%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : SWV019-1 : TPTP v9.3.1. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n002.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 : Fri Sep 25 03:11:02 PM UTC 2026
% Result : Unsatisfiable 6.24s 1.26s
% Output : Proof 6.24s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 10
% Syntax : Number of formulae : 60 ( 23 unt; 0 def)
% Number of atoms : 176 ( 13 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 170 ( 54 ~; 116 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 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 : 32 ( 0 sgn 14 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
cnf(f4,axiom,
( maximal_value = array_value_at(array,index_of_maximal)
| ~ in_array_bounds(array,index_of_maximal) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',this_is_maximal) ).
fof(f4_nnf,plain,
( maximal_value = array_value_at(array,index_of_maximal)
| ~ in_array_bounds(array,index_of_maximal) ),
inference(nnf_transformation,[status(thm)],[f4]) ).
fof(f4_sk,plain,
( maximal_value = array_value_at(array,index_of_maximal)
| ~ in_array_bounds(array,index_of_maximal) ),
inference(skolemisation,[status(esa)],[f4_nnf]) ).
cnf(c4,plain,
( maximal_value = array_value_at(array,index_of_maximal)
| ~ in_array_bounds(array,index_of_maximal) ),
inference(cnf_transformation,[status(esa)],[f4_sk]) ).
cnf(f0,axiom,
( in_array_bounds(array,X1)
| less_than(upper_bound,X1)
| less_than(X1,lower_bound) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',in_bounds) ).
fof(f0_nnf,plain,
! [X1] :
( in_array_bounds(array,X1)
| less_than(upper_bound,X1)
| less_than(X1,lower_bound) ),
inference(nnf_transformation,[status(thm)],[f0]) ).
fof(f0_sk,plain,
! [X1] :
( in_array_bounds(array,X1)
| less_than(upper_bound,X1)
| less_than(X1,lower_bound) ),
inference(skolemisation,[status(esa)],[f0_nnf]) ).
cnf(c0,plain,
( in_array_bounds(array,X0)
| less_than(upper_bound,X0)
| less_than(X0,lower_bound) ),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(p18,plain,
( less_than(upper_bound,index_of_maximal)
| less_than(index_of_maximal,lower_bound)
| maximal_value = array_value_at(array,index_of_maximal) ),
inference(resolution,[status(thm)],[c4,c0]) ).
cnf(f2,axiom,
( less_than(X,Z)
| ~ less_than(Y,Z)
| ~ less_than(X,Y) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',transitivity_of_less) ).
fof(f2_nnf,plain,
! [X,Y,Z] :
( less_than(X,Z)
| ~ less_than(Y,Z)
| ~ less_than(X,Y) ),
inference(nnf_transformation,[status(thm)],[f2]) ).
fof(f2_sk,plain,
! [X,Y,Z] :
( less_than(X,Z)
| ~ less_than(Y,Z)
| ~ less_than(X,Y) ),
inference(skolemisation,[status(esa)],[f2_nnf]) ).
cnf(c2,plain,
( less_than(X0,X2)
| ~ less_than(X1,X2)
| ~ less_than(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f2_sk]) ).
cnf(f5,axiom,
less_than(index_of_maximal,an_index),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',maximal_before_somewhere) ).
fof(f5_nnf,plain,
less_than(index_of_maximal,an_index),
inference(nnf_transformation,[status(thm)],[f5]) ).
cnf(c5,plain,
less_than(index_of_maximal,an_index),
inference(cnf_transformation,[status(esa)],[f5_nnf]) ).
cnf(p11,plain,
( less_than(index_of_maximal,X0)
| ~ less_than(an_index,X0) ),
inference(resolution,[status(thm)],[c2,c5]) ).
cnf(f3,axiom,
less_than(X,successor(X)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',successor_greater) ).
fof(f3_nnf,plain,
! [X] : less_than(X,successor(X)),
inference(nnf_transformation,[status(thm)],[f3]) ).
fof(f3_sk,plain,
! [X] : less_than(X,successor(X)),
inference(skolemisation,[status(esa)],[f3_nnf]) ).
cnf(c3,plain,
less_than(X0,successor(X0)),
inference(cnf_transformation,[status(esa)],[f3_sk]) ).
