TSTP Solution File: LCL450+2 by Otter---3.3
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : LCL450+2 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : otter-tptp-script %s
% Computer : n022.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 13:04:29 EDT 2022
% Result : Unknown 2.12s 2.28s
% Output : None
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.09/0.13 % Problem : LCL450+2 : TPTP v8.1.0. Released v3.3.0.
% 0.09/0.14 % Command : otter-tptp-script %s
% 0.13/0.35 % Computer : n022.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 09:16:20 EDT 2022
% 0.13/0.35 % CPUTime :
% 1.90/2.09 ----- Otter 3.3f, August 2004 -----
% 1.90/2.09 The process was started by sandbox on n022.cluster.edu,
% 1.90/2.09 Wed Jul 27 09:16:20 2022
% 1.90/2.09 The command was "./otter". The process ID is 14769.
% 1.90/2.09
% 1.90/2.09 set(prolog_style_variables).
% 1.90/2.09 set(auto).
% 1.90/2.09 dependent: set(auto1).
% 1.90/2.09 dependent: set(process_input).
% 1.90/2.09 dependent: clear(print_kept).
% 1.90/2.09 dependent: clear(print_new_demod).
% 1.90/2.09 dependent: clear(print_back_demod).
% 1.90/2.09 dependent: clear(print_back_sub).
% 1.90/2.09 dependent: set(control_memory).
% 1.90/2.09 dependent: assign(max_mem, 12000).
% 1.90/2.09 dependent: assign(pick_given_ratio, 4).
% 1.90/2.09 dependent: assign(stats_level, 1).
% 1.90/2.09 dependent: assign(max_seconds, 10800).
% 1.90/2.09 clear(print_given).
% 1.90/2.09
% 1.90/2.09 formula_list(usable).
% 1.90/2.09 all A (A=A).
% 1.90/2.09 modus_ponens<-> (all X Y (is_a_theorem(X)&is_a_theorem(implies(X,Y))->is_a_theorem(Y))).
% 1.90/2.09 substitution_of_e_quivalents<-> (all X Y (is_a_theorem(e_quiv(X,Y))->X=Y)).
% 1.90/2.09 modus_tollens<-> (all X Y is_a_theorem(implies(implies(not(Y),not(X)),implies(X,Y)))).
% 1.90/2.09 implies_1<-> (all X Y is_a_theorem(implies(X,implies(Y,X)))).
% 1.90/2.09 implies_2<-> (all X Y is_a_theorem(implies(implies(X,implies(X,Y)),implies(X,Y)))).
% 1.90/2.09 implies_3<-> (all X Y Z is_a_theorem(implies(implies(X,Y),implies(implies(Y,Z),implies(X,Z))))).
% 1.90/2.09 and_1<-> (all X Y is_a_theorem(implies(and(X,Y),X))).
% 1.90/2.09 and_2<-> (all X Y is_a_theorem(implies(and(X,Y),Y))).
% 1.90/2.09 and_3<-> (all X Y is_a_theorem(implies(X,implies(Y,and(X,Y))))).
% 1.90/2.09 or_1<-> (all X Y is_a_theorem(implies(X,or(X,Y)))).
% 1.90/2.09 or_2<-> (all X Y is_a_theorem(implies(Y,or(X,Y)))).
% 1.90/2.09 or_3<-> (all X Y Z is_a_theorem(implies(implies(X,Z),implies(implies(Y,Z),implies(or(X,Y),Z))))).
% 1.90/2.09 e_quivalence_1<-> (all X Y is_a_theorem(implies(e_quiv(X,Y),implies(X,Y)))).
% 1.90/2.09 e_quivalence_2<-> (all X Y is_a_theorem(implies(e_quiv(X,Y),implies(Y,X)))).
% 1.90/2.09 e_quivalence_3<-> (all X Y is_a_theorem(implies(implies(X,Y),implies(implies(Y,X),e_quiv(X,Y))))).
% 1.90/2.09 kn1<-> (all P is_a_theorem(implies(P,and(P,P)))).
% 1.90/2.09 kn2<-> (all P Q is_a_theorem(implies(and(P,Q),P))).
% 1.90/2.09 kn3<-> (all P Q R is_a_theorem(implies(implies(P,Q),implies(not(and(Q,R)),not(and(R,P)))))).
% 1.90/2.09 cn1<-> (all P Q R is_a_theorem(implies(implies(P,Q),implies(implies(Q,R),implies(P,R))))).
% 1.90/2.09 cn2<-> (all P Q is_a_theorem(implies(P,implies(not(P),Q)))).
% 1.90/2.09 cn3<-> (all P is_a_theorem(implies(implies(not(P),P),P))).
% 1.90/2.09 r1<-> (all P is_a_theorem(implies(or(P,P),P))).
% 1.90/2.09 r2<-> (all P Q is_a_theorem(implies(Q,or(P,Q)))).
% 1.90/2.09 r3<-> (all P Q is_a_theorem(implies(or(P,Q),or(Q,P)))).
% 1.90/2.09 r4<-> (all P Q R is_a_theorem(implies(or(P,or(Q,R)),or(Q,or(P,R))))).
% 1.90/2.09 r5<-> (all P Q R is_a_theorem(implies(implies(Q,R),implies(or(P,Q),or(P,R))))).
% 1.90/2.09 op_or-> (all X Y (or(X,Y)=not(and(not(X),not(Y))))).
% 1.90/2.09 op_and-> (all X Y (and(X,Y)=not(or(not(X),not(Y))))).
% 1.90/2.09 op_implies_and-> (all X Y (implies(X,Y)=not(and(X,not(Y))))).
% 1.90/2.09 op_implies_or-> (all X Y (implies(X,Y)=or(not(X),Y))).
% 1.90/2.09 op_e_quiv-> (all X Y (e_quiv(X,Y)=and(implies(X,Y),implies(Y,X)))).
% 1.90/2.09 op_or.
% 1.90/2.09 op_implies_and.
% 1.90/2.09 op_e_quiv.
% 1.90/2.09 modus_ponens.
% 1.90/2.09 modus_tollens.
% 1.90/2.09 implies_1.
