%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : SWX222-1 : TPTP v9.3.0. Released v9.3.0.
% Transfm : none
% Format : tptp:raw
% Command : otter-tptp-script %s
% Computer : n005.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 07:05:27 PM UTC 2026
% Result : Unsatisfiable 2.11s 2.33s
% Output : Refutation 2.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 13
% Syntax : Number of clauses : 25 ( 25 unt; 0 nHn; 5 RR)
% Number of literals : 25 ( 24 equ; 3 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 20 ( 20 usr; 6 con; 0-4 aty)
% Number of variables : 49 ( 17 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(6,axiom,
e_q4(sat_synth_nf_k(A),bfalse) != btrue,
file('SWX222-1.p',unknown),
[] ).
cnf(7,axiom,
A = A,
file('SWX222-1.p',unknown),
[] ).
cnf(10,axiom,
aux(A,B,C,just(D)) = e_q(D,B),
file('SWX222-1.p',unknown),
[] ).
cnf(12,axiom,
notb(btrue) = bfalse,
file('SWX222-1.p',unknown),
[] ).
cnf(17,axiom,
index(cons(A,B),zero) = just(A),
file('SWX222-1.p',unknown),
[] ).
cnf(21,axiom,
andb(btrue,A) = A,
file('SWX222-1.p',unknown),
[] ).
cnf(31,axiom,
nf(lam(A)) = nf(A),
file('SWX222-1.p',unknown),
[] ).
cnf(33,axiom,
nf(var(A)) = btrue,
file('SWX222-1.p',unknown),
[] ).
cnf(37,axiom,
tc(A,lam(B),arr(C,D)) = tc(cons(C,A),B,D),
file('SWX222-1.p',unknown),
[] ).
cnf(44,axiom,
tc(A,var(B),C) = aux(A,C,B,index(A,B)),
file('SWX222-1.p',unknown),
[] ).
cnf(46,axiom,
sat_synth_nf_k(A) = notb(andb(nf(A),tc(nil,A,arr(a,arr(b,b))))),
file('SWX222-1.p',unknown),
[] ).
cnf(97,axiom,
e_q(A,A) = btrue,
file('SWX222-1.p',unknown),
[] ).
cnf(104,axiom,
e_q4(A,A) = btrue,
file('SWX222-1.p',unknown),
[] ).
cnf(105,plain,
e_q(A,B) = aux(C,B,D,just(A)),
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[10])]),
[iquote('copy,10,flip.1')] ).
cnf(106,plain,
just(A) = index(cons(A,B),zero),
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[17])]),
[iquote('copy,17,flip.1')] ).
cnf(109,plain,
tc(cons(A,B),C,D) = tc(B,lam(C),arr(A,D)),
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[37])]),
[iquote('copy,37,flip.1')] ).
cnf(110,plain,
aux(A,B,C,index(A,C)) = tc(A,var(C),B),
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[44])]),
[iquote('copy,44,flip.1')] ).
cnf(111,plain,
e_q4(notb(andb(nf(A),tc(nil,A,arr(a,arr(b,b))))),bfalse) != btrue,
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[6]),46]),
[iquote('back_demod,6,demod,46')] ).
cnf(220,plain,
aux(A,B,C,just(B)) = btrue,
inference(flip,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[105,97])]),
[iquote('para_into,105.1.1,97.1.1,flip.1')] ).
cnf(251,plain,
aux(A,B,C,index(cons(B,D),zero)) = btrue,
inference(para_into,[status(thm),theory(equality)],[220,106]),
[iquote('para_into,220.1.1.4,106.1.1')] ).
cnf(401,plain,
tc(cons(A,B),var(zero),A) = btrue,
inference(para_into,[status(thm),theory(equality)],[251,110]),
[iquote('para_into,251.1.1,110.1.1')] ).
cnf(416,plain,
tc(A,lam(var(zero)),arr(B,B)) = btrue,
inference(para_into,[status(thm),theory(equality)],[401,109]),
[iquote('para_into,401.1.1,109.1.1')] ).
cnf(422,plain,
tc(A,lam(lam(var(zero))),arr(B,arr(C,C))) = btrue,
inference(para_into,[status(thm),theory(equality)],[416,109]),
[iquote('para_into,416.1.1,109.1.1')] ).
cnf(579,plain,
btrue != btrue,
inference(demod,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[422,111]),31,31,33,21,12,104]),
[iquote('para_from,422.1.1,111.1.1.1.1.2,demod,31,31,33,21,12,104')] ).
cnf(580,plain,
$false,
inference(binary,[status(thm)],[579,7]),
[iquote('binary,579.1,7.1')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.13 % Problem : SWX222-1 : TPTP v9.3.0. Released v9.3.0.
