%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SWV019-1 : TPTP v9.3.1. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n016.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 09:06:40 AM UTC 2026
% Result : Unsatisfiable 0.20s 0.47s
% Output : CNFRefutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 10
% Syntax : Number of formulae : 43 ( 19 unt; 0 def)
% Number of atoms : 97 ( 13 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 103 ( 49 ~; 54 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 6 con; 0-2 aty)
% Number of variables : 18 ( 0 sgn 7 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(in_bounds,axiom,
! [VAR_0] :
( in_array_bounds(array,VAR_0)
| less_than(upper_bound,VAR_0)
| less_than(VAR_0,lower_bound) ),
file('theBenchmark.p',in_bounds) ).
cnf(c_1,plain,
( in_array_bounds(array,A)
| less_than(upper_bound,A)
| less_than(A,lower_bound) ),
inference(clausify,[status(thm)],[in_bounds]) ).
fof(predecessor_less,axiom,
! [VAR_0,VAR_1] :
( less_than(VAR_0,VAR_1)
| ~ less_than(successor(VAR_0),successor(VAR_1)) ),
file('theBenchmark.p',predecessor_less) ).
cnf(c_2,plain,
( less_than(A,B)
| ~ less_than(successor(A),successor(B)) ),
inference(clausify,[status(thm)],[predecessor_less]) ).
fof(transitivity_of_less,axiom,
! [VAR_0,VAR_1,VAR_2] :
( less_than(VAR_0,VAR_2)
| ~ less_than(VAR_1,VAR_2)
| ~ less_than(VAR_0,VAR_1) ),
file('theBenchmark.p',transitivity_of_less) ).
cnf(c_3,plain,
( less_than(A,C)
| ~ less_than(B,C)
| ~ less_than(A,B) ),
inference(clausify,[status(thm)],[transitivity_of_less]) ).
fof(successor_greater,axiom,
! [VAR_0] : less_than(VAR_0,successor(VAR_0)),
file('theBenchmark.p',successor_greater) ).
cnf(c_4,plain,
less_than(A,successor(A)),
inference(clausify,[status(thm)],[successor_greater]) ).
fof(this_is_maximal,axiom,
( maximal_value = array_value_at(array,index_of_maximal)
| ~ in_array_bounds(array,index_of_maximal) ),
file('theBenchmark.p',this_is_maximal) ).
cnf(c_5,plain,
( maximal_value = array_value_at(array,index_of_maximal)
| ~ in_array_bounds(array,index_of_maximal) ),
inference(clausify,[status(thm)],[this_is_maximal]) ).
cnf(c_6,plain,
( array_value_at(array,index_of_maximal) = maximal_value
| ~ in_array_bounds(array,index_of_maximal) ),
inference(copy,[status(thm)],[c_5]) ).
fof(maximal_before_somewhere,axiom,
less_than(index_of_maximal,an_index),
file('theBenchmark.p',maximal_before_somewhere) ).
cnf(c_7,plain,
less_than(index_of_maximal,an_index),
inference(clausify,[status(thm)],[maximal_before_somewhere]) ).
fof(somewhere_above_lower_bound,axiom,
~ less_than(an_index,lower_bound),
file('theBenchmark.p',somewhere_above_lower_bound) ).
cnf(c_8,plain,
~ less_than(an_index,lower_bound),
inference(clausify,[status(thm)],[somewhere_above_lower_bound]) ).
fof(somewhere_below_upper_bound,axiom,
~ less_than(upper_bound,an_index),
file('theBenchmark.p',somewhere_below_upper_bound) ).
cnf(c_9,plain,
~ less_than(upper_bound,an_index),
inference(clausify,[status(thm)],[somewhere_below_upper_bound]) ).
fof(maximal_above_lower_bound,axiom,
~ less_than(index_of_maximal,lower_bound),
file('theBenchmark.p',maximal_above_lower_bound) ).
cnf(c_10,plain,
~ less_than(index_of_maximal,lower_bound),
inference(clausify,[status(thm)],[maximal_above_lower_bound]) ).
fof(prove_this,axiom,
( maximal_value != array_value_at(array,index_of_maximal)
| ~ in_array_bounds(array,index_of_maximal)
| ~ less_than(index_of_maximal,successor(an_index))
| less_than(index_of_maximal,lower_bound)
| less_than(successor(upper_bound),successor(an_index))
| less_than(successor(an_index),lower_bound)
| ~ in_array_bounds(array,an_index) ),
file('theBenchmark.p',prove_this) ).
cnf(c_11,plain,
( maximal_value != array_value_at(array,index_of_maximal)
| ~ in_array_bounds(array,index_of_maximal)
| ~ less_than(index_of_maximal,successor(an_index))
| less_than(index_of_maximal,lower_bound)
| less_than(successor(upper_bound),successor(an_index))
| less_than(successor(an_index),lower_bound)
| ~ in_array_bounds(array,an_index) ),
inference(clausify,[status(thm)],[prove_this]) ).
cnf(c_50,plain,
( array_value_at(array,index_of_maximal) != maximal_value
| ~ in_array_bounds(array,index_of_maximal)
| ~ less_than(index_of_maximal,successor(an_index))
| less_than(index_of_maximal,lower_bound)
| less_than(successor(upper_bound),successor(an_index))
| less_than(successor(an_index),lower_bound)
| ~ in_array_bounds(array,an_index) ),
inference(copy,[status(thm)],[c_11]) ).
