TSTP Solution File: ITP019+2 by Otter---3.3
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- Process Solution
%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : ITP019+2 : TPTP v8.1.0. Bugfixed v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : otter-tptp-script %s
% Computer : n026.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 : Wed Jul 27 12:59:08 EDT 2022
% Result : Theorem 2.30s 2.49s
% Output : Refutation 2.30s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 5
% Syntax : Number of clauses : 11 ( 9 unt; 0 nHn; 10 RR)
% Number of literals : 15 ( 11 equ; 7 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 5 con; 0-2 aty)
% Number of variables : 3 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(27,axiom,
( ~ mem(A,ty_2Epair_2Eprod(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal))
| ap(c_2Ecomplex_2Ecomplex__inv,A) != ap(c_2Ecomplex_2Ecomplex__of__num,c_2Enum_2E0)
| A = ap(c_2Ecomplex_2Ecomplex__of__num,c_2Enum_2E0) ),
file('ITP019+2.p',unknown),
[] ).
cnf(29,axiom,
dollar_c1 != ap(c_2Ecomplex_2Ecomplex__of__num,c_2Enum_2E0),
file('ITP019+2.p',unknown),
[] ).
cnf(30,plain,
ap(c_2Ecomplex_2Ecomplex__of__num,c_2Enum_2E0) != dollar_c1,
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[29])]),
[iquote('copy,29,flip.1')] ).
cnf(43,axiom,
A = A,
file('ITP019+2.p',unknown),
[] ).
cnf(57,axiom,
mem(dollar_c1,ty_2Epair_2Eprod(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal)),
file('ITP019+2.p',unknown),
[] ).
cnf(58,axiom,
ap(c_2Ecomplex_2Ecomplex__inv,dollar_c1) = ap(c_2Ecomplex_2Ecomplex__of__num,c_2Enum_2E0),
file('ITP019+2.p',unknown),
[] ).
cnf(60,plain,
ap(c_2Ecomplex_2Ecomplex__of__num,c_2Enum_2E0) = ap(c_2Ecomplex_2Ecomplex__inv,dollar_c1),
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[58])]),
[iquote('copy,58,flip.1')] ).
cnf(61,plain,
ap(c_2Ecomplex_2Ecomplex__inv,dollar_c1) != dollar_c1,
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[30]),60]),
[iquote('back_demod,30,demod,60')] ).
cnf(63,plain,
( ~ mem(A,ty_2Epair_2Eprod(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal))
| ap(c_2Ecomplex_2Ecomplex__inv,A) != ap(c_2Ecomplex_2Ecomplex__inv,dollar_c1)
| A = ap(c_2Ecomplex_2Ecomplex__inv,dollar_c1) ),
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[27]),60,60]),
[iquote('back_demod,27,demod,60,60')] ).
cnf(3046,plain,
ap(c_2Ecomplex_2Ecomplex__inv,dollar_c1) = dollar_c1,
inference(flip,[status(thm),theory(equality)],[inference(hyper,[status(thm)],[63,57,43])]),
[iquote('hyper,63,57,43,flip.1')] ).
cnf(3048,plain,
$false,
inference(binary,[status(thm)],[3046,61]),
[iquote('binary,3046.1,61.1')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.13 % Problem : ITP019+2 : TPTP v8.1.0. Bugfixed v7.5.0.
% 0.13/0.13 % Command : otter-tptp-script %s
% 0.13/0.35 % Computer : n026.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Wed Jul 27 03:00:24 EDT 2022
% 0.13/0.35 % CPUTime :
% 2.08/2.29 ----- Otter 3.3f, August 2004 -----
% 2.08/2.29 The process was started by sandbox2 on n026.cluster.edu,
% 2.08/2.29 Wed Jul 27 03:00:24 2022
% 2.08/2.29 The command was "./otter". The process ID is 23131.
% 2.08/2.29
% 2.08/2.29 set(prolog_style_variables).
% 2.08/2.29 set(auto).
% 2.08/2.29 dependent: set(auto1).
% 2.08/2.29 dependent: set(process_input).
% 2.08/2.29 dependent: clear(print_kept).
% 2.08/2.29 dependent: clear(print_new_demod).
% 2.08/2.29 dependent: clear(print_back_demod).
% 2.08/2.29 dependent: clear(print_back_sub).
