%------------------------------------------------------------------------------
% File : EQP---0.9e
% Problem : SWX217-1 : TPTP v9.3.0. Released v9.3.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_eqp %s
% Computer : n012.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 07:00:11 PM UTC 2026
% Result : Unsatisfiable 0.63s 1.08s
% Output : Refutation 0.63s
% Verified :
% SZS Type : ERROR: Analysing output (Cycle in a tree)
% Comments :
%------------------------------------------------------------------------------
cnf(1,plain,
equal(cons(o,shw(half(suc(A)))),aux(A,btrue)),
inference(flip,[status(thm),theory(equality)],[1]),
[iquote('flip(1)')] ).
cnf(2,plain,
equal(cons(i,shw(half(suc(A)))),aux(A,bfalse)),
inference(flip,[status(thm),theory(equality)],[1]),
[iquote('flip(1)')] ).
cnf(3,plain,
equal(notb(btrue),bfalse),
file('SWX217-1.p',unknown),
[] ).
cnf(4,plain,
equal(notb(bfalse),btrue),
file('SWX217-1.p',unknown),
[] ).
cnf(5,plain,
equal(half(zero),zero),
file('SWX217-1.p',unknown),
[] ).
cnf(6,plain,
equal(half(suc(zero)),zero),
file('SWX217-1.p',unknown),
[] ).
cnf(7,plain,
equal(half(suc(suc(A))),suc(half(A))),
file('SWX217-1.p',unknown),
[] ).
cnf(8,plain,
equal(evenNat(zero),btrue),
file('SWX217-1.p',unknown),
[] ).
cnf(9,plain,
equal(evenNat(suc(A)),notb(evenNat(A))),
file('SWX217-1.p',unknown),
[] ).
cnf(10,plain,
equal(shw(zero),nil),
file('SWX217-1.p',unknown),
[] ).
cnf(11,plain,
equal(shw(suc(A)),aux(A,notb(evenNat(A)))),
inference(demod,[status(thm),theory(equality)],[9]),
[iquote('demod([9])')] ).
cnf(12,plain,
equal(append(nil,A),A),
file('SWX217-1.p',unknown),
[] ).
cnf(13,plain,
equal(cons(A,append(B,C)),append(cons(A,B),C)),
inference(flip,[status(thm),theory(equality)],[1]),
[iquote('flip(1)')] ).
cnf(14,plain,
equal(addNat(zero,A),A),
file('SWX217-1.p',unknown),
[] ).
cnf(15,plain,
equal(suc(addNat(A,B)),addNat(suc(A),B)),
inference(flip,[status(thm),theory(equality)],[1]),
[iquote('flip(1)')] ).
cnf(16,plain,
equal(double(A),addNat(A,A)),
file('SWX217-1.p',unknown),
[] ).
cnf(17,plain,
equal(rd(nil),zero),
file('SWX217-1.p',unknown),
[] ).
cnf(18,plain,
equal(addNat(suc(rd(A)),rd(A)),rd(cons(i,A))),
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[16,15]),1]),
[iquote('demod([16,15]),flip(1)')] ).
cnf(19,plain,
equal(rd(cons(o,A)),addNat(rd(A),rd(A))),
inference(demod,[status(thm),theory(equality)],[16]),
[iquote('demod([16])')] ).
cnf(20,plain,
equal(rd(append(shw(A),shw(B))),x(A,B)),
inference(flip,[status(thm),theory(equality)],[1]),
[iquote('flip(1)')] ).
cnf(21,plain,
equal(eq(x(A,B),x(B,A)),sat_comm(A,B)),
inference(flip,[status(thm),theory(equality)],[1]),
[iquote('flip(1)')] ).
cnf(26,plain,
equal(eq(suc(A),suc(B)),eq(A,B)),
file('SWX217-1.p',unknown),
[] ).
cnf(27,plain,
equal(eq(zero,suc(A)),bfalse),
file('SWX217-1.p',unknown),
[] ).
cnf(30,plain,
equal(eq2(A,A),btrue),
file('SWX217-1.p',unknown),
[] ).
cnf(32,plain,
~ equal(eq2(sat_comm(A,B),bfalse),btrue),
file('SWX217-1.p',unknown),
[] ).
cnf(33,plain,
equal(cons(o,nil),aux(zero,btrue)),
inference(demod,[status(thm),theory(equality)],[inference(para,[status(thm),theory(equality)],[6,1]),10]),
[iquote('para(6,1),demod([10])')] ).
cnf(34,plain,
equal(cons(i,nil),aux(zero,bfalse)),
inference(demod,[status(thm),theory(equality)],[inference(para,[status(thm),theory(equality)],[6,2]),10]),
[iquote('para(6,2),demod([10])')] ).
cnf(35,plain,
equal(aux(suc(A),btrue),cons(o,aux(half(A),notb(evenNat(half(A)))))),
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(para,[status(thm),theory(equality)],[7,1]),11]),1]),
[iquote('para(7,1),demod([11]),flip(1)')] ).
cnf(37,plain,
equal(cons(A,B),append(cons(A,nil),B)),
inference(para,[status(thm),theory(equality)],[12,13]),
[iquote('para(12,13)')] ).
cnf(38,plain,
equal(append(cons(A,nil),B),cons(A,B)),
inference(flip,[status(thm),theory(equality)],[37]),
[iquote('flip(37)')] ).