% 1.90/2.09 implies_2.
% 1.90/2.09 implies_3.
% 1.90/2.09 and_1.
% 1.90/2.09 and_2.
% 1.90/2.09 and_3.
% 1.90/2.09 or_1.
% 1.90/2.09 or_2.
% 1.90/2.09 or_3.
% 1.90/2.09 e_quivalence_1.
% 1.90/2.09 e_quivalence_2.
% 1.90/2.09 e_quivalence_3.
% 1.90/2.09 -((all X is_a_theorem(e_quiv(X,X)))& (all X Y (is_a_theorem(e_quiv(X,Y))->is_a_theorem(e_quiv(not(X),not(Y)))))& (all X1 X2 Y (is_a_theorem(e_quiv(X1,X2))->is_a_theorem(e_quiv(and(X1,Y),and(X2,Y)))))& (all X1 X2 Y (is_a_theorem(e_quiv(X1,X2))->is_a_theorem(e_quiv(and(Y,X1),and(Y,X2)))))& (all X Y (is_a_theorem(X)&is_a_theorem(e_quiv(X,Y))->is_a_theorem(Y)))).
% 1.90/2.09 end_of_list.
% 1.90/2.09
% 1.90/2.09 -------> usable clausifies to:
% 1.90/2.09
% 1.90/2.09 list(usable).
% 1.90/2.09 0 [] A=A.
% 1.90/2.09 0 [] -modus_ponens| -is_a_theorem(X)| -is_a_theorem(implies(X,Y))|is_a_theorem(Y).
% 1.90/2.09 0 [] modus_ponens|is_a_theorem($c2).
% 1.90/2.09 0 [] modus_ponens|is_a_theorem(implies($c2,$c1)).
% 1.90/2.09 0 [] modus_ponens| -is_a_theorem($c1).
% 1.90/2.09 0 [] -substitution_of_e_quivalents| -is_a_theorem(e_quiv(X,Y))|X=Y.
% 1.90/2.09 0 [] substitution_of_e_quivalents|is_a_theorem(e_quiv($c4,$c3)).
% 1.90/2.09 0 [] substitution_of_e_quivalents|$c4!=$c3.
% 1.90/2.09 0 [] -modus_tollens|is_a_theorem(implies(implies(not(Y),not(X)),implies(X,Y))).
% 1.90/2.09 0 [] modus_tollens| -is_a_theorem(implies(implies(not($c5),not($c6)),implies($c6,$c5))).
% 1.90/2.09 0 [] -implies_1|is_a_theorem(implies(X,implies(Y,X))).
% 1.90/2.09 0 [] implies_1| -is_a_theorem(implies($c8,implies($c7,$c8))).
% 1.90/2.09 0 [] -implies_2|is_a_theorem(implies(implies(X,implies(X,Y)),implies(X,Y))).
% 1.90/2.09 0 [] implies_2| -is_a_theorem(implies(implies($c10,implies($c10,$c9)),implies($c10,$c9))).
% 1.90/2.09 0 [] -implies_3|is_a_theorem(implies(implies(X,Y),implies(implies(Y,Z),implies(X,Z)))).
% 1.90/2.09 0 [] implies_3| -is_a_theorem(implies(implies($c13,$c12),implies(implies($c12,$c11),implies($c13,$c11)))).
% 1.90/2.09 0 [] -and_1|is_a_theorem(implies(and(X,Y),X)).
% 1.90/2.09 0 [] and_1| -is_a_theorem(implies(and($c15,$c14),$c15)).
% 1.90/2.09 0 [] -and_2|is_a_theorem(implies(and(X,Y),Y)).
% 1.90/2.09 0 [] and_2| -is_a_theorem(implies(and($c17,$c16),$c16)).
% 1.90/2.09 0 [] -and_3|is_a_theorem(implies(X,implies(Y,and(X,Y)))).
% 1.90/2.09 0 [] and_3| -is_a_theorem(implies($c19,implies($c18,and($c19,$c18)))).
% 1.90/2.09 0 [] -or_1|is_a_theorem(implies(X,or(X,Y))).
% 1.90/2.09 0 [] or_1| -is_a_theorem(implies($c21,or($c21,$c20))).
% 1.90/2.09 0 [] -or_2|is_a_theorem(implies(Y,or(X,Y))).
% 1.90/2.09 0 [] or_2| -is_a_theorem(implies($c22,or($c23,$c22))).
% 1.90/2.09 0 [] -or_3|is_a_theorem(implies(implies(X,Z),implies(implies(Y,Z),implies(or(X,Y),Z)))).
% 1.90/2.09 0 [] or_3| -is_a_theorem(implies(implies($c26,$c24),implies(implies($c25,$c24),implies(or($c26,$c25),$c24)))).
% 1.90/2.09 0 [] -e_quivalence_1|is_a_theorem(implies(e_quiv(X,Y),implies(X,Y))).
% 1.90/2.09 0 [] e_quivalence_1| -is_a_theorem(implies(e_quiv($c28,$c27),implies($c28,$c27))).
% 1.90/2.09 0 [] -e_quivalence_2|is_a_theorem(implies(e_quiv(X,Y),implies(Y,X))).
% 1.90/2.09 0 [] e_quivalence_2| -is_a_theorem(implies(e_quiv($c30,$c29),implies($c29,$c30))).
% 1.90/2.09 0 [] -e_quivalence_3|is_a_theorem(implies(implies(X,Y),implies(implies(Y,X),e_quiv(X,Y)))).
% 1.90/2.09 0 [] e_quivalence_3| -is_a_theorem(implies(implies($c32,$c31),implies(implies($c31,$c32),e_quiv($c32,$c31)))).
% 1.90/2.09 0 [] -kn1|is_a_theorem(implies(P,and(P,P))).
% 1.90/2.09 0 [] kn1| -is_a_theorem(implies($c33,and($c33,$c33))).
% 1.90/2.09 0 [] -kn2|is_a_theorem(implies(and(P,Q),P)).
% 1.90/2.09 0 [] kn2| -is_a_theorem(implies(and($c35,$c34),$c35)).
