TSTP Solution File: LCL497+1 by Prover9---1109a
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : LCL497+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n021.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 : 600s
% DateTime : Sun Jul 17 13:47:12 EDT 2022
% Result : Theorem 18.06s 18.33s
% Output : Refutation 18.06s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12 % Problem : LCL497+1 : TPTP v8.1.0. Released v3.3.0.
% 0.12/0.13 % Command : tptp2X_and_run_prover9 %d %s
% 0.13/0.34 % Computer : n021.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 600
% 0.13/0.34 % DateTime : Sat Jul 2 20:11:45 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.75/1.01 ============================== Prover9 ===============================
% 0.75/1.01 Prover9 (32) version 2009-11A, November 2009.
% 0.75/1.01 Process 14798 was started by sandbox on n021.cluster.edu,
% 0.75/1.01 Sat Jul 2 20:11:46 2022
% 0.75/1.01 The command was "/export/starexec/sandbox/solver/bin/prover9 -t 300 -f /tmp/Prover9_14643_n021.cluster.edu".
% 0.75/1.01 ============================== end of head ===========================
% 0.75/1.01
% 0.75/1.01 ============================== INPUT =================================
% 0.75/1.01
% 0.75/1.01 % Reading from file /tmp/Prover9_14643_n021.cluster.edu
% 0.75/1.01
% 0.75/1.01 set(prolog_style_variables).
% 0.75/1.01 set(auto2).
% 0.75/1.01 % set(auto2) -> set(auto).
% 0.75/1.01 % set(auto) -> set(auto_inference).
% 0.75/1.01 % set(auto) -> set(auto_setup).
% 0.75/1.01 % set(auto_setup) -> set(predicate_elim).
% 0.75/1.01 % set(auto_setup) -> assign(eq_defs, unfold).
% 0.75/1.01 % set(auto) -> set(auto_limits).
% 0.75/1.01 % set(auto_limits) -> assign(max_weight, "100.000").
% 0.75/1.01 % set(auto_limits) -> assign(sos_limit, 20000).
% 0.75/1.01 % set(auto) -> set(auto_denials).
% 0.75/1.01 % set(auto) -> set(auto_process).
% 0.75/1.01 % set(auto2) -> assign(new_constants, 1).
% 0.75/1.01 % set(auto2) -> assign(fold_denial_max, 3).
% 0.75/1.01 % set(auto2) -> assign(max_weight, "200.000").
% 0.75/1.01 % set(auto2) -> assign(max_hours, 1).
% 0.75/1.01 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 0.75/1.01 % set(auto2) -> assign(max_seconds, 0).
% 0.75/1.01 % set(auto2) -> assign(max_minutes, 5).
% 0.75/1.01 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 0.75/1.01 % set(auto2) -> set(sort_initial_sos).
% 0.75/1.01 % set(auto2) -> assign(sos_limit, -1).
% 0.75/1.01 % set(auto2) -> assign(lrs_ticks, 3000).
% 0.75/1.01 % set(auto2) -> assign(max_megs, 400).
% 0.75/1.01 % set(auto2) -> assign(stats, some).
% 0.75/1.01 % set(auto2) -> clear(echo_input).
% 0.75/1.01 % set(auto2) -> set(quiet).
% 0.75/1.01 % set(auto2) -> clear(print_initial_clauses).
% 0.75/1.01 % set(auto2) -> clear(print_given).
% 0.75/1.01 assign(lrs_ticks,-1).
% 0.75/1.01 assign(sos_limit,10000).
% 0.75/1.01 assign(order,kbo).
% 0.75/1.01 set(lex_order_vars).
% 0.75/1.01 clear(print_given).
% 0.75/1.01
% 0.75/1.01 % formulas(sos). % not echoed (45 formulas)
% 0.75/1.01
% 0.75/1.01 ============================== end of input ==========================
% 0.75/1.01
% 0.75/1.01 % From the command line: assign(max_seconds, 300).
