%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SYO617-1 : TPTP v9.3.1. Released v7.1.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n007.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 03:42:50 PM UTC 2026
% Result : Unsatisfiable 0.09s 0.47s
% Output : CNFRefutation 0.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 7
% Syntax : Number of formulae : 48 ( 7 unt; 0 def)
% Number of atoms : 111 ( 0 equ)
% Maximal formula atoms : 3 ( 2 avg)
% Number of connectives : 149 ( 86 ~; 63 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 6 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 122 ( 122 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [A] : le(A,A),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f2,axiom,
! [A,B,C] :
( le(A,C)
| ~ le(max(A,B),C) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f3,axiom,
! [A,B,C] :
( le(B,C)
| ~ le(max(A,B),C) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f4,axiom,
! [A] :
( eq(f(A),a2)
| eq(f(A),a1)
| eq(f(A),a0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f5,axiom,
! [A0,A1] :
( ~ le(s(A0),A1)
| ~ eq(f(A1),a0)
| ~ eq(f(A0),a0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f6,axiom,
! [A0,A1] :
( ~ le(s(A0),A1)
| ~ eq(f(A1),a1)
| ~ eq(f(A0),a1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f7,axiom,
! [A0,A1] :
( ~ le(s(A0),A1)
| ~ eq(f(A1),a2)
| ~ eq(f(A0),a2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f8,plain,
! [X0] : le(X0,X0),
inference(cnf_transformation,[status(thm)],[f1]) ).
fof(f9,plain,
! [A,C] :
( le(A,C)
| ! [B] : ~ le(max(A,B),C) ),
inference(miniscoping,[status(thm)],[f2]) ).
fof(f10,plain,
! [X0,X1,X2] :
( le(X0,X2)
| ~ le(max(X0,X1),X2) ),
inference(cnf_transformation,[status(thm)],[f9]) ).
fof(f11,plain,
! [B,C] :
( le(B,C)
| ! [A] : ~ le(max(A,B),C) ),
inference(miniscoping,[status(thm)],[f3]) ).
fof(f12,plain,
! [X0,X1,X2] :
( le(X1,X2)
| ~ le(max(X0,X1),X2) ),
inference(cnf_transformation,[status(thm)],[f11]) ).
fof(f13,plain,
! [X0] :
( eq(f(X0),a2)
| eq(f(X0),a1)
| eq(f(X0),a0) ),
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f14,plain,
! [X0,X1] :
( ~ le(s(X0),X1)
| ~ eq(f(X1),a0)
| ~ eq(f(X0),a0) ),
inference(cnf_transformation,[status(thm)],[f5]) ).
fof(f15,plain,
! [X0,X1] :
( ~ le(s(X0),X1)
| ~ eq(f(X1),a1)
| ~ eq(f(X0),a1) ),
inference(cnf_transformation,[status(thm)],[f6]) ).
fof(f16,plain,
! [X0,X1] :
( ~ le(s(X0),X1)
| ~ eq(f(X1),a2)
| ~ eq(f(X0),a2) ),
inference(cnf_transformation,[status(thm)],[f7]) ).
fof(f17,plain,
! [X0,X1,X2] :
( ~ le(max(X2,s(X0)),X1)
| ~ eq(f(X1),a0)
| ~ eq(f(X0),a0) ),
inference(resolution,[status(thm)],[f14,f12]) ).
fof(f18,plain,
! [X0,X1,X2] :
( ~ le(max(s(X0),X2),X1)
| ~ eq(f(X1),a0)
| ~ eq(f(X0),a0) ),
inference(resolution,[status(thm)],[f14,f10]) ).
fof(f22,plain,
! [X0,X1,X2] :
( ~ le(max(s(X0),X2),X1)
| ~ eq(f(X1),a1)
| ~ eq(f(X0),a1) ),
inference(resolution,[status(thm)],[f15,f10]) ).
fof(f25,plain,
! [X0,X1,X2] :
( ~ le(max(s(X0),X2),X1)
| ~ eq(f(X1),a2)
| ~ eq(f(X0),a2) ),
inference(resolution,[status(thm)],[f16,f10]) ).
fof(f29,plain,
! [X0,X1] :
( ~ eq(f(max(X1,s(X0))),a0)
| ~ eq(f(X0),a0) ),
inference(resolution,[status(thm)],[f17,f8]) ).
fof(f30,plain,
! [X0,X1] :
( eq(f(max(X1,s(X0))),a2)
| eq(f(max(X1,s(X0))),a1)
| ~ eq(f(X0),a0) ),
inference(resolution,[status(thm)],[f29,f13]) ).
fof(f33,plain,
! [X0,X1] :
( ~ eq(f(max(s(X0),X1)),a0)
| ~ eq(f(X0),a0) ),
inference(resolution,[status(thm)],[f18,f8]) ).
fof(f34,plain,
! [X0,X1] :
( eq(f(max(s(X0),X1)),a2)
| eq(f(max(s(X0),X1)),a1)
| ~ eq(f(X0),a0) ),
inference(resolution,[status(thm)],[f33,f13]) ).
fof(f39,plain,
! [X0,X1,X2,X3] :
( ~ le(max(max(s(X0),X2),X3),X1)
| ~ eq(f(X1),a1)
| ~ eq(f(X0),a1) ),
inference(resolution,[status(thm)],[f22,f10]) ).
fof(f40,plain,
! [X0,X1] :
( ~ eq(f(max(s(X0),X1)),a1)
| ~ eq(f(X0),a1) ),
inference(resolution,[status(thm)],[f22,f8]) ).