% 0.11/0.14 % Command : otter-tptp-script %s
% 0.16/0.35 % Computer : n005.cluster.edu
% 0.16/0.35 % Model : x86_64 x86_64
% 0.16/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.35 % Memory : 8042.1875MB
% 0.16/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.35 % CPULimit : 300
% 0.16/0.35 % WCLimit : 300
% 0.16/0.35 % DateTime : Tue May 5 12:34:45 EDT 2026
% 0.16/0.35 % CPUTime :
% 2.05/2.29 ----- Otter 3.3f, August 2004 -----
% 2.05/2.29 The process was started by sandbox on n005.cluster.edu,
% 2.05/2.29 Tue May 5 12:34:45 2026
% 2.05/2.29 The command was "./otter". The process ID is 3303.
% 2.05/2.29
% 2.05/2.29 set(prolog_style_variables).
% 2.05/2.29 set(auto).
% 2.05/2.29 dependent: set(auto1).
% 2.05/2.29 dependent: set(process_input).
% 2.05/2.29 dependent: clear(print_kept).
% 2.05/2.29 dependent: clear(print_new_demod).
% 2.05/2.29 dependent: clear(print_back_demod).
% 2.05/2.29 dependent: clear(print_back_sub).
% 2.05/2.29 dependent: set(control_memory).
% 2.05/2.29 dependent: assign(max_mem, 12000).
% 2.05/2.29 dependent: assign(pick_given_ratio, 4).
% 2.05/2.29 dependent: assign(stats_level, 1).
% 2.05/2.29 dependent: assign(max_seconds, 10800).
% 2.05/2.29 clear(print_given).
% 2.05/2.29
% 2.05/2.29 list(usable).
% 2.05/2.29 0 [] A=A.
% 2.05/2.29 0 [] aux(X,Z,X3,nothing)=bfalse.
% 2.05/2.29 0 [] aux(X,Z,X3,just(Tx3))=e_q(Tx3,Z).
% 2.05/2.29 0 [] notb(btrue)=bfalse.
% 2.05/2.29 0 [] notb(bfalse)=btrue.
% 2.05/2.29 0 [] index(nil,Y)=nothing.
% 2.05/2.29 0 [] index(cons(Z,Xs),zero)=just(Z).
% 2.05/2.29 0 [] index(cons(Z,Xs),suc(N))=index(Xs,N).
% 2.05/2.29 0 [] andb(btrue,Q)=Q.
% 2.05/2.29 0 [] andb(bfalse,Q)=bfalse.
% 2.05/2.29 0 [] nf(app(lam(X3),Z,X2))=bfalse.
% 2.05/2.29 0 [] nf(app(app(X,X3,X4),Z,X2))=andb(nf(app(X,X3,X4)),nf(Z)).
% 2.05/2.29 0 [] nf(app(var(X),Z,X2))=andb(nf(var(X)),nf(Z)).
% 2.05/2.29 0 [] nf(lam(E))=nf(E).
% 2.05/2.29 0 [] nf(var(X4))=btrue.
% 2.05/2.29 0 [] tc(X,app(F,X2,Tx),Z)=andb(tc(X,F,arr(Tx,Z)),tc(X,X2,Tx)).
% 2.05/2.29 0 [] tc(X,lam(E),arr(Tx2,T1))=tc(cons(Tx2,X),E,T1).
% 2.05/2.29 0 [] tc(X,lam(E),a)=bfalse.
% 2.05/2.29 0 [] tc(X,lam(E),b)=bfalse.
% 2.05/2.29 0 [] tc(X,lam(E),c)=bfalse.
% 2.05/2.29 0 [] tc(X,var(X3),Z)=aux(X,Z,X3,index(X,X3)).
% 2.05/2.29 0 [] sat_synth_nf_k(X)=notb(andb(nf(X),tc(nil,X,arr(a,arr(b,b))))).