cnf(p13,plain,
less_than(index_of_maximal,successor(an_index)),
inference(resolution,[status(thm)],[p11,c3]) ).
cnf(f9,negated_conjecture,
( 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('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this) ).
fof(f9_nnf,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(nnf_transformation,[status(thm)],[f9]) ).
fof(f9_sk,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(skolemisation,[status(esa)],[f9_nnf]) ).
cnf(c9,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(cnf_transformation,[status(esa)],[f9_sk]) ).
cnf(p10,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)
| less_than(upper_bound,an_index)
| less_than(an_index,lower_bound) ),
inference(resolution,[status(thm)],[c0,c9]) ).
cnf(p14,plain,
( maximal_value != array_value_at(array,index_of_maximal)
| ~ in_array_bounds(array,index_of_maximal)
| less_than(index_of_maximal,lower_bound)
| less_than(successor(upper_bound),successor(an_index))
| less_than(successor(an_index),lower_bound)
| less_than(upper_bound,an_index)
| less_than(an_index,lower_bound) ),
inference(resolution,[status(thm)],[p13,p10]) ).
cnf(p16,plain,
( less_than(upper_bound,index_of_maximal)
| less_than(index_of_maximal,lower_bound)
| maximal_value != array_value_at(array,index_of_maximal)
| less_than(index_of_maximal,lower_bound)
| less_than(successor(upper_bound),successor(an_index))
| less_than(successor(an_index),lower_bound)
| less_than(upper_bound,an_index)
| less_than(an_index,lower_bound) ),
inference(resolution,[status(thm)],[p14,c0]) ).
cnf(p17,plain,
( less_than(upper_bound,index_of_maximal)
| maximal_value != array_value_at(array,index_of_maximal)
| less_than(index_of_maximal,lower_bound)
| less_than(successor(upper_bound),successor(an_index))
| less_than(successor(an_index),lower_bound)
| less_than(upper_bound,an_index)
| less_than(an_index,lower_bound) ),
inference(factoring,[status(thm)],[p16]) ).
cnf(p33,plain,
( less_than(upper_bound,index_of_maximal)
| less_than(index_of_maximal,lower_bound)
| less_than(successor(upper_bound),successor(an_index))
| less_than(successor(an_index),lower_bound)
| less_than(upper_bound,an_index)
| less_than(an_index,lower_bound)
| less_than(upper_bound,index_of_maximal)
| less_than(index_of_maximal,lower_bound) ),
inference(resolution,[status(thm)],[p18,p17]) ).
cnf(p34,plain,
( less_than(upper_bound,index_of_maximal)
| less_than(successor(upper_bound),successor(an_index))
| less_than(successor(an_index),lower_bound)
| less_than(upper_bound,an_index)
| less_than(an_index,lower_bound)
| less_than(upper_bound,index_of_maximal)
| less_than(index_of_maximal,lower_bound) ),
inference(factoring,[status(thm)],[p33]) ).
cnf(p36,plain,
( less_than(successor(upper_bound),successor(an_index))
| less_than(successor(an_index),lower_bound)
| less_than(upper_bound,an_index)
| less_than(an_index,lower_bound)
| less_than(upper_bound,index_of_maximal)
| less_than(index_of_maximal,lower_bound) ),
inference(factoring,[status(thm)],[p34]) ).
cnf(f1,axiom,
( less_than(X,Y)
| ~ less_than(successor(X),successor(Y)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',predecessor_less) ).
fof(f1_nnf,plain,
! [X,Y] :
( less_than(X,Y)
| ~ less_than(successor(X),successor(Y)) ),
inference(nnf_transformation,[status(thm)],[f1]) ).
fof(f1_sk,plain,
! [X,Y] :
( less_than(X,Y)
| ~ less_than(successor(X),successor(Y)) ),
inference(skolemisation,[status(esa)],[f1_nnf]) ).
cnf(c1,plain,
( less_than(X0,X1)
| ~ less_than(successor(X0),successor(X1)) ),
inference(cnf_transformation,[status(esa)],[f1_sk]) ).
