%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : KRS078+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 : n005.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 07:45:59 AM UTC 2026
% Result : Unsatisfiable 0.17s 0.45s
% Output : CNFRefutation 0.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 4
% Syntax : Number of formulae : 29 ( 11 unt; 0 def)
% Number of atoms : 165 ( 15 equ)
% Maximal formula atoms : 65 ( 5 avg)
% Number of connectives : 217 ( 81 ~; 91 |; 40 &)
% ( 2 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 24 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 8 ( 6 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 1 con; 0-3 aty)
% Number of variables : 85 ( 0 sgn 57 !; 9 ?)
% Comments :
%------------------------------------------------------------------------------
fof(rs_substitution_1,axiom,
! [A,B,C] :
( ( rs(A,C)
& A = B )
=> rs(B,C) ),
file('theBenchmark.p',rs_substitution_1) ).
fof(axiom_2,axiom,
! [X] :
( cUnsatisfiable(X)
<=> ( ? [Y] :
( ~ cp(Y)
& ~ cq(Y)
& rs(X,Y) )
& ? [Y] :
( ! [Z0,Z1] :
( ( rinvR(Y,Z1)
& rinvR(Y,Z0) )
=> Z0 = Z1 )
& ? [Z] :
( ! [W] :
( rs(Z,W)
=> cp(W) )
& rinvR(Y,Z) )
& rr(X,Y) ) ) ),
file('theBenchmark.p',axiom_2) ).
fof(axiom_3,axiom,
! [X,Y] :
( rinvR(X,Y)
<=> rr(Y,X) ),
file('theBenchmark.p',axiom_3) ).
cnf(c_27,plain,
( rs(A,C)
| ~ rs(B,C)
| A != B ),
inference(clausify,[status(thm)],[rs_substitution_1]) ).
fof(nnf_16,plain,
! [X] :
( ( ! [Y] :
( cp(Y)
| cq(Y)
| ~ rs(X,Y) )
| ! [X6] :
( ? [Z0,Z1] :
( Z1 != Z0
& rinvR(X6,Z1)
& rinvR(X6,Z0) )
| ! [Z] :
( ? [W] :
( ~ cp(W)
& rs(Z,W) )
| ~ rinvR(X6,Z) )
| ~ rr(X,X6) )
| cUnsatisfiable(X) )
& ( ( ? [X5] :
( ~ cp(X5)
& ~ cq(X5)
& rs(X,X5) )
& ? [X0] :
( ! [X3,X4] :
( X4 = X3
| ~ rinvR(X0,X4)
| ~ rinvR(X0,X3) )
& ? [X1] :
( ! [X2] :
( cp(X2)
| ~ rs(X1,X2) )
& rinvR(X0,X1) )
& rr(X,X0) ) )
| ~ cUnsatisfiable(X) ) ),
inference(fof_nnf,[status(thm)],[axiom_2]) ).
fof(sk_axiom_2_sk,plain,
! [X] :
( ( ! [Y] :
( cp(Y)
| cq(Y)
| ~ rs(X,Y) )
| ! [X6] :
( ( sK5(X,X6) != sK4(X,X6)
& rinvR(X6,sK5(X,X6))
& rinvR(X6,sK4(X,X6)) )
| ! [Z] :
( ( ~ cp(sK3(X,X6,Z))
& rs(Z,sK3(X,X6,Z)) )
| ~ rinvR(X6,Z) )
| ~ rr(X,X6) )
| cUnsatisfiable(X) )
& ( ( ~ cp(sK2(X))
& ~ cq(sK2(X))
& rs(X,sK2(X))
& ! [X3,X4] :
( X4 = X3
| ~ rinvR(sK0(X),X4)
| ~ rinvR(sK0(X),X3) )
& ! [X2] :
( cp(X2)
| ~ rs(sK1(X),X2) )
& rinvR(sK0(X),sK1(X))
& rr(X,sK0(X)) )
| ~ cUnsatisfiable(X) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3,sK4,sK5]),skolemize(X0,sK0(X)),skolemize(X1,sK1(X)),skolemize(X5,sK2(X)),skolemize(W,sK3(X,X6,Z)),skolemize(Z0,sK4(X,X6)),skolemize(Z1,sK5(X,X6))],[nnf_16]) ).
