%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : KRS104+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 : n007.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 07:46:02 AM UTC 2026
% Result : Unsatisfiable 0.18s 0.48s
% Output : CNFRefutation 0.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 20
% Syntax : Number of formulae : 95 ( 8 unt; 0 def)
% Number of atoms : 235 ( 0 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 240 ( 100 ~; 97 |; 24 &)
% ( 17 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 21 ( 20 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 1 con; 0-1 aty)
% Number of variables : 148 ( 22 sgn 61 !; 18 ?)
% Comments :
%------------------------------------------------------------------------------
fof(axiom_2,axiom,
! [X] :
( cUnsatisfiable(X)
<=> ~ ? [Y] : ra_Px5(X,Y) ),
file('theBenchmark.p',axiom_2) ).
fof(axiom_3,axiom,
! [X] :
( cUnsatisfiablexcomp(X)
<=> ( ca_Cx6(X)
& ca_Cx8(X)
& ca_Cx7(X) ) ),
file('theBenchmark.p',axiom_3) ).
fof(axiom_4,axiom,
! [X] :
( cUnsatisfiablexcomp(X)
<=> ? [Y0] : ra_Px5(X,Y0) ),
file('theBenchmark.p',axiom_4) ).
fof(axiom_5,axiom,
! [X] :
( ca(X)
=> ca_Cx1(X) ),
file('theBenchmark.p',axiom_5) ).
fof(axiom_6,axiom,
! [X] :
( cb(X)
<=> ? [Y0] : ra_Px3(X,Y0) ),
file('theBenchmark.p',axiom_6) ).
fof(axiom_7,axiom,
! [X] :
( cb(X)
=> ccxcomp(X) ),
file('theBenchmark.p',axiom_7) ).
fof(axiom_8,axiom,
! [X] :
( cbxcomp(X)
<=> ~ ? [Y] : ra_Px3(X,Y) ),
file('theBenchmark.p',axiom_8) ).
fof(axiom_9,axiom,
! [X] :
( cc(X)
<=> ? [Y0] : ra_Px2(X,Y0) ),
file('theBenchmark.p',axiom_9) ).
fof(axiom_10,axiom,
! [X] :
( ccxcomp(X)
<=> ~ ? [Y] : ra_Px2(X,Y) ),
file('theBenchmark.p',axiom_10) ).
fof(axiom_11,axiom,
! [X] :
( ca_Cx1(X)
<=> ( ccxcomp(X)
& cbxcomp(X) ) ),
file('theBenchmark.p',axiom_11) ).
fof(axiom_14,axiom,
! [X] :
( ca_Cx6(X)
<=> ~ ? [Y] : ra_Px6(X,Y) ),
file('theBenchmark.p',axiom_14) ).
fof(axiom_15,axiom,
! [X] :
( ca_Cx6xcomp(X)
<=> ( cb(X)
& ca(X) ) ),
file('theBenchmark.p',axiom_15) ).
fof(axiom_16,axiom,
! [X] :
( ca_Cx6xcomp(X)
<=> ? [Y0] : ra_Px6(X,Y0) ),
file('theBenchmark.p',axiom_16) ).
fof(axiom_17,axiom,
! [X] :
( ca_Cx7(X)
<=> ? [Y0] : ra_Px7(X,Y0) ),
file('theBenchmark.p',axiom_17) ).
fof(axiom_18,axiom,
! [X] :
( ca_Cx7xcomp(X)
<=> ( ca(X)
& cc(X) ) ),
file('theBenchmark.p',axiom_18) ).
fof(axiom_19,axiom,
! [X] :
( ca_Cx7xcomp(X)
<=> ~ ? [Y] : ra_Px7(X,Y) ),
file('theBenchmark.p',axiom_19) ).
fof(axiom_20,axiom,
! [X] :
( ca_Cx8(X)
<=> ~ ? [Y] : ra_Px8(X,Y) ),
file('theBenchmark.p',axiom_20) ).
