%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SYO691-1.001 : TPTP v9.3.1. Released v7.3.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n005.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 03:43:10 PM UTC 2026
% Result : Unsatisfiable 0.10s 0.42s
% Output : CNFRefutation 0.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 7
% Syntax : Number of formulae : 31 ( 15 unt; 0 def)
% Number of atoms : 50 ( 0 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 43 ( 24 ~; 19 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 6 avg)
% Maximal term depth : 8 ( 2 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-3 aty)
% Number of functors : 4 ( 4 usr; 2 con; 0-2 aty)
% Number of variables : 107 ( 107 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [Z,Y,X] : top(f(f(f(Z,a),Y),f(X,a)),f(f(X,f(f(Y,a),a)),Z)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f2,negated_conjecture,
! [X] : ~ seq(succ(succ(succ(succ(succ(zero))))),X,X),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f3,axiom,
! [X,Y] :
( step(X,Y)
| ~ top(X,Y) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f4,axiom,
! [X,Y,Z] :
( step(f(X,Z),f(Y,Z))
| ~ step(X,Y) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f5,axiom,
! [Y,Z,X] :
( step(f(X,Y),f(X,Z))
| ~ step(Y,Z) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f6,axiom,
! [X] : seq(zero,X,X),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f7,axiom,
! [N,X,Y,Z] :
( seq(succ(N),X,Z)
| ~ step(Y,Z)
| ~ seq(N,X,Y) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f8,plain,
! [X0,X1,X2] : top(f(f(f(X0,a),X1),f(X2,a)),f(f(X2,f(f(X1,a),a)),X0)),
inference(cnf_transformation,[status(thm)],[f1]) ).
fof(f9,plain,
! [X0] : ~ seq(succ(succ(succ(succ(succ(zero))))),X0,X0),
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f10,plain,
! [X0,X1] :
( step(X0,X1)
| ~ top(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f3]) ).
fof(f11,plain,
! [X,Y] :
( ! [Z] : step(f(X,Z),f(Y,Z))
| ~ step(X,Y) ),
inference(miniscoping,[status(thm)],[f4]) ).
fof(f12,plain,
! [X0,X1,X2] :
( step(f(X0,X2),f(X1,X2))
| ~ step(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f11]) ).
fof(f13,plain,
! [Y,Z] :
( ! [X] : step(f(X,Y),f(X,Z))
| ~ step(Y,Z) ),
inference(miniscoping,[status(thm)],[f5]) ).
fof(f14,plain,
! [X0,X1,X2] :
( step(f(X2,X0),f(X2,X1))
| ~ step(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f13]) ).
fof(f15,plain,
! [X0] : seq(zero,X0,X0),
inference(cnf_transformation,[status(thm)],[f6]) ).
fof(f16,plain,
! [N,X,Z] :
( seq(succ(N),X,Z)
| ! [Y] :
( ~ step(Y,Z)
| ~ seq(N,X,Y) ) ),
inference(miniscoping,[status(thm)],[f7]) ).
fof(f17,plain,
! [X0,X1,X2,X3] :
( seq(succ(X0),X1,X3)
| ~ step(X2,X3)
| ~ seq(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f16]) ).
fof(f18,plain,
! [X0,X1,X2] : step(f(f(f(X0,a),X1),f(X2,a)),f(f(X2,f(f(X1,a),a)),X0)),
inference(resolution,[status(thm)],[f8,f10]) ).
fof(f19,plain,
! [X0,X1,X2,X3] : step(f(X0,f(f(f(X1,a),X2),f(X3,a))),f(X0,f(f(X3,f(f(X2,a),a)),X1))),
inference(resolution,[status(thm)],[f18,f14]) ).
fof(f20,plain,
! [X0,X1,X2,X3] : step(f(f(f(f(X0,a),X1),f(X2,a)),X3),f(f(f(X2,f(f(X1,a),a)),X0),X3)),
inference(resolution,[status(thm)],[f18,f12]) ).
