%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : KRS117+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 : n004.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 07:46:04 AM UTC 2026
% Result : Unsatisfiable 0.21s 0.50s
% Output : CNFRefutation 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 12
% Syntax : Number of formulae : 64 ( 22 unt; 0 def)
% Number of atoms : 197 ( 11 equ)
% Maximal formula atoms : 19 ( 3 avg)
% Number of connectives : 218 ( 85 ~; 79 |; 42 &)
% ( 7 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 14 ( 12 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 1 con; 0-1 aty)
% Number of variables : 98 ( 3 sgn 57 !; 10 ?)
% Comments :
%------------------------------------------------------------------------------
fof(ccxcomp_substitution_1,axiom,
! [A,B] :
( ( ccxcomp(A)
& A = B )
=> ccxcomp(B) ),
file('theBenchmark.p',ccxcomp_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) )
& ! [Y] :
( rinvR(X,Y)
=> ca_Vx3(Y) )
& ccxcomp(X) ) ),
file('theBenchmark.p',axiom_2) ).
fof(axiom_3,axiom,
! [X] :
( cc(X)
<=> ~ ? [Y] : ra_Px1(X,Y) ),
file('theBenchmark.p',axiom_3) ).
fof(axiom_4,axiom,
! [X] :
( ccxcomp(X)
<=> ? [Y0] : ra_Px1(X,Y0) ),
file('theBenchmark.p',axiom_4) ).
fof(axiom_5,axiom,
! [X] :
( cd(X)
<=> ( cc(X)
& ? [Y] :
( ccxcomp(Y)
& rf(X,Y) ) ) ),
file('theBenchmark.p',axiom_5) ).
fof(axiom_6,axiom,
! [X] :
( ca_Vx3(X)
<=> ? [Y] :
( cd(Y)
& rinvF(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) ).
fof(axiom_9,axiom,
! [X,Y] :
( rinvR(X,Y)
<=> rr(Y,X) ),
file('theBenchmark.p',axiom_9) ).
fof(axiom_12,axiom,
! [X,Y] :
( rf(X,Y)
=> rr(X,Y) ),
file('theBenchmark.p',axiom_12) ).
cnf(c_35,plain,
( ccxcomp(A)
| ~ ccxcomp(B)
| A != B ),
inference(clausify,[status(thm)],[ccxcomp_substitution_1]) ).
cnf(c_51,plain,
cowlThing(A),
inference(clausify,[status(thm)],[axiom_0]) ).
fof(nnf_22,plain,
! [X] :
( ( ! [Y] :
( ~ cd(Y)
| ~ rinvF(X,Y) )
| ? [X2] :
( ~ ca_Vx3(X2)
& rinvR(X,X2) )
| ~ ccxcomp(X)
| cUnsatisfiable(X) )
& ( ( ? [X1] :
( cd(X1)
& rinvF(X,X1) )
& ! [X0] :
( ca_Vx3(X0)
| ~ rinvR(X,X0) )
& ccxcomp(X) )
| ~ cUnsatisfiable(X) ) ),
inference(fof_nnf,[status(thm)],[axiom_2]) ).
fof(sk_axiom_2_sk,plain,
! [X] :
( ( ! [Y] :
( ~ cd(Y)
| ~ rinvF(X,Y) )
| ( ~ ca_Vx3(sK4(X))
& rinvR(X,sK4(X)) )
| ~ ccxcomp(X)
| cUnsatisfiable(X) )
& ( ( cd(sK0(X))
& rinvF(X,sK0(X))
& ! [X0] :
( ca_Vx3(X0)
| ~ rinvR(X,X0) )
& ccxcomp(X) )
| ~ cUnsatisfiable(X) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK4]),skolemize(X1,sK0(X)),skolemize(X2,sK4(X))],[nnf_22]) ).