fof(axiom_21,axiom,
! [X] :
( ca_Cx8xcomp(X)
<=> ? [Y0] : ra_Px8(X,Y0) ),
file('theBenchmark.p',axiom_21) ).
fof(axiom_22,axiom,
! [X] :
( ca_Cx8xcomp(X)
<=> ( cb(X)
& cc(X) ) ),
file('theBenchmark.p',axiom_22) ).
cnf(c_26,plain,
( ~ ra_Px5(A,B)
| ~ cUnsatisfiable(A) ),
inference(clausify,[status(thm)],[axiom_2]) ).
fof(axiom_23,axiom,
cUnsatisfiable(i2003_11_14_17_20_50869),
file('theBenchmark.p',axiom_23) ).
cnf(c_28,plain,
cUnsatisfiable(i2003_11_14_17_20_50869),
inference(clausify,[status(thm)],[axiom_23]) ).
cnf(c_29,plain,
( ~ ca_Cx6(A)
| ~ ca_Cx8(A)
| ~ ca_Cx7(A)
| cUnsatisfiablexcomp(A) ),
inference(clausify,[status(thm)],[axiom_3]) ).
fof(nnf_5,plain,
! [X] :
( ( ! [Y0] : ~ ra_Px5(X,Y0)
| cUnsatisfiablexcomp(X) )
& ( ? [X0] : ra_Px5(X,X0)
| ~ cUnsatisfiablexcomp(X) ) ),
inference(fof_nnf,[status(thm)],[axiom_4]) ).
fof(sk_axiom_4_sk,plain,
! [X] :
( ( ! [Y0] : ~ ra_Px5(X,Y0)
| cUnsatisfiablexcomp(X) )
& ( ra_Px5(X,sK0(X))
| ~ cUnsatisfiablexcomp(X) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X0,sK0(X))],[nnf_5]) ).
fof(sk_axiom_4,plain,
( ! [VAR_0,VAR_1] :
( ~ ra_Px5(VAR_0,VAR_1)
| cUnsatisfiablexcomp(VAR_0) )
& ! [VAR_0] :
( ra_Px5(VAR_0,sK0(VAR_0))
| ~ cUnsatisfiablexcomp(VAR_0) ) ),
inference(cnf_transformation,[status(thm)],[sk_axiom_4_sk]) ).
cnf(c_33,plain,
( ra_Px5(A,sK0(A))
| ~ cUnsatisfiablexcomp(A) ),
inference(split_conjunct,[status(thm)],[sk_axiom_4]) ).
cnf(c_35,plain,
( ~ ca_Cx6(A)
| ~ ca_Cx8(A)
| ~ ca_Cx7(A)
| ra_Px5(A,sK0(A)) ),
inference(resolve,[status(thm)],[c_33,c_29]) ).
cnf(c_37,plain,
( ~ ra_Px7(A,B)
| ca_Cx7(A) ),
inference(clausify,[status(thm)],[axiom_17]) ).
fof(nnf_21,plain,
! [X] :
( ( ? [Y] : ra_Px8(X,Y)
| ca_Cx8(X) )
& ( ! [X0] : ~ ra_Px8(X,X0)
| ~ ca_Cx8(X) ) ),
inference(fof_nnf,[status(thm)],[axiom_20]) ).
fof(sk_axiom_20_sk,plain,
! [X] :
( ( ra_Px8(X,sK1(X))
| ca_Cx8(X) )
& ( ! [X0] : ~ ra_Px8(X,X0)
| ~ ca_Cx8(X) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(Y,sK1(X))],[nnf_21]) ).
fof(sk_axiom_20,plain,
( ! [VAR_0] :
( ra_Px8(VAR_0,sK1(VAR_0))
| ca_Cx8(VAR_0) )
& ! [VAR_0,VAR_1] :
( ~ ra_Px8(VAR_0,VAR_1)
| ~ ca_Cx8(VAR_0) ) ),
inference(cnf_transformation,[status(thm)],[sk_axiom_20_sk]) ).