% 2.05/2.29 0 [] e_q(a,b)=bfalse.
% 2.05/2.29 0 [] e_q(a,c)=bfalse.
% 2.05/2.29 0 [] e_q(b,a)=bfalse.
% 2.05/2.29 0 [] e_q(b,c)=bfalse.
% 2.05/2.29 0 [] e_q(c,a)=bfalse.
% 2.05/2.29 0 [] e_q(c,b)=bfalse.
% 2.05/2.29 0 [] e_q4(bfalse,btrue)=bfalse.
% 2.05/2.29 0 [] e_q4(btrue,bfalse)=bfalse.
% 2.05/2.29 0 [] e_q2(suc(X),suc(Y))=e_q2(X,Y).
% 2.05/2.29 0 [] e_q2(zero,suc(X))=bfalse.
% 2.05/2.29 0 [] e_q2(suc(X),zero)=bfalse.
% 2.05/2.29 0 [] e_q(X,Z)!=bfalse|e_q(arr(X,Y),arr(Z,X2))=bfalse.
% 2.05/2.29 0 [] e_q(X,Z)!=btrue|e_q(arr(X,Y),arr(Z,X2))=e_q(Y,X2).
% 2.05/2.29 0 [] e_q(arr(X,Y),a)=bfalse.
% 2.05/2.29 0 [] e_q(arr(X,Y),b)=bfalse.
% 2.05/2.29 0 [] e_q(arr(X,Y),c)=bfalse.
% 2.05/2.29 0 [] e_q(a,arr(X,Y))=bfalse.
% 2.05/2.29 0 [] e_q(b,arr(X,Y))=bfalse.
% 2.05/2.29 0 [] e_q(c,arr(X,Y))=bfalse.
% 2.05/2.29 0 [] e_q3(X,X2)!=bfalse|e_q3(app(X,Y,Z),app(X2,X3,X4))=bfalse.
% 2.05/2.29 0 [] e_q3(Y,X3)!=bfalse|e_q3(X,X2)!=btrue|e_q3(app(X,Y,Z),app(X2,X3,X4))=bfalse.
% 2.05/2.29 0 [] e_q3(X,X2)!=btrue|e_q3(Y,X3)!=btrue|e_q3(app(X,Y,Z),app(X2,X3,X4))=e_q(Z,X4).
% 2.05/2.29 0 [] e_q3(lam(X),lam(Y))=e_q3(X,Y).
% 2.05/2.29 0 [] e_q3(var(X),var(Y))=e_q2(X,Y).
% 2.05/2.29 0 [] e_q3(app(X,Y,Z),lam(X2))=bfalse.
% 2.05/2.29 0 [] e_q3(app(X,Y,Z),var(X2))=bfalse.
% 2.05/2.29 0 [] e_q3(lam(X),app(Y,Z,X2))=bfalse.
% 2.05/2.29 0 [] e_q3(lam(X),var(Y))=bfalse.
% 2.05/2.29 0 [] e_q3(var(X),app(Y,Z,X2))=bfalse.
% 2.05/2.29 0 [] e_q3(var(X),lam(Y))=bfalse.
% 2.05/2.29 0 [] e_q(X,X)=btrue.
% 2.05/2.29 0 [] e_q2(X,X)=btrue.
% 2.05/2.29 0 [] e_q3(X,X)=btrue.
% 2.05/2.29 0 [] e_q4(X,X)=btrue.
% 2.05/2.29 0 [] e_q4(sat_synth_nf_k(X),bfalse)!=btrue.
% 2.05/2.29 end_of_list.
% 2.05/2.29
% 2.05/2.29 SCAN INPUT: prop=0, horn=1, equality=1, symmetry=0, max_lits=3.
% 2.05/2.29
% 2.05/2.29 This is a Horn set with equality. The strategy will be
% 2.05/2.29 Knuth-Bendix and hyper_res, with positive clauses in
% 2.05/2.29 sos and nonpositive clauses in usable.
% 2.05/2.29
% 2.05/2.29 dependent: set(knuth_bendix).
% 2.05/2.29 dependent: set(anl_eq).
% 2.05/2.29 dependent: set(para_from).
% 2.05/2.29 dependent: set(para_into).
% 2.05/2.29 dependent: clear(para_from_right).
% 2.05/2.29 dependent: clear(para_into_right).