% 1.90/2.09 0 [] -kn3|is_a_theorem(implies(implies(P,Q),implies(not(and(Q,R)),not(and(R,P))))).
% 1.90/2.09 0 [] kn3| -is_a_theorem(implies(implies($c38,$c37),implies(not(and($c37,$c36)),not(and($c36,$c38))))).
% 1.90/2.09 0 [] -cn1|is_a_theorem(implies(implies(P,Q),implies(implies(Q,R),implies(P,R)))).
% 1.90/2.09 0 [] cn1| -is_a_theorem(implies(implies($c41,$c40),implies(implies($c40,$c39),implies($c41,$c39)))).
% 1.90/2.09 0 [] -cn2|is_a_theorem(implies(P,implies(not(P),Q))).
% 1.90/2.09 0 [] cn2| -is_a_theorem(implies($c43,implies(not($c43),$c42))).
% 1.90/2.09 0 [] -cn3|is_a_theorem(implies(implies(not(P),P),P)).
% 1.90/2.09 0 [] cn3| -is_a_theorem(implies(implies(not($c44),$c44),$c44)).
% 1.90/2.09 0 [] -r1|is_a_theorem(implies(or(P,P),P)).
% 1.90/2.09 0 [] r1| -is_a_theorem(implies(or($c45,$c45),$c45)).
% 1.90/2.09 0 [] -r2|is_a_theorem(implies(Q,or(P,Q))).
% 1.90/2.09 0 [] r2| -is_a_theorem(implies($c46,or($c47,$c46))).
% 1.90/2.09 0 [] -r3|is_a_theorem(implies(or(P,Q),or(Q,P))).
% 1.90/2.09 0 [] r3| -is_a_theorem(implies(or($c49,$c48),or($c48,$c49))).
% 1.90/2.09 0 [] -r4|is_a_theorem(implies(or(P,or(Q,R)),or(Q,or(P,R)))).
% 1.90/2.09 0 [] r4| -is_a_theorem(implies(or($c52,or($c51,$c50)),or($c51,or($c52,$c50)))).
% 1.90/2.09 0 [] -r5|is_a_theorem(implies(implies(Q,R),implies(or(P,Q),or(P,R)))).
% 1.90/2.09 0 [] r5| -is_a_theorem(implies(implies($c54,$c53),implies(or($c55,$c54),or($c55,$c53)))).
% 1.90/2.09 0 [] -op_or|or(X,Y)=not(and(not(X),not(Y))).
% 1.90/2.09 0 [] -op_and|and(X,Y)=not(or(not(X),not(Y))).
% 1.90/2.09 0 [] -op_implies_and|implies(X,Y)=not(and(X,not(Y))).
% 1.90/2.09 0 [] -op_implies_or|implies(X,Y)=or(not(X),Y).
% 1.90/2.09 0 [] -op_e_quiv|e_quiv(X,Y)=and(implies(X,Y),implies(Y,X)).
% 1.90/2.09 0 [] op_or.
% 1.90/2.09 0 [] op_implies_and.
% 1.90/2.09 0 [] op_e_quiv.
% 1.90/2.09 0 [] modus_ponens.
% 1.90/2.09 0 [] modus_tollens.
% 1.90/2.09 0 [] implies_1.
% 1.90/2.09 0 [] implies_2.
% 1.90/2.09 0 [] implies_3.
% 1.90/2.09 0 [] and_1.
% 1.90/2.09 0 [] and_2.
% 1.90/2.09 0 [] and_3.
% 1.90/2.09 0 [] or_1.
% 1.90/2.09 0 [] or_2.
% 1.90/2.09 0 [] or_3.
% 1.90/2.09 0 [] e_quivalence_1.
% 1.90/2.09 0 [] e_quivalence_2.
% 1.90/2.09 0 [] e_quivalence_3.
% 1.90/2.09 0 [] -is_a_theorem(e_quiv($c56,$c56))|is_a_theorem(e_quiv($c58,$c57))|is_a_theorem(e_quiv($c61,$c60))|is_a_theorem(e_quiv($c64,$c63))|is_a_theorem($c66).
% 1.90/2.09 0 [] -is_a_theorem(e_quiv($c56,$c56))|is_a_theorem(e_quiv($c58,$c57))|is_a_theorem(e_quiv($c61,$c60))|is_a_theorem(e_quiv($c64,$c63))|is_a_theorem(e_quiv($c66,$c65)).
% 1.90/2.09 0 [] -is_a_theorem(e_quiv($c56,$c56))|is_a_theorem(e_quiv($c58,$c57))|is_a_theorem(e_quiv($c61,$c60))|is_a_theorem(e_quiv($c64,$c63))| -is_a_theorem($c65).
% 1.90/2.09 0 [] -is_a_theorem(e_quiv($c56,$c56))|is_a_theorem(e_quiv($c58,$c57))|is_a_theorem(e_quiv($c61,$c60))| -is_a_theorem(e_quiv(and($c62,$c64),and($c62,$c63)))|is_a_theorem($c66).
% 1.90/2.09 0 [] -is_a_theorem(e_quiv($c56,$c56))|is_a_theorem(e_quiv($c58,$c57))|is_a_theorem(e_quiv($c61,$c60))| -is_a_theorem(e_quiv(and($c62,$c64),and($c62,$c63)))|is_a_theorem(e_quiv($c66,$c65)).
% 1.90/2.09 0 [] -is_a_theorem(e_quiv($c56,$c56))|is_a_theorem(e_quiv($c58,$c57))|is_a_theorem(e_quiv($c61,$c60))| -is_a_theorem(e_quiv(and($c62,$c64),and($c62,$c63)))| -is_a_theorem($c65).
% 1.90/2.09 0 [] -is_a_theorem(e_quiv($c56,$c56))|is_a_theorem(e_quiv($c58,$c57))| -is_a_theorem(e_quiv(and($c61,$c59),and($c60,$c59)))|is_a_theorem(e_quiv($c64,$c63))|is_a_theorem($c66).
% 1.90/2.09 0 [] -is_a_theorem(e_quiv($c56,$c56))|is_a_theorem(e_quiv($c58,$c57))| -is_a_theorem(e_quiv(and($c61,$c59),and($c60,$c59)))|is_a_theorem(e_quiv($c64,$c63))|is_a_theorem(e_quiv($c66,$c65)).