cnf(c_39,plain,
( ra_Px8(A,sK1(A))
| ca_Cx8(A) ),
inference(split_conjunct,[status(thm)],[sk_axiom_20]) ).
cnf(c_42,plain,
( ~ ca_Cx6(A)
| ~ ca_Cx8(A)
| ra_Px5(A,sK0(A))
| ~ ra_Px7(A,B) ),
inference(resolve,[status(thm)],[c_37,c_35]) ).
cnf(c_45,plain,
( ~ ca_Cx6(A)
| ra_Px5(A,sK0(A))
| ~ ra_Px7(A,B)
| ra_Px8(A,sK1(A)) ),
inference(resolve,[status(thm)],[c_39,c_42]) ).
fof(nnf_15,plain,
! [X] :
( ( ? [Y] : ra_Px6(X,Y)
| ca_Cx6(X) )
& ( ! [X0] : ~ ra_Px6(X,X0)
| ~ ca_Cx6(X) ) ),
inference(fof_nnf,[status(thm)],[axiom_14]) ).
fof(sk_axiom_14_sk,plain,
! [X] :
( ( ra_Px6(X,sK2(X))
| ca_Cx6(X) )
& ( ! [X0] : ~ ra_Px6(X,X0)
| ~ ca_Cx6(X) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2]),skolemize(Y,sK2(X))],[nnf_15]) ).
fof(sk_axiom_14,plain,
( ! [VAR_0] :
( ra_Px6(VAR_0,sK2(VAR_0))
| ca_Cx6(VAR_0) )
& ! [VAR_0,VAR_1] :
( ~ ra_Px6(VAR_0,VAR_1)
| ~ ca_Cx6(VAR_0) ) ),
inference(cnf_transformation,[status(thm)],[sk_axiom_14_sk]) ).
cnf(c_47,plain,
( ra_Px6(A,sK2(A))
| ca_Cx6(A) ),
inference(split_conjunct,[status(thm)],[sk_axiom_14]) ).
cnf(c_49,plain,
( ca(A)
| ~ ca_Cx6xcomp(A) ),
inference(clausify,[status(thm)],[axiom_15]) ).
cnf(c_50,plain,
( ca_Cx1(A)
| ~ ca(A) ),
inference(clausify,[status(thm)],[axiom_5]) ).
cnf(c_52,plain,
( ca(A)
| ~ ca_Cx7xcomp(A) ),
inference(clausify,[status(thm)],[axiom_18]) ).
cnf(c_56,plain,
( ca_Cx1(A)
| ~ ca_Cx6xcomp(A) ),
inference(resolve,[status(thm)],[c_49,c_50]) ).
cnf(c_57,plain,
( ca_Cx1(A)
| ~ ca_Cx7xcomp(A) ),
inference(resolve,[status(thm)],[c_52,c_50]) ).
cnf(c_59,plain,
( ccxcomp(A)
| ~ ca_Cx1(A) ),
inference(clausify,[status(thm)],[axiom_11]) ).
cnf(c_60,plain,
( cbxcomp(A)
| ~ ca_Cx1(A) ),
inference(clausify,[status(thm)],[axiom_11]) ).
fof(nnf_7,plain,
! [X] :
( ( ! [Y0] : ~ ra_Px3(X,Y0)
| cb(X) )
& ( ? [X0] : ra_Px3(X,X0)
| ~ cb(X) ) ),
inference(fof_nnf,[status(thm)],[axiom_6]) ).
fof(sk_axiom_6_sk,plain,
! [X] :
( ( ! [Y0] : ~ ra_Px3(X,Y0)
| cb(X) )
& ( ra_Px3(X,sK3(X))
| ~ cb(X) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3]),skolemize(X0,sK3(X))],[nnf_7]) ).
