%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : KRS010-1 : TPTP v9.3.1. Released v2.0.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox/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 07:45:53 AM UTC 2026
% Result : Unsatisfiable 2.46s 0.76s
% Output : CNFRefutation 2.46s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 13
% Syntax : Number of formulae : 71 ( 18 unt; 0 def)
% Number of atoms : 164 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 193 ( 100 ~; 93 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 3 avg)
% Maximal term depth : 2 ( 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 : 41 ( 0 sgn 16 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(clause_6,axiom,
! [VAR_0,VAR_1,VAR_2] :
( ~ c(VAR_1)
| ~ c(VAR_0)
| ~ r(VAR_2,VAR_1)
| ~ r(VAR_2,VAR_0)
| ~ e(VAR_2)
| equalish(VAR_0,VAR_1) ),
file('theBenchmark.p',clause_6) ).
cnf(c_1,plain,
( ~ c(B)
| ~ c(A)
| ~ r(C,B)
| ~ r(C,A)
| ~ e(C)
| equalish(A,B) ),
inference(clausify,[status(thm)],[clause_6]) ).
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_7,axiom,
! [VAR_0] :
( ~ e(VAR_0)
| r3least(VAR_0) ),
file('theBenchmark.p',clause_7) ).
cnf(c_3,plain,
( ~ e(A)
| r3least(A) ),
inference(clausify,[status(thm)],[clause_7]) ).
fof(clause_8,axiom,
! [VAR_0,VAR_1] :
( ~ r(VAR_1,VAR_0)
| ~ e(VAR_1)
| a(VAR_0) ),
file('theBenchmark.p',clause_8) ).
cnf(c_4,plain,
( ~ r(B,A)
| ~ e(B)
| a(A) ),
inference(clausify,[status(thm)],[clause_8]) ).
fof(clause_31,axiom,
! [VAR_0,VAR_1,VAR_2] :
( ~ d(VAR_2)
| ~ d(VAR_1)
| ~ r(VAR_0,VAR_2)
| ~ r(VAR_0,VAR_1)
| equalish(VAR_1,VAR_2)
| f(VAR_0) ),
file('theBenchmark.p',clause_31) ).
cnf(c_16,plain,
( ~ d(C)
| ~ d(B)
| ~ r(A,C)
| ~ r(A,B)
| equalish(B,C)
| f(A) ),
inference(clausify,[status(thm)],[clause_31]) ).
fof(clause_2,axiom,
~ f(exist),
file('theBenchmark.p',clause_2) ).
cnf(c_21,plain,
~ f(exist),
inference(clausify,[status(thm)],[clause_2]) ).
fof(clause_24,axiom,
! [VAR_0] :
( ~ r3least(VAR_0)
| r(VAR_0,u2r3(VAR_0)) ),
file('theBenchmark.p',clause_24) ).
cnf(c_23,plain,
( ~ r3least(A)
| r(A,u2r3(A)) ),
inference(clausify,[status(thm)],[clause_24]) ).
fof(clause_23,axiom,
! [VAR_0] :
( ~ r3least(VAR_0)
| r(VAR_0,u2r2(VAR_0)) ),
file('theBenchmark.p',clause_23) ).
cnf(c_24,plain,
( ~ r3least(A)
| r(A,u2r2(A)) ),
inference(clausify,[status(thm)],[clause_23]) ).
fof(clause_22,axiom,
! [VAR_0] :
( ~ r3least(VAR_0)
| r(VAR_0,u2r1(VAR_0)) ),
file('theBenchmark.p',clause_22) ).
cnf(c_25,plain,
( ~ r3least(A)
| r(A,u2r1(A)) ),
inference(clausify,[status(thm)],[clause_22]) ).
fof(clause_21,axiom,
! [VAR_0] :
( ~ equalish(u2r3(VAR_0),u2r2(VAR_0))
| ~ r3least(VAR_0) ),
file('theBenchmark.p',clause_21) ).
cnf(c_26,plain,
( ~ equalish(u2r3(A),u2r2(A))
| ~ r3least(A) ),
inference(clausify,[status(thm)],[clause_21]) ).
fof(clause_20,axiom,
! [VAR_0] :
( ~ equalish(u2r3(VAR_0),u2r1(VAR_0))
| ~ r3least(VAR_0) ),
file('theBenchmark.p',clause_20) ).
cnf(c_27,plain,
( ~ equalish(u2r3(A),u2r1(A))
| ~ r3least(A) ),
inference(clausify,[status(thm)],[clause_20]) ).
fof(clause_19,axiom,
! [VAR_0] :
( ~ equalish(u2r2(VAR_0),u2r1(VAR_0))
| ~ r3least(VAR_0) ),
file('theBenchmark.p',clause_19) ).
cnf(c_28,plain,
( ~ equalish(u2r2(A),u2r1(A))
| ~ r3least(A) ),
inference(clausify,[status(thm)],[clause_19]) ).
