%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : KRS072+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 : n018.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 07:45:58 AM UTC 2026
% Result : Unsatisfiable 0.09s 5.39s
% Output : CNFRefutation 0.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 5
% Syntax : Number of formulae : 31 ( 13 unt; 0 def)
% Number of atoms : 119 ( 17 equ)
% Maximal formula atoms : 30 ( 3 avg)
% Number of connectives : 144 ( 56 ~; 56 |; 27 &)
% ( 2 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 10 ( 8 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 1 con; 0-2 aty)
% Number of variables : 55 ( 0 sgn 34 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(cp1_substitution_1,axiom,
! [A,B] :
( ( cp1(A)
& A = B )
=> cp1(B) ),
file('theBenchmark.p',cp1_substitution_1) ).
fof(axiom_2,axiom,
! [X] :
( cUnsatisfiable(X)
<=> ( cp2(X)
& ? [Y] :
( ? [Z] :
( cp1(Z)
& rr(Y,Z) )
& ! [Z0,Z1] :
( ( rr(Y,Z1)
& rr(Y,Z0) )
=> Z0 = Z1 )
& rinvR(X,Y) ) ) ),
file('theBenchmark.p',axiom_2) ).
fof(axiom_3,axiom,
! [X] :
( cp1(X)
=> ~ ( cp5(X)
| cp4(X)
| cp2(X)
| cp3(X) ) ),
file('theBenchmark.p',axiom_3) ).
fof(axiom_7,axiom,
! [X,Y] :
( rinvR(X,Y)
<=> rr(Y,X) ),
file('theBenchmark.p',axiom_7) ).
cnf(c_26,plain,
( cp1(A)
| ~ cp1(B)
| A != B ),
inference(clausify,[status(thm)],[cp1_substitution_1]) ).
fof(nnf_17,plain,
! [X] :
( ( ~ cp2(X)
| ! [Y] :
( ! [Z] :
( ~ cp1(Z)
| ~ rr(Y,Z) )
| ? [Z0,Z1] :
( Z1 != Z0
& rr(Y,Z1)
& rr(Y,Z0) )
| ~ rinvR(X,Y) )
| cUnsatisfiable(X) )
& ( ( cp2(X)
& ? [X0] :
( ? [X3] :
( cp1(X3)
& rr(X0,X3) )
& ! [X1,X2] :
( X2 = X1
| ~ rr(X0,X2)
| ~ rr(X0,X1) )
& rinvR(X,X0) ) )
| ~ cUnsatisfiable(X) ) ),
inference(fof_nnf,[status(thm)],[axiom_2]) ).
fof(sk_axiom_2_sk,plain,
! [X] :
( ( ~ cp2(X)
| ! [Y] :
( ! [Z] :
( ~ cp1(Z)
| ~ rr(Y,Z) )
| ( sK3(X,Y) != sK2(X,Y)
& rr(Y,sK3(X,Y))
& rr(Y,sK2(X,Y)) )
| ~ rinvR(X,Y) )
| cUnsatisfiable(X) )
& ( ( cp2(X)
& cp1(sK1(X))
& rr(sK0(X),sK1(X))
& ! [X1,X2] :
( X2 = X1
| ~ rr(sK0(X),X2)
| ~ rr(sK0(X),X1) )
& rinvR(X,sK0(X)) )
| ~ cUnsatisfiable(X) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3]),skolemize(X0,sK0(X)),skolemize(X3,sK1(X)),skolemize(Z0,sK2(X,Y)),skolemize(Z1,sK3(X,Y))],[nnf_17]) ).
fof(sk_axiom_2,plain,
( ! [VAR_0,VAR_1,VAR_2] :
( ~ cp2(VAR_0)
| ~ cp1(VAR_2)
| ~ rr(VAR_1,VAR_2)
| sK3(VAR_0,VAR_1) != sK2(VAR_0,VAR_1)
| ~ rinvR(VAR_0,VAR_1)
| cUnsatisfiable(VAR_0) )
& ! [VAR_0,VAR_1,VAR_2] :
( ~ cp2(VAR_0)
| ~ cp1(VAR_2)
| ~ rr(VAR_1,VAR_2)
| rr(VAR_1,sK3(VAR_0,VAR_1))
| ~ rinvR(VAR_0,VAR_1)
| cUnsatisfiable(VAR_0) )
& ! [VAR_0,VAR_1,VAR_2] :
( ~ cp2(VAR_0)
| ~ cp1(VAR_2)
| ~ rr(VAR_1,VAR_2)
| rr(VAR_1,sK2(VAR_0,VAR_1))
| ~ rinvR(VAR_0,VAR_1)
| cUnsatisfiable(VAR_0) )
& ! [VAR_0] :
( cp2(VAR_0)
| ~ cUnsatisfiable(VAR_0) )
& ! [VAR_0] :
( cp1(sK1(VAR_0))
| ~ cUnsatisfiable(VAR_0) )
& ! [VAR_0] :
( rr(sK0(VAR_0),sK1(VAR_0))
| ~ cUnsatisfiable(VAR_0) )
& ! [VAR_0,VAR_1,VAR_2] :
( VAR_2 = VAR_1
| ~ rr(sK0(VAR_0),VAR_2)
| ~ rr(sK0(VAR_0),VAR_1)
| ~ cUnsatisfiable(VAR_0) )
& ! [VAR_0] :
( rinvR(VAR_0,sK0(VAR_0))
| ~ cUnsatisfiable(VAR_0) ) ),
inference(cnf_transformation,[status(thm)],[sk_axiom_2_sk]) ).
