%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : KRS090+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 : n016.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 07:46:01 AM UTC 2026
% Result : Unsatisfiable 0.14s 0.39s
% Output : CNFRefutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 6
% Syntax : Number of formulae : 35 ( 7 unt; 0 def)
% Number of atoms : 92 ( 0 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 101 ( 44 ~; 43 |; 8 &)
% ( 0 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 10 ( 9 usr; 1 prp; 0-2 aty)
% Number of functors : 2 ( 2 usr; 1 con; 0-1 aty)
% Number of variables : 32 ( 0 sgn 10 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(axiom_3,axiom,
! [X] :
( cC2(X)
=> ( ( cA(X)
| cB(X) )
& ( cA(X)
| ~ cB(X) ) ) ),
file('theBenchmark.p',axiom_3) ).
fof(axiom_4,axiom,
! [X] :
( cC3(X)
=> ( ( ~ cA(X)
| cB(X) )
& ( ~ cA(X)
| ~ cB(X) ) ) ),
file('theBenchmark.p',axiom_4) ).
fof(axiom_5,axiom,
! [X] :
( cC4(X)
=> ? [Y] :
( cC2(Y)
& rR(X,Y) ) ),
file('theBenchmark.p',axiom_5) ).
fof(axiom_6,axiom,
! [X] :
( cC5(X)
=> ! [Y] :
( rR(X,Y)
=> cC3(Y) ) ),
file('theBenchmark.p',axiom_6) ).
fof(axiom_7,axiom,
! [X] :
( cTEST(X)
=> ( cC5(X)
& cC1(X)
& cC4(X) ) ),
file('theBenchmark.p',axiom_7) ).
fof(nnf_6,plain,
! [X] :
( ? [Y] :
( cC2(Y)
& rR(X,Y) )
| ~ cC4(X) ),
inference(fof_nnf,[status(thm)],[axiom_5]) ).
fof(sk_axiom_5_sk,plain,
! [X] :
( ( cC2(sK0(X))
& rR(X,sK0(X)) )
| ~ cC4(X) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(Y,sK0(X))],[nnf_6]) ).
fof(sk_axiom_5,plain,
( ! [VAR_0] :
( cC2(sK0(VAR_0))
| ~ cC4(VAR_0) )
& ! [VAR_0] :
( rR(VAR_0,sK0(VAR_0))
| ~ cC4(VAR_0) ) ),
inference(cnf_transformation,[status(thm)],[sk_axiom_5_sk]) ).
cnf(c_44,plain,
( cC2(sK0(A))
| ~ cC4(A) ),
inference(split_conjunct,[status(thm)],[sk_axiom_5]) ).
cnf(c_45,plain,
( cA(A)
| cB(A)
| ~ cC2(A) ),
inference(clausify,[status(thm)],[axiom_3]) ).
cnf(c_46,plain,
( cA(A)
| ~ cB(A)
| ~ cC2(A) ),
inference(clausify,[status(thm)],[axiom_3]) ).
cnf(c_47,plain,
( cA(sK0(A))
| cB(sK0(A))
| ~ cC4(A) ),
inference(resolve,[status(thm)],[c_44,c_45]) ).
cnf(c_48,plain,
( cA(sK0(A))
| ~ cB(sK0(A))
| ~ cC4(A) ),
inference(resolve,[status(thm)],[c_44,c_46]) ).
cnf(c_49,plain,
( ~ cA(A)
| cB(A)
| ~ cC3(A) ),
inference(clausify,[status(thm)],[axiom_4]) ).
cnf(c_50,plain,
( ~ cA(A)
| ~ cB(A)
| ~ cC3(A) ),
inference(clausify,[status(thm)],[axiom_4]) ).
cnf(c_51,plain,
( cC3(B)
| ~ rR(A,B)
| ~ cC5(A) ),
inference(clausify,[status(thm)],[axiom_6]) ).
cnf(c_52,plain,
( rR(A,sK0(A))
| ~ cC4(A) ),
inference(split_conjunct,[status(thm)],[sk_axiom_5]) ).
cnf(c_53,plain,
( cC5(A)
| ~ cTEST(A) ),
inference(clausify,[status(thm)],[axiom_7]) ).