cnf(c_29,plain,
r3least(exist),
inference(resolve,[status(thm)],[c_3,c_2]) ).
cnf(c_90,plain,
~ equalish(u2r2(exist),u2r1(exist)),
inference(resolve,[status(thm)],[c_29,c_28]) ).
cnf(c_91,plain,
~ equalish(u2r3(exist),u2r1(exist)),
inference(resolve,[status(thm)],[c_29,c_27]) ).
cnf(c_92,plain,
~ equalish(u2r3(exist),u2r2(exist)),
inference(resolve,[status(thm)],[c_29,c_26]) ).
cnf(c_93,plain,
r(exist,u2r1(exist)),
inference(resolve,[status(thm)],[c_29,c_25]) ).
cnf(c_94,plain,
r(exist,u2r2(exist)),
inference(resolve,[status(thm)],[c_29,c_24]) ).
cnf(c_95,plain,
r(exist,u2r3(exist)),
inference(resolve,[status(thm)],[c_29,c_23]) ).
cnf(c_102,plain,
( ~ r(exist,A)
| a(A) ),
inference(resolve,[status(thm)],[c_4,c_2]) ).
cnf(c_103,plain,
( ~ c(B)
| ~ c(A)
| ~ r(exist,B)
| ~ r(exist,A)
| equalish(A,B) ),
inference(resolve,[status(thm)],[c_1,c_2]) ).
fof(clause_3,axiom,
! [VAR_0] :
( ~ a(VAR_0)
| d(VAR_0)
| c(VAR_0) ),
file('theBenchmark.p',clause_3) ).
cnf(c_106,plain,
( ~ a(A)
| d(A)
| c(A) ),
inference(clausify,[status(thm)],[clause_3]) ).
cnf(c_112,plain,
( ~ d(B)
| ~ d(A)
| ~ r(exist,B)
| ~ r(exist,A)
| equalish(A,B) ),
inference(resolve,[status(thm)],[c_21,c_16]) ).
cnf(c_918,plain,
a(u2r3(exist)),
inference(resolve,[status(thm)],[c_102,c_95]) ).
cnf(c_919,plain,
a(u2r2(exist)),
inference(resolve,[status(thm)],[c_102,c_94]) ).
cnf(c_920,plain,
a(u2r1(exist)),
inference(resolve,[status(thm)],[c_102,c_93]) ).
cnf(c_921,plain,
( ~ c(A)
| ~ c(u2r3(exist))
| ~ r(exist,A)
| equalish(u2r3(exist),A) ),
inference(resolve,[status(thm)],[c_103,c_95]) ).
cnf(c_922,plain,
( ~ c(A)
| ~ c(u2r2(exist))
| ~ r(exist,A)
| equalish(u2r2(exist),A) ),
inference(resolve,[status(thm)],[c_103,c_94]) ).
cnf(c_966,plain,
( ~ d(A)
| ~ d(u2r3(exist))
| ~ r(exist,A)
| equalish(u2r3(exist),A) ),
inference(resolve,[status(thm)],[c_112,c_95]) ).
cnf(c_967,plain,
( ~ d(A)
| ~ d(u2r2(exist))
| ~ r(exist,A)
| equalish(u2r2(exist),A) ),
inference(resolve,[status(thm)],[c_112,c_94]) ).
cnf(c_975,plain,
( d(u2r3(exist))
| c(u2r3(exist)) ),
inference(resolve,[status(thm)],[c_918,c_106]) ).
cnf(c_976,plain,
( d(u2r2(exist))
| c(u2r2(exist)) ),
inference(resolve,[status(thm)],[c_919,c_106]) ).
cnf(c_977,plain,
( d(u2r1(exist))
| c(u2r1(exist)) ),
inference(resolve,[status(thm)],[c_920,c_106]) ).
cnf(c_1001,plain,
( ~ c(u2r2(exist))
| ~ c(u2r3(exist))
| equalish(u2r3(exist),u2r2(exist)) ),
inference(resolve,[status(thm)],[c_921,c_94]) ).
cnf(c_978,plain,
( ~ c(u2r2(exist))
| ~ c(u2r3(exist)) ),
inference(resolve,[status(thm)],[c_92,c_1001]) ).
cnf(c_1002,plain,
( ~ c(u2r1(exist))
| ~ c(u2r3(exist))
| equalish(u2r3(exist),u2r1(exist)) ),
inference(resolve,[status(thm)],[c_921,c_93]) ).
cnf(c_979,plain,
( ~ c(u2r1(exist))
| ~ c(u2r3(exist)) ),
inference(resolve,[status(thm)],[c_91,c_1002]) ).
cnf(c_1003,plain,
( ~ c(u2r1(exist))
| ~ c(u2r2(exist))
| equalish(u2r2(exist),u2r1(exist)) ),
inference(resolve,[status(thm)],[c_922,c_93]) ).