cnf(p37,plain,
( less_than(upper_bound,an_index)
| less_than(successor(an_index),lower_bound)
| less_than(upper_bound,an_index)
| less_than(an_index,lower_bound)
| less_than(upper_bound,index_of_maximal)
| less_than(index_of_maximal,lower_bound) ),
inference(resolution,[status(thm)],[p36,c1]) ).
cnf(p40,plain,
( less_than(successor(an_index),lower_bound)
| less_than(upper_bound,an_index)
| less_than(an_index,lower_bound)
| less_than(upper_bound,index_of_maximal)
| less_than(index_of_maximal,lower_bound) ),
inference(factoring,[status(thm)],[p37]) ).
cnf(p12,plain,
( less_than(X0,X1)
| ~ less_than(successor(X0),X1) ),
inference(resolution,[status(thm)],[c2,c3]) ).
cnf(p43,plain,
( less_than(an_index,lower_bound)
| less_than(upper_bound,an_index)
| less_than(an_index,lower_bound)
| less_than(upper_bound,index_of_maximal)
| less_than(index_of_maximal,lower_bound) ),
inference(resolution,[status(thm)],[p40,p12]) ).
cnf(p45,plain,
( less_than(upper_bound,an_index)
| less_than(an_index,lower_bound)
| less_than(upper_bound,index_of_maximal)
| less_than(index_of_maximal,lower_bound) ),
inference(factoring,[status(thm)],[p43]) ).
cnf(f6,axiom,
~ less_than(an_index,lower_bound),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',somewhere_above_lower_bound) ).
fof(f6_nnf,plain,
~ less_than(an_index,lower_bound),
inference(nnf_transformation,[status(thm)],[f6]) ).
fof(f6_sk,plain,
~ less_than(an_index,lower_bound),
inference(skolemisation,[status(esa)],[f6_nnf]) ).
cnf(c6,plain,
~ less_than(an_index,lower_bound),
inference(cnf_transformation,[status(esa)],[f6_sk]) ).
cnf(p46,plain,
( less_than(upper_bound,an_index)
| less_than(upper_bound,index_of_maximal)
| less_than(index_of_maximal,lower_bound) ),
inference(resolution,[status(thm)],[p45,c6]) ).
cnf(f8,axiom,
~ less_than(index_of_maximal,lower_bound),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',maximal_above_lower_bound) ).
fof(f8_nnf,plain,
~ less_than(index_of_maximal,lower_bound),
inference(nnf_transformation,[status(thm)],[f8]) ).
fof(f8_sk,plain,
~ less_than(index_of_maximal,lower_bound),
inference(skolemisation,[status(esa)],[f8_nnf]) ).
cnf(c8,plain,
~ less_than(index_of_maximal,lower_bound),
inference(cnf_transformation,[status(esa)],[f8_sk]) ).
cnf(p47,plain,
( less_than(upper_bound,an_index)
| less_than(upper_bound,index_of_maximal) ),
inference(resolution,[status(thm)],[p46,c8]) ).
cnf(f7,axiom,
~ less_than(upper_bound,an_index),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',somewhere_below_upper_bound) ).
fof(f7_nnf,plain,
~ less_than(upper_bound,an_index),
inference(nnf_transformation,[status(thm)],[f7]) ).
fof(f7_sk,plain,
~ less_than(upper_bound,an_index),
inference(skolemisation,[status(esa)],[f7_nnf]) ).
cnf(c7,plain,
~ less_than(upper_bound,an_index),
inference(cnf_transformation,[status(esa)],[f7_sk]) ).
cnf(p49,plain,
less_than(upper_bound,index_of_maximal),
inference(resolution,[status(thm)],[p47,c7]) ).
cnf(p50,plain,
( less_than(upper_bound,X0)
| ~ less_than(index_of_maximal,X0) ),
inference(resolution,[status(thm)],[p49,c2]) ).
cnf(p51,plain,
less_than(upper_bound,an_index),
inference(resolution,[status(thm)],[p50,c5]) ).
cnf(p60,plain,
$false,
inference(resolution,[status(thm)],[p51,c7]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SWV019-1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.03 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.10/0.37 % Computer : n002.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Thu Sep 24 18:20:20 UTC 2026
% 0.10/0.38 % CPUTime :
% 0.10/0.38 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 6.24/1.26 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 6.24/1.26 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------