%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : KRS001-1 : TPTP v9.3.1. Released v2.0.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n007.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 07:45:52 AM UTC 2026
% Result : Unsatisfiable 0.15s 0.39s
% Output : CNFRefutation 0.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 9
% Syntax : Number of formulae : 31 ( 9 unt; 0 def)
% Number of atoms : 60 ( 0 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 64 ( 35 ~; 29 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 8 ( 7 usr; 1 prp; 0-2 aty)
% Number of functors : 3 ( 3 usr; 1 con; 0-1 aty)
% Number of variables : 28 ( 0 sgn 10 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(clause_14,axiom,
! [VAR_0] :
( ~ e(VAR_0)
| d(VAR_0) ),
file('theBenchmark.p',clause_14) ).
cnf(c_1,plain,
( ~ e(A)
| d(A) ),
inference(clausify,[status(thm)],[clause_14]) ).
fof(clause_1,axiom,
e(exist),
file('theBenchmark.p',clause_1) ).
cnf(c_2,plain,
e(exist),
inference(clausify,[status(thm)],[clause_1]) ).
fof(clause_15,axiom,
! [VAR_0] :
( ~ e(VAR_0)
| c(VAR_0) ),
file('theBenchmark.p',clause_15) ).
cnf(c_3,plain,
( ~ e(A)
| c(A) ),
inference(clausify,[status(thm)],[clause_15]) ).
fof(clause_6,axiom,
! [VAR_0] :
( ~ r2least(VAR_0)
| r(VAR_0,u1r2(VAR_0)) ),
file('theBenchmark.p',clause_6) ).
cnf(c_5,plain,
( ~ r2least(A)
| r(A,u1r2(A)) ),
inference(clausify,[status(thm)],[clause_6]) ).
fof(clause_5,axiom,
! [VAR_0] :
( ~ r2least(VAR_0)
| r(VAR_0,u1r1(VAR_0)) ),
file('theBenchmark.p',clause_5) ).
cnf(c_7,plain,
( ~ r2least(A)
| r(A,u1r1(A)) ),
inference(clausify,[status(thm)],[clause_5]) ).
fof(clause_4,axiom,
! [VAR_0] :
( ~ equalish(u1r2(VAR_0),u1r1(VAR_0))
| ~ r2least(VAR_0) ),
file('theBenchmark.p',clause_4) ).
cnf(c_8,plain,
( ~ equalish(u1r2(A),u1r1(A))
| ~ r2least(A) ),
inference(clausify,[status(thm)],[clause_4]) ).
fof(clause_2,axiom,
! [VAR_0] :
( ~ c(VAR_0)
| r2least(VAR_0) ),
file('theBenchmark.p',clause_2) ).
cnf(c_10,plain,
( ~ c(A)
| r2least(A) ),
inference(clausify,[status(thm)],[clause_2]) ).
cnf(c_12,plain,
( ~ equalish(u1r2(A),u1r1(A))
| ~ c(A) ),
inference(resolve,[status(thm)],[c_10,c_8]) ).
cnf(c_13,plain,
( r(A,u1r1(A))
| ~ c(A) ),
inference(resolve,[status(thm)],[c_10,c_7]) ).
cnf(c_14,plain,
( r(A,u1r2(A))
| ~ c(A) ),
inference(resolve,[status(thm)],[c_10,c_5]) ).
cnf(c_15,plain,
c(exist),
inference(resolve,[status(thm)],[c_3,c_2]) ).
fof(clause_10,axiom,
! [VAR_0,VAR_1,VAR_2] :
( ~ r(VAR_2,VAR_1)
| ~ r(VAR_2,VAR_0)
| ~ r1most(VAR_2)
| equalish(VAR_0,VAR_1) ),
file('theBenchmark.p',clause_10) ).
cnf(c_16,plain,
( ~ r(C,B)
| ~ r(C,A)
| ~ r1most(C)
| equalish(A,B) ),
inference(clausify,[status(thm)],[clause_10]) ).
fof(clause_8,axiom,
! [VAR_0] :
( ~ d(VAR_0)
| r1most(VAR_0) ),
file('theBenchmark.p',clause_8) ).
cnf(c_21,plain,
( ~ d(A)
| r1most(A) ),
inference(clausify,[status(thm)],[clause_8]) ).
cnf(c_23,plain,
( ~ r(A,C)
| ~ r(A,B)
| equalish(B,C)
| ~ d(A) ),
inference(resolve,[status(thm)],[c_21,c_16]) ).
cnf(c_26,plain,
d(exist),
inference(resolve,[status(thm)],[c_1,c_2]) ).
cnf(c_27,plain,
( ~ r(exist,B)
| ~ r(exist,A)
| equalish(A,B) ),
inference(resolve,[status(thm)],[c_26,c_23]) ).
cnf(c_28,plain,
r(exist,u1r2(exist)),
inference(resolve,[status(thm)],[c_15,c_14]) ).
cnf(c_29,plain,
r(exist,u1r1(exist)),
inference(resolve,[status(thm)],[c_15,c_13]) ).
cnf(c_30,plain,
~ equalish(u1r2(exist),u1r1(exist)),
inference(resolve,[status(thm)],[c_15,c_12]) ).
cnf(c_49,plain,
( ~ r(exist,u1r1(exist))
| ~ r(exist,u1r2(exist)) ),
inference(resolve,[status(thm)],[c_27,c_30]) ).
cnf(c_50,plain,
~ r(exist,u1r2(exist)),
inference(resolve,[status(thm)],[c_49,c_29]) ).
cnf(c_48,plain,
$false,
inference(resolve,[status(thm)],[c_28,c_50]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : KRS001-1 : TPTP v9.3.1. Released v2.0.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.37 % Computer : n007.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 19:29:53 UTC 2026
% 0.09/0.38 % CPUTime :
% 0.09/0.38 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.09/0.38 % Process 1683623 was started by sandbox2 on n007,
% 0.09/0.38 % Fri Sep 25 19:29:53 2026
% 0.09/0.38 % 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 0.00 (+ 0.00) seconds.
% 0.15/0.39 % Length of proof is 20.
% 0.15/0.39 % Level of proof is 3.
% 0.15/0.39 % Maximum clause weight is 9.000.
% 0.15/0.39 % Given clauses 4.
% 0.15/0.39
% 0.15/0.39 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------