% 2.05/2.29 dependent: set(para_from_vars).
% 2.05/2.29 dependent: set(eq_units_both_ways).
% 2.05/2.29 dependent: set(dynamic_demod_all).
% 2.05/2.29 dependent: set(dynamic_demod).
% 2.05/2.29 dependent: set(order_eq).
% 2.05/2.29 dependent: set(back_demod).
% 2.05/2.29 dependent: set(lrpo).
% 2.05/2.29 dependent: set(hyper_res).
% 2.05/2.29 dependent: clear(order_hyper).
% 2.05/2.29
% 2.05/2.29 ------------> process usable:
% 2.05/2.29 ** KEPT (pick-wt=14): 1 [] e_q(A,B)!=bfalse|e_q(arr(A,C),arr(B,D))=bfalse.
% 2.05/2.29 ** KEPT (pick-wt=16): 2 [] e_q(A,B)!=btrue|e_q(arr(A,C),arr(B,D))=e_q(C,D).
% 2.05/2.29 ** KEPT (pick-wt=16): 3 [] e_q3(A,B)!=bfalse|e_q3(app(A,C,D),app(B,E,F))=bfalse.
% 2.05/2.29 ** KEPT (pick-wt=21): 4 [] e_q3(A,B)!=bfalse|e_q3(C,D)!=btrue|e_q3(app(C,A,E),app(D,B,F))=bfalse.
% 2.05/2.29 ** KEPT (pick-wt=23): 5 [] e_q3(A,B)!=btrue|e_q3(C,D)!=btrue|e_q3(app(A,C,E),app(B,D,F))=e_q(E,F).
% 2.05/2.29 ** KEPT (pick-wt=6): 6 [] e_q4(sat_synth_nf_k(A),bfalse)!=btrue.
% 2.05/2.29
% 2.05/2.29 ------------> process sos:
% 2.05/2.29 ** KEPT (pick-wt=3): 7 [] A=A.
% 2.05/2.29 ** KEPT (pick-wt=7): 8 [] aux(A,B,C,nothing)=bfalse.
% 2.05/2.29 ---> New Demodulator: 9 [new_demod,8] aux(A,B,C,nothing)=bfalse.
% 2.05/2.29 ** KEPT (pick-wt=10): 10 [] aux(A,B,C,just(D))=e_q(D,B).
% 2.05/2.29 ** KEPT (pick-wt=4): 11 [] notb(btrue)=bfalse.
% 2.05/2.29 ---> New Demodulator: 12 [new_demod,11] notb(btrue)=bfalse.
% 2.05/2.29 ** KEPT (pick-wt=4): 13 [] notb(bfalse)=btrue.
% 2.05/2.29 ---> New Demodulator: 14 [new_demod,13] notb(bfalse)=btrue.
% 2.05/2.29 ** KEPT (pick-wt=5): 15 [] index(nil,A)=nothing.
% 2.05/2.29 ---> New Demodulator: 16 [new_demod,15] index(nil,A)=nothing.
% 2.05/2.29 ** KEPT (pick-wt=8): 17 [] index(cons(A,B),zero)=just(A).
% 2.05/2.29 ** KEPT (pick-wt=10): 18 [] index(cons(A,B),suc(C))=index(B,C).
% 2.05/2.29 ---> New Demodulator: 19 [new_demod,18] index(cons(A,B),suc(C))=index(B,C).
% 2.05/2.29 ** KEPT (pick-wt=5): 20 [] andb(btrue,A)=A.
% 2.05/2.29 ---> New Demodulator: 21 [new_demod,20] andb(btrue,A)=A.
% 2.05/2.29 ** KEPT (pick-wt=5): 22 [] andb(bfalse,A)=bfalse.
% 2.05/2.29 ---> New Demodulator: 23 [new_demod,22] andb(bfalse,A)=bfalse.
% 2.05/2.29 ** KEPT (pick-wt=8): 24 [] nf(app(lam(A),B,C))=bfalse.
% 2.05/2.29 ---> New Demodulator: 25 [new_demod,24] nf(app(lam(A),B,C))=bfalse.
% 2.05/2.29 ** KEPT (pick-wt=17): 26 [] nf(app(app(A,B,C),D,E))=andb(nf(app(A,B,C)),nf(D)).
