TSTP Solution File: LCL457+1 by Prover9---1109a
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : LCL457+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n012.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 600s
% DateTime : Sun Jul 17 13:46:57 EDT 2022
% Result : Theorem 34.23s 34.50s
% Output : Refutation 34.23s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : LCL457+1 : TPTP v8.1.0. Released v3.3.0.
% 0.06/0.12 % Command : tptp2X_and_run_prover9 %d %s
% 0.13/0.33 % Computer : n012.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 600
% 0.13/0.33 % DateTime : Sun Jul 3 16:29:46 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 9939 was started by sandbox on n012.cluster.edu,
% 0.75/1.01 Sun Jul 3 16:29:47 2022
% 0.75/1.01 The command was "/export/starexec/sandbox/solver/bin/prover9 -t 300 -f /tmp/Prover9_9785_n012.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_9785_n012.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 (53 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].
% 1.12/1.44 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].
% 1.12/1.44 16 kn1 <-> (all P is_a_theorem(implies(P,and(P,P)))) # label(kn1) # label(axiom) # label(non_clause). [assumption].
% 1.12/1.44 17 kn2 <-> (all P all Q is_a_theorem(implies(and(P,Q),P))) # label(kn2) # label(axiom) # label(non_clause). [assumption].
% 1.12/1.44 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].
% 1.12/1.44 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].
% 1.12/1.44 20 cn2 <-> (all P all Q is_a_theorem(implies(P,implies(not(P),Q)))) # label(cn2) # label(axiom) # label(non_clause). [assumption].
% 1.12/1.44 21 cn3 <-> (all P is_a_theorem(implies(implies(not(P),P),P))) # label(cn3) # label(axiom) # label(non_clause). [assumption].
% 1.12/1.44 22 r1 <-> (all P is_a_theorem(implies(or(P,P),P))) # label(r1) # label(axiom) # label(non_clause). [assumption].
% 1.12/1.44 23 r2 <-> (all P all Q is_a_theorem(implies(Q,or(P,Q)))) # label(r2) # label(axiom) # label(non_clause). [assumption].
% 1.12/1.44 24 r3 <-> (all P all Q is_a_theorem(implies(or(P,Q),or(Q,P)))) # label(r3) # label(axiom) # label(non_clause). [assumption].
% 1.12/1.44 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].
% 1.12/1.44 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].
% 1.12/1.44 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].
% 1.12/1.44 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].
% 1.12/1.44 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].
% 1.12/1.44 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].
% 1.12/1.44 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].
% 1.12/1.44
% 1.12/1.44 ============================== end of process non-clausal formulas ===
% 1.12/1.44
% 1.12/1.44 ============================== PROCESS INITIAL CLAUSES ===============
% 1.12/1.44
% 1.12/1.44 ============================== PREDICATE ELIMINATION =================
% 1.12/1.44
% 1.12/1.44 ============================== end predicate elimination =============
% 1.12/1.44
% 1.12/1.44 Auto_denials: (non-Horn, no changes).
% 1.12/1.44
% 1.12/1.44 Term ordering decisions:
% 1.12/1.44
% 1.12/1.44 % Assigning unary symbol not kb_weight 0 and highest precedence (93).
% 1.12/1.44 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.
% 1.12/1.44
% 1.12/1.44 ============================== end of process initial clauses ========
% 1.12/1.44
% 1.12/1.44 ============================== CLAUSES FOR SEARCH ====================
% 1.12/1.44
% 1.12/1.44 ============================== end of clauses for search =============
% 1.12/1.44
% 1.12/1.44 ============================== SEARCH ================================
% 1.12/1.44
% 1.12/1.44 % Starting search at 0.02 seconds.