% 0.75/1.01
% 0.75/1.01 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 0.75/1.01
% 0.75/1.01 % Formulas that are not ordinary clauses:
% 0.75/1.01 1 modus_ponens <-> (all X all Y (is_a_theorem(X) & is_a_theorem(implies(X,Y)) -> is_a_theorem(Y))) # label(modus_ponens) # label(axiom) # label(non_clause). [assumption].
% 0.75/1.01 2 substitution_of_equivalents <-> (all X all Y (is_a_theorem(equiv(X,Y)) -> X = Y)) # label(substitution_of_equivalents) # label(axiom) # label(non_clause). [assumption].
% 0.75/1.01 3 modus_tollens <-> (all X all Y is_a_theorem(implies(implies(not(Y),not(X)),implies(X,Y)))) # label(modus_tollens) # label(axiom) # label(non_clause). [assumption].
% 0.75/1.01 4 implies_1 <-> (all X all Y is_a_theorem(implies(X,implies(Y,X)))) # label(implies_1) # label(axiom) # label(non_clause). [assumption].
% 0.75/1.01 5 implies_2 <-> (all X all Y is_a_theorem(implies(implies(X,implies(X,Y)),implies(X,Y)))) # label(implies_2) # label(axiom) # label(non_clause). [assumption].
% 0.75/1.01 6 implies_3 <-> (all X all Y all Z is_a_theorem(implies(implies(X,Y),implies(implies(Y,Z),implies(X,Z))))) # label(implies_3) # label(axiom) # label(non_clause). [assumption].
% 0.75/1.01 7 and_1 <-> (all X all Y is_a_theorem(implies(and(X,Y),X))) # label(and_1) # label(axiom) # label(non_clause). [assumption].
% 0.75/1.01 8 and_2 <-> (all X all Y is_a_theorem(implies(and(X,Y),Y))) # label(and_2) # label(axiom) # label(non_clause). [assumption].
% 0.75/1.01 9 and_3 <-> (all X all Y is_a_theorem(implies(X,implies(Y,and(X,Y))))) # label(and_3) # label(axiom) # label(non_clause). [assumption].
% 0.75/1.01 10 or_1 <-> (all X all Y is_a_theorem(implies(X,or(X,Y)))) # label(or_1) # label(axiom) # label(non_clause). [assumption].
% 0.75/1.01 11 or_2 <-> (all X all Y is_a_theorem(implies(Y,or(X,Y)))) # label(or_2) # label(axiom) # label(non_clause). [assumption].
% 0.75/1.01 12 or_3 <-> (all X all Y all Z is_a_theorem(implies(implies(X,Z),implies(implies(Y,Z),implies(or(X,Y),Z))))) # label(or_3) # label(axiom) # label(non_clause). [assumption].
% 0.75/1.01 13 equivalence_1 <-> (all X all Y is_a_theorem(implies(equiv(X,Y),implies(X,Y)))) # label(equivalence_1) # label(axiom) # label(non_clause). [assumption].
% 0.75/1.01 14 equivalence_2 <-> (all X all Y is_a_theorem(implies(equiv(X,Y),implies(Y,X)))) # label(equivalence_2) # label(axiom) # label(non_clause). [assumption].
% 1.53/1.80 15 equivalence_3 <-> (all X all Y is_a_theorem(implies(implies(X,Y),implies(implies(Y,X),equiv(X,Y))))) # label(equivalence_3) # label(axiom) # label(non_clause). [assumption].
% 1.53/1.80 16 kn1 <-> (all P is_a_theorem(implies(P,and(P,P)))) # label(kn1) # label(axiom) # label(non_clause). [assumption].
% 1.53/1.80 17 kn2 <-> (all P all Q is_a_theorem(implies(and(P,Q),P))) # label(kn2) # label(axiom) # label(non_clause). [assumption].
% 1.53/1.80 18 kn3 <-> (all P all Q all R is_a_theorem(implies(implies(P,Q),implies(not(and(Q,R)),not(and(R,P)))))) # label(kn3) # label(axiom) # label(non_clause). [assumption].
% 1.53/1.80 19 cn1 <-> (all P all Q all R is_a_theorem(implies(implies(P,Q),implies(implies(Q,R),implies(P,R))))) # label(cn1) # label(axiom) # label(non_clause). [assumption].