cnf(46,plain,
equal(suc(A),addNat(suc(zero),A)),
inference(para,[status(thm),theory(equality)],[14,15]),
[iquote('para(14,15)')] ).
cnf(47,plain,
equal(addNat(suc(zero),A),suc(A)),
inference(flip,[status(thm),theory(equality)],[46]),
[iquote('flip(46)')] ).
cnf(49,plain,
equal(eq(zero,addNat(suc(zero),A)),bfalse),
inference(para,[status(thm),theory(equality)],[46,27]),
[iquote('para(46,27)')] ).
cnf(51,plain,
equal(evenNat(addNat(suc(zero),A)),notb(evenNat(A))),
inference(para,[status(thm),theory(equality)],[46,9]),
[iquote('para(46,9)')] ).
cnf(52,plain,
equal(notb(evenNat(A)),evenNat(addNat(suc(zero),A))),
inference(flip,[status(thm),theory(equality)],[51]),
[iquote('flip(51)')] ).
cnf(54,plain,
equal(evenNat(addNat(suc(zero),zero)),bfalse),
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(para,[status(thm),theory(equality)],[8,52]),3]),1]),
[iquote('para(8,52),demod([3]),flip(1)')] ).
cnf(55,plain,
equal(addNat(suc(zero),zero),rd(aux(zero,bfalse))),
inference(demod,[status(thm),theory(equality)],[inference(para,[status(thm),theory(equality)],[17,18]),17,34]),
[iquote('para(17,18),demod([17,34])')] ).
cnf(56,plain,
equal(evenNat(rd(aux(zero,bfalse))),bfalse),
inference(demod,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[54]),55]),
[iquote('back_demod(54),demod([55])')] ).
cnf(59,plain,
equal(suc(A),addNat(rd(aux(zero,bfalse)),A)),
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(para,[status(thm),theory(equality)],[46,47]),55]),1]),
[iquote('para(46,47),demod([55]),flip(1)')] ).
cnf(61,plain,
equal(addNat(addNat(rd(aux(zero,bfalse)),zero),zero),rd(aux(zero,bfalse))),
inference(demod,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[55]),59]),
[iquote('back_demod(55),demod([59])')] ).
cnf(66,plain,
equal(eq(zero,addNat(addNat(rd(aux(zero,bfalse)),zero),A)),bfalse),
inference(demod,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[49]),59]),
[iquote('back_demod(49),demod([59])')] ).
cnf(67,plain,
equal(addNat(addNat(rd(aux(zero,bfalse)),zero),A),addNat(rd(aux(zero,bfalse)),A)),
inference(demod,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[47]),59,59]),
[iquote('back_demod(47),demod([59,59])')] ).
cnf(68,plain,
equal(eq(zero,addNat(rd(aux(zero,bfalse)),A)),bfalse),
inference(demod,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[66]),67]),
[iquote('back_demod(66),demod([67])')] ).
cnf(72,plain,
equal(addNat(rd(aux(zero,bfalse)),zero),rd(aux(zero,bfalse))),
inference(demod,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[61]),67]),
[iquote('back_demod(61),demod([67])')] ).
cnf(81,plain,
equal(aux(addNat(rd(aux(zero,bfalse)),A),btrue),cons(o,aux(half(A),notb(evenNat(half(A)))))),
inference(demod,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[35]),59]),
[iquote('back_demod(35),demod([59])')] ).
cnf(82,plain,
equal(cons(o,aux(half(A),notb(evenNat(half(A))))),aux(addNat(rd(aux(zero,bfalse)),A),btrue)),
inference(flip,[status(thm),theory(equality)],[81]),
[iquote('flip(81)')] ).
cnf(83,plain,
equal(eq(addNat(rd(aux(zero,bfalse)),A),addNat(rd(aux(zero,bfalse)),B)),eq(A,B)),
inference(demod,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[26]),59,59]),
[iquote('back_demod(26),demod([59,59])')] ).
cnf(84,plain,
equal(rd(cons(i,A)),addNat(addNat(rd(aux(zero,bfalse)),rd(A)),rd(A))),
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[18]),59]),1]),
[iquote('back_demod(18),demod([59]),flip(1)')] ).
cnf(86,plain,
equal(addNat(addNat(rd(aux(zero,bfalse)),A),B),addNat(rd(aux(zero,bfalse)),addNat(A,B))),
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[15]),59,59]),1]),
[iquote('back_demod(15),demod([59,59]),flip(1)')] ).
cnf(87,plain,
equal(rd(cons(i,A)),addNat(rd(aux(zero,bfalse)),addNat(rd(A),rd(A)))),
inference(demod,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[84]),86]),
[iquote('back_demod(84),demod([86])')] ).
cnf(92,plain,
equal(shw(addNat(rd(aux(zero,bfalse)),A)),aux(A,notb(evenNat(A)))),
inference(demod,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[11]),59]),
[iquote('back_demod(11),demod([59])')] ).
cnf(94,plain,
equal(cons(i,shw(half(addNat(rd(aux(zero,bfalse)),A)))),aux(A,bfalse)),
inference(demod,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[2]),59]),
[iquote('back_demod(2),demod([59])')] ).