% 1.12/1.44
% 1.12/1.44 Low Water (keep): wt=40.000, iters=3407
% 1.12/1.44
% 1.12/1.44 Low Water (keep): wt=36.000, iters=3394
% 1.12/1.44
% 1.12/1.44 Low Water (keep): wt=35.000, iters=3369
% 1.12/1.44
% 1.12/1.44 Low Water (keep): wt=34.000, iters=3363
% 1.12/1.44
% 1.12/1.44 Low Water (keep): wt=32.000, iters=3345
% 1.12/1.44
% 1.12/1.44 Low Water (keep): wt=28.000, iters=3496
% 1.12/1.44
% 1.12/1.44 Low Water (keep): wt=27.000, iters=3470
% 1.12/1.44
% 1.12/1.44 Low Water (keep): wt=25.000, iters=3400
% 1.12/1.44
% 1.12/1.44 Low Water (keep): wt=24.000, iters=3649
% 1.12/1.44
% 1.12/1.44 Low Water (keep): wt=21.000, iters=3521
% 1.12/1.44
% 1.12/1.44 Low Water (keep): wt=19.000, iters=3362
% 34.23/34.50
% 34.23/34.50 Low Water (keep): wt=17.000, iters=3357
% 34.23/34.50
% 34.23/34.50 Low Water (keep): wt=16.000, iters=3342
% 34.23/34.50
% 34.23/34.50 Low Water (keep): wt=15.000, iters=3335
% 34.23/34.50
% 34.23/34.50 Low Water (keep): wt=14.000, iters=3341
% 34.23/34.50
% 34.23/34.50 Low Water (keep): wt=13.000, iters=3371
% 34.23/34.50
% 34.23/34.50 NOTE: Back_subsumption disabled, ratio of kept to back_subsumed is 40 (0.00 of 0.96 sec).
% 34.23/34.50
% 34.23/34.50 Low Water (keep): wt=12.000, iters=3343
% 34.23/34.50
% 34.23/34.50 Low Water (displace): id=3493, wt=43.000
% 34.23/34.50
% 34.23/34.50 Low Water (displace): id=3491, wt=42.000
% 34.23/34.50
% 34.23/34.50 Low Water (displace): id=4653, wt=41.000
% 34.23/34.50
% 34.23/34.50 Low Water (displace): id=4651, wt=40.000
% 34.23/34.50
% 34.23/34.50 Low Water (displace): id=1644, wt=39.000
% 34.23/34.50
% 34.23/34.50 Low Water (displace): id=4655, wt=38.000
% 34.23/34.50
% 34.23/34.50 Low Water (displace): id=4981, wt=37.000
% 34.23/34.50
% 34.23/34.50 Low Water (displace): id=4901, wt=36.000
% 34.23/34.50
% 34.23/34.50 Low Water (displace): id=5058, wt=35.000
% 34.23/34.50
% 34.23/34.50 Low Water (displace): id=4899, wt=34.000
% 34.23/34.50
% 34.23/34.50 Low Water (displace): id=5138, wt=33.000
% 34.23/34.50
% 34.23/34.50 Low Water (displace): id=4907, wt=32.000
% 34.23/34.50
% 34.23/34.50 Low Water (displace): id=5155, wt=31.000
% 34.23/34.50
% 34.23/34.50 Low Water (displace): id=5158, wt=30.000
% 34.23/34.50
% 34.23/34.50 Low Water (displace): id=11622, wt=28.000
% 34.23/34.50
% 34.23/34.50 Low Water (displace): id=11626, wt=26.000
% 34.23/34.50
% 34.23/34.50 Low Water (displace): id=8946, wt=25.000
% 34.23/34.50
% 34.23/34.50 Low Water (displace): id=12227, wt=24.000
% 34.23/34.50
% 34.23/34.50 Low Water (displace): id=12418, wt=23.000
% 34.23/34.50
% 34.23/34.50 Low Water (displace): id=12504, wt=15.000
% 34.23/34.50
% 34.23/34.50 Low Water (displace): id=12505, wt=14.000
% 34.23/34.50
% 34.23/34.50 Low Water (displace): id=12656, wt=11.000
% 34.23/34.50
% 34.23/34.50 Low Water (displace): id=12993, wt=9.000
% 34.23/34.50
% 34.23/34.50 Low Water (displace): id=14699, wt=8.000
% 34.23/34.50
% 34.23/34.50 Low Water (keep): wt=11.000, iters=3340
% 34.23/34.50
% 34.23/34.50 Low Water (keep): wt=10.000, iters=3379
% 34.23/34.50
% 34.23/34.50 ============================== PROOF =================================
% 34.23/34.50 % SZS status Theorem
% 34.23/34.50 % SZS output start Refutation
% 34.23/34.50
% 34.23/34.50 % Proof 1 at 31.39 (+ 2.12) seconds.
