%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : KRS076+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 : n008.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 0.15s 0.39s
% Output : CNFRefutation 0.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 9
% Syntax : Number of formulae : 43 ( 15 unt; 0 def)
% Number of atoms : 139 ( 15 equ)
% Maximal formula atoms : 27 ( 3 avg)
% Number of connectives : 157 ( 61 ~; 57 |; 30 &)
% ( 2 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 19 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 9 ( 7 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 1 con; 0-2 aty)
% Number of variables : 78 ( 0 sgn 44 !; 7 ?)
% Comments :
%------------------------------------------------------------------------------
fof(cp_substitution_1,axiom,
! [A,B] :
( ( cp(A)
& A = B )
=> cp(B) ),
file('theBenchmark.p',cp_substitution_1) ).
fof(rf_substitution_2,axiom,
! [A,B,C] :
( ( rf(C,A)
& A = B )
=> rf(C,B) ),
file('theBenchmark.p',rf_substitution_2) ).
fof(axiom_2,axiom,
! [X] :
( cUnsatisfiable(X)
<=> ( ? [Y] :
( ! [Z] :
( rinvF1(Y,Z)
=> ? [W] :
( cowlThing(W)
& rs(Z,W) ) )
& ~ cp(Y)
& rf1(X,Y) )
& ? [Y] :
( cp(Y)
& rf(X,Y) ) ) ),
file('theBenchmark.p',axiom_2) ).
fof(axiom_3,axiom,
! [X,Y,Z] :
( ( rf(X,Z)
& rf(X,Y) )
=> Y = Z ),
file('theBenchmark.p',axiom_3) ).
fof(axiom_4,axiom,
! [X,Y,Z] :
( ( rf1(X,Z)
& rf1(X,Y) )
=> Y = Z ),
file('theBenchmark.p',axiom_4) ).
fof(axiom_6,axiom,
! [X,Y] :
( rinvF1(X,Y)
<=> rf1(Y,X) ),
file('theBenchmark.p',axiom_6) ).
fof(axiom_10,axiom,
! [X,Y] :
( rs(X,Y)
=> rf1(X,Y) ),
file('theBenchmark.p',axiom_10) ).
fof(axiom_11,axiom,
! [X,Y] :
( rs(X,Y)
=> rf(X,Y) ),
file('theBenchmark.p',axiom_11) ).
cnf(c_33,plain,
( cp(A)
| ~ cp(B)
| A != B ),
inference(clausify,[status(thm)],[cp_substitution_1]) ).
cnf(c_35,plain,
( rf(C,A)
| ~ rf(C,B)
| A != B ),
inference(clausify,[status(thm)],[rf_substitution_2]) ).
fof(nnf_21,plain,
! [X] :
( ( ! [Y] :
( ? [Z] :
( ! [W] :
( ~ cowlThing(W)
| ~ rs(Z,W) )
& rinvF1(Y,Z) )
| cp(Y)
| ~ rf1(X,Y) )
| ! [X4] :
( ~ cp(X4)
| ~ rf(X,X4) )
| cUnsatisfiable(X) )
& ( ( ? [X1] :
( ! [X2] :
( ? [X3] :
( cowlThing(X3)
& rs(X2,X3) )
| ~ rinvF1(X1,X2) )
& ~ cp(X1)
& rf1(X,X1) )
& ? [X0] :
( cp(X0)
& rf(X,X0) ) )
| ~ cUnsatisfiable(X) ) ),
inference(fof_nnf,[status(thm)],[axiom_2]) ).
fof(sk_axiom_2_sk,plain,
! [X] :
( ( ! [Y] :
( ( ! [W] :
( ~ cowlThing(W)
| ~ rs(sK3(X,Y),W) )
& rinvF1(Y,sK3(X,Y)) )
| cp(Y)
| ~ rf1(X,Y) )
| ! [X4] :
( ~ cp(X4)
| ~ rf(X,X4) )
| cUnsatisfiable(X) )
& ( ( ! [X2] :
( ( cowlThing(sK2(X,X2))
& rs(X2,sK2(X,X2)) )
| ~ rinvF1(sK1(X),X2) )
& ~ cp(sK1(X))
& rf1(X,sK1(X))
& cp(sK0(X))
& rf(X,sK0(X)) )
| ~ cUnsatisfiable(X) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3]),skolemize(X0,sK0(X)),skolemize(X1,sK1(X)),skolemize(X3,sK2(X,X2)),skolemize(Z,sK3(X,Y))],[nnf_21]) ).