fof(sk_axiom_6,plain,
( ! [VAR_0,VAR_1] :
( ~ ra_Px3(VAR_0,VAR_1)
| cb(VAR_0) )
& ! [VAR_0] :
( ra_Px3(VAR_0,sK3(VAR_0))
| ~ cb(VAR_0) ) ),
inference(cnf_transformation,[status(thm)],[sk_axiom_6_sk]) ).
cnf(c_62,plain,
( ra_Px3(A,sK3(A))
| ~ cb(A) ),
inference(split_conjunct,[status(thm)],[sk_axiom_6]) ).
cnf(c_63,plain,
( ccxcomp(A)
| ~ cb(A) ),
inference(clausify,[status(thm)],[axiom_7]) ).
cnf(c_64,plain,
( cb(A)
| ~ ca_Cx6xcomp(A) ),
inference(clausify,[status(thm)],[axiom_15]) ).
cnf(c_65,plain,
( cb(A)
| ~ ca_Cx8xcomp(A) ),
inference(clausify,[status(thm)],[axiom_22]) ).
cnf(c_68,plain,
( ~ ra_Px2(A,B)
| ~ ccxcomp(A) ),
inference(clausify,[status(thm)],[axiom_10]) ).
cnf(c_72,plain,
( ccxcomp(A)
| ~ ca_Cx8xcomp(A) ),
inference(resolve,[status(thm)],[c_65,c_63]) ).
cnf(c_76,plain,
( ~ ca_Cx7xcomp(A)
| ccxcomp(A) ),
inference(resolve,[status(thm)],[c_59,c_57]) ).
cnf(c_84,plain,
( ~ ca_Cx6xcomp(A)
| cbxcomp(A) ),
inference(resolve,[status(thm)],[c_60,c_56]) ).
cnf(c_86,plain,
( ~ ra_Px3(A,B)
| ~ cbxcomp(A) ),
inference(clausify,[status(thm)],[axiom_8]) ).
cnf(c_88,plain,
( cc(A)
| ~ ca_Cx8xcomp(A) ),
inference(clausify,[status(thm)],[axiom_22]) ).
cnf(c_92,plain,
( cc(A)
| ~ ca_Cx7xcomp(A) ),
inference(clausify,[status(thm)],[axiom_18]) ).
fof(nnf_10,plain,
! [X] :
( ( ! [Y0] : ~ ra_Px2(X,Y0)
| cc(X) )
& ( ? [X0] : ra_Px2(X,X0)
| ~ cc(X) ) ),
inference(fof_nnf,[status(thm)],[axiom_9]) ).
fof(sk_axiom_9_sk,plain,
! [X] :
( ( ! [Y0] : ~ ra_Px2(X,Y0)
| cc(X) )
& ( ra_Px2(X,sK4(X))
| ~ cc(X) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4]),skolemize(X0,sK4(X))],[nnf_10]) ).
fof(sk_axiom_9,plain,
( ! [VAR_0,VAR_1] :
( ~ ra_Px2(VAR_0,VAR_1)
| cc(VAR_0) )
& ! [VAR_0] :
( ra_Px2(VAR_0,sK4(VAR_0))
| ~ cc(VAR_0) ) ),
inference(cnf_transformation,[status(thm)],[sk_axiom_9_sk]) ).
cnf(c_94,plain,
( ra_Px2(A,sK4(A))
| ~ cc(A) ),
inference(split_conjunct,[status(thm)],[sk_axiom_9]) ).
cnf(c_98,plain,
( ~ ca_Cx6xcomp(A)
| ~ ra_Px3(A,B) ),
inference(resolve,[status(thm)],[c_86,c_84]) ).
cnf(c_101,plain,
( ra_Px3(A,sK3(A))
| ~ ca_Cx6xcomp(A) ),
inference(resolve,[status(thm)],[c_64,c_62]) ).
cnf(c_102,plain,
( ~ ra_Px6(A,B)
| ca_Cx6xcomp(A) ),
inference(clausify,[status(thm)],[axiom_16]) ).