% 2.08/2.29 dependent: set(control_memory).
% 2.08/2.29 dependent: assign(max_mem, 12000).
% 2.08/2.29 dependent: assign(pick_given_ratio, 4).
% 2.08/2.29 dependent: assign(stats_level, 1).
% 2.08/2.29 dependent: assign(max_seconds, 10800).
% 2.08/2.29 clear(print_given).
% 2.08/2.29
% 2.08/2.29 formula_list(usable).
% 2.08/2.29 all A (A=A).
% 2.08/2.29 ne(bool).
% 2.08/2.29 ne(ind).
% 2.08/2.29 all A (ne(A)-> (all B (ne(B)->ne(arr(A,B))))).
% 2.08/2.29 all A B F (mem(F,arr(A,B))-> (all X (mem(X,A)->mem(ap(F,X),B)))).
% 2.08/2.29 all Q (mem(Q,bool)-> (all R (mem(R,bool)-> ((p(Q)<->p(R))->Q=R)))).
% 2.08/2.29 all A B F (mem(F,arr(A,B))-> (all G (mem(G,arr(A,B))-> ((all X (mem(X,A)->ap(F,X)=ap(G,X)))->F=G)))).
% 2.08/2.29 all A Y X (mem(X,A)->ap(k(A,Y),X)=Y).
% 2.08/2.29 all A X (mem(X,A)->ap(i(A),X)=X).
% 2.08/2.29 mem(c_2Ebool_2E_7E,arr(bool,bool)).
% 2.08/2.29 all Q (mem(Q,bool)-> (p(ap(c_2Ebool_2E_7E,Q))<-> -p(Q))).
% 2.08/2.29 mem(c_2Ebool_2EF,bool).
% 2.08/2.29 -p(c_2Ebool_2EF).
% 2.08/2.29 mem(c_2Ebool_2ET,bool).
% 2.08/2.29 p(c_2Ebool_2ET).
% 2.08/2.29 mem(c_2Emin_2E_3D_3D_3E,arr(bool,arr(bool,bool))).
% 2.08/2.29 all Q (mem(Q,bool)-> (all R (mem(R,bool)-> (p(ap(ap(c_2Emin_2E_3D_3D_3E,Q),R))<-> (p(Q)->p(R)))))).
% 2.08/2.29 mem(c_2Ebool_2E_2F_5C,arr(bool,arr(bool,bool))).
% 2.08/2.29 all Q (mem(Q,bool)-> (all R (mem(R,bool)-> (p(ap(ap(c_2Ebool_2E_2F_5C,Q),R))<->p(Q)&p(R))))).
% 2.08/2.29 ne(ty_2Enum_2Enum).
% 2.08/2.29 mem(c_2Enum_2E0,ty_2Enum_2Enum).
% 2.08/2.29 ne(ty_2Erealax_2Ereal).
% 2.08/2.29 all A0 (ne(A0)-> (all A1 (ne(A1)->ne(ty_2Epair_2Eprod(A0,A1))))).
% 2.08/2.29 mem(c_2Ecomplex_2Ecomplex__of__num,arr(ty_2Enum_2Enum,ty_2Epair_2Eprod(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal))).
% 2.08/2.29 mem(c_2Ecomplex_2Ecomplex__inv,arr(ty_2Epair_2Eprod(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal),ty_2Epair_2Eprod(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal))).
% 2.08/2.29 all A_27a (ne(A_27a)->mem(c_2Emin_2E_3D(A_27a),arr(A_27a,arr(A_27a,bool)))).
% 2.08/2.29 all A (ne(A)-> (all X (mem(X,A)-> (all Y (mem(Y,A)-> (p(ap(ap(c_2Emin_2E_3D(A),X),Y))<->X=Y)))))).
% 2.08/2.29 all A_27a (ne(A_27a)->mem(c_2Ebool_2E_21(A_27a),arr(arr(A_27a,bool),bool))).
% 2.08/2.29 all A (ne(A)-> (all Q (mem(Q,arr(A,bool))-> (p(ap(c_2Ebool_2E_21(A),Q))<-> (all X (mem(X,A)->p(ap(Q,X)))))))).
% 2.08/2.29 $T.
% 2.08/2.29 all A_27a (ne(A_27a)-> (all V0t (mem(V0t,bool)-> ((all V1x (mem(V1x,A_27a)->p(V0t)))<->p(V0t))))).