fof(sk_axiom_2,plain,
( ! [VAR_0,VAR_1] :
( ~ cd(VAR_1)
| ~ rinvF(VAR_0,VAR_1)
| ~ ca_Vx3(sK4(VAR_0))
| ~ ccxcomp(VAR_0)
| cUnsatisfiable(VAR_0) )
& ! [VAR_0,VAR_1] :
( ~ cd(VAR_1)
| ~ rinvF(VAR_0,VAR_1)
| rinvR(VAR_0,sK4(VAR_0))
| ~ ccxcomp(VAR_0)
| cUnsatisfiable(VAR_0) )
& ! [VAR_0] :
( cd(sK0(VAR_0))
| ~ cUnsatisfiable(VAR_0) )
& ! [VAR_0] :
( rinvF(VAR_0,sK0(VAR_0))
| ~ cUnsatisfiable(VAR_0) )
& ! [VAR_0,VAR_1] :
( ca_Vx3(VAR_1)
| ~ rinvR(VAR_0,VAR_1)
| ~ cUnsatisfiable(VAR_0) )
& ! [VAR_0] :
( ccxcomp(VAR_0)
| ~ cUnsatisfiable(VAR_0) ) ),
inference(cnf_transformation,[status(thm)],[sk_axiom_2_sk]) ).
cnf(c_56,plain,
( ca_Vx3(B)
| ~ rinvR(A,B)
| ~ cUnsatisfiable(A) ),
inference(split_conjunct,[status(thm)],[sk_axiom_2]) ).
cnf(c_57,plain,
( rinvF(A,sK0(A))
| ~ cUnsatisfiable(A) ),
inference(split_conjunct,[status(thm)],[sk_axiom_2]) ).
cnf(c_58,plain,
( cd(sK0(A))
| ~ cUnsatisfiable(A) ),
inference(split_conjunct,[status(thm)],[sk_axiom_2]) ).
cnf(c_61,plain,
( ~ ra_Px1(A,B)
| ~ cc(A) ),
inference(clausify,[status(thm)],[axiom_3]) ).
fof(nnf_24,plain,
! [X] :
( ( ! [Y0] : ~ ra_Px1(X,Y0)
| ccxcomp(X) )
& ( ? [X2] : ra_Px1(X,X2)
| ~ ccxcomp(X) ) ),
inference(fof_nnf,[status(thm)],[axiom_4]) ).
fof(sk_axiom_4_sk,plain,
! [X] :
( ( ! [Y0] : ~ ra_Px1(X,Y0)
| ccxcomp(X) )
& ( ra_Px1(X,sK1(X))
| ~ ccxcomp(X) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(X2,sK1(X))],[nnf_24]) ).
fof(sk_axiom_4,plain,
( ! [VAR_0,VAR_1] :
( ~ ra_Px1(VAR_0,VAR_1)
| ccxcomp(VAR_0) )
& ! [VAR_0] :
( ra_Px1(VAR_0,sK1(VAR_0))
| ~ ccxcomp(VAR_0) ) ),
inference(cnf_transformation,[status(thm)],[sk_axiom_4_sk]) ).
cnf(c_63,plain,
( ra_Px1(A,sK1(A))
| ~ ccxcomp(A) ),
inference(split_conjunct,[status(thm)],[sk_axiom_4]) ).
fof(nnf_25,plain,
! [X] :
( ( ~ cc(X)
| ! [Y] :
( ~ ccxcomp(Y)
| ~ rf(X,Y) )
| cd(X) )
& ( ( cc(X)
& ? [X2] :
( ccxcomp(X2)
& rf(X,X2) ) )
| ~ cd(X) ) ),
inference(fof_nnf,[status(thm)],[axiom_5]) ).
fof(sk_axiom_5_sk,plain,
! [X] :
( ( ~ cc(X)
| ! [Y] :
( ~ ccxcomp(Y)
| ~ rf(X,Y) )
| cd(X) )
& ( ( cc(X)
& ccxcomp(sK2(X))
& rf(X,sK2(X)) )
| ~ cd(X) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2]),skolemize(X2,sK2(X))],[nnf_25]) ).
fof(sk_axiom_5,plain,
( ! [VAR_0,VAR_1] :
( ~ cc(VAR_0)
| ~ ccxcomp(VAR_1)
| ~ rf(VAR_0,VAR_1)
| cd(VAR_0) )
& ! [VAR_0] :
( cc(VAR_0)
| ~ cd(VAR_0) )
& ! [VAR_0] :
( ccxcomp(sK2(VAR_0))
| ~ cd(VAR_0) )
& ! [VAR_0] :
( rf(VAR_0,sK2(VAR_0))
| ~ cd(VAR_0) ) ),
inference(cnf_transformation,[status(thm)],[sk_axiom_5_sk]) ).
cnf(c_65,plain,
( rf(A,sK2(A))
| ~ cd(A) ),
inference(split_conjunct,[status(thm)],[sk_axiom_5]) ).