cnf(c_113,plain,
( ~ ca_Cx7xcomp(A)
| ra_Px2(A,sK4(A)) ),
inference(resolve,[status(thm)],[c_94,c_92]) ).
cnf(c_115,plain,
( ~ ra_Px2(A,B)
| ~ ca_Cx7xcomp(A) ),
inference(resolve,[status(thm)],[c_76,c_68]) ).
fof(nnf_20,plain,
! [X] :
( ( ? [Y] : ra_Px7(X,Y)
| ca_Cx7xcomp(X) )
& ( ! [X0] : ~ ra_Px7(X,X0)
| ~ ca_Cx7xcomp(X) ) ),
inference(fof_nnf,[status(thm)],[axiom_19]) ).
fof(sk_axiom_19_sk,plain,
! [X] :
( ( ra_Px7(X,sK5(X))
| ca_Cx7xcomp(X) )
& ( ! [X0] : ~ ra_Px7(X,X0)
| ~ ca_Cx7xcomp(X) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK5]),skolemize(Y,sK5(X))],[nnf_20]) ).
fof(sk_axiom_19,plain,
( ! [VAR_0] :
( ra_Px7(VAR_0,sK5(VAR_0))
| ca_Cx7xcomp(VAR_0) )
& ! [VAR_0,VAR_1] :
( ~ ra_Px7(VAR_0,VAR_1)
| ~ ca_Cx7xcomp(VAR_0) ) ),
inference(cnf_transformation,[status(thm)],[sk_axiom_19_sk]) ).
cnf(c_118,plain,
( ra_Px7(A,sK5(A))
| ca_Cx7xcomp(A) ),
inference(split_conjunct,[status(thm)],[sk_axiom_19]) ).
cnf(c_130,plain,
( ~ ra_Px8(A,B)
| ca_Cx8xcomp(A) ),
inference(clausify,[status(thm)],[axiom_21]) ).
cnf(c_132,plain,
( ~ ca_Cx8xcomp(A)
| ~ ra_Px2(A,B) ),
inference(resolve,[status(thm)],[c_68,c_72]) ).
cnf(c_133,plain,
( ~ ca_Cx8xcomp(A)
| ra_Px2(A,sK4(A)) ),
inference(resolve,[status(thm)],[c_94,c_88]) ).
cnf(c_135,plain,
( ~ ra_Px8(A,B)
| ra_Px2(A,sK4(A)) ),
inference(resolve,[status(thm)],[c_133,c_130]) ).
cnf(c_137,plain,
( ~ ra_Px8(A,C)
| ~ ra_Px2(A,B) ),
inference(resolve,[status(thm)],[c_132,c_130]) ).
cnf(c_152,plain,
( ~ ra_Px3(A,C)
| ~ ra_Px6(A,B) ),
inference(resolve,[status(thm)],[c_102,c_98]) ).
cnf(c_153,plain,
( ra_Px3(A,sK3(A))
| ~ ra_Px6(A,B) ),
inference(resolve,[status(thm)],[c_102,c_101]) ).
cnf(c_162,plain,
( ra_Px5(A,sK0(A))
| ~ ra_Px7(A,B)
| ra_Px8(A,sK1(A))
| ra_Px6(A,sK2(A)) ),
inference(resolve,[status(thm)],[c_47,c_45]) ).
cnf(c_165,plain,
~ ra_Px5(i2003_11_14_17_20_50869,A),
inference(resolve,[status(thm)],[c_26,c_28]) ).
cnf(c_177,plain,
( ~ ra_Px2(A,B)
| ra_Px7(A,sK5(A)) ),
inference(resolve,[status(thm)],[c_118,c_115]) ).
cnf(c_178,plain,
( ra_Px2(A,sK4(A))
| ra_Px7(A,sK5(A)) ),
inference(resolve,[status(thm)],[c_118,c_113]) ).
