%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SYO620-1 : TPTP v9.3.1. Released v7.1.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n015.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 53.20s 7.17s
% Output : CNFRefutation 53.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 35
% Number of leaves : 8
% Syntax : Number of formulae : 83 ( 8 unt; 0 def)
% Number of atoms : 211 ( 0 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 296 ( 168 ~; 128 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 7 avg)
% Maximal term depth : 8 ( 2 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 4 con; 0-2 aty)
% Number of variables : 258 ( 258 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [A] : le(A,A),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f2,axiom,
! [A,B,C] :
( le(A,C)
| ~ le(max(A,B),C) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f3,axiom,
! [A,B,C] :
( le(B,C)
| ~ le(max(A,B),C) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f4,axiom,
! [A] :
( eq(f(A),a3)
| eq(f(A),a2)
| eq(f(A),a1)
| eq(f(A),a0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f5,axiom,
! [A0,A1] :
( ~ le(s(A0),A1)
| ~ eq(f(A1),a0)
| ~ eq(f(A0),a0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f6,axiom,
! [A0,A1] :
( ~ le(s(A0),A1)
| ~ eq(f(A1),a1)
| ~ eq(f(A0),a1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f7,axiom,
! [A0,A1] :
( ~ le(s(A0),A1)
| ~ eq(f(A1),a2)
| ~ eq(f(A0),a2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f8,axiom,
! [A0,A1] :
( ~ le(s(A0),A1)
| ~ eq(f(A1),a3)
| ~ eq(f(A0),a3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f9,plain,
! [X0] : le(X0,X0),
inference(cnf_transformation,[status(thm)],[f1]) ).
fof(f10,plain,
! [A,C] :
( le(A,C)
| ! [B] : ~ le(max(A,B),C) ),
inference(miniscoping,[status(thm)],[f2]) ).
fof(f11,plain,
! [X0,X1,X2] :
( le(X0,X2)
| ~ le(max(X0,X1),X2) ),
inference(cnf_transformation,[status(thm)],[f10]) ).
fof(f12,plain,
! [B,C] :
( le(B,C)
| ! [A] : ~ le(max(A,B),C) ),
inference(miniscoping,[status(thm)],[f3]) ).
fof(f13,plain,
! [X0,X1,X2] :
( le(X1,X2)
| ~ le(max(X0,X1),X2) ),
inference(cnf_transformation,[status(thm)],[f12]) ).
fof(f14,plain,
! [X0] :
( eq(f(X0),a3)
| eq(f(X0),a2)
| eq(f(X0),a1)
| eq(f(X0),a0) ),
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f15,plain,
! [X0,X1] :
( ~ le(s(X0),X1)
| ~ eq(f(X1),a0)
| ~ eq(f(X0),a0) ),
inference(cnf_transformation,[status(thm)],[f5]) ).
fof(f16,plain,
! [X0,X1] :
( ~ le(s(X0),X1)
| ~ eq(f(X1),a1)
| ~ eq(f(X0),a1) ),
inference(cnf_transformation,[status(thm)],[f6]) ).
fof(f17,plain,
! [X0,X1] :
( ~ le(s(X0),X1)
| ~ eq(f(X1),a2)
| ~ eq(f(X0),a2) ),
inference(cnf_transformation,[status(thm)],[f7]) ).
fof(f18,plain,
! [X0,X1] :
( ~ le(s(X0),X1)
| ~ eq(f(X1),a3)
| ~ eq(f(X0),a3) ),
inference(cnf_transformation,[status(thm)],[f8]) ).
fof(f20,plain,
! [X0,X1,X2] :
( ~ le(max(s(X0),X2),X1)
| ~ eq(f(X1),a0)
| ~ eq(f(X0),a0) ),
inference(resolution,[status(thm)],[f15,f11]) ).
fof(f22,plain,
! [X0,X1,X2] :
( ~ le(max(X2,s(X0)),X1)
| ~ eq(f(X1),a1)
| ~ eq(f(X0),a1) ),
inference(resolution,[status(thm)],[f16,f13]) ).
fof(f23,plain,
! [X0,X1,X2] :
( ~ le(max(s(X0),X2),X1)
| ~ eq(f(X1),a1)
| ~ eq(f(X0),a1) ),
inference(resolution,[status(thm)],[f16,f11]) ).
