%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : KRS082+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 : n015.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 07:45:59 AM UTC 2026
% Result : Unsatisfiable 0.09s 0.39s
% Output : CNFRefutation 0.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 7
% Syntax : Number of formulae : 37 ( 10 unt; 0 def)
% Number of atoms : 157 ( 0 equ)
% Maximal formula atoms : 29 ( 4 avg)
% Number of connectives : 194 ( 74 ~; 66 |; 40 &)
% ( 4 <=>; 10 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 11 ( 10 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 1 con; 0-2 aty)
% Number of variables : 92 ( 0 sgn 47 !; 10 ?)
% Comments :
%------------------------------------------------------------------------------
fof(axiom_2,axiom,
! [X] :
( cUnsatisfiable(X)
=> ? [Y] :
( ? [Z] :
( cowlThing(Z)
& rr(Y,Z) )
& ! [Z] :
( rp(Y,Z)
=> ! [W] :
( rr(Z,W)
=> cc(W) ) )
& ! [Z] :
( rp(Y,Z)
=> ? [W] :
( cowlThing(W)
& rp(Z,W) ) )
& ! [Z] :
( rp(Y,Z)
=> ? [W] :
( cowlThing(W)
& rr(Z,W) ) )
& ! [Z] :
( rr(Y,Z)
=> cc(Z) )
& ? [Z] :
( cowlThing(Z)
& rp(Y,Z) )
& rs(X,Y) ) ),
file('theBenchmark.p',axiom_2) ).
fof(axiom_3,axiom,
! [X] :
( cUnsatisfiable(X)
=> ca(X) ),
file('theBenchmark.p',axiom_3) ).
fof(axiom_4,axiom,
! [X] :
( cc(X)
<=> ! [Y] :
( rinvR(X,Y)
=> ! [Z] :
( rinvP(Y,Z)
=> ! [W] :
( rinvS(Z,W)
=> ~ ca(W) ) ) ) ),
file('theBenchmark.p',axiom_4) ).
fof(axiom_5,axiom,
! [X,Y] :
( rinvP(X,Y)
<=> rp(Y,X) ),
file('theBenchmark.p',axiom_5) ).
fof(axiom_6,axiom,
! [X,Y] :
( rinvR(X,Y)
<=> rr(Y,X) ),
file('theBenchmark.p',axiom_6) ).
fof(axiom_7,axiom,
! [X,Y] :
( rinvS(X,Y)
<=> rs(Y,X) ),
file('theBenchmark.p',axiom_7) ).
cnf(c_12,plain,
( ca(A)
| ~ cUnsatisfiable(A) ),
inference(clausify,[status(thm)],[axiom_3]) ).
fof(axiom_9,axiom,
cUnsatisfiable(i2003_11_14_17_19_28752),
file('theBenchmark.p',axiom_9) ).
cnf(c_13,plain,
cUnsatisfiable(i2003_11_14_17_19_28752),
inference(clausify,[status(thm)],[axiom_9]) ).
fof(nnf_3,plain,
! [X] :
( ? [Y] :
( ? [Z] :
( cowlThing(Z)
& rr(Y,Z) )
& ! [X6] :
( ! [W] :
( cc(W)
| ~ rr(X6,W) )
| ~ rp(Y,X6) )
& ! [X4] :
( ? [X5] :
( cowlThing(X5)
& rp(X4,X5) )
| ~ rp(Y,X4) )
& ! [X2] :
( ? [X3] :
( cowlThing(X3)
& rr(X2,X3) )
| ~ rp(Y,X2) )
& ! [X1] :
( cc(X1)
| ~ rr(Y,X1) )
& ? [X0] :
( cowlThing(X0)
& rp(Y,X0) )
& rs(X,Y) )
| ~ cUnsatisfiable(X) ),
inference(fof_nnf,[status(thm)],[axiom_2]) ).
fof(sk_axiom_2_sk,plain,
! [X] :
( ( cowlThing(sK4(X))
& rr(sK0(X),sK4(X))
& ! [X6] :
( ! [W] :
( cc(W)
| ~ rr(X6,W) )
| ~ rp(sK0(X),X6) )
& ! [X4] :
( ( cowlThing(sK3(X,X4))
& rp(X4,sK3(X,X4)) )
| ~ rp(sK0(X),X4) )
& ! [X2] :
( ( cowlThing(sK1(X,X2))
& rr(X2,sK1(X,X2)) )
| ~ rp(sK0(X),X2) )
& ! [X1] :
( cc(X1)
| ~ rr(sK0(X),X1) )
& cowlThing(sK2(X))
& rp(sK0(X),sK2(X))
& rs(X,sK0(X)) )
| ~ cUnsatisfiable(X) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK2,sK1,sK3,sK4]),skolemize(Y,sK0(X)),skolemize(X0,sK2(X)),skolemize(X3,sK1(X,X2)),skolemize(X5,sK3(X,X4)),skolemize(Z,sK4(X))],[nnf_3]) ).