cnf(c_980,plain,
( ~ c(u2r1(exist))
| ~ c(u2r2(exist)) ),
inference(resolve,[status(thm)],[c_90,c_1003]) ).
cnf(c_1004,plain,
( ~ d(u2r2(exist))
| ~ d(u2r3(exist))
| equalish(u2r3(exist),u2r2(exist)) ),
inference(resolve,[status(thm)],[c_966,c_94]) ).
cnf(c_984,plain,
( ~ d(u2r2(exist))
| ~ d(u2r3(exist)) ),
inference(resolve,[status(thm)],[c_92,c_1004]) ).
cnf(c_1005,plain,
( ~ d(u2r1(exist))
| ~ d(u2r3(exist))
| equalish(u2r3(exist),u2r1(exist)) ),
inference(resolve,[status(thm)],[c_966,c_93]) ).
cnf(c_985,plain,
( ~ d(u2r1(exist))
| ~ d(u2r3(exist)) ),
inference(resolve,[status(thm)],[c_91,c_1005]) ).
cnf(c_1006,plain,
( ~ d(u2r1(exist))
| ~ d(u2r2(exist))
| equalish(u2r2(exist),u2r1(exist)) ),
inference(resolve,[status(thm)],[c_967,c_93]) ).
cnf(c_986,plain,
( ~ d(u2r1(exist))
| ~ d(u2r2(exist)) ),
inference(resolve,[status(thm)],[c_90,c_1006]) ).
cnf(c_987,plain,
( c(u2r3(exist))
| ~ d(u2r2(exist)) ),
inference(resolve,[status(thm)],[c_984,c_975]) ).
cnf(c_988,plain,
( c(u2r3(exist))
| ~ d(u2r1(exist)) ),
inference(resolve,[status(thm)],[c_985,c_975]) ).
cnf(c_989,plain,
( c(u2r2(exist))
| ~ d(u2r1(exist)) ),
inference(resolve,[status(thm)],[c_986,c_976]) ).
cnf(c_990,plain,
( c(u2r2(exist))
| c(u2r3(exist)) ),
inference(resolve,[status(thm)],[c_987,c_976]) ).
cnf(c_991,plain,
( c(u2r1(exist))
| c(u2r3(exist)) ),
inference(resolve,[status(thm)],[c_988,c_977]) ).
cnf(c_992,plain,
( c(u2r1(exist))
| c(u2r2(exist)) ),
inference(resolve,[status(thm)],[c_989,c_977]) ).
cnf(c_993,plain,
( ~ c(u2r1(exist))
| c(u2r2(exist)) ),
inference(resolve,[status(thm)],[c_990,c_979]) ).
cnf(c_995,plain,
( ~ c(u2r2(exist))
| c(u2r1(exist)) ),
inference(resolve,[status(thm)],[c_991,c_978]) ).
cnf(c_1007,plain,
( c(u2r1(exist))
| c(u2r1(exist)) ),
inference(resolve,[status(thm)],[c_995,c_992]) ).
cnf(c_998,plain,
c(u2r1(exist)),
inference(copy,[status(thm)],[c_1007]) ).
cnf(c_999,plain,
c(u2r2(exist)),
inference(resolve,[status(thm)],[c_998,c_993]) ).
cnf(c_1008,plain,
~ c(u2r1(exist)),
inference(resolve,[status(thm)],[c_999,c_980]) ).
cnf(c_1000,plain,
$false,
inference(resolve,[status(thm)],[c_998,c_1008]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : KRS010-1 : TPTP v9.3.1. Released v2.0.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.11/0.36 % Computer : n007.cluster.edu
% 0.11/0.36 % Model : x86_64 x86_64
% 0.11/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.36 % Memory : 8046.5625MB
% 0.11/0.36 % OS : Linux 6.8.0-71-generic
% 0.11/0.36 % CPULimit : 300
% 0.11/0.36 % WCLimit : 300
% 0.11/0.36 % DateTime : Fri Sep 25 19:30:40 UTC 2026
% 0.11/0.36 % CPUTime :
% 0.11/0.36 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.11/0.36 % Process 1685230 was started by sandbox on n007,
% 0.11/0.36 % Fri Sep 25 19:30:40 2026
% 0.11/0.36 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.11/0.37
% 0.11/0.37 % From the command line: assign(max_seconds, 300).
% 2.46/0.76
% 2.46/0.76 % SZS status Unsatisfiable for theBenchmark
% 2.46/0.76
% 2.46/0.76 % Proof 1 at 0.32 (+ 0.06) seconds.
% 2.46/0.76 % Length of proof is 50.
% 2.46/0.76 % Level of proof is 10.
% 2.46/0.76 % Maximum clause weight is 13.000.
% 2.46/0.76 % Given clauses 257.
% 2.46/0.76
% 2.46/0.76 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------