% 2.05/2.29 ---> New Demodulator: 27 [new_demod,26] nf(app(app(A,B,C),D,E))=andb(nf(app(A,B,C)),nf(D)).
% 2.05/2.29 ** KEPT (pick-wt=13): 28 [] nf(app(var(A),B,C))=andb(nf(var(A)),nf(B)).
% 2.05/2.29 ---> New Demodulator: 29 [new_demod,28] nf(app(var(A),B,C))=andb(nf(var(A)),nf(B)).
% 2.05/2.29 ** KEPT (pick-wt=6): 30 [] nf(lam(A))=nf(A).
% 2.05/2.29 ---> New Demodulator: 31 [new_demod,30] nf(lam(A))=nf(A).
% 2.05/2.29 ** KEPT (pick-wt=5): 32 [] nf(var(A))=btrue.
% 2.05/2.29 ---> New Demodulator: 33 [new_demod,32] nf(var(A))=btrue.
% 2.05/2.29 ** KEPT (pick-wt=19): 35 [copy,34,flip.1] andb(tc(A,B,arr(C,D)),tc(A,E,C))=tc(A,app(B,E,C),D).
% 2.05/2.29 ---> New Demodulator: 36 [new_demod,35] andb(tc(A,B,arr(C,D)),tc(A,E,C))=tc(A,app(B,E,C),D).
% 2.05/2.29 ** KEPT (pick-wt=14): 37 [] tc(A,lam(B),arr(C,D))=tc(cons(C,A),B,D).
% 2.05/2.29 ** KEPT (pick-wt=7): 38 [] tc(A,lam(B),a)=bfalse.
% 2.05/2.29 ---> New Demodulator: 39 [new_demod,38] tc(A,lam(B),a)=bfalse.
% 2.05/2.29 ** KEPT (pick-wt=7): 40 [] tc(A,lam(B),b)=bfalse.
% 2.05/2.29 ---> New Demodulator: 41 [new_demod,40] tc(A,lam(B),b)=bfalse.
% 2.05/2.29 ** KEPT (pick-wt=7): 42 [] tc(A,lam(B),c)=bfalse.
% 2.05/2.29 ---> New Demodulator: 43 [new_demod,42] tc(A,lam(B),c)=bfalse.
% 2.05/2.29 ** KEPT (pick-wt=13): 44 [] tc(A,var(B),C)=aux(A,C,B,index(A,B)).
% 2.05/2.29 ** KEPT (pick-wt=15): 45 [] sat_synth_nf_k(A)=notb(andb(nf(A),tc(nil,A,arr(a,arr(b,b))))).
% 2.05/2.29 ---> New Demodulator: 46 [new_demod,45] sat_synth_nf_k(A)=notb(andb(nf(A),tc(nil,A,arr(a,arr(b,b))))).
% 2.05/2.29 ** KEPT (pick-wt=5): 47 [] e_q(a,b)=bfalse.
% 2.05/2.29 ---> New Demodulator: 48 [new_demod,47] e_q(a,b)=bfalse.
% 2.05/2.29 ** KEPT (pick-wt=5): 49 [] e_q(a,c)=bfalse.
% 2.05/2.29 ---> New Demodulator: 50 [new_demod,49] e_q(a,c)=bfalse.
% 2.05/2.29 ** KEPT (pick-wt=5): 51 [] e_q(b,a)=bfalse.
% 2.05/2.29 ---> New Demodulator: 52 [new_demod,51] e_q(b,a)=bfalse.
% 2.05/2.29 ** KEPT (pick-wt=5): 53 [] e_q(b,c)=bfalse.
% 2.05/2.29 ---> New Demodulator: 54 [new_demod,53] e_q(b,c)=bfalse.
% 2.05/2.29 ** KEPT (pick-wt=5): 55 [] e_q(c,a)=bfalse.
% 2.05/2.29 ---> New Demodulator: 56 [new_demod,55] e_q(c,a)=bfalse.
% 2.05/2.29 ** KEPT (pick-wt=5): 57 [] e_q(c,b)=bfalse.
% 2.05/2.29 ---> New Demodulator: 58 [new_demod,57] e_q(c,b)=bfalse.
% 2.05/2.29 ** KEPT (pick-wt=5): 59 [] e_q4(bfalse,btrue)=bfalse.
% 2.05/2.29 ---> New Demodulator: 60 [new_demod,59] e_q4(bfalse,btrue)=bfalse.
