%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : NUN135-1.006 : TPTP v9.3.1. Released v9.3.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n003.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 01:57:19 PM UTC 2026
% Result : Unsatisfiable 0.11s 0.70s
% Output : CNFRefutation 0.88s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 12
% Syntax : Number of formulae : 83 ( 83 unt; 0 def)
% Number of atoms : 83 ( 82 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 2 ( 2 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 3 avg)
% Maximal term depth : 8 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 3 con; 0-4 aty)
% Number of variables : 181 ( 181 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X] : minus(X,zero) = X,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f2,axiom,
! [X,Y] : minus(s(X),s(Y)) = minus(X,Y),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f3,axiom,
! [Y] : '<='(zero,Y) = true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f4,axiom,
! [X] : '<='(s(X),zero) = false,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f5,axiom,
! [X,Y] : '<='(s(X),s(Y)) = '<='(X,Y),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f6,axiom,
! [X,Y] : if(true,X,Y) = X,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f7,axiom,
! [X,Y] : if(false,X,Y) = Y,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f9,axiom,
! [X] : perfectp(s(X)) = f(X,s(zero),s(X),s(X)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f10,axiom,
! [Y,U] : f(zero,Y,zero,U) = true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f12,axiom,
! [X,Z,U] : f(s(X),zero,Z,U) = f(X,U,minus(Z,s(X)),U),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f13,axiom,
! [X,Y,Z,U] : f(s(X),s(Y),Z,U) = if('<='(X,Y),f(s(X),minus(Y,X),Z,U),f(X,U,Z,U)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f14,negated_conjecture,
! [X] : perfectp(X) != true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f15,plain,
! [X0] : minus(X0,zero) = X0,
inference(cnf_transformation,[status(thm)],[f1]) ).
fof(f16,plain,
! [X0,X1] : minus(s(X0),s(X1)) = minus(X0,X1),
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f17,plain,
! [X0] : '<='(zero,X0) = true,
inference(cnf_transformation,[status(thm)],[f3]) ).
fof(f18,plain,
! [X0] : '<='(s(X0),zero) = false,
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f19,plain,
! [X0,X1] : '<='(s(X0),s(X1)) = '<='(X0,X1),
inference(cnf_transformation,[status(thm)],[f5]) ).
fof(f20,plain,
! [X0,X1] : if(true,X0,X1) = X0,
inference(cnf_transformation,[status(thm)],[f6]) ).
fof(f21,plain,
! [X0,X1] : if(false,X0,X1) = X1,
inference(cnf_transformation,[status(thm)],[f7]) ).
fof(f23,plain,
! [X0] : perfectp(s(X0)) = f(X0,s(zero),s(X0),s(X0)),
inference(cnf_transformation,[status(thm)],[f9]) ).
fof(f24,plain,
! [X0,X1] : f(zero,X0,zero,X1) = true,
inference(cnf_transformation,[status(thm)],[f10]) ).
fof(f26,plain,
! [X0,X1,X2] : f(s(X0),zero,X1,X2) = f(X0,X2,minus(X1,s(X0)),X2),
inference(cnf_transformation,[status(thm)],[f12]) ).
fof(f27,plain,
! [X0,X1,X2,X3] : f(s(X0),s(X1),X2,X3) = if('<='(X0,X1),f(s(X0),minus(X1,X0),X2,X3),f(X0,X3,X2,X3)),
inference(cnf_transformation,[status(thm)],[f13]) ).
fof(f28,plain,
! [X0] : perfectp(X0) != true,
inference(cnf_transformation,[status(thm)],[f14]) ).
fof(f33,plain,
! [X0,X1,X2] : f(s(X0),zero,s(X1),X2) = f(X0,X2,minus(X1,X0),X2),
inference(paramodulation,[status(thm)],[f16,f26]) ).
fof(f34,plain,
! [X0,X1,X2] : f(s(s(X0)),zero,s(s(X1)),X2) = f(s(X0),X2,minus(X1,X0),X2),
inference(paramodulation,[status(thm)],[f16,f33]) ).
fof(f35,plain,
! [X0,X1] : f(s(zero),zero,s(X0),X1) = f(zero,X1,X0,X1),
inference(paramodulation,[status(thm)],[f15,f33]) ).
