%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : HWV023-1 : TPTP v9.3.1. Released v2.5.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n012.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 07:34:22 AM UTC 2026
% Result : Unsatisfiable 0.10s 5.51s
% Output : CNFRefutation 0.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 12
% Syntax : Number of formulae : 44 ( 26 unt; 0 def)
% Number of atoms : 82 ( 32 equ)
% Maximal formula atoms : 5 ( 1 avg)
% Number of connectives : 69 ( 31 ~; 38 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 8 ( 6 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 3 con; 0-2 aty)
% Number of variables : 27 ( 3 sgn 10 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(axiom_5,axiom,
! [VAR_0,VAR_1,VAR_2] :
( def_10(VAR_1,VAR_0)
| plus(VAR_2,VAR_1) != VAR_0
| minus(VAR_0,VAR_1) = VAR_2 ),
file('theBenchmark.p',axiom_5) ).
cnf(c_2,plain,
( def_10(B,A)
| plus(C,B) != A
| minus(A,B) = C ),
inference(clausify,[status(thm)],[axiom_5]) ).
fof(axiom_7,axiom,
! [VAR_0,VAR_1] :
( VAR_1 != VAR_0
| ~ def_10(VAR_0,VAR_1) ),
file('theBenchmark.p',axiom_7) ).
cnf(c_4,plain,
( B != A
| ~ def_10(A,B) ),
inference(clausify,[status(thm)],[axiom_7]) ).
fof(axiom_71,axiom,
! [VAR_0] :
( int_level(plus(VAR_0,n1)) = minus(int_level(VAR_0),n1)
| ~ gt(int_level(VAR_0),n0)
| ~ p_Rd(VAR_0)
| p_Wr(VAR_0)
| p_Reset(VAR_0) ),
file('theBenchmark.p',axiom_71) ).
cnf(c_44,plain,
( int_level(plus(A,n1)) = minus(int_level(A),n1)
| ~ gt(int_level(A),n0)
| ~ p_Rd(A)
| p_Wr(A)
| p_Reset(A) ),
inference(clausify,[status(thm)],[axiom_71]) ).
fof(quest_3,axiom,
p_Rd(t_139),
file('theBenchmark.p',quest_3) ).
cnf(c_60,plain,
p_Rd(t_139),
inference(clausify,[status(thm)],[quest_3]) ).
cnf(c_79,plain,
( int_level(plus(t_139,n1)) = minus(int_level(t_139),n1)
| ~ gt(int_level(t_139),n0)
| p_Wr(t_139)
| p_Reset(t_139) ),
inference(resolve,[status(thm)],[c_60,c_44]) ).
cnf(c_577,plain,
( plus(C,B) != A
| minus(A,B) = C
| A != B ),
inference(resolve,[status(thm)],[c_4,c_2]) ).
fof(quest_5,axiom,
~ p_Empty(plus(t_139,n1)),
file('theBenchmark.p',quest_5) ).
cnf(c_580,plain,
~ p_Empty(plus(t_139,n1)),
inference(clausify,[status(thm)],[quest_5]) ).
fof(quest_4,axiom,
~ p_Reset(t_139),
file('theBenchmark.p',quest_4) ).
cnf(c_581,plain,
~ p_Reset(t_139),
inference(clausify,[status(thm)],[quest_4]) ).
fof(quest_2,axiom,
~ p_Wr(t_139),
file('theBenchmark.p',quest_2) ).
cnf(c_582,plain,
~ p_Wr(t_139),
inference(clausify,[status(thm)],[quest_2]) ).
fof(quest_1,axiom,
level(t_139) = n1,
file('theBenchmark.p',quest_1) ).
cnf(c_583,plain,
level(t_139) = n1,
inference(clausify,[status(thm)],[quest_1]) ).
cnf(c_584,plain,
n1 = level(t_139),
inference(copy,[status(thm)],[c_583]) ).
fof(axiom_24,axiom,
! [VAR_0] :
( p_Empty(VAR_0)
| int_level(VAR_0) != n0 ),
file('theBenchmark.p',axiom_24) ).
cnf(c_610,plain,
( p_Empty(A)
| int_level(A) != n0 ),
inference(clausify,[status(thm)],[axiom_24]) ).
fof(axiom_21,axiom,
! [VAR_0] : level(VAR_0) = int_level(VAR_0),
file('theBenchmark.p',axiom_21) ).
cnf(c_611,plain,
level(A) = int_level(A),
inference(clausify,[status(thm)],[axiom_21]) ).
fof(axiom_19,axiom,
! [VAR_0] : plus(n0,VAR_0) = VAR_0,
file('theBenchmark.p',axiom_19) ).
cnf(c_614,plain,
plus(n0,A) = A,
inference(clausify,[status(thm)],[axiom_19]) ).
fof(axiom_2,axiom,
! [VAR_0] : gt(plus(VAR_0,n1),n0),
file('theBenchmark.p',axiom_2) ).
