Y) )
| ~ cowlThing(X) ),
inference(fof_nnf,[status(thm)],[axiom_3]) ).
fof(sk_axiom_3_sk,plain,
! [X] :
( ( ispy = sK3(X)
& rp(X,sK3(X)) )
| ~ cowlThing(X) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3]),skolemize(Y,sK3(X))],[nnf_15]) ).
fof(sk_axiom_3,plain,
( ! [VAR_0] :
( ispy = sK3(VAR_0)
| ~ cowlThing(VAR_0) )
& ! [VAR_0] :
( rp(VAR_0,sK3(VAR_0))
| ~ cowlThing(VAR_0) ) ),
inference(cnf_transformation,[status(thm)],[sk_axiom_3_sk]) ).
cnf(c_39,plain,
( rp(A,sK3(A))
| ~ cowlThing(A) ),
inference(split_conjunct,[status(thm)],[sk_axiom_3]) ).
cnf(c_40,plain,
rp(A,sK3(A)),
inference(resolve,[status(thm)],[c_29,c_39]) ).
cnf(c_41,plain,
( ispy = sK3(A)
| ~ cowlThing(A) ),
inference(split_conjunct,[status(thm)],[sk_axiom_3]) ).
cnf(c_240,plain,
( sK3(A) = ispy
| ~ cowlThing(A) ),
inference(copy,[status(thm)],[c_41]) ).
cnf(c_42,plain,
sK3(A) = ispy,
inference(resolve,[status(thm)],[c_29,c_240]) ).
cnf(c_43,plain,
( rinvP(B,A)
| ~ rp(A,B) ),
inference(clausify,[status(thm)],[axiom_4]) ).
cnf(c_45,plain,
( C = B
| C = A
| B = A
| ~ rinvP(ispy,C)
| ~ rinvP(ispy,B)
| ~ rinvP(ispy,A) ),
inference(clausify,[status(thm)],[axiom_5]) ).
fof(axiom_7,axiom,
cUnsatisfiable(i2003_11_14_17_19_53168),
file('theBenchmark.p',axiom_7) ).
cnf(c_46,plain,
cUnsatisfiable(i2003_11_14_17_19_53168),
inference(clausify,[status(thm)],[axiom_7]) ).
cnf(c_47,plain,
rp(A,ispy),
inference(paramod,[status(thm)],[c_42,c_40]) ).
cnf(c_49,plain,
sK2(i2003_11_14_17_19_53168) != sK0(i2003_11_14_17_19_53168),
inference(resolve,[status(thm)],[c_46,c_38]) ).
cnf(c_50,plain,
sK2(i2003_11_14_17_19_53168) != sK1(i2003_11_14_17_19_53168),
inference(resolve,[status(thm)],[c_46,c_37]) ).
cnf(c_51,plain,
sK0(i2003_11_14_17_19_53168) != sK1(i2003_11_14_17_19_53168),
inference(resolve,[status(thm)],[c_46,c_36]) ).
cnf(c_56,plain,
rinvP(ispy,A),
inference(resolve,[status(thm)],[c_47,c_43]) ).
cnf(c_241,plain,
( B = A
| B = C
| A = C
| ~ rinvP(ispy,B)
| ~ rinvP(ispy,A) ),
inference(resolve,[status(thm)],[c_56,c_45]) ).
cnf(c_242,plain,
( A = B
| A = C
| B = C
| ~ rinvP(ispy,A) ),
inference(resolve,[status(thm)],[c_56,c_241]) ).
cnf(c_58,plain,
( C = A
| C = B
| A = B ),
inference(resolve,[status(thm)],[c_56,c_242]) ).
cnf(c_243,plain,
( A = sK0(i2003_11_14_17_19_53168)
| A = sK1(i2003_11_14_17_19_53168) ),
inference(resolve,[status(thm)],[c_58,c_51]) ).
cnf(c_244,plain,
( A = sK0(i2003_11_14_17_19_53168)
| sK1(i2003_11_14_17_19_53168) = A ),
inference(copy,[status(thm)],[c_243]) ).
cnf(c_69,plain,
( sK0(i2003_11_14_17_19_53168) = A
| sK1(i2003_11_14_17_19_53168) = A ),
inference(copy,[status(thm)],[c_244]) ).
cnf(c_245,plain,
sK0(i2003_11_14_17_19_53168) != sK2(i2003_11_14_17_19_53168),
inference(copy,[status(thm)],[c_49]) ).
cnf(c_246,plain,
sK1(i2003_11_14_17_19_53168) = sK2(i2003_11_14_17_19_53168),
inference(resolve,[status(thm)],[c_69,c_245]) ).
cnf(c_247,plain,
sK2(i2003_11_14_17_19_53168) = sK1(i2003_11_14_17_19_53168),
inference(copy,[status(thm)],[c_246]) ).
cnf(c_239,plain,
$false,
inference(resolve,[status(thm)],[c_50,c_247]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : KRS089+1 : TPTP v9.3.1. Released v3.1.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.35 % Computer : n014.cluster.edu
% 0.09/0.35 % Model : x86_64 x86_64
% 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.35 % Memory : 8046.5625MB
% 0.09/0.35 % OS : Linux 6.8.0-71-generic
% 0.09/0.35 % CPULimit : 300
% 0.09/0.35 % WCLimit : 300
% 0.09/0.35 % DateTime : Fri Sep 25 19:38:48 UTC 2026
% 0.09/0.35 % CPUTime :
% 0.09/0.36 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.09/0.36 % Process 927563 was started by sandbox on n014,
% 0.09/0.36 % Fri Sep 25 19:38:48 2026
% 0.09/0.36 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.13/0.36
% 0.13/0.36 % From the command line: assign(max_seconds, 300).
% 0.13/0.39
% 0.13/0.39 % SZS status Unsatisfiable for theBenchmark
% 0.13/0.39
% 0.13/0.39 % Proof 1 at 0.01 (+ 0.01) seconds.
% 0.13/0.39 % Length of proof is 24.
% 0.13/0.39 % Level of proof is 7.
% 0.13/0.39 % Maximum clause weight is 23.000.
% 0.13/0.39 % Given clauses 56.
% 0.13/0.39
% 0.13/0.39 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------