%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : NUM001-1 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n001.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 01:38:30 PM UTC 2026
% Result : Unsatisfiable 0.12s 0.38s
% Output : CNFRefutation 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 4
% Syntax : Number of formulae : 18 ( 11 unt; 0 def)
% Number of atoms : 28 ( 0 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 30 ( 20 ~; 10 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 3 con; 0-2 aty)
% Number of variables : 23 ( 23 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f2,axiom,
! [A,B,C] :
( equalish(A,C)
| ~ equalish(B,C)
| ~ equalish(A,B) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f3,axiom,
! [A,B] : equalish(add(A,B),add(B,A)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f4,axiom,
! [A,B,C] : equalish(add(A,add(B,C)),add(add(A,B),C)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f13,negated_conjecture,
~ equalish(add(add(a,b),c),add(a,add(b,c))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f15,plain,
! [A,C] :
( equalish(A,C)
| ! [B] :
( ~ equalish(B,C)
| ~ equalish(A,B) ) ),
inference(miniscoping,[status(thm)],[f2]) ).
fof(f16,plain,
! [X0,X1,X2] :
( equalish(X0,X2)
| ~ equalish(X1,X2)
| ~ equalish(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f15]) ).
fof(f17,plain,
! [X0,X1] : equalish(add(X0,X1),add(X1,X0)),
inference(cnf_transformation,[status(thm)],[f3]) ).
fof(f18,plain,
! [X0,X1,X2] : equalish(add(X0,add(X1,X2)),add(add(X0,X1),X2)),
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f31,plain,
~ equalish(add(add(a,b),c),add(a,add(b,c))),
inference(cnf_transformation,[status(thm)],[f13]) ).
fof(f32,plain,
! [X0] :
( ~ equalish(X0,add(a,add(b,c)))
| ~ equalish(add(add(a,b),c),X0) ),
inference(resolution,[status(thm)],[f16,f31]) ).
fof(f33,plain,
~ equalish(add(c,add(a,b)),add(a,add(b,c))),
inference(resolution,[status(thm)],[f32,f17]) ).
fof(f42,plain,
! [X0] :
( ~ equalish(X0,add(a,add(b,c)))
| ~ equalish(add(c,add(a,b)),X0) ),
inference(resolution,[status(thm)],[f33,f16]) ).
fof(f72,plain,
~ equalish(add(c,add(a,b)),add(add(b,c),a)),
inference(resolution,[status(thm)],[f42,f17]) ).
fof(f79,plain,
! [X0] :
( ~ equalish(X0,add(add(b,c),a))
| ~ equalish(add(c,add(a,b)),X0) ),
inference(resolution,[status(thm)],[f72,f16]) ).
fof(f104,plain,
~ equalish(add(c,add(a,b)),add(b,add(c,a))),
inference(resolution,[status(thm)],[f79,f18]) ).
fof(f112,plain,
! [X0] :
( ~ equalish(X0,add(b,add(c,a)))
| ~ equalish(add(c,add(a,b)),X0) ),
inference(resolution,[status(thm)],[f104,f16]) ).
fof(f129,plain,
~ equalish(add(c,add(a,b)),add(add(c,a),b)),
inference(resolution,[status(thm)],[f112,f17]) ).
fof(f134,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f129,f18]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : NUM001-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.03 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.34 % Computer : n001.cluster.edu
% 0.09/0.34 % Model : x86_64 x86_64
% 0.09/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.34 % Memory : 8046.5625MB
% 0.09/0.34 % OS : Linux 6.8.0-71-generic
% 0.09/0.34 % CPULimit : 300
% 0.09/0.34 % WCLimit : 300
% 0.09/0.34 % DateTime : Mon Sep 21 02:03:13 UTC 2026
% 0.09/0.34 % CPUTime :
% 0.09/0.35 % Drodi V4.1.1
% 0.12/0.38 % Refutation found
% 0.12/0.38 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.12/0.38 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.12/0.40 % Elapsed time: 0.047979 seconds
% 0.12/0.40 % CPU time: 0.158679 seconds
% 0.12/0.40 % Total memory used: 34.813 MB
% 0.12/0.40 % Net memory used: 34.240 MB
%------------------------------------------------------------------------------