cnf(97,plain,
equal(rd(shw(A)),x(zero,A)),
inference(demod,[status(thm),theory(equality)],[inference(para,[status(thm),theory(equality)],[10,20]),12]),
[iquote('para(10,20),demod([12])')] ).
cnf(107,plain,
equal(rd(append(aux(zero,btrue),A)),addNat(rd(A),rd(A))),
inference(demod,[status(thm),theory(equality)],[inference(para,[status(thm),theory(equality)],[37,19]),33]),
[iquote('para(37,19),demod([33])')] ).
cnf(112,plain,
equal(cons(o,A),append(aux(zero,btrue),A)),
inference(flip,[status(thm),theory(equality)],[inference(para,[status(thm),theory(equality)],[33,38]),1]),
[iquote('para(33,38),flip(1)')] ).
cnf(115,plain,
equal(append(aux(zero,btrue),aux(half(A),notb(evenNat(half(A))))),aux(addNat(rd(aux(zero,bfalse)),A),btrue)),
inference(demod,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[82]),112]),
[iquote('back_demod(82),demod([112])')] ).
cnf(117,plain,
equal(cons(i,A),append(aux(zero,bfalse),A)),
inference(flip,[status(thm),theory(equality)],[inference(para,[status(thm),theory(equality)],[34,38]),1]),
[iquote('para(34,38),flip(1)')] ).
cnf(118,plain,
equal(append(aux(zero,bfalse),shw(half(addNat(rd(aux(zero,bfalse)),A)))),aux(A,bfalse)),
inference(demod,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[94]),117]),
[iquote('back_demod(94),demod([117])')] ).
cnf(119,plain,
equal(rd(append(aux(zero,bfalse),A)),addNat(rd(aux(zero,bfalse)),addNat(rd(A),rd(A)))),
inference(demod,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[87]),117]),
[iquote('back_demod(87),demod([117])')] ).
cnf(129,plain,
equal(eq(rd(aux(zero,bfalse)),addNat(rd(aux(zero,bfalse)),A)),eq(zero,A)),
inference(para,[status(thm),theory(equality)],[72,83]),
[iquote('para(72,83)')] ).
cnf(135,plain,
equal(rd(append(aux(A,notb(evenNat(A))),shw(B))),x(addNat(rd(aux(zero,bfalse)),A),B)),
inference(para,[status(thm),theory(equality)],[92,20]),
[iquote('para(92,20)')] ).
cnf(137,plain,
equal(append(append(aux(zero,btrue),A),B),append(aux(zero,btrue),append(A,B))),
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(para,[status(thm),theory(equality)],[112,13]),112]),1]),
[iquote('para(112,13),demod([112]),flip(1)')] ).
cnf(139,plain,
equal(shw(rd(aux(zero,bfalse))),aux(zero,bfalse)),
inference(demod,[status(thm),theory(equality)],[inference(para,[status(thm),theory(equality)],[72,92]),8,3]),
[iquote('para(72,92),demod([8,3])')] ).
cnf(140,plain,
equal(x(zero,rd(aux(zero,bfalse))),rd(aux(zero,bfalse))),
inference(flip,[status(thm),theory(equality)],[inference(para,[status(thm),theory(equality)],[139,97]),1]),
[iquote('para(139,97),flip(1)')] ).
cnf(142,plain,
equal(x(rd(aux(zero,bfalse)),A),addNat(rd(aux(zero,bfalse)),addNat(x(zero,A),x(zero,A)))),
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(para,[status(thm),theory(equality)],[139,20]),119,97,97]),1]),
[iquote('para(139,20),demod([119,97,97]),flip(1)')] ).
cnf(144,plain,
equal(rd(aux(A,notb(evenNat(A)))),x(zero,addNat(rd(aux(zero,bfalse)),A))),
inference(para,[status(thm),theory(equality)],[92,97]),
[iquote('para(92,97)')] ).
cnf(165,plain,
equal(rd(aux(rd(aux(zero,bfalse)),btrue)),x(zero,addNat(rd(aux(zero,bfalse)),rd(aux(zero,bfalse))))),
inference(demod,[status(thm),theory(equality)],[inference(para,[status(thm),theory(equality)],[56,144]),4]),
[iquote('para(56,144),demod([4])')] ).
cnf(175,plain,
equal(aux(rd(aux(zero,bfalse)),btrue),append(aux(zero,btrue),aux(zero,bfalse))),
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(para,[status(thm),theory(equality)],[5,115]),5,8,3,72]),1]),
[iquote('para(5,115),demod([5,8,3,72]),flip(1)')] ).
cnf(176,plain,
equal(x(zero,addNat(rd(aux(zero,bfalse)),rd(aux(zero,bfalse)))),addNat(rd(aux(zero,bfalse)),rd(aux(zero,bfalse)))),
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[165]),175,107]),1]),
[iquote('back_demod(165),demod([175,107]),flip(1)')] ).
cnf(192,plain,
equal(rd(aux(A,bfalse)),addNat(rd(aux(zero,bfalse)),addNat(x(zero,half(addNat(rd(aux(zero,bfalse)),A))),x(zero,half(addNat(rd(aux(zero,bfalse)),A)))))),
inference(demod,[status(thm),theory(equality)],[inference(para,[status(thm),theory(equality)],[118,119]),97,97]),
[iquote('para(118,119),demod([97,97])')] ).