fof(sk_axiom_2,plain,
( ! [VAR_0] :
( cowlThing(sK4(VAR_0))
| ~ cUnsatisfiable(VAR_0) )
& ! [VAR_0] :
( rr(sK0(VAR_0),sK4(VAR_0))
| ~ cUnsatisfiable(VAR_0) )
& ! [VAR_0,VAR_1,VAR_2] :
( cc(VAR_2)
| ~ rr(VAR_1,VAR_2)
| ~ rp(sK0(VAR_0),VAR_1)
| ~ cUnsatisfiable(VAR_0) )
& ! [VAR_0,VAR_1] :
( cowlThing(sK3(VAR_0,VAR_1))
| ~ rp(sK0(VAR_0),VAR_1)
| ~ cUnsatisfiable(VAR_0) )
& ! [VAR_0,VAR_1] :
( rp(VAR_1,sK3(VAR_0,VAR_1))
| ~ rp(sK0(VAR_0),VAR_1)
| ~ cUnsatisfiable(VAR_0) )
& ! [VAR_0,VAR_1] :
( cowlThing(sK1(VAR_0,VAR_1))
| ~ rp(sK0(VAR_0),VAR_1)
| ~ cUnsatisfiable(VAR_0) )
& ! [VAR_0,VAR_1] :
( rr(VAR_1,sK1(VAR_0,VAR_1))
| ~ rp(sK0(VAR_0),VAR_1)
| ~ cUnsatisfiable(VAR_0) )
& ! [VAR_0,VAR_1] :
( cc(VAR_1)
| ~ rr(sK0(VAR_0),VAR_1)
| ~ cUnsatisfiable(VAR_0) )
& ! [VAR_0] :
( cowlThing(sK2(VAR_0))
| ~ cUnsatisfiable(VAR_0) )
& ! [VAR_0] :
( rp(sK0(VAR_0),sK2(VAR_0))
| ~ cUnsatisfiable(VAR_0) )
& ! [VAR_0] :
( rs(VAR_0,sK0(VAR_0))
| ~ cUnsatisfiable(VAR_0) ) ),
inference(cnf_transformation,[status(thm)],[sk_axiom_2_sk]) ).
cnf(c_15,plain,
( cc(C)
| ~ rr(B,C)
| ~ rp(sK0(A),B)
| ~ cUnsatisfiable(A) ),
inference(split_conjunct,[status(thm)],[sk_axiom_2]) ).
cnf(c_17,plain,
( rr(B,sK1(A,B))
| ~ rp(sK0(A),B)
| ~ cUnsatisfiable(A) ),
inference(split_conjunct,[status(thm)],[sk_axiom_2]) ).
cnf(c_19,plain,
( rp(sK0(A),sK2(A))
| ~ cUnsatisfiable(A) ),
inference(split_conjunct,[status(thm)],[sk_axiom_2]) ).
cnf(c_20,plain,
( rs(A,sK0(A))
| ~ cUnsatisfiable(A) ),
inference(split_conjunct,[status(thm)],[sk_axiom_2]) ).
cnf(c_21,plain,
( ~ rs(B,A)
| rinvS(A,B) ),
inference(clausify,[status(thm)],[axiom_7]) ).
cnf(c_23,plain,
rs(i2003_11_14_17_19_28752,sK0(i2003_11_14_17_19_28752)),
inference(resolve,[status(thm)],[c_20,c_13]) ).
cnf(c_25,plain,
( ~ rr(B,A)
| rinvR(A,B) ),
inference(clausify,[status(thm)],[axiom_6]) ).
cnf(c_27,plain,
( cc(B)
| ~ rr(A,B)
| ~ rp(sK0(i2003_11_14_17_19_28752),A) ),
inference(resolve,[status(thm)],[c_15,c_13]) ).
cnf(c_28,plain,
( rr(A,sK1(i2003_11_14_17_19_28752,A))
| ~ rp(sK0(i2003_11_14_17_19_28752),A) ),
inference(resolve,[status(thm)],[c_17,c_13]) ).
cnf(c_30,plain,
( ~ ca(D)
| ~ rinvS(C,D)
| ~ rinvP(B,C)
| ~ rinvR(A,B)
| ~ cc(A) ),
inference(clausify,[status(thm)],[axiom_4]) ).
