%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : NUM021-1 : TPTP v9.3.1. Bugfixed v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n014.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 : Thu Sep 24 01:38:32 PM UTC 2026
% Result : Unsatisfiable 0.15s 0.41s
% Output : CNFRefutation 0.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 10
% Syntax : Number of formulae : 36 ( 9 unt; 2 def)
% Number of atoms : 73 ( 0 equ)
% Maximal formula atoms : 3 ( 2 avg)
% Number of connectives : 72 ( 35 ~; 35 |; 0 &)
% ( 2 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 6 ( 5 usr; 3 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 44 ( 44 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f7,axiom,
! [A,B,C] :
( less(C,B)
| ~ less(C,A)
| ~ less(A,B) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f8,axiom,
! [A,B,C] :
( less(B,C)
| ~ equalish(add(successor(A),B),C) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f9,axiom,
! [A,B] :
( equalish(add(successor(predecessor_of_1st_minus_2nd(B,A)),A),B)
| ~ less(A,B) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f10,axiom,
! [A,B] :
( equalish(A,B)
| less(A,B)
| ~ divides(A,B) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f15,axiom,
! [X,Y,Z] :
( equalish(X,Z)
| ~ equalish(Y,Z)
| ~ equalish(X,Y) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f16,hypothesis,
less(b,c),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f17,hypothesis,
~ less(b,a),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f18,negated_conjecture,
divides(c,a),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f26,plain,
! [B,C] :
( less(C,B)
| ! [A] :
( ~ less(C,A)
| ~ less(A,B) ) ),
inference(miniscoping,[status(thm)],[f7]) ).
fof(f27,plain,
! [X0,X1,X2] :
( less(X2,X1)
| ~ less(X2,X0)
| ~ less(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f26]) ).
fof(f28,plain,
! [B,C] :
( less(B,C)
| ! [A] : ~ equalish(add(successor(A),B),C) ),
inference(miniscoping,[status(thm)],[f8]) ).
fof(f29,plain,
! [X0,X1,X2] :
( less(X1,X2)
| ~ equalish(add(successor(X0),X1),X2) ),
inference(cnf_transformation,[status(thm)],[f28]) ).
fof(f30,plain,
! [X0,X1] :
( equalish(add(successor(predecessor_of_1st_minus_2nd(X1,X0)),X0),X1)
| ~ less(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f9]) ).
fof(f31,plain,
! [X0,X1] :
( equalish(X0,X1)
| less(X0,X1)
| ~ divides(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f10]) ).
fof(f36,plain,
! [X,Z] :
( equalish(X,Z)
| ! [Y] :
( ~ equalish(Y,Z)
| ~ equalish(X,Y) ) ),
inference(miniscoping,[status(thm)],[f15]) ).
fof(f37,plain,
! [X0,X1,X2] :
( equalish(X0,X2)
| ~ equalish(X1,X2)
| ~ equalish(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f36]) ).
fof(f38,plain,
less(b,c),
inference(cnf_transformation,[status(thm)],[f16]) ).
fof(f39,plain,
~ less(b,a),
inference(cnf_transformation,[status(thm)],[f17]) ).
fof(f40,plain,
divides(c,a),
inference(cnf_transformation,[status(thm)],[f18]) ).
fof(f47,plain,
! [X0] :
( less(b,X0)
| ~ less(c,X0) ),
inference(resolution,[status(thm)],[f27,f38]) ).
fof(f53,plain,
( equalish(c,a)
| less(c,a) ),
inference(resolution,[status(thm)],[f31,f40]) ).
fof(f56,definition,
( sQ0_spl
<=> less(c,a) ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f57,plain,
( ~ sQ0_spl
| less(c,a) ),
inference(component_clause,[status(thm)],[f56]) ).
fof(f59,definition,
( sQ1_spl
<=> equalish(c,a) ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f60,plain,
( ~ sQ1_spl
| equalish(c,a) ),
inference(component_clause,[status(thm)],[f59]) ).
fof(f62,plain,
( sQ1_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f53,f56,f59]) ).
fof(f63,plain,
( ~ sQ0_spl
| less(b,a) ),
inference(resolution,[status(thm)],[f57,f47]) ).
fof(f66,plain,
( ~ sQ0_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f63,f39]) ).
fof(f67,plain,
~ sQ0_spl,
inference(contradiction_clause,[status(thm)],[f66]) ).
fof(f90,plain,
! [X0,X1,X2,X3] :
( less(X1,X3)
| ~ equalish(X2,X3)
| ~ equalish(add(successor(X0),X1),X2) ),
inference(resolution,[status(thm)],[f37,f29]) ).
fof(f174,plain,
! [X0,X1,X2] :
( ~ less(X2,X0)
| less(X2,X1)
| ~ equalish(X0,X1) ),
inference(resolution,[status(thm)],[f90,f30]) ).
fof(f201,plain,
! [X0] :
( less(b,X0)
| ~ equalish(c,X0) ),
inference(resolution,[status(thm)],[f174,f38]) ).
fof(f205,plain,
( ~ sQ1_spl
| less(b,a) ),
inference(resolution,[status(thm)],[f201,f60]) ).
fof(f209,plain,
( ~ sQ1_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f205,f39]) ).
fof(f210,plain,
~ sQ1_spl,
inference(contradiction_clause,[status(thm)],[f209]) ).
fof(f211,plain,
$false,
inference(sat_refutation,[status(thm)],[f62,f67,f210]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : NUM021-1 : TPTP v9.3.1. Bugfixed v4.0.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.37 % Computer : n014.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 : Mon Sep 21 01:58:50 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.15/0.38 % Drodi V4.1.1
% 0.15/0.41 % Refutation found
% 0.15/0.41 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.15/0.41 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.15/0.42 % Elapsed time: 0.048843 seconds
% 0.15/0.42 % CPU time: 0.183923 seconds
% 0.15/0.42 % Total memory used: 18.012 MB
% 0.15/0.42 % Net memory used: 17.535 MB
%------------------------------------------------------------------------------