%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : KRS083+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 : n011.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 0.11s 0.38s
% Output : CNFRefutation 0.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 9
% Syntax : Number of formulae : 51 ( 19 unt; 0 def)
% Number of atoms : 164 ( 11 equ)
% Maximal formula atoms : 23 ( 3 avg)
% Number of connectives : 188 ( 75 ~; 68 |; 36 &)
% ( 4 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 11 ( 9 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 1 con; 0-2 aty)
% Number of variables : 78 ( 1 sgn 44 !; 7 ?)
% Comments :
%------------------------------------------------------------------------------
fof(cc_substitution_1,axiom,
! [A,B] :
( ( cc(A)
& A = B )
=> cc(B) ),
file('theBenchmark.p',cc_substitution_1) ).
fof(axiom_0,axiom,
! [X] :
( ~ cowlNothing(X)
& cowlThing(X) ),
file('theBenchmark.p',axiom_0) ).
fof(axiom_2,axiom,
! [X] :
( cUnsatisfiable(X)
<=> ( ? [Y] :
( cd(Y)
& rinvF(X,Y) )
& ~ cc(X)
& ! [Y] :
( rinvR(X,Y)
=> ? [Z] :
( cd(Z)
& rinvF(Y,Z) ) ) ) ),
file('theBenchmark.p',axiom_2) ).
fof(axiom_3,axiom,
! [X] :
( cd(X)
<=> ( cc(X)
& ? [Y] :
( ~ cc(Y)
& rf(X,Y) ) ) ),
file('theBenchmark.p',axiom_3) ).
fof(axiom_4,axiom,
! [X] :
( cowlThing(X)
=> ! [Y0,Y1] :
( ( rf(X,Y1)
& rf(X,Y0) )
=> Y0 = Y1 ) ),
file('theBenchmark.p',axiom_4) ).
fof(axiom_5,axiom,
! [X,Y] :
( rinvF(X,Y)
<=> rf(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_9,axiom,
! [X,Y] :
( rf(X,Y)
=> rr(X,Y) ),
file('theBenchmark.p',axiom_9) ).
cnf(c_26,plain,
( cc(A)
| ~ cc(B)
| A != B ),
inference(clausify,[status(thm)],[cc_substitution_1]) ).
cnf(c_40,plain,
cowlThing(A),
inference(clausify,[status(thm)],[axiom_0]) ).
fof(nnf_18,plain,
! [X] :
( ( ! [Y] :
( ~ cd(Y)
| ~ rinvF(X,Y) )
| cc(X)
| ? [X3] :
( ! [Z] :
( ~ cd(Z)
| ~ rinvF(X3,Z) )
& rinvR(X,X3) )
| cUnsatisfiable(X) )
& ( ( ? [X2] :
( cd(X2)
& rinvF(X,X2) )
& ~ cc(X)
& ! [X0] :
( ? [X1] :
( cd(X1)
& rinvF(X0,X1) )
| ~ rinvR(X,X0) ) )
| ~ cUnsatisfiable(X) ) ),
inference(fof_nnf,[status(thm)],[axiom_2]) ).
fof(sk_axiom_2_sk,plain,
! [X] :
( ( ! [Y] :
( ~ cd(Y)
| ~ rinvF(X,Y) )
| cc(X)
| ( ! [Z] :
( ~ cd(Z)
| ~ rinvF(sK3(X),Z) )
& rinvR(X,sK3(X)) )
| cUnsatisfiable(X) )
& ( ( cd(sK1(X))
& rinvF(X,sK1(X))
& ~ cc(X)
& ! [X0] :
( ( cd(sK0(X,X0))
& rinvF(X0,sK0(X,X0)) )
| ~ rinvR(X,X0) ) )
| ~ cUnsatisfiable(X) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK3]),skolemize(X1,sK0(X,X0)),skolemize(X2,sK1(X)),skolemize(X3,sK3(X))],[nnf_18]) ).