cnf(c_66,plain,
( ccxcomp(sK2(A))
| ~ cd(A) ),
inference(split_conjunct,[status(thm)],[sk_axiom_5]) ).
cnf(c_67,plain,
( cc(A)
| ~ cd(A) ),
inference(split_conjunct,[status(thm)],[sk_axiom_5]) ).
fof(nnf_26,plain,
! [X] :
( ( ! [Y] :
( ~ cd(Y)
| ~ rinvF(X,Y) )
| ca_Vx3(X) )
& ( ? [X2] :
( cd(X2)
& rinvF(X,X2) )
| ~ ca_Vx3(X) ) ),
inference(fof_nnf,[status(thm)],[axiom_6]) ).
fof(sk_axiom_6_sk,plain,
! [X] :
( ( ! [Y] :
( ~ cd(Y)
| ~ rinvF(X,Y) )
| ca_Vx3(X) )
& ( ( cd(sK3(X))
& rinvF(X,sK3(X)) )
| ~ ca_Vx3(X) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3]),skolemize(X2,sK3(X))],[nnf_26]) ).
fof(sk_axiom_6,plain,
( ! [VAR_0,VAR_1] :
( ~ cd(VAR_1)
| ~ rinvF(VAR_0,VAR_1)
| ca_Vx3(VAR_0) )
& ! [VAR_0] :
( cd(sK3(VAR_0))
| ~ ca_Vx3(VAR_0) )
& ! [VAR_0] :
( rinvF(VAR_0,sK3(VAR_0))
| ~ ca_Vx3(VAR_0) ) ),
inference(cnf_transformation,[status(thm)],[sk_axiom_6_sk]) ).
cnf(c_69,plain,
( rinvF(A,sK3(A))
| ~ ca_Vx3(A) ),
inference(split_conjunct,[status(thm)],[sk_axiom_6]) ).
cnf(c_70,plain,
( cd(sK3(A))
| ~ ca_Vx3(A) ),
inference(split_conjunct,[status(thm)],[sk_axiom_6]) ).
cnf(c_72,plain,
( C = B
| ~ rf(A,C)
| ~ rf(A,B)
| ~ cowlThing(A) ),
inference(clausify,[status(thm)],[axiom_7]) ).
cnf(c_73,plain,
( C = B
| ~ rf(A,C)
| ~ rf(A,B) ),
inference(resolve,[status(thm)],[c_51,c_72]) ).
cnf(c_74,plain,
( rf(B,A)
| ~ rinvF(A,B) ),
inference(clausify,[status(thm)],[axiom_8]) ).
cnf(c_77,plain,
( ~ rr(B,A)
| rinvR(A,B) ),
inference(clausify,[status(thm)],[axiom_9]) ).
fof(axiom_11,axiom,
cUnsatisfiable(i2003_11_14_17_21_37349),
file('theBenchmark.p',axiom_11) ).
cnf(c_79,plain,
cUnsatisfiable(i2003_11_14_17_21_37349),
inference(clausify,[status(thm)],[axiom_11]) ).
cnf(c_80,plain,
( rr(A,B)
| ~ rf(A,B) ),
inference(clausify,[status(thm)],[axiom_12]) ).
cnf(c_85,plain,
cd(sK0(i2003_11_14_17_21_37349)),
inference(resolve,[status(thm)],[c_79,c_58]) ).
cnf(c_86,plain,
rinvF(i2003_11_14_17_21_37349,sK0(i2003_11_14_17_21_37349)),
inference(resolve,[status(thm)],[c_79,c_57]) ).
cnf(c_87,plain,
( ca_Vx3(A)
| ~ rinvR(i2003_11_14_17_21_37349,A) ),
inference(resolve,[status(thm)],[c_79,c_56]) ).
cnf(c_97,plain,
cc(sK0(i2003_11_14_17_21_37349)),
inference(resolve,[status(thm)],[c_85,c_67]) ).
cnf(c_103,plain,
rf(sK0(i2003_11_14_17_21_37349),i2003_11_14_17_21_37349),
inference(resolve,[status(thm)],[c_86,c_74]) ).
cnf(c_115,plain,
~ ra_Px1(sK0(i2003_11_14_17_21_37349),A),
inference(resolve,[status(thm)],[c_97,c_61]) ).
cnf(c_131,plain,
~ ccxcomp(sK0(i2003_11_14_17_21_37349)),
inference(resolve,[status(thm)],[c_63,c_115]) ).