fof(sk_axiom_2,plain,
( ! [VAR_0,VAR_1,VAR_2,VAR_3] :
( ~ cowlThing(VAR_3)
| ~ rs(sK3(VAR_0,VAR_2),VAR_3)
| cp(VAR_2)
| ~ rf1(VAR_0,VAR_2)
| ~ cp(VAR_1)
| ~ rf(VAR_0,VAR_1)
| cUnsatisfiable(VAR_0) )
& ! [VAR_0,VAR_1,VAR_2] :
( rinvF1(VAR_2,sK3(VAR_0,VAR_2))
| cp(VAR_2)
| ~ rf1(VAR_0,VAR_2)
| ~ cp(VAR_1)
| ~ rf(VAR_0,VAR_1)
| cUnsatisfiable(VAR_0) )
& ! [VAR_0,VAR_1] :
( cowlThing(sK2(VAR_0,VAR_1))
| ~ rinvF1(sK1(VAR_0),VAR_1)
| ~ cUnsatisfiable(VAR_0) )
& ! [VAR_0,VAR_1] :
( rs(VAR_1,sK2(VAR_0,VAR_1))
| ~ rinvF1(sK1(VAR_0),VAR_1)
| ~ cUnsatisfiable(VAR_0) )
& ! [VAR_0] :
( ~ cp(sK1(VAR_0))
| ~ cUnsatisfiable(VAR_0) )
& ! [VAR_0] :
( rf1(VAR_0,sK1(VAR_0))
| ~ cUnsatisfiable(VAR_0) )
& ! [VAR_0] :
( cp(sK0(VAR_0))
| ~ cUnsatisfiable(VAR_0) )
& ! [VAR_0] :
( rf(VAR_0,sK0(VAR_0))
| ~ cUnsatisfiable(VAR_0) ) ),
inference(cnf_transformation,[status(thm)],[sk_axiom_2_sk]) ).
cnf(c_52,plain,
( rf(A,sK0(A))
| ~ cUnsatisfiable(A) ),
inference(split_conjunct,[status(thm)],[sk_axiom_2]) ).
cnf(c_53,plain,
( cp(sK0(A))
| ~ cUnsatisfiable(A) ),
inference(split_conjunct,[status(thm)],[sk_axiom_2]) ).
cnf(c_54,plain,
( rf1(A,sK1(A))
| ~ cUnsatisfiable(A) ),
inference(split_conjunct,[status(thm)],[sk_axiom_2]) ).
cnf(c_55,plain,
( ~ cp(sK1(A))
| ~ cUnsatisfiable(A) ),
inference(split_conjunct,[status(thm)],[sk_axiom_2]) ).
cnf(c_56,plain,
( rs(B,sK2(A,B))
| ~ rinvF1(sK1(A),B)
| ~ cUnsatisfiable(A) ),
inference(split_conjunct,[status(thm)],[sk_axiom_2]) ).
cnf(c_60,plain,
( C = B
| ~ rf(A,C)
| ~ rf(A,B) ),
inference(clausify,[status(thm)],[axiom_3]) ).
cnf(c_61,plain,
( C = B
| ~ rf1(A,C)
| ~ rf1(A,B) ),
inference(clausify,[status(thm)],[axiom_4]) ).
cnf(c_65,plain,
( ~ rf1(B,A)
| rinvF1(A,B) ),
inference(clausify,[status(thm)],[axiom_6]) ).
fof(axiom_9,axiom,
cUnsatisfiable(i2003_11_14_17_19_06193),
file('theBenchmark.p',axiom_9) ).
cnf(c_69,plain,
cUnsatisfiable(i2003_11_14_17_19_06193),
inference(clausify,[status(thm)],[axiom_9]) ).
cnf(c_70,plain,
( rf1(A,B)
| ~ rs(A,B) ),
inference(clausify,[status(thm)],[axiom_10]) ).
cnf(c_71,plain,
( rf(A,B)
| ~ rs(A,B) ),
inference(clausify,[status(thm)],[axiom_11]) ).
cnf(c_74,plain,
rf1(i2003_11_14_17_19_06193,sK1(i2003_11_14_17_19_06193)),
inference(resolve,[status(thm)],[c_69,c_54]) ).
cnf(c_75,plain,
cp(sK0(i2003_11_14_17_19_06193)),
inference(resolve,[status(thm)],[c_69,c_53]) ).