fof(f38,plain,
! [X0] : f(s(zero),zero,s(zero),X0) = true,
inference(paramodulation,[status(thm)],[f24,f35]) ).
fof(f58,plain,
! [X0,X1,X2] : f(s(s(s(X0))),zero,s(s(s(X1))),X2) = f(s(s(X0)),X2,minus(X1,X0),X2),
inference(paramodulation,[status(thm)],[f16,f34]) ).
fof(f59,plain,
! [X0,X1] : f(s(s(zero)),zero,s(s(X0)),X1) = f(s(zero),X1,X0,X1),
inference(paramodulation,[status(thm)],[f15,f34]) ).
fof(f77,plain,
! [X0,X1] : f(s(s(s(zero))),zero,s(s(s(X0))),X1) = f(s(s(zero)),X1,X0,X1),
inference(paramodulation,[status(thm)],[f15,f58]) ).
fof(f93,plain,
! [X0,X1,X2,X3] : f(s(s(X0)),s(s(X1)),X2,X3) = if('<='(X0,X1),f(s(s(X0)),minus(s(X1),s(X0)),X2,X3),f(s(X0),X3,X2,X3)),
inference(paramodulation,[status(thm)],[f19,f27]) ).
fof(f94,plain,
! [X0,X1,X2] : f(s(s(X0)),s(zero),X1,X2) = if(false,f(s(s(X0)),minus(zero,s(X0)),X1,X2),f(s(X0),X2,X1,X2)),
inference(paramodulation,[status(thm)],[f18,f27]) ).
fof(f95,plain,
! [X0,X1,X2] : f(s(zero),s(X0),X1,X2) = if(true,f(s(zero),minus(X0,zero),X1,X2),f(zero,X2,X1,X2)),
inference(paramodulation,[status(thm)],[f17,f27]) ).
fof(f123,plain,
! [X0,X1,X2,X3] : f(s(s(X0)),s(s(X1)),X2,X3) = if('<='(X0,X1),f(s(s(X0)),minus(X1,X0),X2,X3),f(s(X0),X3,X2,X3)),
inference(forward_demodulation,[status(thm)],[f16,f93]) ).
fof(f124,plain,
! [X0,X1,X2] : f(s(s(X0)),s(zero),X1,X2) = f(s(X0),X2,X1,X2),
inference(forward_demodulation,[status(thm)],[f21,f94]) ).
fof(f125,plain,
! [X0,X1,X2] : f(s(zero),s(X0),X1,X2) = f(s(zero),minus(X0,zero),X1,X2),
inference(forward_demodulation,[status(thm)],[f20,f95]) ).
fof(f126,plain,
! [X0,X1,X2] : f(s(zero),s(X0),X1,X2) = f(s(zero),X0,X1,X2),
inference(forward_demodulation,[status(thm)],[f15,f125]) ).
fof(f167,plain,
! [X0,X1] : f(s(s(s(zero))),s(zero),X0,X1) = f(s(s(s(zero))),zero,s(s(s(X0))),X1),
inference(paramodulation,[status(thm)],[f77,f124]) ).
fof(f169,plain,
! [X0,X1] : f(s(s(zero)),s(zero),X0,s(X1)) = f(s(zero),X1,X0,s(X1)),
inference(paramodulation,[status(thm)],[f126,f124]) ).
fof(f170,plain,
! [X0,X1] : f(s(s(zero)),s(zero),X0,X1) = f(s(s(zero)),zero,s(s(X0)),X1),
inference(paramodulation,[status(thm)],[f59,f124]) ).
fof(f354,plain,
! [X0,X1,X2,X3] : f(s(s(s(X0))),s(s(s(X1))),X2,X3) = if('<='(X0,X1),f(s(s(s(X0))),minus(s(X1),s(X0)),X2,X3),f(s(s(X0)),X3,X2,X3)),
inference(paramodulation,[status(thm)],[f19,f123]) ).
fof(f355,plain,
! [X0,X1,X2] : f(s(s(s(X0))),s(s(zero)),X1,X2) = if(false,f(s(s(s(X0))),minus(zero,s(X0)),X1,X2),f(s(s(X0)),X2,X1,X2)),
inference(paramodulation,[status(thm)],[f18,f123]) ).