% 2.05/2.29 ** KEPT (pick-wt=5): 61 [] e_q4(btrue,bfalse)=bfalse.
% 2.05/2.29 ---> New Demodulator: 62 [new_demod,61] e_q4(btrue,bfalse)=bfalse.
% 2.05/2.29 ** KEPT (pick-wt=9): 63 [] e_q2(suc(A),suc(B))=e_q2(A,B).
% 2.05/2.29 ---> New Demodulator: 64 [new_demod,63] e_q2(suc(A),suc(B))=e_q2(A,B).
% 2.05/2.29 ** KEPT (pick-wt=6): 65 [] e_q2(zero,suc(A))=bfalse.
% 2.05/2.29 ---> New Demodulator: 66 [new_demod,65] e_q2(zero,suc(A))=bfalse.
% 2.05/2.29 ** KEPT (pick-wt=6): 67 [] e_q2(suc(A),zero)=bfalse.
% 2.05/2.29 ---> New Demodulator: 68 [new_demod,67] e_q2(suc(A),zero)=bfalse.
% 2.05/2.29 ** KEPT (pick-wt=7): 69 [] e_q(arr(A,B),a)=bfalse.
% 2.05/2.29 ---> New Demodulator: 70 [new_demod,69] e_q(arr(A,B),a)=bfalse.
% 2.05/2.29 ** KEPT (pick-wt=7): 71 [] e_q(arr(A,B),b)=bfalse.
% 2.05/2.29 ---> New Demodulator: 72 [new_demod,71] e_q(arr(A,B),b)=bfalse.
% 2.05/2.29 ** KEPT (pick-wt=7): 73 [] e_q(arr(A,B),c)=bfalse.
% 2.05/2.29 ---> New Demodulator: 74 [new_demod,73] e_q(arr(A,B),c)=bfalse.
% 2.05/2.29 ** KEPT (pick-wt=7): 75 [] e_q(a,arr(A,B))=bfalse.
% 2.05/2.29 ---> New Demodulator: 76 [new_demod,75] e_q(a,arr(A,B))=bfalse.
% 2.05/2.29 ** KEPT (pick-wt=7): 77 [] e_q(b,arr(A,B))=bfalse.
% 2.05/2.29 ---> New Demodulator: 78 [new_demod,77] e_q(b,arr(A,B))=bfalse.
% 2.05/2.29 ** KEPT (pick-wt=7): 79 [] e_q(c,arr(A,B))=bfalse.
% 2.05/2.29 ---> New Demodulator: 80 [new_demod,79] e_q(c,arr(A,B))=bfalse.
% 2.05/2.29 ** KEPT (pick-wt=9): 81 [] e_q3(lam(A),lam(B))=e_q3(A,B).
% 2.05/2.29 ---> New Demodulator: 82 [new_demod,81] e_q3(lam(A),lam(B))=e_q3(A,B).
% 2.05/2.29 ** KEPT (pick-wt=9): 83 [] e_q3(var(A),var(B))=e_q2(A,B).
% 2.05/2.29 ---> New Demodulator: 84 [new_demod,83] e_q3(var(A),var(B))=e_q2(A,B).
% 2.05/2.29 ** KEPT (pick-wt=9): 85 [] e_q3(app(A,B,C),lam(D))=bfalse.
% 2.05/2.29 ---> New Demodulator: 86 [new_demod,85] e_q3(app(A,B,C),lam(D))=bfalse.
% 2.05/2.29 ** KEPT (pick-wt=9): 87 [] e_q3(app(A,B,C),var(D))=bfalse.
% 2.05/2.29 ---> New Demodulator: 88 [new_demod,87] e_q3(app(A,B,C),var(D))=bfalse.
% 2.05/2.29 ** KEPT (pick-wt=9): 89 [] e_q3(lam(A),app(B,C,D))=bfalse.
% 2.05/2.29 ---> New Demodulator: 90 [new_demod,89] e_q3(lam(A),app(B,C,D))=bfalse.
% 2.05/2.29 ** KEPT (pick-wt=7): 91 [] e_q3(lam(A),var(B))=bfalse.
% 2.05/2.29 ---> New Demodulator: 92 [new_demod,91] e_q3(lam(A),var(B))=bfalse.