% 1.53/1.80 20 cn2 <-> (all P all Q is_a_theorem(implies(P,implies(not(P),Q)))) # label(cn2) # label(axiom) # label(non_clause). [assumption].
% 1.53/1.80 21 cn3 <-> (all P is_a_theorem(implies(implies(not(P),P),P))) # label(cn3) # label(axiom) # label(non_clause). [assumption].
% 1.53/1.80 22 r1 <-> (all P is_a_theorem(implies(or(P,P),P))) # label(r1) # label(axiom) # label(non_clause). [assumption].
% 1.53/1.80 23 r2 <-> (all P all Q is_a_theorem(implies(Q,or(P,Q)))) # label(r2) # label(axiom) # label(non_clause). [assumption].
% 1.53/1.80 24 r3 <-> (all P all Q is_a_theorem(implies(or(P,Q),or(Q,P)))) # label(r3) # label(axiom) # label(non_clause). [assumption].
% 1.53/1.80 25 r4 <-> (all P all Q all R is_a_theorem(implies(or(P,or(Q,R)),or(Q,or(P,R))))) # label(r4) # label(axiom) # label(non_clause). [assumption].
% 1.53/1.80 26 r5 <-> (all P all Q all R is_a_theorem(implies(implies(Q,R),implies(or(P,Q),or(P,R))))) # label(r5) # label(axiom) # label(non_clause). [assumption].
% 1.53/1.80 27 op_or -> (all X all Y or(X,Y) = not(and(not(X),not(Y)))) # label(op_or) # label(axiom) # label(non_clause). [assumption].
% 1.53/1.80 28 op_and -> (all X all Y and(X,Y) = not(or(not(X),not(Y)))) # label(op_and) # label(axiom) # label(non_clause). [assumption].
% 1.53/1.80 29 op_implies_and -> (all X all Y implies(X,Y) = not(and(X,not(Y)))) # label(op_implies_and) # label(axiom) # label(non_clause). [assumption].
% 1.53/1.80 30 op_implies_or -> (all X all Y implies(X,Y) = or(not(X),Y)) # label(op_implies_or) # label(axiom) # label(non_clause). [assumption].
% 1.53/1.80 31 op_equiv -> (all X all Y equiv(X,Y) = and(implies(X,Y),implies(Y,X))) # label(op_equiv) # label(axiom) # label(non_clause). [assumption].
% 1.53/1.80
% 1.53/1.80 ============================== end of process non-clausal formulas ===
% 1.53/1.80
% 1.53/1.80 ============================== PROCESS INITIAL CLAUSES ===============
% 1.53/1.80
% 1.53/1.80 ============================== PREDICATE ELIMINATION =================
% 1.53/1.80
% 1.53/1.80 ============================== end predicate elimination =============
% 1.53/1.80
% 1.53/1.80 Auto_denials: (non-Horn, no changes).
% 1.53/1.80
% 1.53/1.80 Term ordering decisions:
% 1.53/1.80
% 1.53/1.80 % Assigning unary symbol not kb_weight 0 and highest precedence (94).
% 1.53/1.80 Function symbol KB weights: c1=1. c2=1. c3=1. c4=1. c5=1. c6=1. c7=1. c8=1. c9=1. c10=1. c11=1. c12=1. c13=1. c14=1. c15=1. c16=1. c17=1. c18=1. c19=1. c20=1. c21=1. c22=1. c23=1. c24=1. c25=1. c26=1. c27=1. c28=1. c29=1. c30=1. c31=1. c32=1. c33=1. c34=1. c35=1. c36=1. c37=1. c38=1. c39=1. c40=1. c41=1. c42=1. c43=1. c44=1. c45=1. c46=1. c47=1. c48=1. c49=1. c50=1. c51=1. c52=1. c53=1. c54=1. c55=1. implies=1. or=1. and=1. equiv=1. not=0.