fof(sk_axiom_2,plain,
( ! [VAR_0,VAR_1,VAR_2,VAR_3] :
( cp(VAR_3)
| cq(VAR_3)
| ~ rs(VAR_0,VAR_3)
| sK5(VAR_0,VAR_1) != sK4(VAR_0,VAR_1)
| ~ cp(sK3(VAR_0,VAR_1,VAR_2))
| ~ rinvR(VAR_1,VAR_2)
| ~ rr(VAR_0,VAR_1)
| cUnsatisfiable(VAR_0) )
& ! [VAR_0,VAR_1,VAR_2,VAR_3] :
( cp(VAR_3)
| cq(VAR_3)
| ~ rs(VAR_0,VAR_3)
| rinvR(VAR_1,sK5(VAR_0,VAR_1))
| ~ cp(sK3(VAR_0,VAR_1,VAR_2))
| ~ rinvR(VAR_1,VAR_2)
| ~ rr(VAR_0,VAR_1)
| cUnsatisfiable(VAR_0) )
& ! [VAR_0,VAR_1,VAR_2,VAR_3] :
( cp(VAR_3)
| cq(VAR_3)
| ~ rs(VAR_0,VAR_3)
| rinvR(VAR_1,sK4(VAR_0,VAR_1))
| ~ cp(sK3(VAR_0,VAR_1,VAR_2))
| ~ rinvR(VAR_1,VAR_2)
| ~ rr(VAR_0,VAR_1)
| cUnsatisfiable(VAR_0) )
& ! [VAR_0,VAR_1,VAR_2,VAR_3] :
( cp(VAR_3)
| cq(VAR_3)
| ~ rs(VAR_0,VAR_3)
| sK5(VAR_0,VAR_1) != sK4(VAR_0,VAR_1)
| rs(VAR_2,sK3(VAR_0,VAR_1,VAR_2))
| ~ rinvR(VAR_1,VAR_2)
| ~ rr(VAR_0,VAR_1)
| cUnsatisfiable(VAR_0) )
& ! [VAR_0,VAR_1,VAR_2,VAR_3] :
( cp(VAR_3)
| cq(VAR_3)
| ~ rs(VAR_0,VAR_3)
| rinvR(VAR_1,sK5(VAR_0,VAR_1))
| rs(VAR_2,sK3(VAR_0,VAR_1,VAR_2))
| ~ rinvR(VAR_1,VAR_2)
| ~ rr(VAR_0,VAR_1)
| cUnsatisfiable(VAR_0) )
& ! [VAR_0,VAR_1,VAR_2,VAR_3] :
( cp(VAR_3)
| cq(VAR_3)
| ~ rs(VAR_0,VAR_3)
| rinvR(VAR_1,sK4(VAR_0,VAR_1))
| rs(VAR_2,sK3(VAR_0,VAR_1,VAR_2))
| ~ rinvR(VAR_1,VAR_2)
| ~ rr(VAR_0,VAR_1)
| cUnsatisfiable(VAR_0) )
& ! [VAR_0] :
( ~ cp(sK2(VAR_0))
| ~ cUnsatisfiable(VAR_0) )
& ! [VAR_0] :
( ~ cq(sK2(VAR_0))
| ~ cUnsatisfiable(VAR_0) )
& ! [VAR_0] :
( rs(VAR_0,sK2(VAR_0))
| ~ cUnsatisfiable(VAR_0) )
& ! [VAR_0,VAR_1,VAR_2] :
( VAR_2 = VAR_1
| ~ rinvR(sK0(VAR_0),VAR_2)
| ~ rinvR(sK0(VAR_0),VAR_1)
| ~ cUnsatisfiable(VAR_0) )
& ! [VAR_0,VAR_1] :
( cp(VAR_1)
| ~ rs(sK1(VAR_0),VAR_1)
| ~ cUnsatisfiable(VAR_0) )
& ! [VAR_0] :
( rinvR(sK0(VAR_0),sK1(VAR_0))
| ~ cUnsatisfiable(VAR_0) )
& ! [VAR_0] :
( rr(VAR_0,sK0(VAR_0))
| ~ cUnsatisfiable(VAR_0) ) ),
inference(cnf_transformation,[status(thm)],[sk_axiom_2_sk]) ).
cnf(c_35,plain,
( rr(A,sK0(A))
| ~ cUnsatisfiable(A) ),
inference(split_conjunct,[status(thm)],[sk_axiom_2]) ).
cnf(c_36,plain,
( rinvR(sK0(A),sK1(A))
| ~ cUnsatisfiable(A) ),
inference(split_conjunct,[status(thm)],[sk_axiom_2]) ).
cnf(c_37,plain,
( cp(B)
| ~ rs(sK1(A),B)
| ~ cUnsatisfiable(A) ),
inference(split_conjunct,[status(thm)],[sk_axiom_2]) ).
cnf(c_38,plain,
( C = B
| ~ rinvR(sK0(A),C)
| ~ rinvR(sK0(A),B)
| ~ cUnsatisfiable(A) ),
inference(split_conjunct,[status(thm)],[sk_axiom_2]) ).