fof(sk_axiom_2,plain,
( ! [VAR_0,VAR_1,VAR_2] :
( ~ cd(VAR_2)
| ~ rinvF(VAR_0,VAR_2)
| cc(VAR_0)
| ~ cd(VAR_1)
| ~ rinvF(sK3(VAR_0),VAR_1)
| cUnsatisfiable(VAR_0) )
& ! [VAR_0,VAR_1] :
( ~ cd(VAR_1)
| ~ rinvF(VAR_0,VAR_1)
| cc(VAR_0)
| rinvR(VAR_0,sK3(VAR_0))
| cUnsatisfiable(VAR_0) )
& ! [VAR_0] :
( cd(sK1(VAR_0))
| ~ cUnsatisfiable(VAR_0) )
& ! [VAR_0] :
( rinvF(VAR_0,sK1(VAR_0))
| ~ cUnsatisfiable(VAR_0) )
& ! [VAR_0] :
( ~ cc(VAR_0)
| ~ cUnsatisfiable(VAR_0) )
& ! [VAR_0,VAR_1] :
( cd(sK0(VAR_0,VAR_1))
| ~ rinvR(VAR_0,VAR_1)
| ~ cUnsatisfiable(VAR_0) )
& ! [VAR_0,VAR_1] :
( rinvF(VAR_1,sK0(VAR_0,VAR_1))
| ~ rinvR(VAR_0,VAR_1)
| ~ cUnsatisfiable(VAR_0) ) ),
inference(cnf_transformation,[status(thm)],[sk_axiom_2_sk]) ).
cnf(c_44,plain,
( rinvF(B,sK0(A,B))
| ~ rinvR(A,B)
| ~ cUnsatisfiable(A) ),
inference(split_conjunct,[status(thm)],[sk_axiom_2]) ).
cnf(c_45,plain,
( cd(sK0(A,B))
| ~ rinvR(A,B)
| ~ cUnsatisfiable(A) ),
inference(split_conjunct,[status(thm)],[sk_axiom_2]) ).
cnf(c_47,plain,
( rinvF(A,sK1(A))
| ~ cUnsatisfiable(A) ),
inference(split_conjunct,[status(thm)],[sk_axiom_2]) ).
cnf(c_48,plain,
( cd(sK1(A))
| ~ cUnsatisfiable(A) ),
inference(split_conjunct,[status(thm)],[sk_axiom_2]) ).
fof(nnf_19,plain,
! [X] :
( ( ~ cc(X)
| ! [Y] :
( cc(Y)
| ~ rf(X,Y) )
| cd(X) )
& ( ( cc(X)
& ? [X3] :
( ~ cc(X3)
& rf(X,X3) ) )
| ~ cd(X) ) ),
inference(fof_nnf,[status(thm)],[axiom_3]) ).
fof(sk_axiom_3_sk,plain,
! [X] :
( ( ~ cc(X)
| ! [Y] :
( cc(Y)
| ~ rf(X,Y) )
| cd(X) )
& ( ( cc(X)
& ~ cc(sK2(X))
& rf(X,sK2(X)) )
| ~ cd(X) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2]),skolemize(X3,sK2(X))],[nnf_19]) ).
fof(sk_axiom_3,plain,
( ! [VAR_0,VAR_1] :
( ~ cc(VAR_0)
| cc(VAR_1)
| ~ rf(VAR_0,VAR_1)
| cd(VAR_0) )
& ! [VAR_0] :
( cc(VAR_0)
| ~ cd(VAR_0) )
& ! [VAR_0] :
( ~ cc(sK2(VAR_0))
| ~ cd(VAR_0) )
& ! [VAR_0] :
( rf(VAR_0,sK2(VAR_0))
| ~ cd(VAR_0) ) ),
inference(cnf_transformation,[status(thm)],[sk_axiom_3_sk]) ).