% 1.90/2.09 0 [] -is_a_theorem(e_quiv($c56,$c56))|is_a_theorem(e_quiv($c58,$c57))| -is_a_theorem(e_quiv(and($c61,$c59),and($c60,$c59)))|is_a_theorem(e_quiv($c64,$c63))| -is_a_theorem($c65).
% 1.90/2.09 0 [] -is_a_theorem(e_quiv($c56,$c56))|is_a_theorem(e_quiv($c58,$c57))| -is_a_theorem(e_quiv(and($c61,$c59),and($c60,$c59)))| -is_a_theorem(e_quiv(and($c62,$c64),and($c62,$c63)))|is_a_theorem($c66).
% 1.90/2.09 0 [] -is_a_theorem(e_quiv($c56,$c56))|is_a_theorem(e_quiv($c58,$c57))| -is_a_theorem(e_quiv(and($c61,$c59),and($c60,$c59)))| -is_a_theorem(e_quiv(and($c62,$c64),and($c62,$c63)))|is_a_theorem(e_quiv($c66,$c65)).
% 1.90/2.09 0 [] -is_a_theorem(e_quiv($c56,$c56))|is_a_theorem(e_quiv($c58,$c57))| -is_a_theorem(e_quiv(and($c61,$c59),and($c60,$c59)))| -is_a_theorem(e_quiv(and($c62,$c64),and($c62,$c63)))| -is_a_theorem($c65).
% 1.90/2.09 0 [] -is_a_theorem(e_quiv($c56,$c56))| -is_a_theorem(e_quiv(not($c58),not($c57)))|is_a_theorem(e_quiv($c61,$c60))|is_a_theorem(e_quiv($c64,$c63))|is_a_theorem($c66).
% 1.90/2.09 0 [] -is_a_theorem(e_quiv($c56,$c56))| -is_a_theorem(e_quiv(not($c58),not($c57)))|is_a_theorem(e_quiv($c61,$c60))|is_a_theorem(e_quiv($c64,$c63))|is_a_theorem(e_quiv($c66,$c65)).
% 1.90/2.09 0 [] -is_a_theorem(e_quiv($c56,$c56))| -is_a_theorem(e_quiv(not($c58),not($c57)))|is_a_theorem(e_quiv($c61,$c60))|is_a_theorem(e_quiv($c64,$c63))| -is_a_theorem($c65).
% 1.90/2.09 0 [] -is_a_theorem(e_quiv($c56,$c56))| -is_a_theorem(e_quiv(not($c58),not($c57)))|is_a_theorem(e_quiv($c61,$c60))| -is_a_theorem(e_quiv(and($c62,$c64),and($c62,$c63)))|is_a_theorem($c66).
% 1.90/2.09 0 [] -is_a_theorem(e_quiv($c56,$c56))| -is_a_theorem(e_quiv(not($c58),not($c57)))|is_a_theorem(e_quiv($c61,$c60))| -is_a_theorem(e_quiv(and($c62,$c64),and($c62,$c63)))|is_a_theorem(e_quiv($c66,$c65)).
% 1.90/2.09 0 [] -is_a_theorem(e_quiv($c56,$c56))| -is_a_theorem(e_quiv(not($c58),not($c57)))|is_a_theorem(e_quiv($c61,$c60))| -is_a_theorem(e_quiv(and($c62,$c64),and($c62,$c63)))| -is_a_theorem($c65).
% 1.90/2.09 0 [] -is_a_theorem(e_quiv($c56,$c56))| -is_a_theorem(e_quiv(not($c58),not($c57)))| -is_a_theorem(e_quiv(and($c61,$c59),and($c60,$c59)))|is_a_theorem(e_quiv($c64,$c63))|is_a_theorem($c66).
% 1.90/2.09 0 [] -is_a_theorem(e_quiv($c56,$c56))| -is_a_theorem(e_quiv(not($c58),not($c57)))| -is_a_theorem(e_quiv(and($c61,$c59),and($c60,$c59)))|is_a_theorem(e_quiv($c64,$c63))|is_a_theorem(e_quiv($c66,$c65)).
% 1.90/2.09 0 [] -is_a_theorem(e_quiv($c56,$c56))| -is_a_theorem(e_quiv(not($c58),not($c57)))| -is_a_theorem(e_quiv(and($c61,$c59),and($c60,$c59)))|is_a_theorem(e_quiv($c64,$c63))| -is_a_theorem($c65).
% 1.90/2.09 0 [] -is_a_theorem(e_quiv($c56,$c56))| -is_a_theorem(e_quiv(not($c58),not($c57)))| -is_a_theorem(e_quiv(and($c61,$c59),and($c60,$c59)))| -is_a_theorem(e_quiv(and($c62,$c64),and($c62,$c63)))|is_a_theorem($c66).
% 1.90/2.09 0 [] -is_a_theorem(e_quiv($c56,$c56))| -is_a_theorem(e_quiv(not($c58),not($c57)))| -is_a_theorem(e_quiv(and($c61,$c59),and($c60,$c59)))| -is_a_theorem(e_quiv(and($c62,$c64),and($c62,$c63)))|is_a_theorem(e_quiv($c66,$c65)).
% 1.90/2.09 0 [] -is_a_theorem(e_quiv($c56,$c56))| -is_a_theorem(e_quiv(not($c58),not($c57)))| -is_a_theorem(e_quiv(and($c61,$c59),and($c60,$c59)))| -is_a_theorem(e_quiv(and($c62,$c64),and($c62,$c63)))| -is_a_theorem($c65).
% 1.90/2.09 end_of_list.
% 1.90/2.09
% 1.90/2.09 SCAN INPUT: prop=0, horn=0, equality=1, symmetry=0, max_lits=5.
% 1.90/2.09
% 1.90/2.09 This ia a non-Horn set with equality. The strategy will be
% 1.90/2.09 Knuth-Bendix, ordered hyper_res, factoring, and unit
% 1.90/2.09 deletion, with positive clauses in sos and nonpositive
% 1.90/2.09 clauses in usable.