fof(f21,plain,
! [X0,X1,X2,X3,X4] :
( seq(succ(X0),X1,f(f(X4,f(f(X3,a),a)),X2))
| ~ seq(X0,X1,f(f(f(X2,a),X3),f(X4,a))) ),
inference(resolution,[status(thm)],[f18,f17]) ).
fof(f22,plain,
! [X0,X1,X2] : ~ seq(succ(succ(succ(succ(zero)))),f(f(X0,f(f(X1,a),a)),X2),f(f(f(X2,a),X1),f(X0,a))),
inference(resolution,[status(thm)],[f21,f9]) ).
fof(f29,plain,
! [X0,X1,X2,X3,X4,X5] :
( seq(succ(X0),X1,f(X2,f(f(X5,f(f(X4,a),a)),X3)))
| ~ seq(X0,X1,f(X2,f(f(f(X3,a),X4),f(X5,a)))) ),
inference(resolution,[status(thm)],[f19,f17]) ).
fof(f31,plain,
! [X0,X1,X2,X3,X4] : step(f(f(f(f(f(X0,a),X1),f(X2,a)),X3),X4),f(f(f(f(X2,f(f(X1,a),a)),X0),X3),X4)),
inference(resolution,[status(thm)],[f20,f12]) ).
fof(f32,plain,
! [X0,X1,X2,X3,X4,X5] :
( seq(succ(X0),X1,f(f(f(X4,f(f(X3,a),a)),X2),X5))
| ~ seq(X0,X1,f(f(f(f(X2,a),X3),f(X4,a)),X5)) ),
inference(resolution,[status(thm)],[f20,f17]) ).
fof(f44,plain,
! [X0,X1,X2,X3,X4,X5,X6] :
( seq(succ(X0),X1,f(f(f(f(X4,f(f(X3,a),a)),X2),X5),X6))
| ~ seq(X0,X1,f(f(f(f(f(X2,a),X3),f(X4,a)),X5),X6)) ),
inference(resolution,[status(thm)],[f31,f17]) ).
fof(f45,plain,
! [X0,X1,X2,X3] : ~ seq(succ(succ(succ(zero))),f(f(f(X0,f(f(X1,a),a)),f(f(X2,a),a)),X3),f(f(f(X3,a),X2),f(f(f(a,a),X1),f(X0,a)))),
inference(resolution,[status(thm)],[f29,f22]) ).
fof(f80,plain,
! [X0,X1,X2,X3] : ~ seq(succ(succ(zero)),f(f(f(X0,f(f(f(f(X1,a),a),a),a)),f(f(X2,a),a)),X3),f(f(f(X3,a),X2),f(f(f(f(X0,a),a),X1),f(f(a,a),a)))),
inference(resolution,[status(thm)],[f45,f29]) ).
fof(f97,plain,
! [X0,X1,X2,X3,X4,X5,X6] :
( ~ seq(X0,X1,f(f(f(f(X5,a),X2),f(f(f(X4,a),X3),a)),X6))
| seq(succ(succ(X0)),X1,f(f(f(f(f(X2,a),f(f(X3,a),a)),X4),X5),X6)) ),
inference(resolution,[status(thm)],[f44,f32]) ).
fof(f368,plain,
! [X0,X1,X2,X3,X4] : seq(succ(succ(zero)),f(f(f(f(X0,a),X1),f(f(f(X2,a),X3),a)),X4),f(f(f(f(f(X1,a),f(f(X3,a),a)),X2),X0),X4)),
inference(resolution,[status(thm)],[f97,f15]) ).
fof(f403,plain,
$false,
inference(resolution,[status(thm)],[f368,f80]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYO691-1.001 : TPTP v9.3.1. Released v7.3.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.37 % Computer : n005.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 12:09:48 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.38 % Drodi V4.1.1
% 0.10/0.42 % Refutation found
% 0.10/0.42 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.10/0.42 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.10/0.46 % Elapsed time: 0.074449 seconds
% 0.10/0.46 % CPU time: 0.360176 seconds
% 0.10/0.46 % Total memory used: 66.076 MB
% 0.10/0.46 % Net memory used: 65.655 MB
%------------------------------------------------------------------------------