fof(f26,plain,
! [X0,X1,X2] :
( ~ le(max(s(X0),X2),X1)
| ~ eq(f(X1),a2)
| ~ eq(f(X0),a2) ),
inference(resolution,[status(thm)],[f17,f11]) ).
fof(f28,plain,
! [X0,X1,X2] :
( ~ le(max(X2,s(X0)),X1)
| ~ eq(f(X1),a3)
| ~ eq(f(X0),a3) ),
inference(resolution,[status(thm)],[f18,f13]) ).
fof(f29,plain,
! [X0,X1,X2] :
( ~ le(max(s(X0),X2),X1)
| ~ eq(f(X1),a3)
| ~ eq(f(X0),a3) ),
inference(resolution,[status(thm)],[f18,f11]) ).
fof(f36,plain,
! [X0,X1,X2,X3] :
( ~ le(max(max(s(X0),X2),X3),X1)
| ~ eq(f(X1),a0)
| ~ eq(f(X0),a0) ),
inference(resolution,[status(thm)],[f20,f11]) ).
fof(f40,plain,
! [X0,X1] :
( ~ eq(f(max(X1,s(X0))),a1)
| ~ eq(f(X0),a1) ),
inference(resolution,[status(thm)],[f22,f9]) ).
fof(f41,plain,
! [X0,X1,X2,X3] :
( ~ le(max(X2,max(s(X0),X3)),X1)
| ~ eq(f(X1),a1)
| ~ eq(f(X0),a1) ),
inference(resolution,[status(thm)],[f23,f13]) ).
fof(f43,plain,
! [X0,X1] :
( ~ eq(f(max(s(X0),X1)),a1)
| ~ eq(f(X0),a1) ),
inference(resolution,[status(thm)],[f23,f9]) ).
fof(f48,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)],[f26,f11]) ).
fof(f49,plain,
! [X0,X1] :
( ~ eq(f(max(s(X0),X1)),a2)
| ~ eq(f(X0),a2) ),
inference(resolution,[status(thm)],[f26,f9]) ).
fof(f52,plain,
! [X0,X1] :
( ~ eq(f(max(X1,s(X0))),a3)
| ~ eq(f(X0),a3) ),
inference(resolution,[status(thm)],[f28,f9]) ).
fof(f53,plain,
! [X0,X1] :
( eq(f(max(X1,s(X0))),a2)
| eq(f(max(X1,s(X0))),a1)
| eq(f(max(X1,s(X0))),a0)
| ~ eq(f(X0),a3) ),
inference(resolution,[status(thm)],[f52,f14]) ).
fof(f56,plain,
! [X0,X1] :
( ~ eq(f(max(s(X0),X1)),a3)
| ~ eq(f(X0),a3) ),
inference(resolution,[status(thm)],[f29,f9]) ).
fof(f58,plain,
! [X0,X1] :
( eq(f(max(s(X0),X1)),a2)
| eq(f(max(s(X0),X1)),a1)
| eq(f(max(s(X0),X1)),a0)
| ~ eq(f(X0),a3) ),
inference(resolution,[status(thm)],[f56,f14]) ).
fof(f68,plain,
! [X0,X1,X2,X3,X4] :
( ~ le(max(X2,max(max(s(X0),X3),X4)),X1)
| ~ eq(f(X1),a0)
| ~ eq(f(X0),a0) ),
inference(resolution,[status(thm)],[f36,f13]) ).
fof(f69,plain,
! [X0,X1,X2,X3,X4] :
( ~ le(max(max(max(s(X0),X2),X3),X4),X1)
| ~ eq(f(X1),a0)
| ~ eq(f(X0),a0) ),
inference(resolution,[status(thm)],[f36,f11]) ).
fof(f78,plain,
! [X0,X1,X2,X3,X4] :
( ~ le(max(max(X2,max(s(X0),X3)),X4),X1)
| ~ eq(f(X1),a1)
| ~ eq(f(X0),a1) ),
inference(resolution,[status(thm)],[f41,f11]) ).