% 2.08/2.29 all V0t (mem(V0t,bool)-> (p(V0t)<->p(V0t))& ((p(V0t)->$T)<->$T)& (($F->p(V0t))<->$T)& ((p(V0t)->p(V0t))<->$T)& (-p(V0t)<-> -p(V0t))).
% 2.08/2.29 all V0z (mem(V0z,ty_2Epair_2Eprod(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal))-> (ap(c_2Ecomplex_2Ecomplex__inv,V0z)=ap(c_2Ecomplex_2Ecomplex__of__num,c_2Enum_2E0)<->V0z=ap(c_2Ecomplex_2Ecomplex__of__num,c_2Enum_2E0))).
% 2.08/2.29 -(all V0z (mem(V0z,ty_2Epair_2Eprod(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal))-> (V0z!=ap(c_2Ecomplex_2Ecomplex__of__num,c_2Enum_2E0)->ap(c_2Ecomplex_2Ecomplex__inv,V0z)!=ap(c_2Ecomplex_2Ecomplex__of__num,c_2Enum_2E0)))).
% 2.08/2.29 end_of_list.
% 2.08/2.29
% 2.08/2.29 -------> usable clausifies to:
% 2.08/2.29
% 2.08/2.29 list(usable).
% 2.08/2.29 0 [] A=A.
% 2.08/2.29 0 [] ne(bool).
% 2.08/2.29 0 [] ne(ind).
% 2.08/2.29 0 [] -ne(A)| -ne(B)|ne(arr(A,B)).
% 2.08/2.29 0 [] -mem(F,arr(A,B))| -mem(X,A)|mem(ap(F,X),B).
% 2.08/2.29 0 [] -mem(Q,bool)| -mem(R,bool)|p(Q)|p(R)|Q=R.
% 2.08/2.29 0 [] -mem(Q,bool)| -mem(R,bool)| -p(Q)| -p(R)|Q=R.
% 2.08/2.29 0 [] -mem(F,arr(A,B))| -mem(G,arr(A,B))|mem($f1(A,B,F,G),A)|F=G.
% 2.08/2.29 0 [] -mem(F,arr(A,B))| -mem(G,arr(A,B))|ap(F,$f1(A,B,F,G))!=ap(G,$f1(A,B,F,G))|F=G.
% 2.08/2.29 0 [] -mem(X,A)|ap(k(A,Y),X)=Y.
% 2.08/2.29 0 [] -mem(X,A)|ap(i(A),X)=X.
% 2.08/2.29 0 [] mem(c_2Ebool_2E_7E,arr(bool,bool)).
% 2.08/2.29 0 [] -mem(Q,bool)| -p(ap(c_2Ebool_2E_7E,Q))| -p(Q).
% 2.08/2.29 0 [] -mem(Q,bool)|p(ap(c_2Ebool_2E_7E,Q))|p(Q).
% 2.08/2.29 0 [] mem(c_2Ebool_2EF,bool).
% 2.08/2.29 0 [] -p(c_2Ebool_2EF).
% 2.08/2.29 0 [] mem(c_2Ebool_2ET,bool).
% 2.08/2.29 0 [] p(c_2Ebool_2ET).
% 2.08/2.29 0 [] mem(c_2Emin_2E_3D_3D_3E,arr(bool,arr(bool,bool))).
% 2.08/2.29 0 [] -mem(Q,bool)| -mem(R,bool)| -p(ap(ap(c_2Emin_2E_3D_3D_3E,Q),R))| -p(Q)|p(R).
% 2.08/2.29 0 [] -mem(Q,bool)| -mem(R,bool)|p(ap(ap(c_2Emin_2E_3D_3D_3E,Q),R))|p(Q).
% 2.08/2.29 0 [] -mem(Q,bool)| -mem(R,bool)|p(ap(ap(c_2Emin_2E_3D_3D_3E,Q),R))| -p(R).
% 2.08/2.29 0 [] mem(c_2Ebool_2E_2F_5C,arr(bool,arr(bool,bool))).
% 2.08/2.29 0 [] -mem(Q,bool)| -mem(R,bool)| -p(ap(ap(c_2Ebool_2E_2F_5C,Q),R))|p(Q).