cnf(193,plain,
equal(addNat(rd(aux(zero,bfalse)),addNat(x(zero,half(addNat(rd(aux(zero,bfalse)),A))),x(zero,half(addNat(rd(aux(zero,bfalse)),A))))),rd(aux(A,bfalse))),
inference(flip,[status(thm),theory(equality)],[192]),
[iquote('flip(192)')] ).
cnf(198,plain,
equal(x(addNat(rd(aux(zero,bfalse)),rd(aux(zero,bfalse))),A),addNat(rd(aux(zero,bfalse)),addNat(addNat(x(zero,A),x(zero,A)),addNat(rd(aux(zero,bfalse)),addNat(x(zero,A),x(zero,A)))))),
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(para,[status(thm),theory(equality)],[56,135]),4,175,137,107,119,97,97,119,97,97,86]),1]),
[iquote('para(56,135),demod([4,175,137,107,119,97,97,119,97,97,86]),flip(1)')] ).
cnf(256,plain,
equal(eq(addNat(rd(aux(zero,bfalse)),addNat(x(zero,A),x(zero,A))),x(A,rd(aux(zero,bfalse)))),sat_comm(rd(aux(zero,bfalse)),A)),
inference(para,[status(thm),theory(equality)],[142,21]),
[iquote('para(142,21)')] ).
cnf(450,plain,
equal(eq(zero,rd(aux(A,bfalse))),bfalse),
inference(para,[status(thm),theory(equality)],[193,68]),
[iquote('para(193,68)')] ).
cnf(1228,plain,
equal(sat_comm(rd(aux(zero,bfalse)),addNat(rd(aux(zero,bfalse)),rd(aux(zero,bfalse)))),bfalse),
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(para,[status(thm),theory(equality)],[176,256]),176,86,198,140,140,140,140,86,83,83,83,83,129,450]),1]),
[iquote('para(176,256),demod([176,86,198,140,140,140,140,86,83,83,83,83,129,450]),flip(1)')] ).
cnf(1229,plain,
~ equal(btrue,btrue),
inference(demod,[status(thm),theory(equality)],[inference(para,[status(thm),theory(equality)],[1228,32]),30]),
[iquote('para(1228,32),demod([30])')] ).
cnf(1230,plain,
$false,
inference(conflict,[status(thm)],[1229]),
[iquote('xx_conflict(1229)')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.06 % Problem : SWX217-1 : TPTP v9.3.0. Released v9.3.0.
% 0.00/0.07 % Command : tptp2X_and_run_eqp %s
% 0.07/0.25 % Computer : n012.cluster.edu
% 0.07/0.25 % Model : x86_64 x86_64
% 0.07/0.25 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.25 % Memory : 8042.1875MB
% 0.07/0.25 % OS : Linux 3.10.0-693.el7.x86_64
% 0.07/0.25 % CPULimit : 300
% 0.07/0.25 % WCLimit : 300
% 0.07/0.25 % DateTime : Tue May 5 12:15:30 EDT 2026
% 0.07/0.25 % CPUTime :
% 0.38/0.79 ----- EQP 0.9e, May 2009 -----
% 0.38/0.79 The job began on n012.cluster.edu, Tue May 5 12:15:31 2026
% 0.38/0.79 The command was "./eqp09e".
% 0.38/0.79
% 0.38/0.79 set(prolog_style_variables).
% 0.38/0.79 set(lrpo).
% 0.38/0.79 set(basic_paramod).
% 0.38/0.79 set(functional_subsume).
% 0.38/0.79 set(ordered_paramod).
% 0.38/0.79 set(prime_paramod).
% 0.38/0.79 set(para_pairs).
% 0.38/0.79 assign(pick_given_ratio,4).
% 0.38/0.79 clear(print_kept).
% 0.38/0.79 clear(print_new_demod).
% 0.38/0.79 clear(print_back_demod).
% 0.38/0.79 clear(print_given).
% 0.38/0.79 assign(max_mem,64000).
% 0.38/0.79 end_of_commands.
% 0.38/0.79
% 0.38/0.79 Usable:
% 0.38/0.79 end_of_list.
% 0.38/0.79
% 0.38/0.79 Sos:
% 0.38/0.79 0 (wt=-1) [] aux(A,btrue) = cons(o,shw(half(suc(A)))).
% 0.38/0.79 0 (wt=-1) [] aux(A,bfalse) = cons(i,shw(half(suc(A)))).
% 0.38/0.79 0 (wt=-1) [] notb(btrue) = bfalse.
% 0.38/0.79 0 (wt=-1) [] notb(bfalse) = btrue.
% 0.38/0.79 0 (wt=-1) [] half(zero) = zero.
% 0.38/0.79 0 (wt=-1) [] half(suc(zero)) = zero.
% 0.38/0.79 0 (wt=-1) [] half(suc(suc(A))) = suc(half(A)).
% 0.38/0.79 0 (wt=-1) [] evenNat(zero) = btrue.
% 0.38/0.79 0 (wt=-1) [] evenNat(suc(A)) = notb(evenNat(A)).
% 0.38/0.79 0 (wt=-1) [] shw(zero) = nil.
% 0.38/0.79 0 (wt=-1) [] shw(suc(A)) = aux(A,evenNat(suc(A))).
% 0.38/0.79 0 (wt=-1) [] append(nil,A) = A.