cnf(c_636,plain,
gt(plus(A,n1),n0),
inference(clausify,[status(thm)],[axiom_2]) ).
cnf(c_1154,plain,
gt(plus(A,level(t_139)),n0),
inference(paramod,[status(thm)],[c_584,c_636]) ).
cnf(c_637,plain,
gt(plus(A,int_level(t_139)),n0),
inference(paramod,[status(thm)],[c_611,c_1154]) ).
cnf(c_1155,plain,
( int_level(plus(t_139,level(t_139))) = minus(int_level(t_139),n1)
| ~ gt(int_level(t_139),n0)
| p_Wr(t_139)
| p_Reset(t_139) ),
inference(paramod,[status(thm)],[c_584,c_79]) ).
cnf(c_1156,plain,
( int_level(plus(t_139,int_level(t_139))) = minus(int_level(t_139),n1)
| ~ gt(int_level(t_139),n0)
| p_Wr(t_139)
| p_Reset(t_139) ),
inference(paramod,[status(thm)],[c_611,c_1155]) ).
cnf(c_1157,plain,
( int_level(plus(t_139,int_level(t_139))) = minus(int_level(t_139),level(t_139))
| ~ gt(int_level(t_139),n0)
| p_Wr(t_139)
| p_Reset(t_139) ),
inference(paramod,[status(thm)],[c_584,c_1156]) ).
cnf(c_1158,plain,
( int_level(plus(t_139,int_level(t_139))) = minus(int_level(t_139),int_level(t_139))
| ~ gt(int_level(t_139),n0)
| p_Wr(t_139)
| p_Reset(t_139) ),
inference(paramod,[status(thm)],[c_611,c_1157]) ).
cnf(c_1159,plain,
( int_level(plus(t_139,int_level(t_139))) = minus(int_level(t_139),int_level(t_139))
| ~ gt(int_level(t_139),n0)
| p_Wr(t_139) ),
inference(resolve,[status(thm)],[c_581,c_1158]) ).
cnf(c_667,plain,
( int_level(plus(t_139,int_level(t_139))) = minus(int_level(t_139),int_level(t_139))
| ~ gt(int_level(t_139),n0) ),
inference(resolve,[status(thm)],[c_582,c_1159]) ).
cnf(c_1160,plain,
~ p_Empty(plus(t_139,level(t_139))),
inference(paramod,[status(thm)],[c_584,c_580]) ).
cnf(c_669,plain,
~ p_Empty(plus(t_139,int_level(t_139))),
inference(paramod,[status(thm)],[c_611,c_1160]) ).
cnf(c_1161,plain,
( minus(A,A) = n0
| A != A ),
inference(resolve,[status(thm)],[c_614,c_577]) ).
cnf(c_845,plain,
minus(A,A) = n0,
inference(copy,[status(thm)],[c_1161]) ).
cnf(c_847,plain,
( int_level(plus(t_139,int_level(t_139))) = n0
| ~ gt(int_level(t_139),n0) ),
inference(paramod,[status(thm)],[c_845,c_667]) ).
cnf(c_891,plain,
gt(int_level(t_139),n0),
inference(paramod,[status(thm)],[c_614,c_637]) ).
cnf(c_892,plain,
int_level(plus(t_139,int_level(t_139))) = n0,
inference(resolve,[status(thm)],[c_891,c_847]) ).
cnf(c_1162,plain,
p_Empty(plus(t_139,int_level(t_139))),
inference(resolve,[status(thm)],[c_892,c_610]) ).
cnf(c_1153,plain,
$false,
inference(resolve,[status(thm)],[c_669,c_1162]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : HWV023-1 : TPTP v9.3.1. Released v2.5.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.07/5.35 % Computer : n012.cluster.edu
% 0.07/5.35 % Model : x86_64 x86_64
% 0.07/5.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/5.35 % Memory : 8046.5625MB
% 0.07/5.35 % OS : Linux 6.8.0-71-generic
% 0.07/5.35 % CPULimit : 300
% 0.07/5.35 % WCLimit : 300
% 0.07/5.35 % DateTime : Fri Sep 25 16:01:45 UTC 2026
% 0.07/5.35 % CPUTime :
% 0.07/5.35 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.07/5.35 % Process 2497702 was started by sandbox on n012,
% 0.07/5.35 % Fri Sep 25 16:01:45 2026
% 0.07/5.35 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.07/5.35
% 0.07/5.35 % From the command line: assign(max_seconds, 300).
% 0.10/5.51
% 0.10/5.51 % SZS status Unsatisfiable for theBenchmark
% 0.10/5.51
% 0.10/5.51 % Proof 1 at 0.14 (+ 0.01) seconds.
% 0.10/5.51 % Length of proof is 23.
% 0.10/5.51 % Level of proof is 5.
% 0.10/5.51 % Maximum clause weight is 17.000.
% 0.10/5.51 % Given clauses 231.
% 0.10/5.51
% 0.10/5.51 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------