% 2.08/2.29 0 [] -mem(Q,bool)| -mem(R,bool)| -p(ap(ap(c_2Ebool_2E_2F_5C,Q),R))|p(R).
% 2.08/2.29 0 [] -mem(Q,bool)| -mem(R,bool)|p(ap(ap(c_2Ebool_2E_2F_5C,Q),R))| -p(Q)| -p(R).
% 2.08/2.29 0 [] ne(ty_2Enum_2Enum).
% 2.08/2.29 0 [] mem(c_2Enum_2E0,ty_2Enum_2Enum).
% 2.08/2.29 0 [] ne(ty_2Erealax_2Ereal).
% 2.08/2.29 0 [] -ne(A0)| -ne(A1)|ne(ty_2Epair_2Eprod(A0,A1)).
% 2.08/2.29 0 [] mem(c_2Ecomplex_2Ecomplex__of__num,arr(ty_2Enum_2Enum,ty_2Epair_2Eprod(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal))).
% 2.08/2.29 0 [] mem(c_2Ecomplex_2Ecomplex__inv,arr(ty_2Epair_2Eprod(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal),ty_2Epair_2Eprod(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal))).
% 2.08/2.29 0 [] -ne(A_27a)|mem(c_2Emin_2E_3D(A_27a),arr(A_27a,arr(A_27a,bool))).
% 2.08/2.29 0 [] -ne(A)| -mem(X,A)| -mem(Y,A)| -p(ap(ap(c_2Emin_2E_3D(A),X),Y))|X=Y.
% 2.08/2.29 0 [] -ne(A)| -mem(X,A)| -mem(Y,A)|p(ap(ap(c_2Emin_2E_3D(A),X),Y))|X!=Y.
% 2.08/2.29 0 [] -ne(A_27a)|mem(c_2Ebool_2E_21(A_27a),arr(arr(A_27a,bool),bool)).
% 2.08/2.29 0 [] -ne(A)| -mem(Q,arr(A,bool))| -p(ap(c_2Ebool_2E_21(A),Q))| -mem(X,A)|p(ap(Q,X)).
% 2.08/2.29 0 [] -ne(A)| -mem(Q,arr(A,bool))|p(ap(c_2Ebool_2E_21(A),Q))|mem($f2(A,Q),A).
% 2.08/2.29 0 [] -ne(A)| -mem(Q,arr(A,bool))|p(ap(c_2Ebool_2E_21(A),Q))| -p(ap(Q,$f2(A,Q))).
% 2.08/2.29 0 [] $T.
% 2.08/2.29 0 [] -ne(A_27a)| -mem(V0t,bool)|mem($f3(A_27a,V0t),A_27a)|p(V0t).
% 2.08/2.29 0 [] -mem(V0t,bool)| -$F|p(V0t)| -$T.
% 2.08/2.29 0 [] -mem(V0t,bool)|$T.
% 2.08/2.29 0 [] -mem(V0z,ty_2Epair_2Eprod(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal))|ap(c_2Ecomplex_2Ecomplex__inv,V0z)!=ap(c_2Ecomplex_2Ecomplex__of__num,c_2Enum_2E0)|V0z=ap(c_2Ecomplex_2Ecomplex__of__num,c_2Enum_2E0).
% 2.08/2.29 0 [] -mem(V0z,ty_2Epair_2Eprod(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal))|ap(c_2Ecomplex_2Ecomplex__inv,V0z)=ap(c_2Ecomplex_2Ecomplex__of__num,c_2Enum_2E0)|V0z!=ap(c_2Ecomplex_2Ecomplex__of__num,c_2Enum_2E0).
% 2.08/2.29 0 [] mem($c1,ty_2Epair_2Eprod(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal)).
% 2.08/2.29 0 [] $c1!=ap(c_2Ecomplex_2Ecomplex__of__num,c_2Enum_2E0).
% 2.08/2.29 0 [] ap(c_2Ecomplex_2Ecomplex__inv,$c1)=ap(c_2Ecomplex_2Ecomplex__of__num,c_2Enum_2E0).
% 2.08/2.29 end_of_list.
% 2.08/2.29
% 2.08/2.29 SCAN INPUT: prop=0, horn=0, equality=1, symmetry=0, max_lits=5.