fof(f79,plain,
! [X0,X1,X2] :
( ~ eq(f(max(X1,max(s(X0),X2))),a1)
| ~ eq(f(X0),a1) ),
inference(resolution,[status(thm)],[f41,f9]) ).
fof(f94,plain,
! [X0,X1,X2] :
( ~ eq(f(max(max(s(X0),X1),X2)),a2)
| ~ eq(f(X0),a2) ),
inference(resolution,[status(thm)],[f48,f9]) ).
fof(f114,plain,
! [X0,X1,X2] :
( ~ eq(f(X1),a2)
| eq(f(max(max(s(X1),X2),s(X0))),a1)
| eq(f(max(max(s(X1),X2),s(X0))),a0)
| ~ eq(f(X0),a3) ),
inference(resolution,[status(thm)],[f53,f94]) ).
fof(f134,plain,
! [X0,X1,X2,X3,X4,X5] :
( ~ le(max(X2,max(X3,max(max(s(X0),X4),X5))),X1)
| ~ eq(f(X1),a0)
| ~ eq(f(X0),a0) ),
inference(resolution,[status(thm)],[f68,f13]) ).
fof(f141,plain,
! [X0,X1,X2,X3,X4,X5] :
( ~ le(max(X2,max(max(max(s(X0),X3),X4),X5)),X1)
| ~ eq(f(X1),a0)
| ~ eq(f(X0),a0) ),
inference(resolution,[status(thm)],[f69,f13]) ).
fof(f142,plain,
! [X0,X1,X2,X3,X4,X5] :
( ~ le(max(max(max(max(s(X0),X2),X3),X4),X5),X1)
| ~ eq(f(X1),a0)
| ~ eq(f(X0),a0) ),
inference(resolution,[status(thm)],[f69,f11]) ).
fof(f161,plain,
! [X0,X1,X2,X3] :
( ~ eq(f(max(max(X1,max(s(X0),X2)),X3)),a1)
| ~ eq(f(X0),a1) ),
inference(resolution,[status(thm)],[f78,f9]) ).
fof(f315,plain,
! [X0,X1,X2,X3,X4,X5,X6] :
( ~ le(max(max(X2,max(X3,max(max(s(X0),X4),X5))),X6),X1)
| ~ eq(f(X1),a0)
| ~ eq(f(X0),a0) ),
inference(resolution,[status(thm)],[f134,f11]) ).
fof(f318,plain,
! [X0,X1,X2,X3] :
( ~ eq(f(X2),a1)
| ~ eq(f(X1),a2)
| eq(f(max(max(s(X1),max(s(X2),X3)),s(X0))),a0)
| ~ eq(f(X0),a3) ),
inference(resolution,[status(thm)],[f114,f161]) ).
fof(f325,plain,
! [X0,X1,X2,X3,X4,X5,X6] :
( ~ le(max(X2,max(X3,max(max(max(s(X0),X4),X5),X6))),X1)
| ~ eq(f(X1),a0)
| ~ eq(f(X0),a0) ),
inference(resolution,[status(thm)],[f141,f13]) ).
fof(f326,plain,
! [X0,X1,X2,X3,X4,X5,X6] :
( ~ le(max(max(X2,max(max(max(s(X0),X3),X4),X5)),X6),X1)
| ~ eq(f(X1),a0)
| ~ eq(f(X0),a0) ),
inference(resolution,[status(thm)],[f141,f11]) ).
fof(f328,plain,
! [X0,X1,X2,X3,X4,X5,X6] :
( ~ le(max(X2,max(max(max(max(s(X0),X3),X4),X5),X6)),X1)
| ~ eq(f(X1),a0)
| ~ eq(f(X0),a0) ),
inference(resolution,[status(thm)],[f142,f13]) ).
fof(f329,plain,
! [X0,X1,X2,X3,X4,X5,X6] :
( ~ le(max(max(max(max(max(s(X0),X2),X3),X4),X5),X6),X1)
| ~ eq(f(X1),a0)
| ~ eq(f(X0),a0) ),
inference(resolution,[status(thm)],[f142,f11]) ).