fof(f356,plain,
! [X0,X1,X2] : f(s(s(zero)),s(s(X0)),X1,X2) = if(true,f(s(s(zero)),minus(X0,zero),X1,X2),f(s(zero),X2,X1,X2)),
inference(paramodulation,[status(thm)],[f17,f123]) ).
fof(f383,plain,
! [X0,X1,X2,X3] : f(s(s(s(X0))),s(s(s(X1))),X2,X3) = if('<='(X0,X1),f(s(s(s(X0))),minus(X1,X0),X2,X3),f(s(s(X0)),X3,X2,X3)),
inference(forward_demodulation,[status(thm)],[f16,f354]) ).
fof(f384,plain,
! [X0,X1,X2] : f(s(s(s(X0))),s(s(zero)),X1,X2) = f(s(s(X0)),X2,X1,X2),
inference(forward_demodulation,[status(thm)],[f21,f355]) ).
fof(f385,plain,
! [X0,X1,X2] : f(s(s(zero)),s(s(X0)),X1,X2) = f(s(s(zero)),minus(X0,zero),X1,X2),
inference(forward_demodulation,[status(thm)],[f20,f356]) ).
fof(f386,plain,
! [X0,X1,X2] : f(s(s(zero)),s(s(X0)),X1,X2) = f(s(s(zero)),X0,X1,X2),
inference(forward_demodulation,[status(thm)],[f15,f385]) ).
fof(f416,plain,
! [X0,X1] : f(s(s(zero)),X0,X1,s(s(X0))) = f(s(s(s(zero))),s(zero),X1,s(s(X0))),
inference(paramodulation,[status(thm)],[f124,f386]) ).
fof(f422,plain,
! [X0,X1,X2] : f(s(s(s(zero))),s(s(X0)),X1,s(s(X2))) = if('<='(s(zero),X0),f(s(s(s(zero))),minus(X0,s(zero)),X1,s(s(X2))),f(s(s(zero)),X2,X1,s(s(X2)))),
inference(paramodulation,[status(thm)],[f386,f123]) ).
fof(f435,plain,
! [X0,X1] : f(s(s(zero)),s(zero),X0,s(s(X1))) = f(s(zero),X1,X0,s(s(X1))),
inference(paramodulation,[status(thm)],[f126,f169]) ).
fof(f496,plain,
! [X0,X1] : f(s(s(zero)),s(zero),X0,s(s(s(X1)))) = f(s(zero),X1,X0,s(s(s(X1)))),
inference(paramodulation,[status(thm)],[f126,f435]) ).
fof(f542,plain,
! [X0,X1,X2] : f(s(s(s(X0))),s(s(zero)),X1,X2) = f(s(s(s(X0))),s(zero),X1,X2),
inference(paramodulation,[status(thm)],[f124,f384]) ).
fof(f1026,plain,
! [X0,X1] : f(s(s(s(zero))),s(zero),X0,s(s(s(s(X1))))) = f(s(s(zero)),X1,X0,s(s(s(s(X1))))),
inference(paramodulation,[status(thm)],[f386,f416]) ).
fof(f1063,plain,
! [X0,X1] : f(s(s(zero)),s(zero),X0,s(s(s(s(X1))))) = f(s(zero),X1,X0,s(s(s(s(X1))))),
inference(paramodulation,[status(thm)],[f126,f496]) ).
fof(f1511,plain,
! [X0,X1] : f(s(s(zero)),s(zero),X0,s(s(s(s(s(X1)))))) = f(s(zero),X1,X0,s(s(s(s(s(X1)))))),
inference(paramodulation,[status(thm)],[f126,f1063]) ).
fof(f2250,plain,
! [X0,X1] : f(s(s(s(zero))),s(zero),X0,s(s(s(s(s(s(X1))))))) = f(s(s(zero)),X1,X0,s(s(s(s(s(s(X1))))))),
inference(paramodulation,[status(thm)],[f386,f1026]) ).
fof(f2311,plain,
! [X0,X1] : f(s(s(zero)),s(zero),X0,s(s(s(s(s(s(X1))))))) = f(s(zero),X1,X0,s(s(s(s(s(s(X1))))))),
inference(paramodulation,[status(thm)],[f126,f1511]) ).
