%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : KRS015-1 : 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 07:45:54 AM UTC 2026
% Result : Unsatisfiable 0.17s 5.50s
% Output : CNFRefutation 0.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 11
% Syntax : Number of formulae : 40 ( 11 unt; 0 def)
% Number of atoms : 82 ( 0 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 91 ( 49 ~; 42 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 10 ( 9 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 1 con; 0-1 aty)
% Number of variables : 40 ( 0 sgn 15 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(clause_14,axiom,
! [VAR_0] :
( ~ e(VAR_0)
| r(VAR_0,u4r4(VAR_0)) ),
file('theBenchmark.p',clause_14) ).
cnf(c_1,plain,
( ~ e(A)
| r(A,u4r4(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_0,VAR_1)
| ~ e(VAR_0)
| s(VAR_0,VAR_1) ),
file('theBenchmark.p',clause_15) ).
cnf(c_3,plain,
( ~ r(A,B)
| ~ e(A)
| s(A,B) ),
inference(clausify,[status(thm)],[clause_15]) ).
fof(clause_17,axiom,
! [VAR_0,VAR_1] :
( ~ s(VAR_1,VAR_0)
| ~ e(VAR_1)
| d(VAR_0) ),
file('theBenchmark.p',clause_17) ).
cnf(c_5,plain,
( ~ s(B,A)
| ~ e(B)
| d(A) ),
inference(clausify,[status(thm)],[clause_17]) ).
fof(clause_18,axiom,
! [VAR_0,VAR_1] :
( ~ r(VAR_1,VAR_0)
| ~ e(VAR_1)
| c(VAR_0) ),
file('theBenchmark.p',clause_18) ).
cnf(c_6,plain,
( ~ r(B,A)
| ~ e(B)
| c(A) ),
inference(clausify,[status(thm)],[clause_18]) ).
fof(clause_6,axiom,
! [VAR_0] :
( ~ t2least(VAR_0)
| t(VAR_0,u1r2(VAR_0)) ),
file('theBenchmark.p',clause_6) ).
cnf(c_15,plain,
( ~ t2least(A)
| t(A,u1r2(A)) ),
inference(clausify,[status(thm)],[clause_6]) ).
fof(clause_5,axiom,
! [VAR_0] :
( ~ t2least(VAR_0)
| t(VAR_0,u1r1(VAR_0)) ),
file('theBenchmark.p',clause_5) ).
cnf(c_17,plain,
( ~ t2least(A)
| t(A,u1r1(A)) ),
inference(clausify,[status(thm)],[clause_5]) ).
fof(clause_4,axiom,
! [VAR_0] :
( ~ equalish(u1r2(VAR_0),u1r1(VAR_0))
| ~ t2least(VAR_0) ),
file('theBenchmark.p',clause_4) ).
cnf(c_18,plain,
( ~ equalish(u1r2(A),u1r1(A))
| ~ t2least(A) ),
inference(clausify,[status(thm)],[clause_4]) ).
fof(clause_2,axiom,
! [VAR_0] :
( ~ c(VAR_0)
| t2least(VAR_0) ),
file('theBenchmark.p',clause_2) ).
cnf(c_20,plain,
( ~ c(A)
| t2least(A) ),
inference(clausify,[status(thm)],[clause_2]) ).
fof(clause_8,axiom,
! [VAR_0] :
( ~ d(VAR_0)
| t1most(VAR_0) ),
file('theBenchmark.p',clause_8) ).
cnf(c_22,plain,
( ~ d(A)
| t1most(A) ),
inference(clausify,[status(thm)],[clause_8]) ).
fof(clause_10,axiom,
! [VAR_0,VAR_1,VAR_2] :
( ~ t(VAR_2,VAR_1)
| ~ t(VAR_2,VAR_0)
| ~ t1most(VAR_2)
| equalish(VAR_0,VAR_1) ),
file('theBenchmark.p',clause_10) ).
cnf(c_23,plain,
( ~ t(C,B)
| ~ t(C,A)
| ~ t1most(C)
| equalish(A,B) ),
inference(clausify,[status(thm)],[clause_10]) ).
cnf(c_33,plain,
( ~ d(C)
| ~ t(C,B)
| ~ t(C,A)
| equalish(A,B) ),
inference(resolve,[status(thm)],[c_23,c_22]) ).