fof(f893,plain,
! [X0,X1,X2,X3,X4,X5] :
( ~ eq(f(max(max(X1,max(X2,max(max(s(X0),X3),X4))),X5)),a0)
| ~ eq(f(X0),a0) ),
inference(resolution,[status(thm)],[f315,f9]) ).
fof(f928,plain,
! [X0,X1,X2,X3,X4,X5] :
( ~ eq(f(max(X1,max(X2,max(max(max(s(X0),X3),X4),X5)))),a0)
| ~ eq(f(X0),a0) ),
inference(resolution,[status(thm)],[f325,f9]) ).
fof(f931,plain,
! [X0,X1,X2,X3,X4,X5] :
( ~ eq(f(max(max(X1,max(max(max(s(X0),X2),X3),X4)),X5)),a0)
| ~ eq(f(X0),a0) ),
inference(resolution,[status(thm)],[f326,f9]) ).
fof(f934,plain,
! [X0,X1,X2,X3,X4,X5] :
( ~ eq(f(max(X1,max(max(max(max(s(X0),X2),X3),X4),X5))),a0)
| ~ eq(f(X0),a0) ),
inference(resolution,[status(thm)],[f328,f9]) ).
fof(f963,plain,
! [X0,X1,X2,X3,X4,X5] :
( ~ eq(f(max(max(max(max(max(s(X0),X1),X2),X3),X4),X5)),a0)
| ~ eq(f(X0),a0) ),
inference(resolution,[status(thm)],[f329,f9]) ).
fof(f4001,plain,
! [X0,X1,X2,X3] :
( ~ eq(f(X3),a0)
| ~ eq(f(X2),a1)
| ~ eq(f(X1),a2)
| ~ eq(f(X0),a3) ),
inference(resolution,[status(thm)],[f318,f893]) ).
fof(f4151,plain,
! [X0,X1,X2] :
( ~ eq(f(X2),a1)
| ~ eq(f(X1),a2)
| ~ eq(f(X0),a3) ),
inference(backward_subsumption_resolution,[status(thm)],[f318,f4001]) ).
fof(f4244,plain,
! [X0,X1,X2] :
( ~ eq(f(X1),a2)
| eq(f(max(max(s(X1),X2),s(X0))),a0)
| ~ eq(f(X0),a3) ),
inference(backward_subsumption_resolution,[status(thm)],[f114,f4151]) ).
fof(f4295,plain,
! [X0,X1,X2] :
( ~ eq(f(X2),a0)
| ~ eq(f(X1),a2)
| ~ eq(f(X0),a3) ),
inference(resolution,[status(thm)],[f4244,f931]) ).
fof(f4328,plain,
! [X0,X1] :
( ~ eq(f(X1),a2)
| ~ eq(f(X0),a3) ),
inference(backward_subsumption_resolution,[status(thm)],[f4244,f4295]) ).
fof(f4352,plain,
! [X0,X1] :
( eq(f(max(s(X0),X1)),a1)
| eq(f(max(s(X0),X1)),a0)
| ~ eq(f(X0),a3) ),
inference(backward_subsumption_resolution,[status(thm)],[f58,f4328]) ).
fof(f4379,plain,
! [X0,X1,X2] :
( ~ eq(f(X1),a1)
| eq(f(max(s(X0),max(s(X1),X2))),a0)
| ~ eq(f(X0),a3) ),
inference(resolution,[status(thm)],[f4352,f79]) ).
fof(f4747,plain,
! [X0,X1,X2] :
( ~ eq(f(X2),a0)
| ~ eq(f(X1),a1)
| ~ eq(f(X0),a3) ),
inference(resolution,[status(thm)],[f4379,f928]) ).
fof(f4762,plain,
! [X0,X1] :
( ~ eq(f(X1),a1)
| ~ eq(f(X0),a3) ),
inference(backward_subsumption_resolution,[status(thm)],[f4379,f4747]) ).
fof(f4775,plain,
! [X0,X1] :
( eq(f(max(s(X0),X1)),a0)
| ~ eq(f(X0),a3) ),
inference(backward_subsumption_resolution,[status(thm)],[f4352,f4762]) ).
fof(f4783,plain,
! [X0,X1] :
( ~ eq(f(X1),a0)
| ~ eq(f(X0),a3) ),
inference(resolution,[status(thm)],[f4775,f934]) ).