% 2.05/2.29 ** KEPT (pick-wt=9): 93 [] e_q3(var(A),app(B,C,D))=bfalse.
% 2.05/2.29 ---> New Demodulator: 94 [new_demod,93] e_q3(var(A),app(B,C,D))=bfalse.
% 2.05/2.29 ** KEPT (pick-wt=7): 95 [] e_q3(var(A),lam(B))=bfalse.
% 2.05/2.29 ---> New Demodulator: 96 [new_demod,95] e_q3(var(A),lam(B))=bfalse.
% 2.05/2.29 ** KEPT (pick-wt=5): 97 [] e_q(A,A)=btrue.
% 2.05/2.29 ---> New Demodulator: 98 [new_demod,97] e_q(A,A)=btrue.
% 2.05/2.29 ** KEPT (pick-wt=5): 99 [] e_q2(A,A)=btrue.
% 2.05/2.29 ---> New Demodulator: 100 [new_demod,99] e_q2(A,A)=btrue.
% 2.05/2.29 ** KEPT (pick-wt=5): 101 [] e_q3(A,A)=btrue.
% 2.05/2.29 ---> New Demodulator: 102 [new_demod,101] e_q3(A,A)=btrue.
% 2.05/2.29 ** KEPT (pick-wt=5): 103 [] e_q4(A,A)=btrue.
% 2.05/2.29 ---> New Demodulator: 104 [new_demod,103] e_q4(A,A)=btrue.
% 2.05/2.29 Following clause subsumed by 7 during input processing: 0 [copy,7,flip.1] A=A.
% 2.05/2.29 >>>> Starting back demodulation with 9.
% 2.05/2.29 ** KEPT (pick-wt=10): 105 [copy,10,flip.1] e_q(A,B)=aux(C,B,D,just(A)).
% 2.05/2.29 >>>> Starting back demodulation with 12.
% 2.05/2.29 >>>> Starting back demodulation with 14.
% 2.05/2.29 >>>> Starting back demodulation with 16.
% 2.05/2.29 ** KEPT (pick-wt=8): 106 [copy,17,flip.1] just(A)=index(cons(A,B),zero).
% 2.05/2.29 >>>> Starting back demodulation with 19.
% 2.05/2.29 >>>> Starting back demodulation with 21.
% 2.05/2.29 >>>> Starting back demodulation with 23.
% 2.05/2.29 >>>> Starting back demodulation with 25.
% 2.05/2.29 >>>> Starting back demodulation with 27.
% 2.05/2.29 >>>> Starting back demodulation with 29.
% 2.05/2.29 >>>> Starting back demodulation with 31.
% 2.05/2.29 >>>> Starting back demodulation with 33.
% 2.05/2.29 >> back demodulating 28 with 33.
% 2.05/2.29 >>>> Starting back demodulation with 36.
% 2.05/2.29 ** KEPT (pick-wt=14): 109 [copy,37,flip.1] tc(cons(A,B),C,D)=tc(B,lam(C),arr(A,D)).
% 2.05/2.29 >>>> Starting back demodulation with 39.
% 2.05/2.29 >>>> Starting back demodulation with 41.
% 2.05/2.29 >>>> Starting back demodulation with 43.
% 2.05/2.29 ** KEPT (pick-wt=13): 110 [copy,44,flip.1] aux(A,B,C,index(A,C))=tc(A,var(C),B).
% 2.05/2.29 >>>> Starting back demodulation with 46.
% 2.05/2.29 >> back demodulating 6 with 46.
% 2.05/2.29 >>>> Starting back demodulation with 48.
% 2.05/2.29 >>>> Starting back demodulation with 50.
% 2.05/2.29 >>>> Starting back demodulation with 52.
% 2.05/2.29 >>>> Starting back demodulation with 54.
% 2.05/2.29 >>>> Starting back demodulation with 56.
% 2.05/2.29 >>>> Starting back demodulation with 58.
% 2.05/2.29 >>>> Starting back demodulation with 60.
% 2.05/2.29 >>>> Starting back demodulation with 62.
% 2.05/2.29 >>>> Starting back demodulation with 64.
% 2.05/2.29 >>>> Starting back demodulation with 66.
% 2.05/2.29 >>>> Starting back demodulation with 68.
% 2.05/2.29 >>>> Starting back demodulation with 70.