cnf(c_54,plain,
( ~ cC4(A)
| cC3(sK0(A))
| ~ cC5(A) ),
inference(resolve,[status(thm)],[c_51,c_52]) ).
fof(axiom_8,axiom,
cTEST(i2003_11_14_17_19_57994),
file('theBenchmark.p',axiom_8) ).
cnf(c_55,plain,
cTEST(i2003_11_14_17_19_57994),
inference(clausify,[status(thm)],[axiom_8]) ).
cnf(c_56,plain,
( cC4(A)
| ~ cTEST(A) ),
inference(clausify,[status(thm)],[axiom_7]) ).
cnf(c_57,plain,
( ~ cC4(A)
| cC3(sK0(A))
| ~ cTEST(A) ),
inference(resolve,[status(thm)],[c_53,c_54]) ).
cnf(c_58,plain,
( ~ cC4(i2003_11_14_17_19_57994)
| cC3(sK0(i2003_11_14_17_19_57994)) ),
inference(resolve,[status(thm)],[c_55,c_57]) ).
cnf(c_59,plain,
cC4(i2003_11_14_17_19_57994),
inference(resolve,[status(thm)],[c_55,c_56]) ).
cnf(c_60,plain,
( cA(sK0(A))
| ~ cC4(A)
| cA(sK0(A))
| ~ cC4(A) ),
inference(resolve,[status(thm)],[c_47,c_48]) ).
cnf(c_67,plain,
( cA(sK0(A))
| cA(sK0(A))
| ~ cC4(A) ),
inference(copy,[status(thm)],[c_60]) ).
cnf(c_61,plain,
( cA(sK0(A))
| ~ cC4(A) ),
inference(copy,[status(thm)],[c_67]) ).
cnf(c_62,plain,
( ~ cA(A)
| ~ cC3(A)
| ~ cA(A)
| ~ cC3(A) ),
inference(resolve,[status(thm)],[c_50,c_49]) ).
cnf(c_68,plain,
( ~ cA(A)
| ~ cA(A)
| ~ cC3(A) ),
inference(copy,[status(thm)],[c_62]) ).
cnf(c_63,plain,
( ~ cA(A)
| ~ cC3(A) ),
inference(copy,[status(thm)],[c_68]) ).
cnf(c_64,plain,
cC3(sK0(i2003_11_14_17_19_57994)),
inference(resolve,[status(thm)],[c_59,c_58]) ).
cnf(c_65,plain,
cA(sK0(i2003_11_14_17_19_57994)),
inference(resolve,[status(thm)],[c_61,c_59]) ).
cnf(c_69,plain,
~ cA(sK0(i2003_11_14_17_19_57994)),
inference(resolve,[status(thm)],[c_64,c_63]) ).
cnf(c_66,plain,
$false,
inference(resolve,[status(thm)],[c_65,c_69]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : KRS090+1 : TPTP v9.3.1. Released v3.1.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.37 % Computer : n016.cluster.edu
% 0.09/0.37 % Model : x86_64 x86_64
% 0.09/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.37 % Memory : 8046.5625MB
% 0.09/0.37 % OS : Linux 6.8.0-71-generic
% 0.09/0.37 % CPULimit : 300
% 0.09/0.37 % WCLimit : 300
% 0.09/0.37 % DateTime : Fri Sep 25 19:44:00 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.37 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.09/0.37 % Process 3125953 was started by sandbox2 on n016,
% 0.09/0.37 % Fri Sep 25 19:44:00 2026
% 0.09/0.37 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.14/0.38
% 0.14/0.38 % From the command line: assign(max_seconds, 300).
% 0.14/0.39
% 0.14/0.39 % SZS status Unsatisfiable for theBenchmark
% 0.14/0.39
% 0.14/0.39 % Proof 1 at 0.00 (+ 0.00) seconds.
% 0.14/0.39 % Length of proof is 28.
% 0.14/0.39 % Level of proof is 6.
% 0.14/0.39 % Maximum clause weight is 5.000.
% 0.14/0.39 % Given clauses 4.
% 0.14/0.39
% 0.14/0.39 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------