%------------------------------------------------------------------------------
% File : MaedMax---1.4
% Problem : DAT436-1 : TPTP v9.3.0. Released v9.3.0.
% Transfm : none
% Format : tptp
% Command : run_maedmax %d %s
% Computer : n013.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue May 5 06:23:44 PM UTC 2026
% Result : Unsatisfiable 36.33s 36.55s
% Output : CNFRefutation 36.33s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 20
% Syntax : Number of clauses : 69 ( 69 unt; 0 nHn; 18 RR)
% Number of literals : 69 ( 68 equ; 9 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 10 ( 3 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 17 ( 17 usr; 7 con; 0-4 aty)
% Number of variables : 104 ( 13 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(eq_0,axiom,
eq(zero,zero) = true,
file('/tmp/MaedMax_9177') ).
cnf(eq_1,axiom,
eq(zero,s(Y)) = false,
file('/tmp/MaedMax_9177') ).
cnf(eq_2,axiom,
eq(s(Y),zero) = false,
file('/tmp/MaedMax_9177') ).
cnf(eq_3,axiom,
eq(Y,X) = eq(s(Y),s(X)),
file('/tmp/MaedMax_9177') ).
cnf(eq_4,axiom,
true = le(zero,Y),
file('/tmp/MaedMax_9177') ).
cnf(eq_5,axiom,
false = le(s(Y),zero),
file('/tmp/MaedMax_9177') ).
cnf(eq_6,axiom,
le(Y,X) = le(s(Y),s(X)),
file('/tmp/MaedMax_9177') ).
cnf(eq_7,axiom,
zero = min(cons(zero,nil)),
file('/tmp/MaedMax_9177') ).
cnf(eq_8,axiom,
s(Y) = min(cons(s(Y),nil)),
file('/tmp/MaedMax_9177') ).
cnf(eq_9,axiom,
min(cons(Y,cons(X,N))) = ifmin(le(Y,X),cons(Y,cons(X,N))),
file('/tmp/MaedMax_9177') ).
cnf(eq_10,axiom,
min(cons(Y,X)) = ifmin(true,cons(Y,cons(N,X))),
file('/tmp/MaedMax_9177') ).
cnf(eq_11,axiom,
min(cons(Y,X)) = ifmin(false,cons(N,cons(Y,X))),
file('/tmp/MaedMax_9177') ).
cnf(eq_12,axiom,
replace(Y,X,cons(N,M)) = ifrepl(eq(Y,N),Y,X,cons(N,M)),
file('/tmp/MaedMax_9177') ).
cnf(eq_13,axiom,
cons(Y,X) = ifrepl(true,N,Y,cons(M,X)),
file('/tmp/MaedMax_9177') ).
cnf(eq_14,axiom,
cons(Y,replace(X,N,M)) = ifrepl(false,X,N,cons(Y,M)),
file('/tmp/MaedMax_9177') ).
cnf(eq_15,axiom,
nil = selsort(nil),
file('/tmp/MaedMax_9177') ).
cnf(eq_16,axiom,
selsort(cons(Y,X)) = ifselsort(eq(Y,min(cons(Y,X))),cons(Y,X)),
file('/tmp/MaedMax_9177') ).
cnf(eq_17,axiom,
cons(Y,selsort(X)) = ifselsort(true,cons(Y,X)),
file('/tmp/MaedMax_9177') ).
cnf(eq_18,axiom,
cons(min(cons(Y,X)),selsort(replace(min(cons(Y,X)),Y,X))) = ifselsort(false,cons(Y,X)),
file('/tmp/MaedMax_9177') ).
cnf(eq_19,negated_conjecture,
cons(zero,cons(s(zero),cons(s(s(zero)),cons(s(s(s(zero))),cons(s(s(s(s(zero)))),nil))))) != selsort(cons(s(s(s(zero))),cons(s(zero),cons(s(s(zero)),cons(s(s(s(s(zero)))),cons(zero,nil)))))),
file('/tmp/MaedMax_9177') ).
cnf(eq_20,plain,
ifmin(le(Y,X),cons(s(Y),cons(s(X),x102))) = min(cons(s(Y),cons(s(X),x102))),
inference(cp,[status(thm)],[eq_6,eq_9]) ).
cnf(eq_21,plain,
ifrepl(eq(Y,X),s(Y),x102,cons(s(X),x103)) = replace(s(Y),x102,cons(s(X),x103)),
inference(cp,[status(thm)],[eq_3,eq_12]) ).