cnf(c_200,plain,
( ra_Px7(A,sK5(A))
| ra_Px7(A,sK5(A)) ),
inference(resolve,[status(thm)],[c_178,c_177]) ).
cnf(c_183,plain,
ra_Px7(A,sK5(A)),
inference(copy,[status(thm)],[c_200]) ).
cnf(c_185,plain,
( ra_Px5(A,sK0(A))
| ra_Px8(A,sK1(A))
| ra_Px6(A,sK2(A)) ),
inference(resolve,[status(thm)],[c_183,c_162]) ).
cnf(c_187,plain,
( ra_Px8(i2003_11_14_17_20_50869,sK1(i2003_11_14_17_20_50869))
| ra_Px6(i2003_11_14_17_20_50869,sK2(i2003_11_14_17_20_50869)) ),
inference(resolve,[status(thm)],[c_185,c_165]) ).
cnf(c_191,plain,
( ~ ra_Px2(i2003_11_14_17_20_50869,A)
| ra_Px6(i2003_11_14_17_20_50869,sK2(i2003_11_14_17_20_50869)) ),
inference(resolve,[status(thm)],[c_187,c_137]) ).
cnf(c_192,plain,
( ra_Px2(i2003_11_14_17_20_50869,sK4(i2003_11_14_17_20_50869))
| ra_Px6(i2003_11_14_17_20_50869,sK2(i2003_11_14_17_20_50869)) ),
inference(resolve,[status(thm)],[c_187,c_135]) ).
cnf(c_201,plain,
( ra_Px6(i2003_11_14_17_20_50869,sK2(i2003_11_14_17_20_50869))
| ra_Px6(i2003_11_14_17_20_50869,sK2(i2003_11_14_17_20_50869)) ),
inference(resolve,[status(thm)],[c_192,c_191]) ).
cnf(c_194,plain,
ra_Px6(i2003_11_14_17_20_50869,sK2(i2003_11_14_17_20_50869)),
inference(copy,[status(thm)],[c_201]) ).
cnf(c_195,plain,
ra_Px3(i2003_11_14_17_20_50869,sK3(i2003_11_14_17_20_50869)),
inference(resolve,[status(thm)],[c_194,c_153]) ).
cnf(c_198,plain,
~ ra_Px3(i2003_11_14_17_20_50869,A),
inference(resolve,[status(thm)],[c_152,c_194]) ).
cnf(c_199,plain,
$false,
inference(resolve,[status(thm)],[c_198,c_195]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : KRS104+1 : TPTP v9.3.1. Released v3.1.0.
% 0.00/0.06 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.18/0.44 % Computer : n007.cluster.edu
% 0.18/0.44 % Model : x86_64 x86_64
% 0.18/0.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.44 % Memory : 8046.5625MB
% 0.18/0.44 % OS : Linux 6.8.0-71-generic
% 0.18/0.44 % CPULimit : 300
% 0.18/0.44 % WCLimit : 300
% 0.18/0.44 % DateTime : Fri Sep 25 19:37:38 UTC 2026
% 0.18/0.44 % CPUTime :
% 0.18/0.44 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.18/0.44 % Process 1697909 was started by sandbox on n007,
% 0.18/0.44 % Fri Sep 25 19:37:38 2026
% 0.18/0.44 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.18/0.46
% 0.18/0.46 % From the command line: assign(max_seconds, 300).
% 0.18/0.48
% 0.18/0.48 % SZS status Unsatisfiable for theBenchmark
% 0.18/0.48
% 0.18/0.48 % Proof 1 at 0.01 (+ 0.01) seconds.
% 0.18/0.48 % Length of proof is 74.
% 0.18/0.48 % Level of proof is 12.
% 0.18/0.48 % Maximum clause weight is 15.000.
% 0.18/0.48 % Given clauses 48.
% 0.18/0.48
% 0.18/0.48 % SZS output start CNFRefutation for theBenchmark
% See solution above
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