fof(f3803,plain,
! [X0,X1,X2] : f(s(s(s(zero))),s(s(s(X0))),X1,s(s(X2))) = if('<='(zero,X0),f(s(s(s(zero))),minus(s(X0),s(zero)),X1,s(s(X2))),f(s(s(zero)),X2,X1,s(s(X2)))),
inference(paramodulation,[status(thm)],[f19,f422]) ).
fof(f3819,plain,
! [X0,X1,X2] : f(s(s(s(zero))),s(s(s(X0))),X1,s(s(X2))) = if(true,f(s(s(s(zero))),minus(s(X0),s(zero)),X1,s(s(X2))),f(s(s(zero)),X2,X1,s(s(X2)))),
inference(forward_demodulation,[status(thm)],[f17,f3803]) ).
fof(f3820,plain,
! [X0,X1,X2] : f(s(s(s(zero))),s(s(s(X0))),X1,s(s(X2))) = f(s(s(s(zero))),minus(s(X0),s(zero)),X1,s(s(X2))),
inference(forward_demodulation,[status(thm)],[f20,f3819]) ).
fof(f3821,plain,
! [X0,X1,X2] : f(s(s(s(zero))),s(s(s(X0))),X1,s(s(X2))) = f(s(s(s(zero))),minus(X0,zero),X1,s(s(X2))),
inference(forward_demodulation,[status(thm)],[f16,f3820]) ).
fof(f3822,plain,
! [X0,X1,X2] : f(s(s(s(zero))),s(s(s(X0))),X1,s(s(X2))) = f(s(s(s(zero))),X0,X1,s(s(X2))),
inference(forward_demodulation,[status(thm)],[f15,f3821]) ).
fof(f3839,plain,
! [X0,X1] : f(s(s(s(zero))),X0,X1,s(s(s(X0)))) = f(s(s(s(s(zero)))),s(zero),X1,s(s(s(X0)))),
inference(paramodulation,[status(thm)],[f124,f3822]) ).
fof(f3948,plain,
! [X0,X1,X2,X3] : f(s(s(s(s(X0)))),s(s(s(s(X1)))),X2,X3) = if('<='(X0,X1),f(s(s(s(s(X0)))),minus(s(X1),s(X0)),X2,X3),f(s(s(s(X0))),X3,X2,X3)),
inference(paramodulation,[status(thm)],[f19,f383]) ).
fof(f3950,plain,
! [X0,X1,X2] : f(s(s(s(zero))),s(s(s(X0))),X1,X2) = if(true,f(s(s(s(zero))),minus(X0,zero),X1,X2),f(s(s(zero)),X2,X1,X2)),
inference(paramodulation,[status(thm)],[f17,f383]) ).
fof(f3989,plain,
! [X0,X1,X2,X3] : f(s(s(s(s(X0)))),s(s(s(s(X1)))),X2,X3) = if('<='(X0,X1),f(s(s(s(s(X0)))),minus(X1,X0),X2,X3),f(s(s(s(X0))),X3,X2,X3)),
inference(forward_demodulation,[status(thm)],[f16,f3948]) ).
fof(f3991,plain,
! [X0,X1,X2] : f(s(s(s(zero))),s(s(s(X0))),X1,X2) = f(s(s(s(zero))),minus(X0,zero),X1,X2),
inference(forward_demodulation,[status(thm)],[f20,f3950]) ).
fof(f3992,plain,
! [X0,X1,X2] : f(s(s(s(zero))),s(s(s(X0))),X1,X2) = f(s(s(s(zero))),X0,X1,X2),
inference(forward_demodulation,[status(thm)],[f15,f3991]) ).
fof(f4014,plain,
! [X0,X1] : f(s(s(s(zero))),X0,X1,s(s(s(s(s(s(X0))))))) = f(s(s(s(s(zero)))),s(zero),X1,s(s(s(s(s(s(X0))))))),
inference(paramodulation,[status(thm)],[f3839,f3992]) ).
fof(f8994,plain,
! [X0,X1,X2] : f(s(s(s(s(zero)))),s(s(s(s(X0)))),X1,X2) = if(true,f(s(s(s(s(zero)))),minus(X0,zero),X1,X2),f(s(s(s(zero))),X2,X1,X2)),
inference(paramodulation,[status(thm)],[f17,f3989]) ).