% 1.90/2.09
% 1.90/2.09 dependent: set(knuth_bendix).
% 1.90/2.09 dependent: set(anl_eq).
% 1.90/2.09 dependent: set(para_from).
% 1.90/2.09 dependent: set(para_into).
% 1.90/2.09 dependent: clear(para_from_right).
% 1.90/2.09 dependent: clear(para_into_right).
% 1.90/2.09 dependent: set(para_from_vars).
% 1.90/2.09 dependent: set(eq_units_both_ways).
% 1.90/2.09 dependent: set(dynamic_demod_all).
% 1.90/2.09 dependent: set(dynamic_demod).
% 1.90/2.09 dependent: set(order_eq).
% 1.90/2.09 dependent: set(back_demod).
% 1.90/2.09 dependent: set(lrpo).
% 1.90/2.09 dependent: set(hyper_res).
% 1.90/2.09 dependent: set(unit_deletion).
% 1.90/2.09 dependent: set(factor).
% 1.90/2.09
% 1.90/2.09 ------------> process usable:
% 1.90/2.09 ** KEPT (pick-wt=9): 1 [] -modus_ponens| -is_a_theorem(A)| -is_a_theorem(implies(A,B))|is_a_theorem(B).
% 1.90/2.09 ** KEPT (pick-wt=3): 2 [] modus_ponens| -is_a_theorem($c1).
% 1.90/2.09 ** KEPT (pick-wt=8): 3 [] -substitution_of_e_quivalents| -is_a_theorem(e_quiv(A,B))|A=B.
% 1.90/2.09 ** KEPT (pick-wt=4): 4 [] substitution_of_e_quivalents|$c4!=$c3.
% 1.90/2.09 ** KEPT (pick-wt=11): 5 [] -modus_tollens|is_a_theorem(implies(implies(not(A),not(B)),implies(B,A))).
% 1.90/2.09 ** KEPT (pick-wt=11): 6 [] modus_tollens| -is_a_theorem(implies(implies(not($c5),not($c6)),implies($c6,$c5))).
% 1.90/2.09 ** KEPT (pick-wt=7): 7 [] -implies_1|is_a_theorem(implies(A,implies(B,A))).
% 1.90/2.09 ** KEPT (pick-wt=7): 8 [] implies_1| -is_a_theorem(implies($c8,implies($c7,$c8))).
% 1.90/2.09 ** KEPT (pick-wt=11): 9 [] -implies_2|is_a_theorem(implies(implies(A,implies(A,B)),implies(A,B))).
% 1.90/2.09 ** KEPT (pick-wt=11): 10 [] implies_2| -is_a_theorem(implies(implies($c10,implies($c10,$c9)),implies($c10,$c9))).
% 1.90/2.09 ** KEPT (pick-wt=13): 11 [] -implies_3|is_a_theorem(implies(implies(A,B),implies(implies(B,C),implies(A,C)))).
% 1.90/2.09 ** KEPT (pick-wt=13): 12 [] implies_3| -is_a_theorem(implies(implies($c13,$c12),implies(implies($c12,$c11),implies($c13,$c11)))).
% 1.90/2.09 ** KEPT (pick-wt=7): 13 [] -and_1|is_a_theorem(implies(and(A,B),A)).
% 1.90/2.09 ** KEPT (pick-wt=7): 14 [] and_1| -is_a_theorem(implies(and($c15,$c14),$c15)).
% 1.90/2.09 ** KEPT (pick-wt=7): 15 [] -and_2|is_a_theorem(implies(and(A,B),B)).
% 1.90/2.09 ** KEPT (pick-wt=7): 16 [] and_2| -is_a_theorem(implies(and($c17,$c16),$c16)).
% 1.90/2.09 ** KEPT (pick-wt=9): 17 [] -and_3|is_a_theorem(implies(A,implies(B,and(A,B)))).
% 1.90/2.09 ** KEPT (pick-wt=9): 18 [] and_3| -is_a_theorem(implies($c19,implies($c18,and($c19,$c18)))).
% 1.90/2.09 ** KEPT (pick-wt=7): 19 [] -or_1|is_a_theorem(implies(A,or(A,B))).
% 1.90/2.09 ** KEPT (pick-wt=7): 20 [] or_1| -is_a_theorem(implies($c21,or($c21,$c20))).
% 1.90/2.09 ** KEPT (pick-wt=7): 21 [] -or_2|is_a_theorem(implies(A,or(B,A))).
% 1.90/2.09 ** KEPT (pick-wt=7): 22 [] or_2| -is_a_theorem(implies($c22,or($c23,$c22))).
% 1.90/2.09 ** KEPT (pick-wt=15): 23 [] -or_3|is_a_theorem(implies(implies(A,B),implies(implies(C,B),implies(or(A,C),B)))).
% 1.90/2.09 ** KEPT (pick-wt=15): 24 [] or_3| -is_a_theorem(implies(implies($c26,$c24),implies(implies($c25,$c24),implies(or($c26,$c25),$c24)))).
% 1.90/2.09 ** KEPT (pick-wt=9): 25 [] -e_quivalence_1|is_a_theorem(implies(e_quiv(A,B),implies(A,B))).
% 1.90/2.09 ** KEPT (pick-wt=9): 26 [] e_quivalence_1| -is_a_theorem(implies(e_quiv($c28,$c27),implies($c28,$c27))).
% 1.90/2.09 ** KEPT (pick-wt=9): 27 [] -e_quivalence_2|is_a_theorem(implies(e_quiv(A,B),implies(B,A))).
% 1.90/2.09 ** KEPT (pick-wt=9): 28 [] e_quivalence_2| -is_a_theorem(implies(e_quiv($c30,$c29),implies($c29,$c30))).
% 1.90/2.09 ** KEPT (pick-wt=13): 29 [] -e_quivalence_3|is_a_theorem(implies(implies(A,B),implies(implies(B,A),e_quiv(A,B)))).
% 1.90/2.09 ** KEPT (pick-wt=13): 30 [] e_quivalence_3| -is_a_theorem(implies(implies($c32,$c31),implies(implies($c31,$c32),e_quiv($c32,$c31)))).
