%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : KRS002-1 : 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 : n006.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 0.13s 15.65s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 10
% Syntax : Number of formulae : 36 ( 10 unt; 0 def)
% Number of atoms : 73 ( 0 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 81 ( 44 ~; 37 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 9 ( 8 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 1 con; 0-1 aty)
% Number of variables : 35 ( 0 sgn 13 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(clause_14,axiom,
! [VAR_0] :
( ~ e(VAR_0)
| r(VAR_0,u4r2(VAR_0)) ),
file('theBenchmark.p',clause_14) ).
cnf(c_1,plain,
( ~ e(A)
| r(A,u4r2(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,VAR_1] :
( ~ r(VAR_1,VAR_0)
| ~ e(VAR_1)
| d(VAR_0) ),
file('theBenchmark.p',clause_15) ).
cnf(c_3,plain,
( ~ r(B,A)
| ~ e(B)
| d(A) ),
inference(clausify,[status(thm)],[clause_15]) ).
fof(clause_16,axiom,
! [VAR_0,VAR_1] :
( ~ r(VAR_1,VAR_0)
| ~ e(VAR_1)
| c(VAR_0) ),
file('theBenchmark.p',clause_16) ).
cnf(c_4,plain,
( ~ r(B,A)
| ~ e(B)
| c(A) ),
inference(clausify,[status(thm)],[clause_16]) ).
fof(clause_6,axiom,
! [VAR_0] :
( ~ s2least(VAR_0)
| s(VAR_0,u1r2(VAR_0)) ),
file('theBenchmark.p',clause_6) ).
cnf(c_7,plain,
( ~ s2least(A)
| s(A,u1r2(A)) ),
inference(clausify,[status(thm)],[clause_6]) ).
fof(clause_5,axiom,
! [VAR_0] :
( ~ s2least(VAR_0)
| s(VAR_0,u1r1(VAR_0)) ),
file('theBenchmark.p',clause_5) ).
cnf(c_9,plain,
( ~ s2least(A)
| s(A,u1r1(A)) ),
inference(clausify,[status(thm)],[clause_5]) ).
fof(clause_4,axiom,
! [VAR_0] :
( ~ equalish(u1r2(VAR_0),u1r1(VAR_0))
| ~ s2least(VAR_0) ),
file('theBenchmark.p',clause_4) ).
cnf(c_10,plain,
( ~ equalish(u1r2(A),u1r1(A))
| ~ s2least(A) ),
inference(clausify,[status(thm)],[clause_4]) ).
fof(clause_2,axiom,
! [VAR_0] :
( ~ c(VAR_0)
| s2least(VAR_0) ),
file('theBenchmark.p',clause_2) ).
cnf(c_12,plain,
( ~ c(A)
| s2least(A) ),
inference(clausify,[status(thm)],[clause_2]) ).
fof(clause_8,axiom,
! [VAR_0] :
( ~ d(VAR_0)
| s1most(VAR_0) ),
file('theBenchmark.p',clause_8) ).
cnf(c_14,plain,
( ~ d(A)
| s1most(A) ),
inference(clausify,[status(thm)],[clause_8]) ).
fof(clause_10,axiom,
! [VAR_0,VAR_1,VAR_2] :
( ~ s(VAR_2,VAR_1)
| ~ s(VAR_2,VAR_0)
| ~ s1most(VAR_2)
| equalish(VAR_0,VAR_1) ),
file('theBenchmark.p',clause_10) ).
cnf(c_15,plain,
( ~ s(C,B)
| ~ s(C,A)
| ~ s1most(C)
| equalish(A,B) ),
inference(clausify,[status(thm)],[clause_10]) ).
cnf(c_25,plain,
( ~ d(C)
| ~ s(C,B)
| ~ s(C,A)
| equalish(A,B) ),
inference(resolve,[status(thm)],[c_15,c_14]) ).
cnf(c_32,plain,
( ~ r(exist,A)
| c(A) ),
inference(resolve,[status(thm)],[c_4,c_2]) ).
cnf(c_33,plain,
( ~ r(exist,A)
| d(A) ),
inference(resolve,[status(thm)],[c_3,c_2]) ).
cnf(c_34,plain,
r(exist,u4r2(exist)),
inference(resolve,[status(thm)],[c_1,c_2]) ).
cnf(c_39,plain,
( ~ equalish(u1r2(A),u1r1(A))
| ~ c(A) ),
inference(resolve,[status(thm)],[c_12,c_10]) ).
cnf(c_40,plain,
( s(A,u1r1(A))
| ~ c(A) ),
inference(resolve,[status(thm)],[c_12,c_9]) ).
cnf(c_41,plain,
( s(A,u1r2(A))
| ~ c(A) ),
inference(resolve,[status(thm)],[c_12,c_7]) ).
cnf(c_54,plain,
d(u4r2(exist)),
inference(resolve,[status(thm)],[c_34,c_33]) ).
cnf(c_55,plain,
c(u4r2(exist)),
inference(resolve,[status(thm)],[c_34,c_32]) ).
cnf(c_74,plain,
s(u4r2(exist),u1r2(u4r2(exist))),
inference(resolve,[status(thm)],[c_55,c_41]) ).
cnf(c_75,plain,
s(u4r2(exist),u1r1(u4r2(exist))),
inference(resolve,[status(thm)],[c_55,c_40]) ).
cnf(c_76,plain,
~ equalish(u1r2(u4r2(exist)),u1r1(u4r2(exist))),
inference(resolve,[status(thm)],[c_39,c_55]) ).
cnf(c_90,plain,
( ~ d(A)
| ~ s(A,u1r1(u4r2(exist)))
| ~ s(A,u1r2(u4r2(exist))) ),
inference(resolve,[status(thm)],[c_25,c_76]) ).
cnf(c_91,plain,
( ~ d(u4r2(exist))
| ~ s(u4r2(exist),u1r1(u4r2(exist))) ),
inference(resolve,[status(thm)],[c_90,c_74]) ).
cnf(c_92,plain,
~ s(u4r2(exist),u1r1(u4r2(exist))),
inference(resolve,[status(thm)],[c_91,c_54]) ).
cnf(c_89,plain,
$false,
inference(resolve,[status(thm)],[c_75,c_92]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : KRS002-1 : TPTP v9.3.1. Released v2.0.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.13/15.62 % Computer : n006.cluster.edu
% 0.13/15.62 % Model : x86_64 x86_64
% 0.13/15.62 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/15.62 % Memory : 8046.5625MB
% 0.13/15.62 % OS : Linux 6.8.0-71-generic
% 0.13/15.62 % CPULimit : 300
% 0.13/15.62 % WCLimit : 300
% 0.13/15.62 % DateTime : Fri Sep 25 19:32:00 UTC 2026
% 0.13/15.62 % CPUTime :
% 0.13/15.62 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.13/15.62 % Process 3555359 was started by sandbox2 on n006,
% 0.13/15.62 % Fri Sep 25 19:32:00 2026
% 0.13/15.62 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.13/15.63
% 0.13/15.63 % From the command line: assign(max_seconds, 300).
% 0.13/15.65
% 0.13/15.65 % SZS status Unsatisfiable for theBenchmark
% 0.13/15.65
% 0.13/15.65 % Proof 1 at 0.00 (+ 0.00) seconds.
% 0.13/15.65 % Length of proof is 23.
% 0.13/15.65 % Level of proof is 4.
% 0.13/15.65 % Maximum clause weight is 22.000.
% 0.13/15.65 % Given clauses 46.
% 0.13/15.65
% 0.13/15.65 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------