fof(f9045,plain,
! [X0,X1,X2] : f(s(s(s(s(zero)))),s(s(s(s(X0)))),X1,X2) = f(s(s(s(s(zero)))),minus(X0,zero),X1,X2),
inference(forward_demodulation,[status(thm)],[f20,f8994]) ).
fof(f9046,plain,
! [X0,X1,X2] : f(s(s(s(s(zero)))),s(s(s(s(X0)))),X1,X2) = f(s(s(s(s(zero)))),X0,X1,X2),
inference(forward_demodulation,[status(thm)],[f15,f9045]) ).
fof(f9073,plain,
! [X0,X1] : f(s(s(s(s(zero)))),X0,X1,s(s(s(s(X0))))) = f(s(s(s(s(s(zero))))),s(zero),X1,s(s(s(s(X0))))),
inference(paramodulation,[status(thm)],[f124,f9046]) ).
fof(f9195,plain,
f(s(s(s(s(zero)))),s(s(zero)),s(s(s(s(s(s(zero)))))),s(s(s(s(s(s(zero))))))) = perfectp(s(s(s(s(s(s(zero))))))),
inference(paramodulation,[status(thm)],[f23,f9073]) ).
fof(f9222,plain,
f(s(s(s(s(zero)))),s(zero),s(s(s(s(s(s(zero)))))),s(s(s(s(s(s(zero))))))) = perfectp(s(s(s(s(s(s(zero))))))),
inference(forward_demodulation,[status(thm)],[f542,f9195]) ).
fof(f10073,plain,
f(s(s(s(zero))),zero,s(s(s(s(s(s(zero)))))),s(s(s(s(s(s(zero))))))) = perfectp(s(s(s(s(s(s(zero))))))),
inference(forward_demodulation,[status(thm)],[f4014,f9222]) ).
fof(f10074,plain,
f(s(s(s(zero))),s(zero),s(s(s(zero))),s(s(s(s(s(s(zero))))))) = perfectp(s(s(s(s(s(s(zero))))))),
inference(forward_demodulation,[status(thm)],[f167,f10073]) ).
fof(f10075,plain,
f(s(s(zero)),zero,s(s(s(zero))),s(s(s(s(s(s(zero))))))) = perfectp(s(s(s(s(s(s(zero))))))),
inference(forward_demodulation,[status(thm)],[f2250,f10074]) ).
fof(f10076,plain,
f(s(s(zero)),s(zero),s(zero),s(s(s(s(s(s(zero))))))) = perfectp(s(s(s(s(s(s(zero))))))),
inference(forward_demodulation,[status(thm)],[f170,f10075]) ).
fof(f10077,plain,
f(s(zero),zero,s(zero),s(s(s(s(s(s(zero))))))) = perfectp(s(s(s(s(s(s(zero))))))),
inference(forward_demodulation,[status(thm)],[f2311,f10076]) ).
fof(f10078,plain,
true = perfectp(s(s(s(s(s(s(zero))))))),
inference(forward_demodulation,[status(thm)],[f38,f10077]) ).
fof(f10079,plain,
$false,
inference(resolution,[status(thm)],[f10078,f28]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUN135-1.006 : TPTP v9.3.1. Released v9.3.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.11/0.38 % Computer : n003.cluster.edu
% 0.11/0.38 % Model : x86_64 x86_64
% 0.11/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.38 % Memory : 8046.5625MB
% 0.11/0.38 % OS : Linux 6.8.0-71-generic
% 0.11/0.38 % CPULimit : 300
% 0.11/0.38 % WCLimit : 300
% 0.11/0.38 % DateTime : Mon Sep 21 03:30:30 UTC 2026
% 0.11/0.38 % CPUTime :
% 0.11/0.39 % Drodi V4.1.1
% 0.11/0.70 % Refutation found
% 0.11/0.70 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.11/0.70 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.88/0.72 % Elapsed time: 0.335933 seconds
% 0.88/0.72 % CPU time: 2.387868 seconds
% 0.88/0.72 % Total memory used: 54.005 MB
% 0.88/0.72 % Net memory used: 53.154 MB
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