% 0.38/0.79 0 (wt=-1) [] append(cons(A,B),C) = cons(A,append(B,C)).
% 0.38/0.79 0 (wt=-1) [] addNat(zero,A) = A.
% 0.38/0.79 0 (wt=-1) [] addNat(suc(A),B) = suc(addNat(A,B)).
% 0.38/0.79 0 (wt=-1) [] double(A) = addNat(A,A).
% 0.38/0.79 0 (wt=-1) [] rd(nil) = zero.
% 0.38/0.79 0 (wt=-1) [] rd(cons(i,A)) = suc(double(rd(A))).
% 0.38/0.79 0 (wt=-1) [] rd(cons(o,A)) = double(rd(A)).
% 0.38/0.79 0 (wt=-1) [] x(A,B) = rd(append(shw(A),shw(B))).
% 0.38/0.79 0 (wt=-1) [] sat_comm(A,B) = eq(x(A,B),x(B,A)).
% 0.38/0.79 0 (wt=-1) [] eq2(bfalse,btrue) = bfalse.
% 0.38/0.79 0 (wt=-1) [] eq2(btrue,bfalse) = bfalse.
% 0.38/0.79 0 (wt=-1) [] eq3(i,o) = bfalse.
% 0.38/0.79 0 (wt=-1) [] eq3(o,i) = bfalse.
% 0.38/0.79 0 (wt=-1) [] eq(suc(A),suc(B)) = eq(A,B).
% 0.38/0.79 0 (wt=-1) [] eq(zero,suc(A)) = bfalse.
% 0.38/0.79 0 (wt=-1) [] eq(suc(A),zero) = bfalse.
% 0.38/0.79 0 (wt=-1) [] eq(A,A) = btrue.
% 0.38/0.79 0 (wt=-1) [] eq2(A,A) = btrue.
% 0.38/0.79 0 (wt=-1) [] eq3(A,A) = btrue.
% 0.38/0.79 0 (wt=-1) [] -(eq2(sat_comm(A,B),bfalse) = btrue).
% 0.38/0.79 end_of_list.
% 0.38/0.79
% 0.38/0.79 Demodulators:
% 0.38/0.79 end_of_list.
% 0.38/0.79
% 0.38/0.79 Passive:
% 0.38/0.79 end_of_list.
% 0.38/0.79
% 0.38/0.79 Starting to process input.
% 0.38/0.79
% 0.38/0.79 ** KEPT: 1 (wt=10) [flip(1)] cons(o,shw(half(suc(A)))) = aux(A,btrue).
% 0.38/0.79 1 is a new demodulator.
% 0.38/0.79
% 0.38/0.79 ** KEPT: 2 (wt=10) [flip(1)] cons(i,shw(half(suc(A)))) = aux(A,bfalse).
% 0.38/0.79 2 is a new demodulator.
% 0.38/0.79
% 0.38/0.79 ** KEPT: 3 (wt=4) [] notb(btrue) = bfalse.
% 0.38/0.79 3 is a new demodulator.
% 0.38/0.79
% 0.38/0.79 ** KEPT: 4 (wt=4) [] notb(bfalse) = btrue.
% 0.38/0.79 4 is a new demodulator.
% 0.38/0.79
% 0.38/0.79 ** KEPT: 5 (wt=4) [] half(zero) = zero.
% 0.38/0.79 5 is a new demodulator.
% 0.38/0.79
% 0.38/0.79 ** KEPT: 6 (wt=5) [] half(suc(zero)) = zero.
% 0.38/0.79 6 is a new demodulator.
% 0.38/0.79
% 0.38/0.79 ** KEPT: 7 (wt=8) [] half(suc(suc(A))) = suc(half(A)).
% 0.38/0.79 7 is a new demodulator.
% 0.38/0.79
% 0.38/0.79 ** KEPT: 8 (wt=4) [] evenNat(zero) = btrue.
% 0.38/0.79 8 is a new demodulator.
% 0.38/0.79
% 0.38/0.79 ** KEPT: 9 (wt=7) [] evenNat(suc(A)) = notb(evenNat(A)).
% 0.38/0.79 9 is a new demodulator.
% 0.38/0.79
% 0.38/0.79 ** KEPT: 10 (wt=4) [] shw(zero) = nil.
% 0.38/0.79 10 is a new demodulator.
% 0.38/0.79
% 0.38/0.79 ** KEPT: 11 (wt=9) [demod([9])] shw(suc(A)) = aux(A,notb(evenNat(A))).
% 0.38/0.79 11 is a new demodulator.
% 0.38/0.79
% 0.38/0.79 ** KEPT: 12 (wt=5) [] append(nil,A) = A.
% 0.38/0.79 12 is a new demodulator.
% 0.38/0.79
% 0.38/0.79 ** KEPT: 13 (wt=11) [flip(1)] cons(A,append(B,C)) = append(cons(A,B),C).
% 0.38/0.79 13 is a new demodulator.
% 0.38/0.79
% 0.38/0.79 ** KEPT: 14 (wt=5) [] addNat(zero,A) = A.
% 0.38/0.79 14 is a new demodulator.
% 0.38/0.79
% 0.38/0.79 ** KEPT: 15 (wt=9) [flip(1)] suc(addNat(A,B)) = addNat(suc(A),B).