% 1.53/1.80
% 1.53/1.80 ============================== end of process initial clauses ========
% 1.53/1.80
% 1.53/1.80 ============================== CLAUSES FOR SEARCH ====================
% 1.53/1.80
% 1.53/1.80 ============================== end of clauses for search =============
% 1.53/1.80
% 1.53/1.80 ============================== SEARCH ================================
% 1.53/1.80
% 1.53/1.80 % Starting search at 0.02 seconds.
% 1.53/1.80
% 1.53/1.80 Low Water (keep): wt=29.000, iters=3458
% 1.53/1.80
% 1.53/1.80 Low Water (keep): wt=25.000, iters=3394
% 1.53/1.80
% 1.53/1.80 Low Water (keep): wt=23.000, iters=3367
% 1.53/1.80
% 1.53/1.80 Low Water (keep): wt=22.000, iters=3443
% 1.53/1.80
% 1.53/1.80 Low Water (keep): wt=20.000, iters=3337
% 1.53/1.80
% 1.53/1.80 Low Water (keep): wt=19.000, iters=3341
% 1.53/1.80
% 1.53/1.80 Low Water (keep): wt=18.000, iters=3369
% 1.53/1.80
% 1.53/1.80 Low Water (keep): wt=17.000, iters=3589
% 1.53/1.80
% 1.53/1.80 Low Water (keep): wt=16.000, iters=3405
% 1.53/1.80
% 1.53/1.80 Low Water (keep): wt=15.000, iters=3351
% 1.53/1.80
% 18.06/18.33 Low Water (keep): wt=14.000, iters=3345
% 18.06/18.33
% 18.06/18.33 Low Water (displace): id=2781, wt=47.000
% 18.06/18.33
% 18.06/18.33 Low Water (displace): id=1418, wt=39.000
% 18.06/18.33
% 18.06/18.33 Low Water (displace): id=1469, wt=37.000
% 18.06/18.33
% 18.06/18.33 Low Water (displace): id=1468, wt=33.000
% 18.06/18.33
% 18.06/18.33 Low Water (displace): id=1466, wt=32.000
% 18.06/18.33
% 18.06/18.33 Low Water (displace): id=3757, wt=31.000
% 18.06/18.33
% 18.06/18.33 Low Water (displace): id=3696, wt=29.000
% 18.06/18.33
% 18.06/18.33 Low Water (displace): id=5562, wt=28.000
% 18.06/18.33
% 18.06/18.33 Low Water (displace): id=2062, wt=27.000
% 18.06/18.33
% 18.06/18.33 Low Water (displace): id=11171, wt=26.000
% 18.06/18.33
% 18.06/18.33 Low Water (displace): id=11464, wt=13.000
% 18.06/18.33
% 18.06/18.33 Low Water (displace): id=12002, wt=12.000
% 18.06/18.33
% 18.06/18.33 Low Water (displace): id=13775, wt=11.000
% 18.06/18.33
% 18.06/18.33 Low Water (displace): id=13816, wt=10.000
% 18.06/18.33
% 18.06/18.33 Low Water (displace): id=15525, wt=9.000
% 18.06/18.33
% 18.06/18.33 Low Water (keep): wt=13.000, iters=3441
% 18.06/18.33
% 18.06/18.33 Low Water (keep): wt=12.000, iters=3343
% 18.06/18.33
% 18.06/18.33 Low Water (keep): wt=11.000, iters=3335
% 18.06/18.33
% 18.06/18.33 ============================== PROOF =================================
% 18.06/18.33 % SZS status Theorem
% 18.06/18.33 % SZS output start Refutation
% 18.06/18.33
% 18.06/18.33 % Proof 1 at 16.15 (+ 1.18) seconds.
% 18.06/18.33 % Length of proof is 74.
% 18.06/18.33 % Level of proof is 21.
% 18.06/18.33 % Maximum clause weight is 12.000.
% 18.06/18.33 % Given clauses 3172.
% 18.06/18.33
% 18.06/18.33 1 modus_ponens <-> (all X all Y (is_a_theorem(X) & is_a_theorem(implies(X,Y)) -> is_a_theorem(Y))) # label(modus_ponens) # label(axiom) # label(non_clause). [assumption].