cnf(c_33,plain,
( cc(sK1(i2003_11_14_17_19_28752,A))
| ~ rp(sK0(i2003_11_14_17_19_28752),A)
| ~ rp(sK0(i2003_11_14_17_19_28752),A) ),
inference(resolve,[status(thm)],[c_28,c_27]) ).
cnf(c_46,plain,
( ~ rp(sK0(i2003_11_14_17_19_28752),A)
| ~ rp(sK0(i2003_11_14_17_19_28752),A)
| ~ ca(D)
| ~ rinvS(C,D)
| ~ rinvP(B,C)
| ~ rinvR(sK1(i2003_11_14_17_19_28752,A),B) ),
inference(resolve,[status(thm)],[c_30,c_33]) ).
cnf(c_47,plain,
( ~ rp(sK0(i2003_11_14_17_19_28752),A)
| ~ ca(D)
| ~ rinvS(C,D)
| ~ rinvP(B,C)
| ~ rinvR(sK1(i2003_11_14_17_19_28752,A),B) ),
inference(copy,[status(thm)],[c_46]) ).
cnf(c_49,plain,
rinvS(sK0(i2003_11_14_17_19_28752),i2003_11_14_17_19_28752),
inference(resolve,[status(thm)],[c_21,c_23]) ).
cnf(c_51,plain,
( ~ rp(B,A)
| rinvP(A,B) ),
inference(clausify,[status(thm)],[axiom_5]) ).
cnf(c_53,plain,
ca(i2003_11_14_17_19_28752),
inference(resolve,[status(thm)],[c_12,c_13]) ).
cnf(c_55,plain,
rp(sK0(i2003_11_14_17_19_28752),sK2(i2003_11_14_17_19_28752)),
inference(resolve,[status(thm)],[c_19,c_13]) ).
cnf(c_57,plain,
( rinvR(sK1(i2003_11_14_17_19_28752,A),A)
| ~ rp(sK0(i2003_11_14_17_19_28752),A) ),
inference(resolve,[status(thm)],[c_28,c_25]) ).
cnf(c_130,plain,
rinvP(sK2(i2003_11_14_17_19_28752),sK0(i2003_11_14_17_19_28752)),
inference(resolve,[status(thm)],[c_51,c_55]) ).
cnf(c_137,plain,
rinvR(sK1(i2003_11_14_17_19_28752,sK2(i2003_11_14_17_19_28752)),sK2(i2003_11_14_17_19_28752)),
inference(resolve,[status(thm)],[c_57,c_55]) ).
cnf(c_147,plain,
( ~ rp(sK0(i2003_11_14_17_19_28752),A)
| ~ ca(B)
| ~ rinvS(sK0(i2003_11_14_17_19_28752),B)
| ~ rinvR(sK1(i2003_11_14_17_19_28752,A),sK2(i2003_11_14_17_19_28752)) ),
inference(resolve,[status(thm)],[c_47,c_130]) ).
cnf(c_148,plain,
( ~ rp(sK0(i2003_11_14_17_19_28752),A)
| ~ ca(i2003_11_14_17_19_28752)
| ~ rinvR(sK1(i2003_11_14_17_19_28752,A),sK2(i2003_11_14_17_19_28752)) ),
inference(resolve,[status(thm)],[c_147,c_49]) ).
cnf(c_149,plain,
( ~ rp(sK0(i2003_11_14_17_19_28752),A)
| ~ rinvR(sK1(i2003_11_14_17_19_28752,A),sK2(i2003_11_14_17_19_28752)) ),
inference(resolve,[status(thm)],[c_148,c_53]) ).
cnf(c_150,plain,
~ rinvR(sK1(i2003_11_14_17_19_28752,sK2(i2003_11_14_17_19_28752)),sK2(i2003_11_14_17_19_28752)),
inference(resolve,[status(thm)],[c_149,c_55]) ).
cnf(c_146,plain,
$false,
inference(resolve,[status(thm)],[c_137,c_150]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : KRS082+1 : TPTP v9.3.1. Released v3.1.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n015.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Fri Sep 25 19:41:57 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.37 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.09/0.37 % Process 2080411 was started by sandbox on n015,
% 0.09/0.37 % Fri Sep 25 19:41:57 2026
% 0.09/0.37 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.09/0.37
% 0.09/0.37 % From the command line: assign(max_seconds, 300).
% 0.09/0.39
% 0.09/0.39 % SZS status Unsatisfiable for theBenchmark
% 0.09/0.39
% 0.09/0.39 % Proof 1 at 0.01 (+ 0.00) seconds.
% 0.09/0.39 % Length of proof is 29.
% 0.09/0.39 % Level of proof is 6.
% 0.09/0.39 % Maximum clause weight is 27.000.
% 0.09/0.39 % Given clauses 22.
% 0.09/0.39
% 0.09/0.39 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------