cnf(c_39,plain,
( rs(A,sK2(A))
| ~ cUnsatisfiable(A) ),
inference(split_conjunct,[status(thm)],[sk_axiom_2]) ).
cnf(c_41,plain,
( ~ cp(sK2(A))
| ~ cUnsatisfiable(A) ),
inference(split_conjunct,[status(thm)],[sk_axiom_2]) ).
cnf(c_49,plain,
( ~ rr(B,A)
| rinvR(A,B) ),
inference(clausify,[status(thm)],[axiom_3]) ).
fof(axiom_4,axiom,
cUnsatisfiable(i2003_11_14_17_19_13721),
file('theBenchmark.p',axiom_4) ).
cnf(c_50,plain,
cUnsatisfiable(i2003_11_14_17_19_13721),
inference(clausify,[status(thm)],[axiom_4]) ).
cnf(c_52,plain,
~ cp(sK2(i2003_11_14_17_19_13721)),
inference(resolve,[status(thm)],[c_50,c_41]) ).
cnf(c_54,plain,
rs(i2003_11_14_17_19_13721,sK2(i2003_11_14_17_19_13721)),
inference(resolve,[status(thm)],[c_50,c_39]) ).
cnf(c_57,plain,
rinvR(sK0(i2003_11_14_17_19_13721),sK1(i2003_11_14_17_19_13721)),
inference(resolve,[status(thm)],[c_50,c_36]) ).
cnf(c_58,plain,
rr(i2003_11_14_17_19_13721,sK0(i2003_11_14_17_19_13721)),
inference(resolve,[status(thm)],[c_50,c_35]) ).
cnf(c_77,plain,
( cp(A)
| ~ rs(sK1(i2003_11_14_17_19_13721),A) ),
inference(resolve,[status(thm)],[c_37,c_50]) ).
cnf(c_60,plain,
~ rs(sK1(i2003_11_14_17_19_13721),sK2(i2003_11_14_17_19_13721)),
inference(resolve,[status(thm)],[c_77,c_52]) ).
cnf(c_78,plain,
( rs(A,sK2(i2003_11_14_17_19_13721))
| A != i2003_11_14_17_19_13721 ),
inference(resolve,[status(thm)],[c_27,c_54]) ).
cnf(c_63,plain,
sK1(i2003_11_14_17_19_13721) != i2003_11_14_17_19_13721,
inference(resolve,[status(thm)],[c_78,c_60]) ).
cnf(c_64,plain,
rinvR(sK0(i2003_11_14_17_19_13721),i2003_11_14_17_19_13721),
inference(resolve,[status(thm)],[c_58,c_49]) ).
cnf(c_79,plain,
( B = A
| ~ rinvR(sK0(i2003_11_14_17_19_13721),B)
| ~ rinvR(sK0(i2003_11_14_17_19_13721),A) ),
inference(resolve,[status(thm)],[c_38,c_50]) ).
cnf(c_80,plain,
( A = i2003_11_14_17_19_13721
| ~ rinvR(sK0(i2003_11_14_17_19_13721),A) ),
inference(resolve,[status(thm)],[c_79,c_64]) ).
cnf(c_81,plain,
~ rinvR(sK0(i2003_11_14_17_19_13721),sK1(i2003_11_14_17_19_13721)),
inference(resolve,[status(thm)],[c_80,c_63]) ).
cnf(c_76,plain,
$false,
inference(resolve,[status(thm)],[c_57,c_81]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : KRS078+1 : TPTP v9.3.1. Released v3.1.0.
% 0.00/0.06 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.17/0.42 % Computer : n005.cluster.edu
% 0.17/0.42 % Model : x86_64 x86_64
% 0.17/0.42 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.42 % Memory : 8046.5625MB
% 0.17/0.42 % OS : Linux 6.8.0-71-generic
% 0.17/0.42 % CPULimit : 300
% 0.17/0.42 % WCLimit : 300
% 0.17/0.42 % DateTime : Fri Sep 25 19:38:17 UTC 2026
% 0.17/0.42 % CPUTime :
% 0.17/0.43 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.17/0.43 % Process 401 was started by sandbox2 on n005,
% 0.17/0.43 % Fri Sep 25 19:38:17 2026
% 0.17/0.43 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.17/0.44
% 0.17/0.44 % From the command line: assign(max_seconds, 300).
% 0.17/0.45
% 0.17/0.45 % SZS status Unsatisfiable for theBenchmark
% 0.17/0.45
% 0.17/0.45 % Proof 1 at 0.00 (+ 0.00) seconds.
% 0.17/0.45 % Length of proof is 20.
% 0.17/0.45 % Level of proof is 5.
% 0.17/0.45 % Maximum clause weight is 23.000.
% 0.17/0.45 % Given clauses 40.
% 0.17/0.45
% 0.17/0.45 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------