% 18.06/18.33 20 cn2 <-> (all P all Q is_a_theorem(implies(P,implies(not(P),Q)))) # label(cn2) # label(axiom) # label(non_clause). [assumption].
% 18.06/18.33 22 r1 <-> (all P is_a_theorem(implies(or(P,P),P))) # label(r1) # label(axiom) # label(non_clause). [assumption].
% 18.06/18.33 23 r2 <-> (all P all Q is_a_theorem(implies(Q,or(P,Q)))) # label(r2) # label(axiom) # label(non_clause). [assumption].
% 18.06/18.33 24 r3 <-> (all P all Q is_a_theorem(implies(or(P,Q),or(Q,P)))) # label(r3) # label(axiom) # label(non_clause). [assumption].
% 18.06/18.33 26 r5 <-> (all P all Q all R is_a_theorem(implies(implies(Q,R),implies(or(P,Q),or(P,R))))) # label(r5) # label(axiom) # label(non_clause). [assumption].
% 18.06/18.33 27 op_or -> (all X all Y or(X,Y) = not(and(not(X),not(Y)))) # label(op_or) # label(axiom) # label(non_clause). [assumption].
% 18.06/18.33 28 op_and -> (all X all Y and(X,Y) = not(or(not(X),not(Y)))) # label(op_and) # label(axiom) # label(non_clause). [assumption].
% 18.06/18.33 30 op_implies_or -> (all X all Y implies(X,Y) = or(not(X),Y)) # label(op_implies_or) # label(axiom) # label(non_clause). [assumption].
% 18.06/18.33 32 op_implies_or # label(principia_op_implies_or) # label(axiom). [assumption].
% 18.06/18.33 33 op_and # label(principia_op_and) # label(axiom). [assumption].
% 18.06/18.33 35 modus_ponens # label(principia_modus_ponens) # label(axiom). [assumption].
% 18.06/18.33 36 r1 # label(principia_r1) # label(axiom). [assumption].
% 18.06/18.33 37 r2 # label(principia_r2) # label(axiom). [assumption].
% 18.06/18.33 38 r3 # label(principia_r3) # label(axiom). [assumption].
% 18.06/18.33 40 r5 # label(principia_r5) # label(axiom). [assumption].
% 18.06/18.33 42 op_or # label(luka_op_or) # label(axiom). [assumption].
% 18.06/18.33 44 -cn2 # label(luka_cn2) # label(negated_conjecture). [assumption].
% 18.06/18.33 59 -r1 | is_a_theorem(implies(or(A,A),A)) # label(r1) # label(axiom). [clausify(22)].
% 18.06/18.33 60 is_a_theorem(implies(or(A,A),A)). [copy(59),unit_del(a,36)].
% 18.06/18.33 62 -r2 | is_a_theorem(implies(A,or(B,A))) # label(r2) # label(axiom). [clausify(23)].
% 18.06/18.33 63 is_a_theorem(implies(A,or(B,A))). [copy(62),unit_del(a,37)].
% 18.06/18.33 67 cn2 | -is_a_theorem(implies(c42,implies(not(c42),c43))) # label(cn2) # label(axiom). [clausify(20)].
% 18.06/18.33 68 -is_a_theorem(implies(c42,implies(not(c42),c43))). [copy(67),unit_del(a,44)].
% 18.06/18.33 71 -modus_ponens | -is_a_theorem(A) | -is_a_theorem(implies(A,B)) | is_a_theorem(B) # label(modus_ponens) # label(axiom). [clausify(1)].
% 18.06/18.33 72 -is_a_theorem(A) | -is_a_theorem(implies(A,B)) | is_a_theorem(B). [copy(71),unit_del(a,35)].
% 18.06/18.33 79 -r3 | is_a_theorem(implies(or(A,B),or(B,A))) # label(r3) # label(axiom). [clausify(24)].
% 18.06/18.33 80 is_a_theorem(implies(or(A,B),or(B,A))). [copy(79),unit_del(a,38)].
% 18.06/18.33 82 -op_implies_or | or(not(A),B) = implies(A,B) # label(op_implies_or) # label(axiom). [clausify(30)].
