%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : KRS113+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 : n009.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 0.11s 0.38s
% Output : CNFRefutation 0.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 8
% Syntax : Number of formulae : 42 ( 14 unt; 0 def)
% Number of atoms : 155 ( 14 equ)
% Maximal formula atoms : 35 ( 3 avg)
% Number of connectives : 187 ( 74 ~; 70 |; 34 &)
% ( 5 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 19 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 10 ( 8 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 1 con; 0-1 aty)
% Number of variables : 76 ( 1 sgn 47 !; 9 ?)
% Comments :
%------------------------------------------------------------------------------
fof(ca_Vx2_substitution_1,axiom,
! [A,B] :
( ( ca_Vx2(A)
& A = B )
=> ca_Vx2(B) ),
file('theBenchmark.p',ca_Vx2_substitution_1) ).
fof(axiom_2,axiom,
! [X] :
( cUnsatisfiable(X)
<=> ( cpxcomp(X)
& ? [Y] :
( cp(Y)
& rs(X,Y) )
& ? [Y] :
( ca_Vx2(Y)
& rr(X,Y) )
& ! [Y0,Y1] :
( ( rr(X,Y1)
& rr(X,Y0) )
=> Y0 = Y1 ) ) ),
file('theBenchmark.p',axiom_2) ).
fof(axiom_3,axiom,
! [X] :
( cp(X)
<=> ~ ? [Y] : ra_Px1(X,Y) ),
file('theBenchmark.p',axiom_3) ).
fof(axiom_4,axiom,
! [X] :
( cpxcomp(X)
<=> ? [Y0] : ra_Px1(X,Y0) ),
file('theBenchmark.p',axiom_4) ).
fof(axiom_5,axiom,
! [X] :
( ca_Vx2(X)
<=> ! [Y] :
( rinvS(X,Y)
=> cp(Y) ) ),
file('theBenchmark.p',axiom_5) ).
fof(axiom_6,axiom,
! [X,Y] :
( rinvS(X,Y)
<=> rs(Y,X) ),
file('theBenchmark.p',axiom_6) ).
fof(axiom_8,axiom,
! [X,Y] :
( rs(X,Y)
=> rr(X,Y) ),
file('theBenchmark.p',axiom_8) ).
cnf(c_26,plain,
( ca_Vx2(A)
| ~ ca_Vx2(B)
| A != B ),
inference(clausify,[status(thm)],[ca_Vx2_substitution_1]) ).
fof(nnf_19,plain,
! [X] :
( ( ~ cpxcomp(X)
| ! [Y] :
( ~ cp(Y)
| ~ rs(X,Y) )
| ! [X4] :
( ~ ca_Vx2(X4)
| ~ rr(X,X4) )
| ? [Y0,Y1] :
( Y1 != Y0
& rr(X,Y1)
& rr(X,Y0) )
| cUnsatisfiable(X) )
& ( ( cpxcomp(X)
& ? [X3] :
( cp(X3)
& rs(X,X3) )
& ? [X2] :
( ca_Vx2(X2)
& rr(X,X2) )
& ! [X0,X1] :
( X1 = X0
| ~ rr(X,X1)
| ~ rr(X,X0) ) )
| ~ cUnsatisfiable(X) ) ),
inference(fof_nnf,[status(thm)],[axiom_2]) ).
fof(sk_axiom_2_sk,plain,
! [X] :
( ( ~ cpxcomp(X)
| ! [Y] :
( ~ cp(Y)
| ~ rs(X,Y) )
| ! [X4] :
( ~ ca_Vx2(X4)
| ~ rr(X,X4) )
| ( sK4(X) != sK3(X)
& rr(X,sK4(X))
& rr(X,sK3(X)) )
| cUnsatisfiable(X) )
& ( ( cpxcomp(X)
& cp(sK1(X))
& rs(X,sK1(X))
& ca_Vx2(sK0(X))
& rr(X,sK0(X))
& ! [X0,X1] :
( X1 = X0
| ~ rr(X,X1)
| ~ rr(X,X0) ) )
| ~ cUnsatisfiable(X) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK3,sK4]),skolemize(X2,sK0(X)),skolemize(X3,sK1(X)),skolemize(Y0,sK3(X)),skolemize(Y1,sK4(X))],[nnf_19]) ).