cnf(c_136,plain,
rr(sK0(i2003_11_14_17_21_37349),i2003_11_14_17_21_37349),
inference(resolve,[status(thm)],[c_103,c_80]) ).
cnf(c_147,plain,
rinvR(i2003_11_14_17_21_37349,sK0(i2003_11_14_17_21_37349)),
inference(resolve,[status(thm)],[c_136,c_77]) ).
cnf(c_168,plain,
ca_Vx3(sK0(i2003_11_14_17_21_37349)),
inference(resolve,[status(thm)],[c_147,c_87]) ).
cnf(c_171,plain,
cd(sK3(sK0(i2003_11_14_17_21_37349))),
inference(resolve,[status(thm)],[c_168,c_70]) ).
cnf(c_172,plain,
rinvF(sK0(i2003_11_14_17_21_37349),sK3(sK0(i2003_11_14_17_21_37349))),
inference(resolve,[status(thm)],[c_168,c_69]) ).
cnf(c_208,plain,
ccxcomp(sK2(sK3(sK0(i2003_11_14_17_21_37349)))),
inference(resolve,[status(thm)],[c_171,c_66]) ).
cnf(c_209,plain,
rf(sK3(sK0(i2003_11_14_17_21_37349)),sK2(sK3(sK0(i2003_11_14_17_21_37349)))),
inference(resolve,[status(thm)],[c_171,c_65]) ).
cnf(c_214,plain,
rf(sK3(sK0(i2003_11_14_17_21_37349)),sK0(i2003_11_14_17_21_37349)),
inference(resolve,[status(thm)],[c_172,c_74]) ).
cnf(c_325,plain,
( ccxcomp(A)
| A != sK2(sK3(sK0(i2003_11_14_17_21_37349))) ),
inference(resolve,[status(thm)],[c_35,c_208]) ).
cnf(c_326,plain,
sK0(i2003_11_14_17_21_37349) != sK2(sK3(sK0(i2003_11_14_17_21_37349))),
inference(resolve,[status(thm)],[c_325,c_131]) ).
cnf(c_251,plain,
sK2(sK3(sK0(i2003_11_14_17_21_37349))) != sK0(i2003_11_14_17_21_37349),
inference(copy,[status(thm)],[c_326]) ).
cnf(c_257,plain,
( sK0(i2003_11_14_17_21_37349) = A
| ~ rf(sK3(sK0(i2003_11_14_17_21_37349)),A) ),
inference(resolve,[status(thm)],[c_214,c_73]) ).
cnf(c_327,plain,
sK0(i2003_11_14_17_21_37349) = sK2(sK3(sK0(i2003_11_14_17_21_37349))),
inference(resolve,[status(thm)],[c_257,c_209]) ).
cnf(c_328,plain,
sK2(sK3(sK0(i2003_11_14_17_21_37349))) = sK0(i2003_11_14_17_21_37349),
inference(copy,[status(thm)],[c_327]) ).
cnf(c_324,plain,
$false,
inference(resolve,[status(thm)],[c_251,c_328]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : KRS117+1 : TPTP v9.3.1. Released v3.1.0.
% 0.00/0.06 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.19/0.43 % Computer : n004.cluster.edu
% 0.19/0.43 % Model : x86_64 x86_64
% 0.19/0.43 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.19/0.43 % Memory : 8046.5625MB
% 0.19/0.43 % OS : Linux 6.8.0-71-generic
% 0.19/0.43 % CPULimit : 300
% 0.19/0.43 % WCLimit : 300
% 0.19/0.43 % DateTime : Fri Sep 25 19:40:05 UTC 2026
% 0.19/0.43 % CPUTime :
% 0.19/0.43 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.19/0.43 % Process 3916341 was started by sandbox on n004,
% 0.19/0.43 % Fri Sep 25 19:40:05 2026
% 0.19/0.43 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.19/0.45
% 0.19/0.45 % From the command line: assign(max_seconds, 300).
% 0.21/0.50
% 0.21/0.50 % SZS status Unsatisfiable for theBenchmark
% 0.21/0.50
% 0.21/0.50 % Proof 1 at 0.03 (+ 0.01) seconds.
% 0.21/0.50 % Length of proof is 47.
% 0.21/0.50 % Level of proof is 10.
% 0.21/0.50 % Maximum clause weight is 28.000.
% 0.21/0.50 % Given clauses 197.
% 0.21/0.50
% 0.21/0.50 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------