%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : NUM002-1 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n004.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 0.09s 0.39s
% Output : CNFRefutation 0.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 6
% Syntax : Number of formulae : 21 ( 12 unt; 0 def)
% Number of atoms : 36 ( 0 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 38 ( 23 ~; 15 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 40 ( 40 !; 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(f7,axiom,
! [A,B,C] : equalish(add(subtract(A,B),C),subtract(add(A,C),B)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f8,axiom,
! [A,B,C] : equalish(subtract(add(A,B),C),add(subtract(A,C),B)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f11,axiom,
! [A,B,C,D] :
( equalish(C,subtract(B,D))
| ~ equalish(C,subtract(A,D))
| ~ equalish(A,B) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f13,negated_conjecture,
~ equalish(add(subtract(a,b),c),add(a,subtract(c,b))),
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(f21,plain,
! [X0,X1,X2] : equalish(add(subtract(X0,X1),X2),subtract(add(X0,X2),X1)),
inference(cnf_transformation,[status(thm)],[f7]) ).
fof(f22,plain,
! [X0,X1,X2] : equalish(subtract(add(X0,X1),X2),add(subtract(X0,X2),X1)),
inference(cnf_transformation,[status(thm)],[f8]) ).
fof(f27,plain,
! [B,C,D] :
( equalish(C,subtract(B,D))
| ! [A] :
( ~ equalish(C,subtract(A,D))
| ~ equalish(A,B) ) ),
inference(miniscoping,[status(thm)],[f11]) ).
fof(f28,plain,
! [X0,X1,X2,X3] :
( equalish(X2,subtract(X1,X3))
| ~ equalish(X2,subtract(X0,X3))
| ~ equalish(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f27]) ).
fof(f31,plain,
~ equalish(add(subtract(a,b),c),add(a,subtract(c,b))),
inference(cnf_transformation,[status(thm)],[f13]) ).
fof(f32,plain,
! [X0] :
( ~ equalish(X0,add(a,subtract(c,b)))
| ~ equalish(add(subtract(a,b),c),X0) ),
inference(resolution,[status(thm)],[f16,f31]) ).
fof(f36,plain,
~ equalish(add(subtract(a,b),c),add(subtract(c,b),a)),
inference(resolution,[status(thm)],[f32,f17]) ).
fof(f46,plain,
! [X0] :
( ~ equalish(X0,add(subtract(c,b),a))
| ~ equalish(add(subtract(a,b),c),X0) ),
inference(resolution,[status(thm)],[f36,f16]) ).
fof(f56,plain,
~ equalish(add(subtract(a,b),c),subtract(add(c,a),b)),
inference(resolution,[status(thm)],[f46,f22]) ).
fof(f64,plain,
! [X0] :
( ~ equalish(add(subtract(a,b),c),subtract(X0,b))
| ~ equalish(X0,add(c,a)) ),
inference(resolution,[status(thm)],[f56,f28]) ).
fof(f69,plain,
~ equalish(add(a,c),add(c,a)),
inference(resolution,[status(thm)],[f64,f21]) ).
fof(f74,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f69,f17]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM002-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n004.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Mon Sep 21 01:57:35 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.37 % Drodi V4.1.1
% 0.09/0.39 % Refutation found
% 0.09/0.39 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.09/0.39 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.09/0.41 % Elapsed time: 0.047508 seconds
% 0.09/0.41 % CPU time: 0.149599 seconds
% 0.09/0.41 % Total memory used: 56.321 MB
% 0.09/0.41 % Net memory used: 55.764 MB
%------------------------------------------------------------------------------