% 0.38/0.79 15 is a new demodulator.
% 0.38/0.79
% 0.38/0.79 ** KEPT: 16 (wt=6) [] double(A) = addNat(A,A).
% 0.38/0.79 16 is a new demodulator.
% 0.38/0.79
% 0.38/0.79 ** KEPT: 17 (wt=4) [] rd(nil) = zero.
% 0.38/0.79 17 is a new demodulator.
% 0.38/0.79
% 0.38/0.79 ** KEPT: 18 (wt=11) [demod([16,15]),flip(1)] addNat(suc(rd(A)),rd(A)) = rd(cons(i,A)).
% 0.38/0.79 18 is a new demodulator.
% 0.38/0.79
% 0.38/0.79 ** KEPT: 19 (wt=10) [demod([16])] rd(cons(o,A)) = addNat(rd(A),rd(A)).
% 0.38/0.79 19 is a new demodulator.
% 0.38/0.79
% 0.38/0.79 ** KEPT: 20 (wt=10) [flip(1)] rd(append(shw(A),shw(B))) = x(A,B).
% 0.38/0.79 20 is a new demodulator.
% 0.38/0.79
% 0.38/0.79 ** KEPT: 21 (wt=11) [flip(1)] eq(x(A,B),x(B,A)) = sat_comm(A,B).
% 0.38/0.79 21 is a new demodulator.
% 0.38/0.79
% 0.38/0.79 ** KEPT: 22 (wt=5) [] eq2(bfalse,btrue) = bfalse.
% 0.38/0.79 22 is a new demodulator.
% 0.38/0.79
% 0.38/0.79 ** KEPT: 23 (wt=5) [] eq2(btrue,bfalse) = bfalse.
% 0.38/0.79 23 is a new demodulator.
% 0.38/0.79
% 0.38/0.79 ** KEPT: 24 (wt=5) [] eq3(i,o) = bfalse.
% 0.38/0.79 24 is a new demodulator.
% 0.38/0.79
% 0.38/0.79 ** KEPT: 25 (wt=5) [] eq3(o,i) = bfalse.
% 0.38/0.79 25 is a new demodulator.
% 0.38/0.79
% 0.38/0.79 ** KEPT: 26 (wt=9) [] eq(suc(A),suc(B)) = eq(A,B).
% 0.38/0.79 26 is a new demodulator.
% 0.38/0.79
% 0.38/0.79 ** KEPT: 27 (wt=6) [] eq(zero,suc(A)) = bfalse.
% 0.38/0.79 27 is a new demodulator.
% 0.38/0.79
% 0.38/0.79 ** KEPT: 28 (wt=6) [] eq(suc(A),zero) = bfalse.
% 0.38/0.79 28 is a new demodulator.
% 0.38/0.79
% 0.38/0.79 ** KEPT: 29 (wt=5) [] eq(A,A) = btrue.
% 0.63/1.08 29 is a new demodulator.
% 0.63/1.08
% 0.63/1.08 ** KEPT: 30 (wt=5) [] eq2(A,A) = btrue.
% 0.63/1.08 30 is a new demodulator.
% 0.63/1.08
% 0.63/1.08 ** KEPT: 31 (wt=5) [] eq3(A,A) = btrue.
% 0.63/1.08 31 is a new demodulator.
% 0.63/1.08
% 0.63/1.08 ** KEPT: 32 (wt=7) [] -(eq2(sat_comm(A,B),bfalse) = btrue).
% 0.63/1.08 ---------------- PROOF FOUND ----------------
% 0.63/1.08 % SZS status Unsatisfiable
% 0.63/1.08
% 0.63/1.08
% 0.63/1.08 After processing input:
% 0.63/1.08
% 0.63/1.08 Usable:
% 0.63/1.08 end_of_list.
% 0.63/1.08
% 0.63/1.08 Sos:
% 0.63/1.08 3 (wt=4) [] notb(btrue) = bfalse.
% 0.63/1.08 4 (wt=4) [] notb(bfalse) = btrue.
% 0.63/1.08 5 (wt=4) [] half(zero) = zero.
% 0.63/1.08 8 (wt=4) [] evenNat(zero) = btrue.
% 0.63/1.08 10 (wt=4) [] shw(zero) = nil.
% 0.63/1.08 17 (wt=4) [] rd(nil) = zero.
% 0.63/1.08 6 (wt=5) [] half(suc(zero)) = zero.
% 0.63/1.08 12 (wt=5) [] append(nil,A) = A.
% 0.63/1.08 14 (wt=5) [] addNat(zero,A) = A.
% 0.63/1.08 22 (wt=5) [] eq2(bfalse,btrue) = bfalse.
% 0.63/1.08 23 (wt=5) [] eq2(btrue,bfalse) = bfalse.
% 0.63/1.08 24 (wt=5) [] eq3(i,o) = bfalse.
% 0.63/1.08 25 (wt=5) [] eq3(o,i) = bfalse.
% 0.63/1.08 29 (wt=5) [] eq(A,A) = btrue.
% 0.63/1.08 30 (wt=5) [] eq2(A,A) = btrue.
% 0.63/1.08 31 (wt=5) [] eq3(A,A) = btrue.
% 0.63/1.08 16 (wt=6) [] double(A) = addNat(A,A).