% 2.08/2.29
% 2.08/2.29 This ia a non-Horn set with equality. The strategy will be
% 2.08/2.29 Knuth-Bendix, ordered hyper_res, factoring, and unit
% 2.08/2.29 deletion, with positive clauses in sos and nonpositive
% 2.08/2.29 clauses in usable.
% 2.08/2.29
% 2.08/2.29 dependent: set(knuth_bendix).
% 2.08/2.29 dependent: set(anl_eq).
% 2.08/2.29 dependent: set(para_from).
% 2.08/2.29 dependent: set(para_into).
% 2.08/2.29 dependent: clear(para_from_right).
% 2.08/2.29 dependent: clear(para_into_right).
% 2.08/2.29 dependent: set(para_from_vars).
% 2.08/2.29 dependent: set(eq_units_both_ways).
% 2.08/2.29 dependent: set(dynamic_demod_all).
% 2.08/2.29 dependent: set(dynamic_demod).
% 2.08/2.29 dependent: set(order_eq).
% 2.08/2.29 dependent: set(back_demod).
% 2.08/2.29 dependent: set(lrpo).
% 2.08/2.29 dependent: set(hyper_res).
% 2.08/2.29 dependent: set(unit_deletion).
% 2.08/2.29 dependent: set(factor).
% 2.08/2.29
% 2.08/2.29 ------------> process usable:
% 2.08/2.29 ** KEPT (pick-wt=8): 1 [] -ne(A)| -ne(B)|ne(arr(A,B)).
% 2.08/2.29 ** KEPT (pick-wt=13): 2 [] -mem(A,arr(B,C))| -mem(D,B)|mem(ap(A,D),C).
% 2.08/2.29 ** KEPT (pick-wt=13): 3 [] -mem(A,bool)| -mem(B,bool)|p(A)|p(B)|A=B.
% 2.08/2.29 ** KEPT (pick-wt=13): 4 [] -mem(A,bool)| -mem(B,bool)| -p(A)| -p(B)|A=B.
% 2.08/2.29 ** KEPT (pick-wt=20): 5 [] -mem(A,arr(B,C))| -mem(D,arr(B,C))|mem($f1(B,C,A,D),B)|A=D.
% 2.08/2.29 ** KEPT (pick-wt=28): 6 [] -mem(A,arr(B,C))| -mem(D,arr(B,C))|ap(A,$f1(B,C,A,D))!=ap(D,$f1(B,C,A,D))|A=D.
% 2.08/2.30 ** KEPT (pick-wt=10): 7 [] -mem(A,B)|ap(k(B,C),A)=C.
% 2.08/2.30 ** KEPT (pick-wt=9): 8 [] -mem(A,B)|ap(i(B),A)=A.
% 2.08/2.30 ** KEPT (pick-wt=9): 9 [] -mem(A,bool)| -p(ap(c_2Ebool_2E_7E,A))| -p(A).
% 2.08/2.30 ** KEPT (pick-wt=9): 10 [] -mem(A,bool)|p(ap(c_2Ebool_2E_7E,A))|p(A).
% 2.08/2.30 ** KEPT (pick-wt=2): 11 [] -p(c_2Ebool_2EF).
% 2.08/2.30 ** KEPT (pick-wt=16): 12 [] -mem(A,bool)| -mem(B,bool)| -p(ap(ap(c_2Emin_2E_3D_3D_3E,A),B))| -p(A)|p(B).
% 2.08/2.30 ** KEPT (pick-wt=14): 13 [] -mem(A,bool)| -mem(B,bool)|p(ap(ap(c_2Emin_2E_3D_3D_3E,A),B))|p(A).
% 2.08/2.30 ** KEPT (pick-wt=14): 14 [] -mem(A,bool)| -mem(B,bool)|p(ap(ap(c_2Emin_2E_3D_3D_3E,A),B))| -p(B).
% 2.08/2.30 ** KEPT (pick-wt=14): 15 [] -mem(A,bool)| -mem(B,bool)| -p(ap(ap(c_2Ebool_2E_2F_5C,A),B))|p(A).
% 2.08/2.30 ** KEPT (pick-wt=14): 16 [] -mem(A,bool)| -mem(B,bool)| -p(ap(ap(c_2Ebool_2E_2F_5C,A),B))|p(B).
% 2.08/2.30 ** KEPT (pick-wt=16): 17 [] -mem(A,bool)| -mem(B,bool)|p(ap(ap(c_2Ebool_2E_2F_5C,A),B))| -p(A)| -p(B).