fof(f44,plain,
! [X0,X1,X2,X3] :
( ~ le(max(X2,max(s(X0),X3)),X1)
| ~ eq(f(X1),a2)
| ~ eq(f(X0),a2) ),
inference(resolution,[status(thm)],[f25,f12]) ).
fof(f45,plain,
! [X0,X1,X2,X3] :
( ~ le(max(max(s(X0),X2),X3),X1)
| ~ eq(f(X1),a2)
| ~ eq(f(X0),a2) ),
inference(resolution,[status(thm)],[f25,f10]) ).
fof(f77,plain,
! [X0,X1,X2] :
( ~ eq(f(max(max(s(X0),X1),X2)),a1)
| ~ eq(f(X0),a1) ),
inference(resolution,[status(thm)],[f39,f8]) ).
fof(f85,plain,
! [X0,X1,X2,X3,X4] :
( ~ le(max(max(X2,max(s(X0),X3)),X4),X1)
| ~ eq(f(X1),a2)
| ~ eq(f(X0),a2) ),
inference(resolution,[status(thm)],[f44,f10]) ).
fof(f87,plain,
! [X0,X1,X2,X3,X4] :
( ~ le(max(X2,max(max(s(X0),X3),X4)),X1)
| ~ eq(f(X1),a2)
| ~ eq(f(X0),a2) ),
inference(resolution,[status(thm)],[f45,f12]) ).
fof(f88,plain,
! [X0,X1,X2,X3,X4] :
( ~ le(max(max(max(s(X0),X2),X3),X4),X1)
| ~ eq(f(X1),a2)
| ~ eq(f(X0),a2) ),
inference(resolution,[status(thm)],[f45,f10]) ).
fof(f90,plain,
! [X0,X1,X2] :
( ~ eq(f(X1),a1)
| eq(f(max(max(s(X1),X2),s(X0))),a2)
| ~ eq(f(X0),a0) ),
inference(resolution,[status(thm)],[f30,f77]) ).
fof(f216,plain,
! [X0,X1,X2,X3] :
( ~ eq(f(max(max(X1,max(s(X0),X2)),X3)),a2)
| ~ eq(f(X0),a2) ),
inference(resolution,[status(thm)],[f85,f8]) ).
fof(f219,plain,
! [X0,X1,X2,X3] :
( ~ eq(f(max(X1,max(max(s(X0),X2),X3))),a2)
| ~ eq(f(X0),a2) ),
inference(resolution,[status(thm)],[f87,f8]) ).
fof(f222,plain,
! [X0,X1,X2,X3] :
( ~ eq(f(max(max(max(s(X0),X1),X2),X3)),a2)
| ~ eq(f(X0),a2) ),
inference(resolution,[status(thm)],[f88,f8]) ).
fof(f282,plain,
! [X0,X1,X2] :
( ~ eq(f(X2),a2)
| ~ eq(f(X1),a1)
| ~ eq(f(X0),a0) ),
inference(resolution,[status(thm)],[f90,f216]) ).
fof(f298,plain,
! [X0,X1] :
( ~ eq(f(X1),a1)
| ~ eq(f(X0),a0) ),
inference(backward_subsumption_resolution,[status(thm)],[f90,f282]) ).
fof(f309,plain,
! [X0,X1] :
( eq(f(max(s(X0),X1)),a2)
| ~ eq(f(X0),a0) ),
inference(backward_subsumption_resolution,[status(thm)],[f34,f298]) ).
fof(f317,plain,
! [X0,X1] :
( ~ eq(f(X1),a2)
| ~ eq(f(X0),a0) ),
inference(resolution,[status(thm)],[f309,f219]) ).
fof(f324,plain,
! [X0] : ~ eq(f(X0),a0),
inference(backward_subsumption_resolution,[status(thm)],[f309,f317]) ).
fof(f327,plain,
! [X0] :
( eq(f(X0),a2)
| eq(f(X0),a1) ),
inference(backward_subsumption_resolution,[status(thm)],[f13,f324]) ).
fof(f334,plain,
! [X0,X1] :
( ~ eq(f(X0),a1)
| eq(f(max(s(X0),X1)),a2) ),
inference(resolution,[status(thm)],[f327,f40]) ).
fof(f346,plain,
! [X0,X1] :
( ~ eq(f(X1),a2)
| ~ eq(f(X0),a1) ),
inference(resolution,[status(thm)],[f334,f219]) ).
fof(f361,plain,
! [X0] : ~ eq(f(X0),a1),
inference(backward_subsumption_resolution,[status(thm)],[f334,f346]) ).
fof(f365,plain,
! [X0] : eq(f(X0),a2),
inference(backward_subsumption_resolution,[status(thm)],[f327,f361]) ).
fof(f366,plain,
! [X0,X1,X2,X3] : ~ eq(f(max(max(max(s(X0),X1),X2),X3)),a2),
inference(backward_subsumption_resolution,[status(thm)],[f222,f365]) ).
fof(f396,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f366,f365]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SYO617-1 : TPTP v9.3.1. Released v7.1.0.
% 0.00/0.03 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n007.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 12:02:21 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.37 % Drodi V4.1.1
% 0.09/0.47 % Refutation found
% 0.09/0.47 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.09/0.47 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.09/0.48 % Elapsed time: 0.116645 seconds
% 0.09/0.48 % CPU time: 0.782457 seconds
% 0.09/0.48 % Total memory used: 15.175 MB
% 0.09/0.48 % Net memory used: 13.022 MB
%------------------------------------------------------------------------------