cnf(eq_22,plain,
ifrepl(false,zero,x102,cons(s(Y),x103)) = replace(zero,x102,cons(s(Y),x103)),
inference(cp,[status(thm)],[eq_1,eq_12]) ).
cnf(eq_23,plain,
ifrepl(true,zero,x102,cons(zero,x103)) = replace(zero,x102,cons(zero,x103)),
inference(cp,[status(thm)],[eq_0,eq_12]) ).
cnf(eq_24,plain,
ifselsort(eq(s(Y),s(Y)),cons(s(Y),nil)) = selsort(cons(s(Y),nil)),
inference(cp,[status(thm)],[eq_8,eq_16]) ).
cnf(eq_25,plain,
replace(zero,Y,cons(s(X),N)) = ifrepl(false,zero,Y,cons(s(X),N)),
eq_22 ).
cnf(eq_26,plain,
selsort(cons(s(Y),nil)) = ifselsort(eq(Y,Y),cons(s(Y),nil)),
inference(rw,[status(thm)],[eq_24,eq_3]) ).
cnf(eq_27,plain,
min(cons(s(Y),cons(s(X),N))) = ifmin(le(Y,X),cons(s(Y),cons(s(X),N))),
eq_20 ).
cnf(eq_28,plain,
cons(Y,X) = replace(zero,Y,cons(zero,X)),
inference(rw,[status(thm)],[eq_23,eq_13]) ).
cnf(eq_29,plain,
replace(s(Y),X,cons(s(N),M)) = ifrepl(eq(Y,N),s(Y),X,cons(s(N),M)),
eq_21 ).
cnf(eq_30,plain,
cons(x100,nil) = ifselsort(true,cons(x100,nil)),
inference(cp,[status(thm)],[eq_15,eq_17]) ).
cnf(eq_31,plain,
ifselsort(eq(X,X),cons(s(s(X)),nil)) = selsort(cons(s(s(X)),nil)),
inference(cp,[status(thm)],[eq_3,eq_26]) ).
cnf(eq_32,plain,
selsort(cons(s(s(Y)),nil)) = ifselsort(eq(Y,Y),cons(s(s(Y)),nil)),
eq_31 ).
cnf(eq_33,plain,
cons(Y,nil) = ifselsort(true,cons(Y,nil)),
eq_30 ).
cnf(eq_34,plain,
ifselsort(eq(X,X),cons(s(s(s(X))),nil)) = selsort(cons(s(s(s(X))),nil)),
inference(cp,[status(thm)],[eq_3,eq_32]) ).
cnf(eq_35,plain,
selsort(cons(s(s(s(Y))),nil)) = ifselsort(eq(Y,Y),cons(s(s(s(Y))),nil)),
eq_34 ).
cnf(eq_36,plain,
ifselsort(eq(X,X),cons(s(s(s(s(X)))),nil)) = selsort(cons(s(s(s(s(X)))),nil)),
inference(cp,[status(thm)],[eq_3,eq_35]) ).
cnf(eq_37,plain,
selsort(cons(s(s(s(s(Y)))),nil)) = ifselsort(eq(Y,Y),cons(s(s(s(s(Y)))),nil)),
eq_36 ).
cnf(eq_38,plain,
eq(zero,zero) = le(zero,Y),
inference(rw,[status(thm)],[eq_4,eq_0]) ).
cnf(eq_39,plain,
cons(Y,selsort(X)) = ifselsort(eq(zero,zero),cons(Y,X)),
inference(rw,[status(thm)],[eq_17,eq_0]) ).
cnf(eq_40,plain,
min(cons(Y,X)) = ifmin(eq(zero,zero),cons(Y,cons(N,X))),
inference(rw,[status(thm)],[eq_10,eq_0]) ).
cnf(eq_41,plain,
ifmin(le(Y,X),cons(s(s(Y)),cons(s(s(X)),x102))) = min(cons(s(s(Y)),cons(s(s(X)),x102))),
inference(cp,[status(thm)],[eq_6,eq_27]) ).
cnf(eq_42,plain,
ifmin(true,cons(s(zero),cons(s(Y),x102))) = min(cons(s(zero),cons(s(Y),x102))),
inference(cp,[status(thm)],[eq_4,eq_27]) ).
cnf(eq_43,plain,
ifrepl(eq(Y,X),s(s(Y)),x102,cons(s(s(X)),x103)) = replace(s(s(Y)),x102,cons(s(s(X)),x103)),
inference(cp,[status(thm)],[eq_3,eq_29]) ).