% 2.08/2.30 ** KEPT (pick-wt=8): 18 [] -ne(A)| -ne(B)|ne(ty_2Epair_2Eprod(A,B)).
% 2.30/2.49 ** KEPT (pick-wt=10): 19 [] -ne(A)|mem(c_2Emin_2E_3D(A),arr(A,arr(A,bool))).
% 2.30/2.49 ** KEPT (pick-wt=18): 20 [] -ne(A)| -mem(B,A)| -mem(C,A)| -p(ap(ap(c_2Emin_2E_3D(A),B),C))|B=C.
% 2.30/2.49 ** KEPT (pick-wt=18): 21 [] -ne(A)| -mem(B,A)| -mem(C,A)|p(ap(ap(c_2Emin_2E_3D(A),B),C))|B!=C.
% 2.30/2.49 ** KEPT (pick-wt=10): 22 [] -ne(A)|mem(c_2Ebool_2E_21(A),arr(arr(A,bool),bool)).
% 2.30/2.49 ** KEPT (pick-wt=19): 23 [] -ne(A)| -mem(B,arr(A,bool))| -p(ap(c_2Ebool_2E_21(A),B))| -mem(C,A)|p(ap(B,C)).
% 2.30/2.49 ** KEPT (pick-wt=17): 24 [] -ne(A)| -mem(B,arr(A,bool))|p(ap(c_2Ebool_2E_21(A),B))|mem($f2(A,B),A).
% 2.30/2.49 ** KEPT (pick-wt=18): 25 [] -ne(A)| -mem(B,arr(A,bool))|p(ap(c_2Ebool_2E_21(A),B))| -p(ap(B,$f2(A,B))).
% 2.30/2.49 ** KEPT (pick-wt=12): 26 [] -ne(A)| -mem(B,bool)|mem($f3(A,B),A)|p(B).
% 2.30/2.49 ** KEPT (pick-wt=17): 27 [] -mem(A,ty_2Epair_2Eprod(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal))|ap(c_2Ecomplex_2Ecomplex__inv,A)!=ap(c_2Ecomplex_2Ecomplex__of__num,c_2Enum_2E0)|A=ap(c_2Ecomplex_2Ecomplex__of__num,c_2Enum_2E0).
% 2.30/2.49 ** KEPT (pick-wt=17): 28 [] -mem(A,ty_2Epair_2Eprod(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal))|ap(c_2Ecomplex_2Ecomplex__inv,A)=ap(c_2Ecomplex_2Ecomplex__of__num,c_2Enum_2E0)|A!=ap(c_2Ecomplex_2Ecomplex__of__num,c_2Enum_2E0).
% 2.30/2.49 ** KEPT (pick-wt=5): 30 [copy,29,flip.1] ap(c_2Ecomplex_2Ecomplex__of__num,c_2Enum_2E0)!=$c1.
% 2.30/2.49
% 2.30/2.49 ------------> process sos:
% 2.30/2.49 ** KEPT (pick-wt=3): 43 [] A=A.
% 2.30/2.49 ** KEPT (pick-wt=2): 44 [] ne(bool).
% 2.30/2.49 ** KEPT (pick-wt=2): 45 [] ne(ind).
% 2.30/2.49 ** KEPT (pick-wt=5): 46 [] mem(c_2Ebool_2E_7E,arr(bool,bool)).
% 2.30/2.49 ** KEPT (pick-wt=3): 47 [] mem(c_2Ebool_2EF,bool).
% 2.30/2.49 ** KEPT (pick-wt=3): 48 [] mem(c_2Ebool_2ET,bool).
% 2.30/2.49 ** KEPT (pick-wt=2): 49 [] p(c_2Ebool_2ET).
% 2.30/2.49 ** KEPT (pick-wt=7): 50 [] mem(c_2Emin_2E_3D_3D_3E,arr(bool,arr(bool,bool))).
% 2.30/2.49 ** KEPT (pick-wt=7): 51 [] mem(c_2Ebool_2E_2F_5C,arr(bool,arr(bool,bool))).
% 2.30/2.49 ** KEPT (pick-wt=2): 52 [] ne(ty_2Enum_2Enum).
% 2.30/2.49 ** KEPT (pick-wt=3): 53 [] mem(c_2Enum_2E0,ty_2Enum_2Enum).