% 18.06/18.33 83 or(not(A),B) = implies(A,B). [copy(82),unit_del(a,32)].
% 18.06/18.33 89 -op_or | or(A,B) = not(and(not(A),not(B))) # label(op_or) # label(axiom). [clausify(27)].
% 18.06/18.33 90 not(and(not(A),not(B))) = or(A,B). [copy(89),flip(b),unit_del(a,42)].
% 18.06/18.33 91 -op_and | and(A,B) = not(or(not(A),not(B))) # label(op_and) # label(axiom). [clausify(28)].
% 18.06/18.33 92 not(implies(A,not(B))) = and(A,B). [copy(91),rewrite([83(5)]),flip(b),unit_del(a,33)].
% 18.06/18.33 104 -r5 | is_a_theorem(implies(implies(A,B),implies(or(C,A),or(C,B)))) # label(r5) # label(axiom). [clausify(26)].
% 18.06/18.33 105 is_a_theorem(implies(implies(A,B),implies(or(C,A),or(C,B)))). [copy(104),unit_del(a,40)].
% 18.06/18.33 117 -is_a_theorem(or(A,B)) | is_a_theorem(or(B,A)). [resolve(80,a,72,b)].
% 18.06/18.33 120 is_a_theorem(implies(A,implies(B,A))). [para(83(a,1),63(a,1,2))].
% 18.06/18.33 121 is_a_theorem(implies(implies(A,B),or(B,not(A)))). [para(83(a,1),80(a,1,1))].
% 18.06/18.33 122 is_a_theorem(implies(or(A,not(B)),implies(B,A))). [para(83(a,1),80(a,1,2))].
% 18.06/18.33 137 -is_a_theorem(implies(A,B)) | is_a_theorem(implies(or(C,A),or(C,B))). [resolve(105,a,72,b)].
% 18.06/18.33 185 -is_a_theorem(implies(A,B)) | is_a_theorem(or(B,not(A))). [para(83(a,1),117(a,1))].
% 18.06/18.33 386 is_a_theorem(implies(implies(A,not(B)),implies(B,not(A)))). [para(83(a,1),121(a,1,2))].
% 18.06/18.33 512 -is_a_theorem(or(A,not(B))) | is_a_theorem(implies(B,A)). [resolve(122,a,72,b)].
% 18.06/18.33 1132 -is_a_theorem(implies(A,not(B))) | is_a_theorem(implies(B,not(A))). [para(83(a,1),512(a,1))].
% 18.06/18.33 4224 is_a_theorem(implies(or(A,B),or(A,implies(C,B)))). [resolve(137,a,120,a)].
% 18.06/18.33 4230 is_a_theorem(implies(or(A,or(B,B)),or(A,B))). [resolve(137,a,60,a)].
% 18.06/18.33 5832 -is_a_theorem(or(A,B)) | is_a_theorem(or(A,implies(C,B))). [resolve(4224,a,72,b)].
% 18.06/18.33 5892 -is_a_theorem(or(A,or(B,B))) | is_a_theorem(or(A,B)). [resolve(4230,a,72,b)].
% 18.06/18.33 6822 -is_a_theorem(implies(A,or(B,B))) | is_a_theorem(implies(A,B)). [para(83(a,1),5892(a,1)),rewrite([83(5)])].
% 18.06/18.33 8251 is_a_theorem(implies(A,A)). [resolve(6822,a,63,a)].
% 18.06/18.33 8263 is_a_theorem(implies(A,not(not(A)))). [resolve(8251,a,1132,a)].
% 18.06/18.33 8264 is_a_theorem(or(A,not(A))). [resolve(8251,a,185,a)].
% 18.06/18.33 8497 is_a_theorem(or(A,implies(B,not(A)))). [resolve(8264,a,5832,a)].
% 18.06/18.33 8940 is_a_theorem(implies(or(A,B),or(A,not(not(B))))). [resolve(8263,a,137,a)].
% 18.06/18.33 18082 -is_a_theorem(or(A,B)) | is_a_theorem(or(A,not(not(B)))). [resolve(8940,a,72,b)].