cnf(c_41,plain,
( rinvR(A,sK0(A))
| ~ cUnsatisfiable(A) ),
inference(split_conjunct,[status(thm)],[sk_axiom_2]) ).
cnf(c_42,plain,
( C = B
| ~ rr(sK0(A),C)
| ~ rr(sK0(A),B)
| ~ cUnsatisfiable(A) ),
inference(split_conjunct,[status(thm)],[sk_axiom_2]) ).
cnf(c_43,plain,
( rr(sK0(A),sK1(A))
| ~ cUnsatisfiable(A) ),
inference(split_conjunct,[status(thm)],[sk_axiom_2]) ).
cnf(c_44,plain,
( cp1(sK1(A))
| ~ cUnsatisfiable(A) ),
inference(split_conjunct,[status(thm)],[sk_axiom_2]) ).
cnf(c_45,plain,
( cp2(A)
| ~ cUnsatisfiable(A) ),
inference(split_conjunct,[status(thm)],[sk_axiom_2]) ).
cnf(c_50,plain,
( ~ cp2(A)
| ~ cp1(A) ),
inference(clausify,[status(thm)],[axiom_3]) ).
cnf(c_59,plain,
( rr(B,A)
| ~ rinvR(A,B) ),
inference(clausify,[status(thm)],[axiom_7]) ).
fof(axiom_8,axiom,
cUnsatisfiable(i2003_11_14_17_18_50190),
file('theBenchmark.p',axiom_8) ).
cnf(c_61,plain,
cUnsatisfiable(i2003_11_14_17_18_50190),
inference(clausify,[status(thm)],[axiom_8]) ).
cnf(c_63,plain,
cp2(i2003_11_14_17_18_50190),
inference(resolve,[status(thm)],[c_61,c_45]) ).
cnf(c_64,plain,
cp1(sK1(i2003_11_14_17_18_50190)),
inference(resolve,[status(thm)],[c_61,c_44]) ).
cnf(c_65,plain,
rr(sK0(i2003_11_14_17_18_50190),sK1(i2003_11_14_17_18_50190)),
inference(resolve,[status(thm)],[c_61,c_43]) ).
cnf(c_66,plain,
rinvR(i2003_11_14_17_18_50190,sK0(i2003_11_14_17_18_50190)),
inference(resolve,[status(thm)],[c_61,c_41]) ).
cnf(c_68,plain,
~ cp1(i2003_11_14_17_18_50190),
inference(resolve,[status(thm)],[c_63,c_50]) ).
cnf(c_78,plain,
rr(sK0(i2003_11_14_17_18_50190),i2003_11_14_17_18_50190),
inference(resolve,[status(thm)],[c_66,c_59]) ).
cnf(c_93,plain,
( i2003_11_14_17_18_50190 = A
| ~ rr(sK0(i2003_11_14_17_18_50190),A)
| ~ cUnsatisfiable(i2003_11_14_17_18_50190) ),
inference(resolve,[status(thm)],[c_78,c_42]) ).
cnf(c_81,plain,
( i2003_11_14_17_18_50190 = A
| ~ rr(sK0(i2003_11_14_17_18_50190),A) ),
inference(resolve,[status(thm)],[c_61,c_93]) ).
cnf(c_94,plain,
( cp1(A)
| A != sK1(i2003_11_14_17_18_50190) ),
inference(resolve,[status(thm)],[c_26,c_64]) ).
cnf(c_95,plain,
i2003_11_14_17_18_50190 != sK1(i2003_11_14_17_18_50190),
inference(resolve,[status(thm)],[c_94,c_68]) ).
cnf(c_88,plain,
sK1(i2003_11_14_17_18_50190) != i2003_11_14_17_18_50190,
inference(copy,[status(thm)],[c_95]) ).
cnf(c_96,plain,
i2003_11_14_17_18_50190 = sK1(i2003_11_14_17_18_50190),
inference(resolve,[status(thm)],[c_81,c_65]) ).
cnf(c_97,plain,
sK1(i2003_11_14_17_18_50190) = i2003_11_14_17_18_50190,
inference(copy,[status(thm)],[c_96]) ).
cnf(c_92,plain,
$false,
inference(resolve,[status(thm)],[c_88,c_97]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : KRS072+1 : TPTP v9.3.1. Released v3.1.0.
% 0.00/0.03 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/5.36 % Computer : n018.cluster.edu
% 0.09/5.36 % Model : x86_64 x86_64
% 0.09/5.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/5.36 % Memory : 8046.5625MB
% 0.09/5.36 % OS : Linux 6.8.0-71-generic
% 0.09/5.36 % CPULimit : 300
% 0.09/5.36 % WCLimit : 300
% 0.09/5.36 % DateTime : Fri Sep 25 19:40:11 UTC 2026
% 0.09/5.36 % CPUTime :
% 0.09/5.37 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.09/5.37 % Process 2673689 was started by sandbox on n018,
% 0.09/5.37 % Fri Sep 25 19:40:11 2026
% 0.09/5.37 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.09/5.37
% 0.09/5.37 % From the command line: assign(max_seconds, 300).
% 0.09/5.39
% 0.09/5.39 % SZS status Unsatisfiable for theBenchmark
% 0.09/5.39
% 0.09/5.39 % Proof 1 at 0.00 (+ 0.00) seconds.
% 0.09/5.39 % Length of proof is 22.
% 0.09/5.39 % Level of proof is 5.
% 0.09/5.39 % Maximum clause weight is 13.000.
% 0.09/5.39 % Given clauses 59.
% 0.09/5.39
% 0.09/5.39 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------