cnf(eq_44,plain,
replace(s(s(Y)),X,cons(s(s(N)),M)) = ifrepl(eq(Y,N),s(s(Y)),X,cons(s(s(N)),M)),
eq_43 ).
cnf(eq_45,plain,
min(cons(s(zero),Y)) = min(cons(s(zero),cons(s(X),Y))),
inference(rw,[status(thm)],[eq_42,eq_10]) ).
cnf(eq_46,plain,
min(cons(s(s(Y)),cons(s(s(X)),N))) = ifmin(le(Y,X),cons(s(s(Y)),cons(s(s(X)),N))),
eq_41 ).
cnf(eq_47,plain,
cons(s(Y),replace(zero,X,N)) = replace(zero,X,cons(s(Y),N)),
inference(rw,[status(thm)],[eq_25,eq_14]) ).
cnf(eq_48,plain,
ifselsort(true,cons(s(s(s(s(zero)))),nil)) = selsort(cons(s(s(s(s(zero)))),nil)),
inference(cp,[status(thm)],[eq_0,eq_37]) ).
cnf(eq_49,plain,
cons(s(s(s(s(zero)))),nil) = selsort(cons(s(s(s(s(zero)))),nil)),
inference(rw,[status(thm)],[eq_48,eq_33]) ).
cnf(eq_50,plain,
ifrepl(eq(Y,X),s(s(s(Y))),x102,cons(s(s(s(X))),x103)) = replace(s(s(s(Y))),x102,cons(s(s(s(X))),x103)),
inference(cp,[status(thm)],[eq_3,eq_44]) ).
cnf(eq_51,plain,
replace(s(s(s(Y))),X,cons(s(s(s(N))),M)) = ifrepl(eq(Y,N),s(s(s(Y))),X,cons(s(s(s(N))),M)),
eq_50 ).
cnf(eq_52,plain,
ifrepl(true,s(s(s(zero))),x102,cons(s(s(s(zero))),x103)) = replace(s(s(s(zero))),x102,cons(s(s(s(zero))),x103)),
inference(cp,[status(thm)],[eq_0,eq_51]) ).
cnf(eq_53,plain,
cons(Y,X) = replace(s(s(s(zero))),Y,cons(s(s(s(zero))),X)),
inference(rw,[status(thm)],[eq_52,eq_13]) ).
cnf(eq_54,negated_conjecture,
cons(zero,cons(s(zero),cons(s(s(zero)),cons(s(s(s(zero))),cons(s(s(s(s(zero)))),nil))))) != ifselsort(false,cons(s(s(s(zero))),cons(s(zero),cons(s(s(zero)),cons(s(s(s(s(zero)))),cons(zero,nil)))))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[eq_19,eq_16]),eq_9]),eq_6]),eq_5]),eq_11]),eq_9]),eq_6]),eq_4]),eq_10]),eq_9]),eq_6]),eq_4]),eq_10]),eq_9]),eq_5]),eq_11]),eq_7]),eq_2]) ).
cnf(eq_55,negated_conjecture,
cons(zero,cons(s(zero),cons(s(s(zero)),cons(s(s(s(zero))),cons(s(s(s(s(zero)))),nil))))) != cons(zero,selsort(cons(s(zero),cons(s(s(zero)),cons(s(s(s(s(zero)))),cons(s(s(s(zero))),nil)))))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[eq_54,eq_18]),eq_9]),eq_9]),eq_6]),eq_6]),eq_5]),eq_5]),eq_11]),eq_11]),eq_9]),eq_9]),eq_6]),eq_6]),eq_4]),eq_4]),eq_10]),eq_10]),eq_9]),eq_9]),eq_6]),eq_6]),eq_4]),eq_4]),eq_10]),eq_10]),eq_9]),eq_9]),eq_5]),eq_5]),eq_11]),eq_11]),eq_7]),eq_7]),eq_47]),eq_47]),eq_47]),eq_28]) ).
cnf(eq_56,negated_conjecture,
cons(zero,cons(s(zero),cons(s(s(zero)),cons(s(s(s(zero))),cons(s(s(s(s(zero)))),nil))))) != cons(zero,ifselsort(eq(zero,zero),cons(s(zero),cons(s(s(zero)),cons(s(s(s(s(zero)))),cons(s(s(s(zero))),nil)))))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[eq_55,eq_16]),eq_45]),eq_45]),eq_45]),eq_8]),eq_3]) ).
cnf(eq_57,negated_conjecture,
cons(zero,cons(s(zero),cons(s(s(zero)),cons(s(s(s(zero))),cons(s(s(s(s(zero)))),nil))))) != cons(zero,cons(s(zero),selsort(cons(s(s(zero)),cons(s(s(s(s(zero)))),cons(s(s(s(zero))),nil)))))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[eq_56,eq_0]),eq_17]) ).