% 0.63/1.08 27 (wt=6) [] eq(zero,suc(A)) = bfalse.
% 0.63/1.08 28 (wt=6) [] eq(suc(A),zero) = bfalse.
% 0.63/1.08 9 (wt=7) [] evenNat(suc(A)) = notb(evenNat(A)).
% 0.63/1.08 32 (wt=7) [] -(eq2(sat_comm(A,B),bfalse) = btrue).
% 0.63/1.08 7 (wt=8) [] half(suc(suc(A))) = suc(half(A)).
% 0.63/1.08 11 (wt=9) [demod([9])] shw(suc(A)) = aux(A,notb(evenNat(A))).
% 0.63/1.08 15 (wt=9) [flip(1)] suc(addNat(A,B)) = addNat(suc(A),B).
% 0.63/1.08 26 (wt=9) [] eq(suc(A),suc(B)) = eq(A,B).
% 0.63/1.08 1 (wt=10) [flip(1)] cons(o,shw(half(suc(A)))) = aux(A,btrue).
% 0.63/1.08 2 (wt=10) [flip(1)] cons(i,shw(half(suc(A)))) = aux(A,bfalse).
% 0.63/1.08 19 (wt=10) [demod([16])] rd(cons(o,A)) = addNat(rd(A),rd(A)).
% 0.63/1.08 20 (wt=10) [flip(1)] rd(append(shw(A),shw(B))) = x(A,B).
% 0.63/1.08 13 (wt=11) [flip(1)] cons(A,append(B,C)) = append(cons(A,B),C).
% 0.63/1.08 18 (wt=11) [demod([16,15]),flip(1)] addNat(suc(rd(A)),rd(A)) = rd(cons(i,A)).
% 0.63/1.08 21 (wt=11) [flip(1)] eq(x(A,B),x(B,A)) = sat_comm(A,B).
% 0.63/1.08 end_of_list.
% 0.63/1.08
% 0.63/1.08 Demodulators:
% 0.63/1.08 1 (wt=10) [flip(1)] cons(o,shw(half(suc(A)))) = aux(A,btrue).
% 0.63/1.08 2 (wt=10) [flip(1)] cons(i,shw(half(suc(A)))) = aux(A,bfalse).
% 0.63/1.08 3 (wt=4) [] notb(btrue) = bfalse.
% 0.63/1.08 4 (wt=4) [] notb(bfalse) = btrue.
% 0.63/1.08 5 (wt=4) [] half(zero) = zero.
% 0.63/1.08 6 (wt=5) [] half(suc(zero)) = zero.
% 0.63/1.08 7 (wt=8) [] half(suc(suc(A))) = suc(half(A)).
% 0.63/1.08 8 (wt=4) [] evenNat(zero) = btrue.
% 0.63/1.08 9 (wt=7) [] evenNat(suc(A)) = notb(evenNat(A)).
% 0.63/1.08 10 (wt=4) [] shw(zero) = nil.
% 0.63/1.08 11 (wt=9) [demod([9])] shw(suc(A)) = aux(A,notb(evenNat(A))).
% 0.63/1.08 12 (wt=5) [] append(nil,A) = A.
% 0.63/1.08 13 (wt=11) [flip(1)] cons(A,append(B,C)) = append(cons(A,B),C).
% 0.63/1.08 14 (wt=5) [] addNat(zero,A) = A.
% 0.63/1.08 15 (wt=9) [flip(1)] suc(addNat(A,B)) = addNat(suc(A),B).
% 0.63/1.08 16 (wt=6) [] double(A) = addNat(A,A).
% 0.63/1.08 17 (wt=4) [] rd(nil) = zero.
% 0.63/1.08 18 (wt=11) [demod([16,15]),flip(1)] addNat(suc(rd(A)),rd(A)) = rd(cons(i,A)).
% 0.63/1.08 19 (wt=10) [demod([16])] rd(cons(o,A)) = addNat(rd(A),rd(A)).
% 0.63/1.08 20 (wt=10) [flip(1)] rd(append(shw(A),shw(B))) = x(A,B).
% 0.63/1.08 21 (wt=11) [flip(1)] eq(x(A,B),x(B,A)) = sat_comm(A,B).
% 0.63/1.08 22 (wt=5) [] eq2(bfalse,btrue) = bfalse.
% 0.63/1.08 23 (wt=5) [] eq2(btrue,bfalse) = bfalse.
% 0.63/1.08 24 (wt=5) [] eq3(i,o) = bfalse.
% 0.63/1.08 25 (wt=5) [] eq3(o,i) = bfalse.
% 0.63/1.08 26 (wt=9) [] eq(suc(A),suc(B)) = eq(A,B).
% 0.63/1.08 27 (wt=6) [] eq(zero,suc(A)) = bfalse.
% 0.63/1.08 28 (wt=6) [] eq(suc(A),zero) = bfalse.
% 0.63/1.08 29 (wt=5) [] eq(A,A) = btrue.
% 0.63/1.08 30 (wt=5) [] eq2(A,A) = btrue.
% 0.63/1.08 31 (wt=5) [] eq3(A,A) = btrue.
% 0.63/1.08 end_of_list.
% 0.63/1.08
% 0.63/1.08 Passive:
% 0.63/1.08 end_of_list.
% 0.63/1.08
% 0.63/1.08 UNIT CONFLICT from 1229 and x=x at 0.13 seconds.