fof(sk_axiom_2,plain,
( ! [VAR_0,VAR_1,VAR_2] :
( ~ cpxcomp(VAR_0)
| ~ cp(VAR_2)
| ~ rs(VAR_0,VAR_2)
| ~ ca_Vx2(VAR_1)
| ~ rr(VAR_0,VAR_1)
| sK4(VAR_0) != sK3(VAR_0)
| cUnsatisfiable(VAR_0) )
& ! [VAR_0,VAR_1,VAR_2] :
( ~ cpxcomp(VAR_0)
| ~ cp(VAR_2)
| ~ rs(VAR_0,VAR_2)
| ~ ca_Vx2(VAR_1)
| ~ rr(VAR_0,VAR_1)
| rr(VAR_0,sK4(VAR_0))
| cUnsatisfiable(VAR_0) )
& ! [VAR_0,VAR_1,VAR_2] :
( ~ cpxcomp(VAR_0)
| ~ cp(VAR_2)
| ~ rs(VAR_0,VAR_2)
| ~ ca_Vx2(VAR_1)
| ~ rr(VAR_0,VAR_1)
| rr(VAR_0,sK3(VAR_0))
| cUnsatisfiable(VAR_0) )
& ! [VAR_0] :
( cpxcomp(VAR_0)
| ~ cUnsatisfiable(VAR_0) )
& ! [VAR_0] :
( cp(sK1(VAR_0))
| ~ cUnsatisfiable(VAR_0) )
& ! [VAR_0] :
( rs(VAR_0,sK1(VAR_0))
| ~ cUnsatisfiable(VAR_0) )
& ! [VAR_0] :
( ca_Vx2(sK0(VAR_0))
| ~ cUnsatisfiable(VAR_0) )
& ! [VAR_0] :
( rr(VAR_0,sK0(VAR_0))
| ~ cUnsatisfiable(VAR_0) )
& ! [VAR_0,VAR_1,VAR_2] :
( VAR_2 = VAR_1
| ~ rr(VAR_0,VAR_2)
| ~ rr(VAR_0,VAR_1)
| ~ cUnsatisfiable(VAR_0) ) ),
inference(cnf_transformation,[status(thm)],[sk_axiom_2_sk]) ).
cnf(c_45,plain,
( C = B
| ~ rr(A,C)
| ~ rr(A,B)
| ~ cUnsatisfiable(A) ),
inference(split_conjunct,[status(thm)],[sk_axiom_2]) ).
cnf(c_46,plain,
( rr(A,sK0(A))
| ~ cUnsatisfiable(A) ),
inference(split_conjunct,[status(thm)],[sk_axiom_2]) ).
cnf(c_47,plain,
( ca_Vx2(sK0(A))
| ~ cUnsatisfiable(A) ),
inference(split_conjunct,[status(thm)],[sk_axiom_2]) ).
cnf(c_48,plain,
( rs(A,sK1(A))
| ~ cUnsatisfiable(A) ),
inference(split_conjunct,[status(thm)],[sk_axiom_2]) ).
cnf(c_50,plain,
( cpxcomp(A)
| ~ cUnsatisfiable(A) ),
inference(split_conjunct,[status(thm)],[sk_axiom_2]) ).
cnf(c_54,plain,
( ~ ra_Px1(A,B)
| ~ cp(A) ),
inference(clausify,[status(thm)],[axiom_3]) ).
fof(nnf_21,plain,
! [X] :
( ( ! [Y0] : ~ ra_Px1(X,Y0)
| cpxcomp(X) )
& ( ? [X4] : ra_Px1(X,X4)
| ~ cpxcomp(X) ) ),
inference(fof_nnf,[status(thm)],[axiom_4]) ).
fof(sk_axiom_4_sk,plain,
! [X] :
( ( ! [Y0] : ~ ra_Px1(X,Y0)
| cpxcomp(X) )
& ( ra_Px1(X,sK2(X))
| ~ cpxcomp(X) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2]),skolemize(X4,sK2(X))],[nnf_21]) ).
fof(sk_axiom_4,plain,
( ! [VAR_0,VAR_1] :
( ~ ra_Px1(VAR_0,VAR_1)
| cpxcomp(VAR_0) )
& ! [VAR_0] :
( ra_Px1(VAR_0,sK2(VAR_0))
| ~ cpxcomp(VAR_0) ) ),
inference(cnf_transformation,[status(thm)],[sk_axiom_4_sk]) ).
cnf(c_56,plain,
( ra_Px1(A,sK2(A))
| ~ cpxcomp(A) ),
inference(split_conjunct,[status(thm)],[sk_axiom_4]) ).