% 1.90/2.09 ** KEPT (pick-wt=7): 31 [] -kn1|is_a_theorem(implies(A,and(A,A))).
% 1.90/2.09 ** KEPT (pick-wt=7): 32 [] kn1| -is_a_theorem(implies($c33,and($c33,$c33))).
% 1.90/2.09 ** KEPT (pick-wt=7): 33 [] -kn2|is_a_theorem(implies(and(A,B),A)).
% 1.90/2.09 ** KEPT (pick-wt=7): 34 [] kn2| -is_a_theorem(implies(and($c35,$c34),$c35)).
% 1.90/2.09 ** KEPT (pick-wt=15): 35 [] -kn3|is_a_theorem(implies(implies(A,B),implies(not(and(B,C)),not(and(C,A))))).
% 1.90/2.09 ** KEPT (pick-wt=15): 36 [] kn3| -is_a_theorem(implies(implies($c38,$c37),implies(not(and($c37,$c36)),not(and($c36,$c38))))).
% 1.90/2.09 ** KEPT (pick-wt=13): 37 [] -cn1|is_a_theorem(implies(implies(A,B),implies(implies(B,C),implies(A,C)))).
% 1.90/2.09 ** KEPT (pick-wt=13): 38 [] cn1| -is_a_theorem(implies(implies($c41,$c40),implies(implies($c40,$c39),implies($c41,$c39)))).
% 1.90/2.09 ** KEPT (pick-wt=8): 39 [] -cn2|is_a_theorem(implies(A,implies(not(A),B))).
% 1.90/2.09 ** KEPT (pick-wt=8): 40 [] cn2| -is_a_theorem(implies($c43,implies(not($c43),$c42))).
% 1.90/2.09 ** KEPT (pick-wt=8): 41 [] -cn3|is_a_theorem(implies(implies(not(A),A),A)).
% 1.90/2.09 ** KEPT (pick-wt=8): 42 [] cn3| -is_a_theorem(implies(implies(not($c44),$c44),$c44)).
% 1.90/2.09 ** KEPT (pick-wt=7): 43 [] -r1|is_a_theorem(implies(or(A,A),A)).
% 1.90/2.09 ** KEPT (pick-wt=7): 44 [] r1| -is_a_theorem(implies(or($c45,$c45),$c45)).
% 1.90/2.09 ** KEPT (pick-wt=7): 45 [] -r2|is_a_theorem(implies(A,or(B,A))).
% 1.90/2.09 ** KEPT (pick-wt=7): 46 [] r2| -is_a_theorem(implies($c46,or($c47,$c46))).
% 1.90/2.09 ** KEPT (pick-wt=9): 47 [] -r3|is_a_theorem(implies(or(A,B),or(B,A))).
% 1.90/2.09 ** KEPT (pick-wt=9): 48 [] r3| -is_a_theorem(implies(or($c49,$c48),or($c48,$c49))).
% 1.90/2.09 ** KEPT (pick-wt=13): 49 [] -r4|is_a_theorem(implies(or(A,or(B,C)),or(B,or(A,C)))).
% 1.90/2.09 ** KEPT (pick-wt=13): 50 [] r4| -is_a_theorem(implies(or($c52,or($c51,$c50)),or($c51,or($c52,$c50)))).
% 1.90/2.09 ** KEPT (pick-wt=13): 51 [] -r5|is_a_theorem(implies(implies(A,B),implies(or(C,A),or(C,B)))).
% 1.90/2.09 ** KEPT (pick-wt=13): 52 [] r5| -is_a_theorem(implies(implies($c54,$c53),implies(or($c55,$c54),or($c55,$c53)))).
% 1.90/2.09 ** KEPT (pick-wt=11): 54 [copy,53,flip.2] -op_or|not(and(not(A),not(B)))=or(A,B).
% 1.90/2.09 ** KEPT (pick-wt=11): 56 [copy,55,flip.2] -op_and|not(or(not(A),not(B)))=and(A,B).
% 1.90/2.09 ** KEPT (pick-wt=10): 58 [copy,57,flip.2] -op_implies_and|not(and(A,not(B)))=implies(A,B).
% 1.90/2.09 ** KEPT (pick-wt=9): 60 [copy,59,flip.2] -op_implies_or|or(not(A),B)=implies(A,B).
% 1.90/2.09 ** KEPT (pick-wt=12): 62 [copy,61,flip.2] -op_e_quiv|and(implies(A,B),implies(B,A))=e_quiv(A,B).
% 1.90/2.09 ** KEPT (pick-wt=18): 63 [] -is_a_theorem(e_quiv($c56,$c56))|is_a_theorem(e_quiv($c58,$c57))|is_a_theorem(e_quiv($c61,$c60))|is_a_theorem(e_quiv($c64,$c63))|is_a_theorem($c66).
% 1.90/2.09 ** KEPT (pick-wt=20): 64 [] -is_a_theorem(e_quiv($c56,$c56))|is_a_theorem(e_quiv($c58,$c57))|is_a_theorem(e_quiv($c61,$c60))|is_a_theorem(e_quiv($c64,$c63))|is_a_theorem(e_quiv($c66,$c65)).
% 1.90/2.09 ** KEPT (pick-wt=18): 65 [] -is_a_theorem(e_quiv($c56,$c56))|is_a_theorem(e_quiv($c58,$c57))|is_a_theorem(e_quiv($c61,$c60))|is_a_theorem(e_quiv($c64,$c63))| -is_a_theorem($c65).
% 1.90/2.09 ** KEPT (pick-wt=22): 66 [] -is_a_theorem(e_quiv($c56,$c56))|is_a_theorem(e_quiv($c58,$c57))|is_a_theorem(e_quiv($c61,$c60))| -is_a_theorem(e_quiv(and($c62,$c64),and($c62,$c63)))|is_a_theorem($c66).
% 1.90/2.09 ** KEPT (pick-wt=24): 67 [] -is_a_theorem(e_quiv($c56,$c56))|is_a_theorem(e_quiv($c58,$c57))|is_a_theorem(e_quiv($c61,$c60))| -is_a_theorem(e_quiv(and($c62,$c64),and($c62,$c63)))|is_a_theorem(e_quiv($c66,$c65)).