% 0.63/1.08
% 0.63/1.08 ---------------- PROOF ----------------
% 0.63/1.08 % SZS output start Refutation
% See solution above
% 0.63/1.08 ------------ end of proof -------------
% 0.63/1.08
% 0.63/1.08
% 0.63/1.08 ------------- memory usage ------------
% 0.63/1.08 Memory dynamically allocated (tp_alloc): 2929.
% 0.63/1.08 type (bytes each) gets frees in use avail bytes
% 0.63/1.08 sym_ent ( 96) 75 0 75 0 7.0 K
% 0.63/1.08 term ( 16) 259895 225396 34499 110 671.1 K
% 0.63/1.08 gen_ptr ( 8) 195790 30521 165269 76 1291.8 K
% 0.63/1.08 context ( 808) 746727 746725 2 7 7.1 K
% 0.63/1.08 trail ( 12) 889 889 0 7 0.1 K
% 0.63/1.08 bt_node ( 68) 334382 334379 3 21 1.6 K
% 0.63/1.08 ac_position (285432) 0 0 0 0 0.0 K
% 0.63/1.08 ac_match_pos (14044) 0 0 0 0 0.0 K
% 0.63/1.08 ac_match_free_vars_pos (4020)
% 0.63/1.08 0 0 0 0 0.0 K
% 0.63/1.08 discrim ( 12) 21490 1622 19868 0 232.8 K
% 0.63/1.08 flat ( 40) 590462 590462 0 71 2.8 K
% 0.63/1.08 discrim_pos ( 12) 13458 13458 0 1 0.0 K
% 0.63/1.08 fpa_head ( 12) 6908 0 6908 0 81.0 K
% 0.63/1.08 fpa_tree ( 28) 2397 2397 0 31 0.8 K
% 0.63/1.08 fpa_pos ( 36) 1546 1546 0 1 0.0 K
% 0.63/1.08 literal ( 12) 10454 9225 1229 0 14.4 K
% 0.63/1.08 clause ( 24) 10454 9225 1229 0 28.8 K
% 0.63/1.08 list ( 12) 377 321 56 3 0.7 K
% 0.63/1.08 list_pos ( 20) 4318 662 3656 0 71.4 K
% 0.63/1.08 pair_index ( 40) 2 0 2 0 0.1 K
% 0.63/1.08
% 0.63/1.08 -------------- statistics -------------
% 0.63/1.08 Clauses input 32
% 0.63/1.08 Usable input 0
% 0.63/1.08 Sos input 32
% 0.63/1.08 Demodulators input 0
% 0.63/1.08 Passive input 0
% 0.63/1.08
% 0.63/1.08 Processed BS (before search) 32
% 0.63/1.08 Forward subsumed BS 0
% 0.63/1.08 Kept BS 32
% 0.63/1.08 New demodulators BS 31
% 0.63/1.08 Back demodulated BS 0
% 0.63/1.08
% 0.63/1.08 Clauses or pairs given 37891
% 0.63/1.08 Clauses generated 5157
% 0.63/1.08 Forward subsumed 3960
% 0.63/1.08 Deleted by weight 0
% 0.63/1.08 Deleted by variable count 0
% 0.63/1.08 Kept 1197
% 0.63/1.08 New demodulators 287
% 0.63/1.08 Back demodulated 142
% 0.63/1.08 Ordered paramod prunes 0
% 0.63/1.08 Basic paramod prunes 120984
% 0.63/1.08 Prime paramod prunes 0
% 0.63/1.08 Semantic prunes 0
% 0.63/1.08
% 0.63/1.08 Rewrite attmepts 136446
% 0.63/1.08 Rewrites 10383
% 0.63/1.08
% 0.63/1.08 FPA overloads 0
% 0.63/1.08 FPA underloads 0
% 0.63/1.08
% 0.63/1.08 Usable size 0
% 0.63/1.08 Sos size 1086
% 0.63/1.08 Demodulators size 256
% 0.63/1.08 Passive size 0
% 0.63/1.08 Disabled size 142
% 0.63/1.08
% 0.63/1.08 Proofs found 1
% 0.63/1.08
% 0.63/1.08 ----------- times (seconds) ----------- Tue May 5 12:15:31 2026
% 0.63/1.08
% 0.63/1.08 user CPU time 0.13 (0 hr, 0 min, 0 sec)
% 0.63/1.08 system CPU time 0.17 (0 hr, 0 min, 0 sec)
% 0.63/1.08 wall-clock time 0 (0 hr, 0 min, 0 sec)
% 0.63/1.08 input time 0.00
% 0.63/1.08 paramodulation time 0.04
% 0.63/1.08 demodulation time 0.01
% 0.63/1.08 orient time 0.01
% 0.63/1.08 weigh time 0.01
% 0.63/1.08 forward subsume time 0.01
% 0.63/1.08 back demod find time 0.00
% 0.63/1.08 conflict time 0.00
% 0.63/1.08 LRPO time 0.00
% 0.63/1.08 store clause time 0.01
% 0.63/1.08 disable clause time 0.00
% 0.63/1.08 prime paramod time 0.00
% 0.63/1.08 semantics time 0.00
% 0.63/1.08
% 0.63/1.08 EQP interrupted
%------------------------------------------------------------------------------