% 2.30/2.49 ** KEPT (pick-wt=2): 54 [] ne(ty_2Erealax_2Ereal).
% 2.30/2.49 ** KEPT (pick-wt=7): 55 [] mem(c_2Ecomplex_2Ecomplex__of__num,arr(ty_2Enum_2Enum,ty_2Epair_2Eprod(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal))).
% 2.30/2.49 ** KEPT (pick-wt=9): 56 [] mem(c_2Ecomplex_2Ecomplex__inv,arr(ty_2Epair_2Eprod(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal),ty_2Epair_2Eprod(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal))).
% 2.30/2.49 ** KEPT (pick-wt=5): 57 [] mem($c1,ty_2Epair_2Eprod(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal)).
% 2.30/2.49 ** KEPT (pick-wt=7): 59 [copy,58,flip.1] ap(c_2Ecomplex_2Ecomplex__of__num,c_2Enum_2E0)=ap(c_2Ecomplex_2Ecomplex__inv,$c1).
% 2.30/2.49 ---> New Demodulator: 60 [new_demod,59] ap(c_2Ecomplex_2Ecomplex__of__num,c_2Enum_2E0)=ap(c_2Ecomplex_2Ecomplex__inv,$c1).
% 2.30/2.49 Following clause subsumed by 43 during input processing: 0 [copy,43,flip.1] A=A.
% 2.30/2.49 43 back subsumes 41.
% 2.30/2.49 43 back subsumes 35.
% 2.30/2.49 43 back subsumes 34.
% 2.30/2.49 43 back subsumes 33.
% 2.30/2.49 43 back subsumes 32.
% 2.30/2.49 >>>> Starting back demodulation with 60.
% 2.30/2.49 >> back demodulating 30 with 60.
% 2.30/2.49 >> back demodulating 28 with 60.
% 2.30/2.49 >> back demodulating 27 with 60.
% 2.30/2.49
% 2.30/2.49 ======= end of input processing =======
% 2.30/2.49
% 2.30/2.49 =========== start of search ===========
% 2.30/2.49
% 2.30/2.49
% 2.30/2.49 Resetting weight limit to 6.
% 2.30/2.49
% 2.30/2.49
% 2.30/2.49 Resetting weight limit to 6.
% 2.30/2.49
% 2.30/2.49 sos_size=2872
% 2.30/2.49
% 2.30/2.49 -------- PROOF --------
% 2.30/2.49
% 2.30/2.49 ----> UNIT CONFLICT at 0.20 sec ----> 3048 [binary,3046.1,61.1] $F.
% 2.30/2.49
% 2.30/2.49 Length of proof is 5. Level of proof is 3.
% 2.30/2.49
% 2.30/2.49 ---------------- PROOF ----------------
% 2.30/2.49 % SZS status Theorem
% 2.30/2.49 % SZS output start Refutation
% See solution above
% 2.30/2.49 ------------ end of proof -------------
% 2.30/2.49
% 2.30/2.49
% 2.30/2.49 Search stopped by max_proofs option.
% 2.30/2.49
% 2.30/2.49
% 2.30/2.49 Search stopped by max_proofs option.
% 2.30/2.49
% 2.30/2.49 ============ end of search ============
% 2.30/2.49
% 2.30/2.49 -------------- statistics -------------
% 2.30/2.49 clauses given 51
% 2.30/2.49 clauses generated 4748
% 2.30/2.49 clauses kept 3025
% 2.30/2.49 clauses forward subsumed 1193
% 2.30/2.49 clauses back subsumed 5
% 2.30/2.49 Kbytes malloced 4882
% 2.30/2.49
% 2.30/2.49 ----------- times (seconds) -----------
% 2.30/2.49 user CPU time 0.20 (0 hr, 0 min, 0 sec)
% 2.30/2.49 system CPU time 0.00 (0 hr, 0 min, 0 sec)
% 2.30/2.49 wall-clock time 2 (0 hr, 0 min, 2 sec)
% 2.30/2.49
% 2.30/2.49 That finishes the proof of the theorem.
% 2.30/2.49
% 2.30/2.49 Process 23131 finished Wed Jul 27 03:00:26 2022
% 2.30/2.49 Otter interrupted
% 2.30/2.49 PROOF FOUND
%------------------------------------------------------------------------------