cnf(c_58,plain,
( cp(B)
| ~ rinvS(A,B)
| ~ ca_Vx2(A) ),
inference(clausify,[status(thm)],[axiom_5]) ).
cnf(c_62,plain,
( ~ rs(B,A)
| rinvS(A,B) ),
inference(clausify,[status(thm)],[axiom_6]) ).
fof(axiom_7,axiom,
cUnsatisfiable(i2003_11_14_17_21_22376),
file('theBenchmark.p',axiom_7) ).
cnf(c_63,plain,
cUnsatisfiable(i2003_11_14_17_21_22376),
inference(clausify,[status(thm)],[axiom_7]) ).
cnf(c_64,plain,
( rr(A,B)
| ~ rs(A,B) ),
inference(clausify,[status(thm)],[axiom_8]) ).
cnf(c_72,plain,
cpxcomp(i2003_11_14_17_21_22376),
inference(resolve,[status(thm)],[c_63,c_50]) ).
cnf(c_74,plain,
rs(i2003_11_14_17_21_22376,sK1(i2003_11_14_17_21_22376)),
inference(resolve,[status(thm)],[c_63,c_48]) ).
cnf(c_75,plain,
ca_Vx2(sK0(i2003_11_14_17_21_22376)),
inference(resolve,[status(thm)],[c_63,c_47]) ).
cnf(c_76,plain,
rr(i2003_11_14_17_21_22376,sK0(i2003_11_14_17_21_22376)),
inference(resolve,[status(thm)],[c_63,c_46]) ).
cnf(c_78,plain,
ra_Px1(i2003_11_14_17_21_22376,sK2(i2003_11_14_17_21_22376)),
inference(resolve,[status(thm)],[c_72,c_56]) ).
cnf(c_88,plain,
rr(i2003_11_14_17_21_22376,sK1(i2003_11_14_17_21_22376)),
inference(resolve,[status(thm)],[c_74,c_64]) ).
cnf(c_89,plain,
rinvS(sK1(i2003_11_14_17_21_22376),i2003_11_14_17_21_22376),
inference(resolve,[status(thm)],[c_74,c_62]) ).
cnf(c_95,plain,
~ cp(i2003_11_14_17_21_22376),
inference(resolve,[status(thm)],[c_78,c_54]) ).
cnf(c_127,plain,
( cp(i2003_11_14_17_21_22376)
| ~ ca_Vx2(sK1(i2003_11_14_17_21_22376)) ),
inference(resolve,[status(thm)],[c_89,c_58]) ).
cnf(c_106,plain,
~ ca_Vx2(sK1(i2003_11_14_17_21_22376)),
inference(resolve,[status(thm)],[c_95,c_127]) ).
cnf(c_128,plain,
( ca_Vx2(A)
| A != sK0(i2003_11_14_17_21_22376) ),
inference(resolve,[status(thm)],[c_26,c_75]) ).
cnf(c_116,plain,
sK1(i2003_11_14_17_21_22376) != sK0(i2003_11_14_17_21_22376),
inference(resolve,[status(thm)],[c_128,c_106]) ).
cnf(c_129,plain,
( A = sK0(i2003_11_14_17_21_22376)
| ~ rr(i2003_11_14_17_21_22376,A)
| ~ cUnsatisfiable(i2003_11_14_17_21_22376) ),
inference(resolve,[status(thm)],[c_45,c_76]) ).
cnf(c_130,plain,
( sK1(i2003_11_14_17_21_22376) = sK0(i2003_11_14_17_21_22376)
| ~ cUnsatisfiable(i2003_11_14_17_21_22376) ),
inference(resolve,[status(thm)],[c_129,c_88]) ).
cnf(c_131,plain,
~ cUnsatisfiable(i2003_11_14_17_21_22376),
inference(resolve,[status(thm)],[c_130,c_116]) ).
cnf(c_126,plain,
$false,
inference(resolve,[status(thm)],[c_63,c_131]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : KRS113+1 : TPTP v9.3.1. Released v3.1.0.
% 0.00/0.03 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.07/0.34 % Computer : n009.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 19:39:59 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 2369970 was started by sandbox2 on n009,
% 0.07/0.34 % Fri Sep 25 19:39:59 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 30.
% 0.11/0.38 % Level of proof is 7.
% 0.11/0.38 % Maximum clause weight is 11.000.
% 0.11/0.38 % Given clauses 73.
% 0.11/0.38
% 0.11/0.38 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------