% 2.05/2.29 >>>> Starting back demodulation with 72.
% 2.05/2.29 >>>> Starting back demodulation with 74.
% 2.05/2.29 >>>> Starting back demodulation with 76.
% 2.05/2.29 >>>> Starting back demodulation with 78.
% 2.05/2.29 >>>> Starting back demodulation with 80.
% 2.05/2.29 >>>> Starting back demodulation with 82.
% 2.05/2.29 >>>> Starting back demodulation with 84.
% 2.05/2.29 >>>> Starting back demodulation with 86.
% 2.05/2.29 >>>> Starting back demodulation with 88.
% 2.05/2.29 >>>> Starting back demodulation with 90.
% 2.05/2.29 >>>> Starting back demodulation with 92.
% 2.05/2.29 >>>> Starting back demodulation with 94.
% 2.05/2.29 >>>> Starting back demodulation with 96.
% 2.05/2.29 >>>> Starting back demodulation with 98.
% 2.05/2.29 >>>> Starting back demodulation with 100.
% 2.05/2.29 >>>> Starting back demodulation with 102.
% 2.05/2.29 >>>> Starting back demodulation with 104.
% 2.05/2.29 Following clause subsumed by 10 during input processing: 0 [copy,105,flip.1] aux(A,B,C,just(D))=e_q(D,B).
% 2.05/2.29 Following clause subsumed by 17 during input processing: 0 [copy,106,flip.1] index(cons(A,B),zero)=just(A).
% 2.11/2.33 >>>> Starting back demodulation with 108.
% 2.11/2.33 Following clause subsumed by 37 during input processing: 0 [copy,109,flip.1] tc(A,lam(B),arr(C,D))=tc(cons(C,A),B,D).
% 2.11/2.33 Following clause subsumed by 44 during input processing: 0 [copy,110,flip.1] tc(A,var(B),C)=aux(A,C,B,index(A,B)).
% 2.11/2.33
% 2.11/2.33 ======= end of input processing =======
% 2.11/2.33
% 2.11/2.33 =========== start of search ===========
% 2.11/2.33
% 2.11/2.33
% 2.11/2.33 Resetting weight limit to 12.
% 2.11/2.33
% 2.11/2.33
% 2.11/2.33 Resetting weight limit to 12.
% 2.11/2.33
% 2.11/2.33 sos_size=225
% 2.11/2.33
% 2.11/2.33 -------- PROOF --------
% 2.11/2.33
% 2.11/2.33 ----> UNIT CONFLICT at 0.04 sec ----> 580 [binary,579.1,7.1] $F.
% 2.11/2.33
% 2.11/2.33 Length of proof is 11. Level of proof is 7.
% 2.11/2.33
% 2.11/2.33 ---------------- PROOF ----------------
% 2.11/2.33 % SZS status Unsatisfiable
% 2.11/2.33 % SZS output start Refutation
% See solution above
% 2.11/2.33 ------------ end of proof -------------
% 2.11/2.33
% 2.11/2.33
% 2.11/2.33 Search stopped by max_proofs option.
% 2.11/2.33
% 2.11/2.33
% 2.11/2.33 Search stopped by max_proofs option.
% 2.11/2.33
% 2.11/2.33 ============ end of search ============
% 2.11/2.33
% 2.11/2.33 -------------- statistics -------------
% 2.11/2.33 clauses given 194
% 2.11/2.33 clauses generated 2695
% 2.11/2.33 clauses kept 392
% 2.11/2.33 clauses forward subsumed 1227
% 2.11/2.33 clauses back subsumed 12
% 2.11/2.33 Kbytes malloced 4882
% 2.11/2.33
% 2.11/2.33 ----------- times (seconds) -----------
% 2.11/2.33 user CPU time 0.04 (0 hr, 0 min, 0 sec)
% 2.11/2.33 system CPU time 0.00 (0 hr, 0 min, 0 sec)
% 2.11/2.33 wall-clock time 2 (0 hr, 0 min, 2 sec)
% 2.11/2.33
% 2.11/2.33 That finishes the proof of the theorem.
% 2.11/2.33
% 2.11/2.33 Process 3303 finished Tue May 5 12:34:47 2026
% 2.11/2.33 Otter interrupted
% 2.11/2.33 PROOF FOUND
%------------------------------------------------------------------------------