cnf(eq_58,plain,
ifmin(le(Y,X),cons(s(s(s(Y))),cons(s(s(s(X))),x102))) = min(cons(s(s(s(Y))),cons(s(s(s(X))),x102))),
inference(cp,[status(thm)],[eq_6,eq_46]) ).
cnf(eq_59,plain,
ifmin(eq(zero,zero),cons(s(s(zero)),cons(s(s(Y)),x102))) = min(cons(s(s(zero)),cons(s(s(Y)),x102))),
inference(cp,[status(thm)],[eq_38,eq_46]) ).
cnf(eq_60,plain,
min(cons(s(s(zero)),Y)) = min(cons(s(s(zero)),cons(s(s(X)),Y))),
inference(rw,[status(thm)],[eq_59,eq_40]) ).
cnf(eq_61,plain,
min(cons(s(s(s(Y))),cons(s(s(s(X))),N))) = ifmin(le(Y,X),cons(s(s(s(Y))),cons(s(s(s(X))),N))),
eq_58 ).
cnf(eq_62,plain,
ifmin(false,cons(s(s(s(s(Y)))),cons(s(s(s(zero))),x102))) = min(cons(s(s(s(s(Y)))),cons(s(s(s(zero))),x102))),
inference(cp,[status(thm)],[eq_5,eq_61]) ).
cnf(eq_63,plain,
min(cons(s(s(s(zero))),Y)) = min(cons(s(s(s(s(X)))),cons(s(s(s(zero))),Y))),
inference(rw,[status(thm)],[eq_62,eq_11]) ).
cnf(eq_64,negated_conjecture,
cons(zero,cons(s(zero),cons(s(s(zero)),cons(s(s(s(zero))),cons(s(s(s(s(zero)))),nil))))) != cons(zero,cons(s(zero),ifselsort(eq(zero,zero),cons(s(s(zero)),cons(s(s(s(s(zero)))),cons(s(s(s(zero))),nil)))))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[eq_57,eq_16]),eq_60]),eq_60]),eq_8]),eq_3]),eq_3]) ).
cnf(eq_65,negated_conjecture,
cons(zero,cons(s(zero),cons(s(s(zero)),cons(s(s(s(zero))),cons(s(s(s(s(zero)))),nil))))) != cons(zero,cons(s(zero),cons(s(s(zero)),selsort(cons(s(s(s(s(zero)))),cons(s(s(s(zero))),nil)))))),
inference(rw,[status(thm)],[eq_64,eq_39]) ).
cnf(eq_66,negated_conjecture,
cons(zero,cons(s(zero),cons(s(s(zero)),cons(s(s(s(zero))),cons(s(s(s(s(zero)))),nil))))) != cons(zero,cons(s(zero),cons(s(s(zero)),ifselsort(false,cons(s(s(s(s(zero)))),cons(s(s(s(zero))),nil)))))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[eq_65,eq_16]),eq_63]),eq_8]),eq_3]),eq_3]),eq_3]),eq_2]) ).
cnf(eq_67,negated_conjecture,
cons(zero,cons(s(zero),cons(s(s(zero)),cons(s(s(s(zero))),cons(s(s(s(s(zero)))),nil))))) != cons(zero,cons(s(zero),cons(s(s(zero)),cons(s(s(s(zero))),cons(s(s(s(s(zero)))),nil))))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[eq_66,eq_18]),eq_63]),eq_63]),eq_8]),eq_8]),eq_53]),eq_49]) ).
cnf(bot,negated_conjecture,
$false,
inference(cn,[status(thm)],[eq_67]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : DAT436-1 : TPTP v9.3.0. Released v9.3.0.
% 0.00/0.12 % Command : run_maedmax %d %s
% 0.16/0.33 % Computer : n013.cluster.edu
% 0.16/0.33 % Model : x86_64 x86_64
% 0.16/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.33 % Memory : 8042.1875MB
% 0.16/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.33 % CPULimit : 300
% 0.16/0.33 % WCLimit : 300
% 0.16/0.33 % DateTime : Mon May 4 20:56:40 EDT 2026
% 0.16/0.33 % CPUTime :
% 36.33/36.55 % SZS status Unsatisfiable
% 36.33/36.55 % SZS output start CNFRefutation for /tmp/MaedMax_9177
% See solution above
% 36.33/36.55
%------------------------------------------------------------------------------