%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : NUM024-1 : TPTP v9.3.1. Bugfixed v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n017.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 0.17s 0.49s
% Output : CNFRefutation 0.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 8
% Syntax : Number of formulae : 26 ( 12 unt; 0 def)
% Number of atoms : 43 ( 0 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 37 ( 20 ~; 17 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 44 ( 44 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [A] : equalish(add(A,n0),A),
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(f11,axiom,
! [X,Y] :
( equalish(Y,X)
| ~ equalish(X,Y) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f12,axiom,
! [X,Y,Z] :
( equalish(X,Z)
| ~ equalish(Y,Z)
| ~ equalish(X,Y) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f13,axiom,
! [A,B,C] :
( equalish(A,C)
| ~ equalish(add(A,B),add(C,B)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f14,axiom,
! [A,B] : equalish(add(A,B),add(B,A)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f15,hypothesis,
less(a,a),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f16,negated_conjecture,
! [A] : ~ equalish(successor(A),n0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f17,plain,
! [X0] : equalish(add(X0,n0),X0),
inference(cnf_transformation,[status(thm)],[f1]) ).
fof(f27,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(f29,plain,
! [X0,X1] :
( equalish(X1,X0)
| ~ equalish(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f11]) ).
fof(f30,plain,
! [X,Z] :
( equalish(X,Z)
| ! [Y] :
( ~ equalish(Y,Z)
| ~ equalish(X,Y) ) ),
inference(miniscoping,[status(thm)],[f12]) ).
fof(f31,plain,
! [X0,X1,X2] :
( equalish(X0,X2)
| ~ equalish(X1,X2)
| ~ equalish(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f30]) ).
fof(f32,plain,
! [A,C] :
( equalish(A,C)
| ! [B] : ~ equalish(add(A,B),add(C,B)) ),
inference(miniscoping,[status(thm)],[f13]) ).
fof(f33,plain,
! [X0,X1,X2] :
( equalish(X0,X2)
| ~ equalish(add(X0,X1),add(X2,X1)) ),
inference(cnf_transformation,[status(thm)],[f32]) ).
fof(f34,plain,
! [X0,X1] : equalish(add(X0,X1),add(X1,X0)),
inference(cnf_transformation,[status(thm)],[f14]) ).
fof(f35,plain,
less(a,a),
inference(cnf_transformation,[status(thm)],[f15]) ).
fof(f36,plain,
! [X0] : ~ equalish(successor(X0),n0),
inference(cnf_transformation,[status(thm)],[f16]) ).
fof(f46,plain,
! [X0,X1] :
( equalish(X0,X1)
| ~ equalish(X0,add(X1,n0)) ),
inference(resolution,[status(thm)],[f31,f17]) ).
fof(f86,plain,
! [X0] : equalish(add(n0,X0),X0),
inference(resolution,[status(thm)],[f34,f46]) ).
fof(f93,plain,
! [X0] : equalish(X0,add(n0,X0)),
inference(resolution,[status(thm)],[f86,f29]) ).
fof(f96,plain,
! [X0,X1] :
( equalish(X0,add(n0,X1))
| ~ equalish(X0,X1) ),
inference(resolution,[status(thm)],[f93,f31]) ).
fof(f285,plain,
! [X0,X1] :
( ~ equalish(add(X0,X1),X1)
| equalish(X0,n0) ),
inference(resolution,[status(thm)],[f33,f96]) ).
fof(f324,plain,
! [X0] :
( ~ less(X0,X0)
| equalish(successor(predecessor_of_1st_minus_2nd(X0,X0)),n0) ),
inference(resolution,[status(thm)],[f285,f27]) ).
fof(f335,plain,
! [X0] : ~ less(X0,X0),
inference(forward_subsumption_resolution,[status(thm)],[f324,f36]) ).
fof(f337,plain,
$false,
inference(backward_subsumption_resolution,[status(thm)],[f35,f335]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : NUM024-1 : TPTP v9.3.1. Bugfixed v4.0.0.
% 0.00/0.06 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.17/0.43 % Computer : n017.cluster.edu
% 0.17/0.43 % Model : x86_64 x86_64
% 0.17/0.43 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.43 % Memory : 8046.5625MB
% 0.17/0.43 % OS : Linux 6.8.0-71-generic
% 0.17/0.43 % CPULimit : 300
% 0.17/0.43 % WCLimit : 300
% 0.17/0.43 % DateTime : Mon Sep 21 01:54:26 UTC 2026
% 0.17/0.43 % CPUTime :
% 0.17/0.45 % Drodi V4.1.1
% 0.17/0.49 % Refutation found
% 0.17/0.49 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.17/0.49 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.23/0.53 % Elapsed time: 0.073321 seconds
% 0.23/0.53 % CPU time: 0.229793 seconds
% 0.23/0.53 % Total memory used: 56.703 MB
% 0.23/0.53 % Net memory used: 56.132 MB
%------------------------------------------------------------------------------