cnf(c_51,plain,
( rf(A,sK2(A))
| ~ cd(A) ),
inference(split_conjunct,[status(thm)],[sk_axiom_3]) ).
cnf(c_52,plain,
( ~ cc(sK2(A))
| ~ cd(A) ),
inference(split_conjunct,[status(thm)],[sk_axiom_3]) ).
cnf(c_53,plain,
( cc(A)
| ~ cd(A) ),
inference(split_conjunct,[status(thm)],[sk_axiom_3]) ).
cnf(c_55,plain,
( C = B
| ~ rf(A,C)
| ~ rf(A,B)
| ~ cowlThing(A) ),
inference(clausify,[status(thm)],[axiom_4]) ).
cnf(c_56,plain,
( C = B
| ~ rf(A,C)
| ~ rf(A,B) ),
inference(resolve,[status(thm)],[c_40,c_55]) ).
cnf(c_57,plain,
( rf(B,A)
| ~ rinvF(A,B) ),
inference(clausify,[status(thm)],[axiom_5]) ).
cnf(c_60,plain,
( ~ rr(B,A)
| rinvR(A,B) ),
inference(clausify,[status(thm)],[axiom_6]) ).
fof(axiom_8,axiom,
cUnsatisfiable(i2003_11_14_17_19_32337),
file('theBenchmark.p',axiom_8) ).
cnf(c_62,plain,
cUnsatisfiable(i2003_11_14_17_19_32337),
inference(clausify,[status(thm)],[axiom_8]) ).
cnf(c_63,plain,
( rr(A,B)
| ~ rf(A,B) ),
inference(clausify,[status(thm)],[axiom_9]) ).
cnf(c_66,plain,
cd(sK1(i2003_11_14_17_19_32337)),
inference(resolve,[status(thm)],[c_62,c_48]) ).
cnf(c_67,plain,
rinvF(i2003_11_14_17_19_32337,sK1(i2003_11_14_17_19_32337)),
inference(resolve,[status(thm)],[c_62,c_47]) ).
cnf(c_71,plain,
cc(sK1(i2003_11_14_17_19_32337)),
inference(resolve,[status(thm)],[c_66,c_53]) ).
cnf(c_140,plain,
( cc(A)
| A != sK1(i2003_11_14_17_19_32337) ),
inference(resolve,[status(thm)],[c_71,c_26]) ).
cnf(c_77,plain,
( cc(A)
| sK1(i2003_11_14_17_19_32337) != A ),
inference(copy,[status(thm)],[c_140]) ).
cnf(c_78,plain,
rf(sK1(i2003_11_14_17_19_32337),i2003_11_14_17_19_32337),
inference(resolve,[status(thm)],[c_67,c_57]) ).
cnf(c_81,plain,
rr(sK1(i2003_11_14_17_19_32337),i2003_11_14_17_19_32337),
inference(resolve,[status(thm)],[c_78,c_63]) ).
cnf(c_90,plain,
rinvR(i2003_11_14_17_19_32337,sK1(i2003_11_14_17_19_32337)),
inference(resolve,[status(thm)],[c_81,c_60]) ).
cnf(c_141,plain,
( cd(sK0(i2003_11_14_17_19_32337,sK1(i2003_11_14_17_19_32337)))
| ~ cUnsatisfiable(i2003_11_14_17_19_32337) ),
inference(resolve,[status(thm)],[c_90,c_45]) ).
cnf(c_93,plain,
cd(sK0(i2003_11_14_17_19_32337,sK1(i2003_11_14_17_19_32337))),
inference(resolve,[status(thm)],[c_62,c_141]) ).
cnf(c_142,plain,
( rinvF(sK1(i2003_11_14_17_19_32337),sK0(i2003_11_14_17_19_32337,sK1(i2003_11_14_17_19_32337)))
| ~ cUnsatisfiable(i2003_11_14_17_19_32337) ),
inference(resolve,[status(thm)],[c_90,c_44]) ).