% 1.90/2.09 ** KEPT (pick-wt=22): 68 [] -is_a_theorem(e_quiv($c56,$c56))|is_a_theorem(e_quiv($c58,$c57))|is_a_theorem(e_quiv($c61,$c60))| -is_a_theorem(e_quiv(and($c62,$c64),and($c62,$c63)))| -is_a_theorem($c65).
% 1.90/2.09 ** KEPT (pick-wt=22): 69 [] -is_a_theorem(e_quiv($c56,$c56))|is_a_theorem(e_quiv($c58,$c57))| -is_a_theorem(e_quiv(and($c61,$c59),and($c60,$c59)))|is_a_theorem(e_quiv($c64,$c63))|is_a_theorem($c66).
% 1.90/2.09 ** KEPT (pick-wt=24): 70 [] -is_a_theorem(e_quiv($c56,$c56))|is_a_theorem(e_quiv($c58,$c57))| -is_a_theorem(e_quiv(and($c61,$c59),and($c60,$c59)))|is_a_theorem(e_quiv($c64,$c63))|is_a_theorem(e_quiv($c66,$c65)).
% 1.90/2.09 ** KEPT (pick-wt=22): 71 [] -is_a_theorem(e_quiv($c56,$c56))|is_a_theorem(e_quiv($c58,$c57))| -is_a_theorem(e_quiv(and($c61,$c59),and($c60,$c59)))|is_a_theorem(e_quiv($c64,$c63))| -is_a_theorem($c65).
% 1.90/2.09 ** KEPT (pick-wt=26): 72 [] -is_a_theorem(e_quiv($c56,$c56))|is_a_theorem(e_quiv($c58,$c57))| -is_a_theorem(e_quiv(and($c61,$c59),and($c60,$c59)))| -is_a_theorem(e_quiv(and($c62,$c64),and($c62,$c63)))|is_a_theorem($c66).
% 1.90/2.09 ** KEPT (pick-wt=28): 73 [] -is_a_theorem(e_quiv($c56,$c56))|is_a_theorem(e_quiv($c58,$c57))| -is_a_theorem(e_quiv(and($c61,$c59),and($c60,$c59)))| -is_a_theorem(e_quiv(and($c62,$c64),and($c62,$c63)))|is_a_theorem(e_quiv($c66,$c65)).
% 1.90/2.09 ** KEPT (pick-wt=26): 74 [] -is_a_theorem(e_quiv($c56,$c56))|is_a_theorem(e_quiv($c58,$c57))| -is_a_theorem(e_quiv(and($c61,$c59),and($c60,$c59)))| -is_a_theorem(e_quiv(and($c62,$c64),and($c62,$c63)))| -is_a_theorem($c65).
% 1.90/2.10 ** KEPT (pick-wt=20): 75 [] -is_a_theorem(e_quiv($c56,$c56))| -is_a_theorem(e_quiv(not($c58),not($c57)))|is_a_theorem(e_quiv($c61,$c60))|is_a_theorem(e_quiv($c64,$c63))|is_a_theorem($c66).
% 1.90/2.10 ** KEPT (pick-wt=22): 76 [] -is_a_theorem(e_quiv($c56,$c56))| -is_a_theorem(e_quiv(not($c58),not($c57)))|is_a_theorem(e_quiv($c61,$c60))|is_a_theorem(e_quiv($c64,$c63))|is_a_theorem(e_quiv($c66,$c65)).
% 1.90/2.10 ** KEPT (pick-wt=20): 77 [] -is_a_theorem(e_quiv($c56,$c56))| -is_a_theorem(e_quiv(not($c58),not($c57)))|is_a_theorem(e_quiv($c61,$c60))|is_a_theorem(e_quiv($c64,$c63))| -is_a_theorem($c65).
% 1.90/2.10 ** KEPT (pick-wt=24): 78 [] -is_a_theorem(e_quiv($c56,$c56))| -is_a_theorem(e_quiv(not($c58),not($c57)))|is_a_theorem(e_quiv($c61,$c60))| -is_a_theorem(e_quiv(and($c62,$c64),and($c62,$c63)))|is_a_theorem($c66).
% 1.90/2.10 ** KEPT (pick-wt=26): 79 [] -is_a_theorem(e_quiv($c56,$c56))| -is_a_theorem(e_quiv(not($c58),not($c57)))|is_a_theorem(e_quiv($c61,$c60))| -is_a_theorem(e_quiv(and($c62,$c64),and($c62,$c63)))|is_a_theorem(e_quiv($c66,$c65)).
% 1.90/2.10 ** KEPT (pick-wt=24): 80 [] -is_a_theorem(e_quiv($c56,$c56))| -is_a_theorem(e_quiv(not($c58),not($c57)))|is_a_theorem(e_quiv($c61,$c60))| -is_a_theorem(e_quiv(and($c62,$c64),and($c62,$c63)))| -is_a_theorem($c65).
% 1.90/2.10 ** KEPT (pick-wt=24): 81 [] -is_a_theorem(e_quiv($c56,$c56))| -is_a_theorem(e_quiv(not($c58),not($c57)))| -is_a_theorem(e_quiv(and($c61,$c59),and($c60,$c59)))|is_a_theorem(e_quiv($c64,$c63))|is_a_theorem($c66).
% 1.90/2.10 ** KEPT (pick-wt=26): 82 [] -is_a_theorem(e_quiv($c56,$c56))| -is_a_theorem(e_quiv(not($c58),not($c57)))| -is_a_theorem(e_quiv(and($c61,$c59),and($c60,$c59)))|is_a_theorem(e_quiv($c64,$c63))|is_a_theorem(e_quiv($c66,$c65)).
% 1.90/2.10 ** KEPT (pick-wt=24): 83 [] -is_a_theorem(e_quiv($c56,$c56))| -is_a_theorem(e_quiv(not($c58),not($c57)))| -is_a_theorem(e_quiv(and($c61,$c59),and($c60,$c59)))|is_a_theorem(e_quiv($c64,$c63))| -is_a_theorem($c65).