% 18.06/18.33 18085 is_a_theorem(implies(implies(A,B),implies(A,not(not(B))))). [para(83(a,1),8940(a,1,1)),rewrite([83(5)])].
% 18.06/18.33 31186 is_a_theorem(or(A,not(and(B,A)))). [resolve(18082,a,8497,a),rewrite([92(3)])].
% 18.06/18.33 31208 -is_a_theorem(implies(A,B)) | is_a_theorem(implies(A,not(not(B)))). [para(83(a,1),18082(a,1)),rewrite([83(6)])].
% 18.06/18.33 31242 is_a_theorem(implies(and(A,B),B)). [resolve(31186,a,512,a)].
% 18.06/18.33 31310 is_a_theorem(implies(or(A,and(B,C)),or(A,C))). [resolve(31242,a,137,a)].
% 18.06/18.33 48243 is_a_theorem(implies(implies(A,B),not(and(A,not(B))))). [resolve(31208,a,18085,a),rewrite([92(5)])].
% 18.06/18.33 48333 is_a_theorem(implies(implies(A,not(B)),not(and(B,A)))). [resolve(31208,a,386,a),rewrite([92(5)])].
% 18.06/18.33 48807 -is_a_theorem(or(A,and(B,C))) | is_a_theorem(or(A,C)). [resolve(31310,a,72,b)].
% 18.06/18.33 65155 is_a_theorem(implies(implies(not(A),B),or(A,B))). [para(90(a,1),48243(a,1,2))].
% 18.06/18.33 65208 -is_a_theorem(implies(not(A),B)) | is_a_theorem(or(A,B)). [resolve(65155,a,72,b)].
% 18.06/18.33 68203 is_a_theorem(implies(and(A,B),and(B,A))). [resolve(48333,a,1132,a),rewrite([92(4)])].
% 18.06/18.33 69034 -is_a_theorem(implies(A,and(B,C))) | is_a_theorem(implies(A,C)). [para(83(a,1),48807(a,1)),rewrite([83(5)])].
% 18.06/18.33 107834 is_a_theorem(implies(and(A,B),A)). [resolve(69034,a,68203,a)].
% 18.06/18.33 108041 is_a_theorem(or(A,not(and(A,B)))). [resolve(107834,a,185,a)].
% 18.06/18.33 109829 is_a_theorem(implies(A,or(A,B))). [para(90(a,1),108041(a,1,2)),rewrite([83(3)])].
% 18.06/18.33 109840 is_a_theorem(or(A,implies(A,B))). [resolve(109829,a,65208,a),rewrite([83(2)])].
% 18.06/18.33 110031 is_a_theorem(implies(A,implies(not(A),B))). [para(83(a,1),109840(a,1))].
% 18.06/18.33 110032 $F. [resolve(110031,a,68,a)].
% 18.06/18.33
% 18.06/18.33 % SZS output end Refutation
% 18.06/18.33 ============================== end of proof ==========================
% 18.06/18.33
% 18.06/18.33 ============================== STATISTICS ============================
% 18.06/18.33
% 18.06/18.33 Given=3172. Generated=2152332. Kept=109983. proofs=1.
% 18.06/18.33 Usable=2943. Sos=9999. Demods=11. Limbo=87, Disabled=97027. Hints=0.
% 18.06/18.33 Megabytes=72.61.
% 18.06/18.33 User_CPU=16.15, System_CPU=1.18, Wall_clock=17.
% 18.06/18.33
% 18.06/18.33 ============================== end of statistics =====================
% 18.06/18.33
% 18.06/18.33 ============================== end of search =========================
% 18.06/18.33
% 18.06/18.33 THEOREM PROVED
% 18.06/18.33 % SZS status Theorem
% 18.06/18.33
% 18.06/18.33 Exiting with 1 proof.
% 18.06/18.33
% 18.06/18.33 Process 14798 exit (max_proofs) Sat Jul 2 20:12:03 2022
% 18.06/18.33 Prover9 interrupted
%------------------------------------------------------------------------------