cnf(c_74,plain,
( ~ r(exist,A)
| c(A) ),
inference(resolve,[status(thm)],[c_6,c_2]) ).
cnf(c_75,plain,
( ~ s(exist,A)
| d(A) ),
inference(resolve,[status(thm)],[c_5,c_2]) ).
cnf(c_77,plain,
( ~ r(exist,A)
| s(exist,A) ),
inference(resolve,[status(thm)],[c_3,c_2]) ).
cnf(c_78,plain,
r(exist,u4r4(exist)),
inference(resolve,[status(thm)],[c_1,c_2]) ).
cnf(c_83,plain,
( ~ equalish(u1r2(A),u1r1(A))
| ~ c(A) ),
inference(resolve,[status(thm)],[c_20,c_18]) ).
cnf(c_84,plain,
( t(A,u1r1(A))
| ~ c(A) ),
inference(resolve,[status(thm)],[c_20,c_17]) ).
cnf(c_85,plain,
( t(A,u1r2(A))
| ~ c(A) ),
inference(resolve,[status(thm)],[c_20,c_15]) ).
cnf(c_148,plain,
s(exist,u4r4(exist)),
inference(resolve,[status(thm)],[c_78,c_77]) ).
cnf(c_149,plain,
c(u4r4(exist)),
inference(resolve,[status(thm)],[c_78,c_74]) ).
cnf(c_172,plain,
d(u4r4(exist)),
inference(resolve,[status(thm)],[c_148,c_75]) ).
cnf(c_173,plain,
t(u4r4(exist),u1r2(u4r4(exist))),
inference(resolve,[status(thm)],[c_149,c_85]) ).
cnf(c_174,plain,
t(u4r4(exist),u1r1(u4r4(exist))),
inference(resolve,[status(thm)],[c_149,c_84]) ).
cnf(c_175,plain,
~ equalish(u1r2(u4r4(exist)),u1r1(u4r4(exist))),
inference(resolve,[status(thm)],[c_83,c_149]) ).
cnf(c_189,plain,
( ~ d(A)
| ~ t(A,u1r1(u4r4(exist)))
| ~ t(A,u1r2(u4r4(exist))) ),
inference(resolve,[status(thm)],[c_33,c_175]) ).
cnf(c_190,plain,
( ~ d(u4r4(exist))
| ~ t(u4r4(exist),u1r1(u4r4(exist))) ),
inference(resolve,[status(thm)],[c_189,c_173]) ).
cnf(c_191,plain,
~ t(u4r4(exist),u1r1(u4r4(exist))),
inference(resolve,[status(thm)],[c_190,c_172]) ).
cnf(c_188,plain,
$false,
inference(resolve,[status(thm)],[c_174,c_191]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : KRS015-1 : TPTP v9.3.1. Released v2.0.0.
% 0.00/0.06 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.17/5.45 % Computer : n007.cluster.edu
% 0.17/5.45 % Model : x86_64 x86_64
% 0.17/5.45 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/5.45 % Memory : 8046.5625MB
% 0.17/5.45 % OS : Linux 6.8.0-71-generic
% 0.17/5.46 % CPULimit : 300
% 0.17/5.46 % WCLimit : 300
% 0.17/5.46 % DateTime : Fri Sep 25 19:31:14 UTC 2026
% 0.17/5.46 % CPUTime :
% 0.17/5.46 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.17/5.46 % Process 1686192 was started by sandbox on n007,
% 0.17/5.46 % Fri Sep 25 19:31:14 2026
% 0.17/5.46 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.17/5.47
% 0.17/5.47 % From the command line: assign(max_seconds, 300).
% 0.17/5.50
% 0.17/5.50 % SZS status Unsatisfiable for theBenchmark
% 0.17/5.50
% 0.17/5.50 % Proof 1 at 0.01 (+ 0.01) seconds.
% 0.17/5.50 % Length of proof is 26.
% 0.17/5.50 % Level of proof is 4.
% 0.17/5.50 % Maximum clause weight is 22.000.
% 0.17/5.50 % Given clauses 101.
% 0.17/5.50
% 0.17/5.50 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------