cnf(c_12,plain,
( array_value_at(array,index_of_maximal) != maximal_value
| ~ in_array_bounds(array,index_of_maximal)
| ~ less_than(index_of_maximal,successor(an_index))
| less_than(successor(upper_bound),successor(an_index))
| less_than(successor(an_index),lower_bound)
| ~ in_array_bounds(array,an_index) ),
inference(resolve,[status(thm)],[c_10,c_50]) ).
cnf(c_51,plain,
( less_than(upper_bound,index_of_maximal)
| less_than(index_of_maximal,lower_bound)
| array_value_at(array,index_of_maximal) = maximal_value ),
inference(resolve,[status(thm)],[c_6,c_1]) ).
cnf(c_21,plain,
( less_than(upper_bound,index_of_maximal)
| array_value_at(array,index_of_maximal) = maximal_value ),
inference(resolve,[status(thm)],[c_10,c_51]) ).
cnf(c_23,plain,
( less_than(index_of_maximal,A)
| ~ less_than(an_index,A) ),
inference(resolve,[status(thm)],[c_7,c_3]) ).
cnf(c_52,plain,
( in_array_bounds(array,an_index)
| less_than(upper_bound,an_index) ),
inference(resolve,[status(thm)],[c_8,c_1]) ).
cnf(c_24,plain,
in_array_bounds(array,an_index),
inference(resolve,[status(thm)],[c_9,c_52]) ).
cnf(c_53,plain,
( less_than(A,B)
| ~ less_than(successor(A),B) ),
inference(resolve,[status(thm)],[c_3,c_4]) ).
cnf(c_25,plain,
~ less_than(successor(an_index),lower_bound),
inference(resolve,[status(thm)],[c_53,c_8]) ).
cnf(c_54,plain,
( array_value_at(array,index_of_maximal) != maximal_value
| ~ in_array_bounds(array,index_of_maximal)
| ~ less_than(index_of_maximal,successor(an_index))
| less_than(successor(upper_bound),successor(an_index))
| less_than(successor(an_index),lower_bound) ),
inference(resolve,[status(thm)],[c_24,c_12]) ).
cnf(c_27,plain,
( array_value_at(array,index_of_maximal) != maximal_value
| ~ in_array_bounds(array,index_of_maximal)
| ~ less_than(index_of_maximal,successor(an_index))
| less_than(successor(upper_bound),successor(an_index)) ),
inference(resolve,[status(thm)],[c_25,c_54]) ).
cnf(c_55,plain,
( less_than(A,an_index)
| ~ less_than(A,index_of_maximal) ),
inference(resolve,[status(thm)],[c_3,c_7]) ).
cnf(c_28,plain,
~ less_than(upper_bound,index_of_maximal),
inference(resolve,[status(thm)],[c_55,c_9]) ).
cnf(c_30,plain,
~ less_than(successor(upper_bound),successor(an_index)),
inference(resolve,[status(thm)],[c_2,c_9]) ).
cnf(c_31,plain,
array_value_at(array,index_of_maximal) = maximal_value,
inference(resolve,[status(thm)],[c_28,c_21]) ).
cnf(c_56,plain,
( array_value_at(array,index_of_maximal) != maximal_value
| ~ in_array_bounds(array,index_of_maximal)
| ~ less_than(index_of_maximal,successor(an_index)) ),
inference(resolve,[status(thm)],[c_30,c_27]) ).
cnf(c_32,plain,
( ~ in_array_bounds(array,index_of_maximal)
| ~ less_than(index_of_maximal,successor(an_index)) ),
inference(resolve,[status(thm)],[c_31,c_56]) ).
cnf(c_57,plain,
( in_array_bounds(array,index_of_maximal)
| less_than(upper_bound,index_of_maximal) ),
inference(resolve,[status(thm)],[c_10,c_1]) ).
cnf(c_33,plain,
in_array_bounds(array,index_of_maximal),
inference(resolve,[status(thm)],[c_28,c_57]) ).
cnf(c_36,plain,
~ less_than(index_of_maximal,successor(an_index)),
inference(resolve,[status(thm)],[c_33,c_32]) ).
cnf(c_58,plain,
less_than(index_of_maximal,successor(an_index)),
inference(resolve,[status(thm)],[c_23,c_4]) ).
cnf(c_49,plain,
$false,
inference(resolve,[status(thm)],[c_36,c_58]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SWV019-1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.06 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.20/0.44 % Computer : n016.cluster.edu
% 0.20/0.44 % Model : x86_64 x86_64
% 0.20/0.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.20/0.44 % Memory : 8046.5625MB
% 0.20/0.44 % OS : Linux 6.8.0-71-generic
% 0.20/0.45 % CPULimit : 300
% 0.20/0.45 % WCLimit : 300
% 0.20/0.45 % DateTime : Sat Sep 26 13:11:01 UTC 2026
% 0.20/0.45 % CPUTime :
% 0.20/0.45 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.20/0.45 % Process 942612 was started by sandbox2 on n016,
% 0.20/0.45 % Sat Sep 26 13:11:01 2026
% 0.20/0.45 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.20/0.45
% 0.20/0.45 % From the command line: assign(max_seconds, 300).
% 0.20/0.47
% 0.20/0.47 % SZS status Unsatisfiable for theBenchmark
% 0.20/0.47
% 0.20/0.47 % Proof 1 at 0.00 (+ 0.00) seconds.
% 0.20/0.47 % Length of proof is 24.
% 0.20/0.47 % Level of proof is 6.
% 0.20/0.47 % Maximum clause weight is 34.000.
% 0.20/0.47 % Given clauses 20.
% 0.20/0.47
% 0.20/0.47 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------