cnf(c_76,plain,
rf(i2003_11_14_17_19_06193,sK0(i2003_11_14_17_19_06193)),
inference(resolve,[status(thm)],[c_69,c_52]) ).
cnf(c_78,plain,
~ cp(sK1(i2003_11_14_17_19_06193)),
inference(resolve,[status(thm)],[c_55,c_69]) ).
cnf(c_79,plain,
rinvF1(sK1(i2003_11_14_17_19_06193),i2003_11_14_17_19_06193),
inference(resolve,[status(thm)],[c_74,c_65]) ).
cnf(c_80,plain,
( sK1(i2003_11_14_17_19_06193) = A
| ~ rf1(i2003_11_14_17_19_06193,A) ),
inference(resolve,[status(thm)],[c_74,c_61]) ).
cnf(c_114,plain,
( cp(A)
| A != sK0(i2003_11_14_17_19_06193) ),
inference(resolve,[status(thm)],[c_33,c_75]) ).
cnf(c_84,plain,
sK1(i2003_11_14_17_19_06193) != sK0(i2003_11_14_17_19_06193),
inference(resolve,[status(thm)],[c_114,c_78]) ).
cnf(c_115,plain,
( rs(i2003_11_14_17_19_06193,sK2(i2003_11_14_17_19_06193,i2003_11_14_17_19_06193))
| ~ cUnsatisfiable(i2003_11_14_17_19_06193) ),
inference(resolve,[status(thm)],[c_79,c_56]) ).
cnf(c_89,plain,
rs(i2003_11_14_17_19_06193,sK2(i2003_11_14_17_19_06193,i2003_11_14_17_19_06193)),
inference(resolve,[status(thm)],[c_69,c_115]) ).
cnf(c_116,plain,
( A = sK0(i2003_11_14_17_19_06193)
| ~ rf(i2003_11_14_17_19_06193,A) ),
inference(resolve,[status(thm)],[c_60,c_76]) ).
cnf(c_95,plain,
~ rf(i2003_11_14_17_19_06193,sK1(i2003_11_14_17_19_06193)),
inference(resolve,[status(thm)],[c_116,c_84]) ).
cnf(c_101,plain,
rf(i2003_11_14_17_19_06193,sK2(i2003_11_14_17_19_06193,i2003_11_14_17_19_06193)),
inference(resolve,[status(thm)],[c_89,c_71]) ).
cnf(c_102,plain,
rf1(i2003_11_14_17_19_06193,sK2(i2003_11_14_17_19_06193,i2003_11_14_17_19_06193)),
inference(resolve,[status(thm)],[c_89,c_70]) ).
cnf(c_117,plain,
( rf(i2003_11_14_17_19_06193,A)
| A != sK2(i2003_11_14_17_19_06193,i2003_11_14_17_19_06193) ),
inference(resolve,[status(thm)],[c_35,c_101]) ).
cnf(c_112,plain,
sK1(i2003_11_14_17_19_06193) != sK2(i2003_11_14_17_19_06193,i2003_11_14_17_19_06193),
inference(resolve,[status(thm)],[c_117,c_95]) ).
cnf(c_118,plain,
sK1(i2003_11_14_17_19_06193) = sK2(i2003_11_14_17_19_06193,i2003_11_14_17_19_06193),
inference(resolve,[status(thm)],[c_102,c_80]) ).
cnf(c_113,plain,
$false,
inference(resolve,[status(thm)],[c_112,c_118]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : KRS076+1 : TPTP v9.3.1. Released v3.1.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.36 % Computer : n008.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Fri Sep 25 19:38:54 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.10/0.37 % Process 1700413 was started by sandbox2 on n008,
% 0.10/0.37 % Fri Sep 25 19:38:54 2026
% 0.10/0.37 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.15/0.38
% 0.15/0.38 % From the command line: assign(max_seconds, 300).
% 0.15/0.39
% 0.15/0.39 % SZS status Unsatisfiable for theBenchmark
% 0.15/0.39
% 0.15/0.39 % Proof 1 at 0.01 (+ 0.00) seconds.
% 0.15/0.39 % Length of proof is 34.
% 0.15/0.39 % Level of proof is 7.
% 0.15/0.39 % Maximum clause weight is 21.000.
% 0.15/0.39 % Given clauses 59.
% 0.15/0.39
% 0.15/0.39 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------