%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : NUM022-1 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n009.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 01:38:33 PM UTC 2026
% Result : Unsatisfiable 0.13s 0.40s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 10
% Syntax : Number of formulae : 36 ( 10 unt; 2 def)
% Number of atoms : 72 ( 0 equ)
% Maximal formula atoms : 3 ( 2 avg)
% Number of connectives : 72 ( 36 ~; 34 |; 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(f1,axiom,
! [A,B,C] :
( less(C,B)
| ~ less(C,A)
| ~ less(A,B) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f2,axiom,
! [A,B,C] :
( less(B,C)
| ~ equalish(add(successor(A),B),C) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f3,axiom,
! [A,B] :
( equalish(add(successor(predecessor_of_1st_minus_2nd(B,A)),A),B)
| ~ less(A,B) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f4,axiom,
! [A,B] :
( equalish(A,B)
| less(A,B)
| ~ divides(A,B) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f7,axiom,
! [A,B,C] :
( equalish(C,B)
| ~ equalish(C,A)
| ~ equalish(A,B) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f8,hypothesis,
less(a,b),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f9,hypothesis,
divides(b,d),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f10,negated_conjecture,
~ less(a,d),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f11,plain,
! [B,C] :
( less(C,B)
| ! [A] :
( ~ less(C,A)
| ~ less(A,B) ) ),
inference(miniscoping,[status(thm)],[f1]) ).
fof(f12,plain,
! [X0,X1,X2] :
( less(X2,X1)
| ~ less(X2,X0)
| ~ less(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f11]) ).
fof(f13,plain,
! [B,C] :
( less(B,C)
| ! [A] : ~ equalish(add(successor(A),B),C) ),
inference(miniscoping,[status(thm)],[f2]) ).
fof(f14,plain,
! [X0,X1,X2] :
( less(X1,X2)
| ~ equalish(add(successor(X0),X1),X2) ),
inference(cnf_transformation,[status(thm)],[f13]) ).
fof(f15,plain,
! [X0,X1] :
( equalish(add(successor(predecessor_of_1st_minus_2nd(X1,X0)),X0),X1)
| ~ less(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f3]) ).
fof(f16,plain,
! [X0,X1] :
( equalish(X0,X1)
| less(X0,X1)
| ~ divides(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f19,plain,
! [B,C] :
( equalish(C,B)
| ! [A] :
( ~ equalish(C,A)
| ~ equalish(A,B) ) ),
inference(miniscoping,[status(thm)],[f7]) ).
fof(f20,plain,
! [X0,X1,X2] :
( equalish(X2,X1)
| ~ equalish(X2,X0)
| ~ equalish(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f19]) ).
fof(f21,plain,
less(a,b),
inference(cnf_transformation,[status(thm)],[f8]) ).
fof(f22,plain,
divides(b,d),
inference(cnf_transformation,[status(thm)],[f9]) ).
fof(f23,plain,
~ less(a,d),
inference(cnf_transformation,[status(thm)],[f10]) ).
fof(f24,plain,
! [X0] :
( less(a,X0)
| ~ less(b,X0) ),
inference(resolution,[status(thm)],[f21,f12]) ).
fof(f30,plain,
! [X0,X1,X2,X3] :
( less(X3,X1)
| ~ equalish(add(successor(X2),X3),X0)
| ~ equalish(X0,X1) ),
inference(resolution,[status(thm)],[f20,f14]) ).
fof(f31,plain,
! [X0,X1,X2] :
( ~ less(X2,X0)
| less(X2,X1)
| ~ equalish(X0,X1) ),
inference(resolution,[status(thm)],[f30,f15]) ).
fof(f35,plain,
! [X0] :
( ~ less(a,X0)
| ~ equalish(X0,d) ),
inference(resolution,[status(thm)],[f31,f23]) ).
fof(f41,plain,
~ equalish(b,d),
inference(resolution,[status(thm)],[f35,f21]) ).
fof(f44,plain,
( less(b,d)
| ~ divides(b,d) ),
inference(resolution,[status(thm)],[f41,f16]) ).
fof(f45,definition,
( sQ0_spl
<=> divides(b,d) ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f47,plain,
( sQ0_spl
| ~ divides(b,d) ),
inference(component_clause,[status(thm)],[f45]) ).
fof(f48,definition,
( sQ1_spl
<=> less(b,d) ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f49,plain,
( ~ sQ1_spl
| less(b,d) ),
inference(component_clause,[status(thm)],[f48]) ).
fof(f51,plain,
( sQ1_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f44,f45,f48]) ).
fof(f52,plain,
( sQ0_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f47,f22]) ).
fof(f53,plain,
sQ0_spl,
inference(contradiction_clause,[status(thm)],[f52]) ).
fof(f56,plain,
( ~ sQ1_spl
| less(a,d) ),
inference(resolution,[status(thm)],[f49,f24]) ).
fof(f58,plain,
( ~ sQ1_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f56,f23]) ).
fof(f59,plain,
~ sQ1_spl,
inference(contradiction_clause,[status(thm)],[f58]) ).
fof(f60,plain,
$false,
inference(sat_refutation,[status(thm)],[f51,f53,f59]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM022-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.37 % Computer : n009.cluster.edu
% 0.09/0.37 % Model : x86_64 x86_64
% 0.09/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.37 % Memory : 8046.5625MB
% 0.09/0.37 % OS : Linux 6.8.0-71-generic
% 0.09/0.37 % CPULimit : 300
% 0.09/0.37 % WCLimit : 300
% 0.09/0.37 % DateTime : Mon Sep 21 01:59:28 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.13/0.38 % Drodi V4.1.1
% 0.13/0.40 % Refutation found
% 0.13/0.40 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.13/0.40 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.13/0.44 % Elapsed time: 0.049588 seconds
% 0.13/0.44 % CPU time: 0.147974 seconds
% 0.13/0.44 % Total memory used: 17.072 MB
% 0.13/0.44 % Net memory used: 16.548 MB
%------------------------------------------------------------------------------