fof(f4846,plain,
! [X0] : ~ eq(f(X0),a3),
inference(backward_subsumption_resolution,[status(thm)],[f4775,f4783]) ).
fof(f4850,plain,
! [X0] :
( eq(f(X0),a2)
| eq(f(X0),a1)
| eq(f(X0),a0) ),
inference(backward_subsumption_resolution,[status(thm)],[f14,f4846]) ).
fof(f4881,plain,
! [X0,X1] :
( ~ eq(f(X0),a2)
| eq(f(max(s(X0),X1)),a1)
| eq(f(max(s(X0),X1)),a0) ),
inference(resolution,[status(thm)],[f4850,f49]) ).
fof(f4930,plain,
! [X0,X1,X2] :
( ~ eq(f(X1),a1)
| ~ eq(f(X0),a2)
| eq(f(max(s(X0),max(s(X1),X2))),a0) ),
inference(resolution,[status(thm)],[f4881,f79]) ).
fof(f4946,plain,
! [X0,X1] :
( ~ eq(f(X1),a1)
| ~ eq(f(X0),a2)
| eq(f(max(s(X0),s(X1))),a0) ),
inference(resolution,[status(thm)],[f4881,f40]) ).
fof(f5207,plain,
! [X0,X1,X2] :
( ~ eq(f(X2),a0)
| ~ eq(f(X1),a1)
| ~ eq(f(X0),a2) ),
inference(resolution,[status(thm)],[f4930,f928]) ).
fof(f5257,plain,
! [X0,X1] :
( ~ eq(f(X1),a1)
| ~ eq(f(X0),a2) ),
inference(backward_subsumption_resolution,[status(thm)],[f4946,f5207]) ).
fof(f5270,plain,
! [X0,X1] :
( ~ eq(f(X0),a2)
| eq(f(max(s(X0),X1)),a0) ),
inference(backward_subsumption_resolution,[status(thm)],[f4881,f5257]) ).
fof(f5279,plain,
! [X0,X1] :
( ~ eq(f(X1),a0)
| ~ eq(f(X0),a2) ),
inference(resolution,[status(thm)],[f5270,f934]) ).
fof(f5310,plain,
! [X0] : ~ eq(f(X0),a2),
inference(backward_subsumption_resolution,[status(thm)],[f5270,f5279]) ).
fof(f5313,plain,
! [X0] :
( eq(f(X0),a1)
| eq(f(X0),a0) ),
inference(backward_subsumption_resolution,[status(thm)],[f4850,f5310]) ).
fof(f5344,plain,
! [X0,X1] :
( ~ eq(f(X0),a1)
| eq(f(max(s(X0),X1)),a0) ),
inference(resolution,[status(thm)],[f5313,f43]) ).
fof(f5379,plain,
! [X0,X1] :
( ~ eq(f(X1),a0)
| ~ eq(f(X0),a1) ),
inference(resolution,[status(thm)],[f5344,f934]) ).
fof(f5443,plain,
! [X0] : ~ eq(f(X0),a1),
inference(backward_subsumption_resolution,[status(thm)],[f5344,f5379]) ).
fof(f5447,plain,
! [X0] : eq(f(X0),a0),
inference(backward_subsumption_resolution,[status(thm)],[f5313,f5443]) ).
fof(f5448,plain,
! [X0,X1,X2,X3,X4,X5] : ~ eq(f(max(max(max(max(max(s(X0),X1),X2),X3),X4),X5)),a0),
inference(backward_subsumption_resolution,[status(thm)],[f963,f5447]) ).
fof(f5574,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f5448,f5447]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYO620-1 : TPTP v9.3.1. Released v7.1.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.36 % Computer : n015.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Mon Sep 21 12:07:52 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 % Drodi V4.1.1
% 53.20/7.17 % Refutation found
% 53.20/7.17 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 53.20/7.17 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 3.17/7.20 % Elapsed time: 6.830063 seconds
% 3.17/7.20 % CPU time: 53.935455 seconds
% 3.17/7.20 % Total memory used: 206.148 MB
% 3.17/7.20 % Net memory used: 170.075 MB
%------------------------------------------------------------------------------