cnf(c_94,plain,
rinvF(sK1(i2003_11_14_17_19_32337),sK0(i2003_11_14_17_19_32337,sK1(i2003_11_14_17_19_32337))),
inference(resolve,[status(thm)],[c_62,c_142]) ).
cnf(c_98,plain,
rf(sK0(i2003_11_14_17_19_32337,sK1(i2003_11_14_17_19_32337)),sK2(sK0(i2003_11_14_17_19_32337,sK1(i2003_11_14_17_19_32337)))),
inference(resolve,[status(thm)],[c_93,c_51]) ).
cnf(c_100,plain,
~ cc(sK2(sK0(i2003_11_14_17_19_32337,sK1(i2003_11_14_17_19_32337)))),
inference(resolve,[status(thm)],[c_52,c_93]) ).
cnf(c_143,plain,
sK1(i2003_11_14_17_19_32337) != sK2(sK0(i2003_11_14_17_19_32337,sK1(i2003_11_14_17_19_32337))),
inference(resolve,[status(thm)],[c_77,c_100]) ).
cnf(c_120,plain,
sK2(sK0(i2003_11_14_17_19_32337,sK1(i2003_11_14_17_19_32337))) != sK1(i2003_11_14_17_19_32337),
inference(copy,[status(thm)],[c_143]) ).
cnf(c_130,plain,
rf(sK0(i2003_11_14_17_19_32337,sK1(i2003_11_14_17_19_32337)),sK1(i2003_11_14_17_19_32337)),
inference(resolve,[status(thm)],[c_94,c_57]) ).
cnf(c_144,plain,
( sK1(i2003_11_14_17_19_32337) = A
| ~ rf(sK0(i2003_11_14_17_19_32337,sK1(i2003_11_14_17_19_32337)),A) ),
inference(resolve,[status(thm)],[c_56,c_130]) ).
cnf(c_145,plain,
sK1(i2003_11_14_17_19_32337) != sK2(sK0(i2003_11_14_17_19_32337,sK1(i2003_11_14_17_19_32337))),
inference(copy,[status(thm)],[c_120]) ).
cnf(c_146,plain,
~ rf(sK0(i2003_11_14_17_19_32337,sK1(i2003_11_14_17_19_32337)),sK2(sK0(i2003_11_14_17_19_32337,sK1(i2003_11_14_17_19_32337)))),
inference(resolve,[status(thm)],[c_144,c_145]) ).
cnf(c_139,plain,
$false,
inference(resolve,[status(thm)],[c_98,c_146]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : KRS083+1 : TPTP v9.3.1. Released v3.1.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.07/0.34 % Computer : n011.cluster.edu
% 0.07/0.34 % Model : x86_64 x86_64
% 0.07/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.34 % Memory : 8046.5625MB
% 0.07/0.34 % OS : Linux 6.8.0-71-generic
% 0.07/0.34 % CPULimit : 300
% 0.07/0.34 % WCLimit : 300
% 0.07/0.34 % DateTime : Fri Sep 25 19:38:44 UTC 2026
% 0.07/0.34 % CPUTime :
% 0.07/0.34 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.07/0.34 % Process 2708696 was started by sandbox2 on n011,
% 0.07/0.34 % Fri Sep 25 19:38:44 2026
% 0.07/0.34 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.07/0.35
% 0.07/0.35 % From the command line: assign(max_seconds, 300).
% 0.11/0.38
% 0.11/0.38 % SZS status Unsatisfiable for theBenchmark
% 0.11/0.38
% 0.11/0.38 % Proof 1 at 0.01 (+ 0.00) seconds.
% 0.11/0.38 % Length of proof is 37.
% 0.11/0.38 % Level of proof is 9.
% 0.11/0.38 % Maximum clause weight is 10.000.
% 0.11/0.38 % Given clauses 84.
% 0.11/0.38
% 0.11/0.38 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------