% 1.90/2.10 ** KEPT (pick-wt=28): 84 [] -is_a_theorem(e_quiv($c56,$c56))| -is_a_theorem(e_quiv(not($c58),not($c57)))| -is_a_theorem(e_quiv(and($c61,$c59),and($c60,$c59)))| -is_a_theorem(e_quiv(and($c62,$c64),and($c62,$c63)))|is_a_theorem($c66).
% 1.90/2.10 ** KEPT (pick-wt=30): 85 [] -is_a_theorem(e_quiv($c56,$c56))| -is_a_theorem(e_quiv(not($c58),not($c57)))| -is_a_theorem(e_quiv(and($c61,$c59),and($c60,$c59)))| -is_a_theorem(e_quiv(and($c62,$c64),and($c62,$c63)))|is_a_theorem(e_quiv($c66,$c65)).
% 1.90/2.10 ** KEPT (pick-wt=28): 86 [] -is_a_theorem(e_quiv($c56,$c56))| -is_a_theorem(e_quiv(not($c58),not($c57)))| -is_a_theorem(e_quiv(and($c61,$c59),and($c60,$c59)))| -is_a_theorem(e_quiv(and($c62,$c64),and($c62,$c63)))| -is_a_theorem($c65).
% 1.90/2.10
% 1.90/2.10 ------------> process sos:
% 1.90/2.10 ** KEPT (pick-wt=3): 87 [] A=A.
% 1.90/2.10 ** KEPT (pick-wt=3): 88 [] modus_ponens|is_a_theorem($c2).
% 1.90/2.10 ** KEPT (pick-wt=5): 89 [] modus_ponens|is_a_theorem(implies($c2,$c1)).
% 1.90/2.10 ** KEPT (pick-wt=5): 90 [] substitution_of_e_quivalents|is_a_theorem(e_quiv($c4,$c3)).
% 1.90/2.10 ** KEPT (pick-wt=1): 91 [] op_or.
% 1.90/2.10 ** KEPT (pick-wt=1): 92 [] op_implies_and.
% 1.90/2.10 ** KEPT (pick-wt=1): 93 [] op_e_quiv.
% 1.90/2.10 ** KEPT (pick-wt=1): 94 [] modus_ponens.
% 1.90/2.10 ** KEPT (pick-wt=1): 95 [] modus_tollens.
% 1.90/2.10 ** KEPT (pick-wt=1): 96 [] implies_1.
% 1.90/2.10 ** KEPT (pick-wt=1): 97 [] implies_2.
% 1.90/2.10 ** KEPT (pick-wt=1): 98 [] implies_3.
% 1.90/2.10 ** KEPT (pick-wt=1): 99 [] and_1.
% 1.90/2.10 ** KEPT (pick-wt=1): 100 [] and_2.
% 1.90/2.10 ** KEPT (pick-wt=1): 101 [] and_3.
% 1.90/2.10 ** KEPT (pick-wt=1): 102 [] or_1.
% 1.90/2.10 ** KEPT (pick-wt=1): 103 [] or_2.
% 1.90/2.10 ** KEPT (pick-wt=1): 104 [] or_3.
% 1.90/2.10 ** KEPT (pick-wt=1): 105 [] e_quivalence_1.
% 1.90/2.10 ** KEPT (pick-wt=1): 106 [] e_quivalence_2.
% 1.90/2.10 ** KEPT (pick-wt=1): 107 [] e_quivalence_3.
% 1.90/2.10 Following clause subsumed by 87 during input processing: 0 [copy,87,flip.1] A=A.
% 1.90/2.10 94 back subsumes 89.
% 1.90/2.10 94 back subsumes 88.
% 1.90/2.10 94 back subsumes 2.
% 1.90/2.10 95 back subsumes 6.
% 1.90/2.10 96 back subsumes 8.
% 1.90/2.10 97 back subsumes 10.
% 1.90/2.10 98 back subsumes 12.
% 1.90/2.10 99 back subsumes 14.
% 1.90/2.10 100 back subsumes 16.
% 1.90/2.10 101 back subsumes 18.
% 1.90/2.10 102 back subsumes 20.
% 1.90/2.10 103 back subsumes 22.
% 1.90/2.10 104 back subsumes 24.
% 1.90/2.10 105 back subsumes 26.
% 1.90/2.10 106 back subsumes 28.
% 1.90/2.10 107 back subsumes 30.
% 1.90/2.10
% 1.90/2.10 ======= end of input processing =======
% 1.90/2.10
% 1.90/2.10 =========== start of search ===========
% 1.90/2.10
% 1.90/2.10
% 1.90/2.10 Resetting weight limit to 8.
% 1.90/2.10
% 1.90/2.10
% 1.90/2.10 Resetting weight limit to 8.
% 2.12/2.28
% 2.12/2.28 sos_size=186
% 2.12/2.28
% 2.12/2.28 Search stopped because sos empty.
% 2.12/2.28
% 2.12/2.28
% 2.12/2.28 Search stopped because sos empty.
% 2.12/2.28
% 2.12/2.28 ============ end of search ============
% 2.12/2.28
% 2.12/2.28 -------------- statistics -------------
% 2.12/2.28 clauses given 293
% 2.12/2.28 clauses generated 20258
% 2.12/2.28 clauses kept 381
% 2.12/2.28 clauses forward subsumed 4460
% 2.12/2.28 clauses back subsumed 46
% 2.12/2.28 Kbytes malloced 6835
% 2.12/2.28
% 2.12/2.28 ----------- times (seconds) -----------
% 2.12/2.28 user CPU time 0.19 (0 hr, 0 min, 0 sec)
% 2.12/2.28 system CPU time 0.01 (0 hr, 0 min, 0 sec)
% 2.12/2.28 wall-clock time 2 (0 hr, 0 min, 2 sec)
% 2.12/2.28
% 2.12/2.28 Process 14769 finished Wed Jul 27 09:16:22 2022
% 2.12/2.28 Otter interrupted
% 2.12/2.28 PROOF NOT FOUND
%------------------------------------------------------------------------------