% 34.23/34.50 % Length of proof is 264.
% 34.23/34.50 % Level of proof is 45.
% 34.23/34.50 % Maximum clause weight is 19.000.
% 34.23/34.50 % Given clauses 5186.
% 34.23/34.50
% 34.23/34.50 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].
% 34.23/34.50 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].
% 34.23/34.50 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].
% 34.23/34.50 4 implies_1 <-> (all X all Y is_a_theorem(implies(X,implies(Y,X)))) # label(implies_1) # label(axiom) # label(non_clause). [assumption].
% 34.23/34.50 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].
% 34.23/34.50 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].
% 34.23/34.50 7 and_1 <-> (all X all Y is_a_theorem(implies(and(X,Y),X))) # label(and_1) # label(axiom) # label(non_clause). [assumption].
% 34.23/34.50 8 and_2 <-> (all X all Y is_a_theorem(implies(and(X,Y),Y))) # label(and_2) # label(axiom) # label(non_clause). [assumption].
% 34.23/34.50 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].
% 34.23/34.50 10 or_1 <-> (all X all Y is_a_theorem(implies(X,or(X,Y)))) # label(or_1) # label(axiom) # label(non_clause). [assumption].
% 34.23/34.50 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].
% 34.23/34.50 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].
% 34.23/34.50 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].
% 34.23/34.50 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].
% 34.23/34.50 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].
% 34.23/34.50 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].
% 34.23/34.50 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].
% 34.23/34.50 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].
% 34.23/34.50 32 op_or # label(hilbert_op_or) # label(axiom). [assumption].
% 34.23/34.50 33 op_implies_and # label(hilbert_op_implies_and) # label(axiom). [assumption].
% 34.23/34.50 34 op_equiv # label(hilbert_op_equiv) # label(axiom). [assumption].
% 34.23/34.50 35 modus_ponens # label(hilbert_modus_ponens) # label(axiom). [assumption].
% 34.23/34.50 36 modus_tollens # label(hilbert_modus_tollens) # label(axiom). [assumption].
% 34.23/34.50 37 implies_1 # label(hilbert_implies_1) # label(axiom). [assumption].
% 34.23/34.50 38 implies_2 # label(hilbert_implies_2) # label(axiom). [assumption].
% 34.23/34.50 39 implies_3 # label(hilbert_implies_3) # label(axiom). [assumption].
% 34.23/34.50 40 and_1 # label(hilbert_and_1) # label(axiom). [assumption].
% 34.23/34.50 41 and_2 # label(hilbert_and_2) # label(axiom). [assumption].
% 34.23/34.50 42 and_3 # label(hilbert_and_3) # label(axiom). [assumption].
% 34.23/34.50 43 or_1 # label(hilbert_or_1) # label(axiom). [assumption].
% 34.23/34.50 45 or_3 # label(hilbert_or_3) # label(axiom). [assumption].
% 34.23/34.50 48 equivalence_3 # label(hilbert_equivalence_3) # label(axiom). [assumption].
% 34.23/34.50 49 substitution_of_equivalents # label(substitution_of_equivalents) # label(axiom). [assumption].
% 34.23/34.50 50 op_implies_or # label(principia_op_implies_or) # label(axiom). [assumption].
% 34.23/34.50 51 op_and # label(principia_op_and) # label(axiom). [assumption].
% 34.23/34.50 52 -r4 # label(principia_r4) # label(negated_conjecture). [assumption].
% 34.23/34.50 53 -implies_1 | is_a_theorem(implies(A,implies(B,A))) # label(implies_1) # label(axiom). [clausify(4)].
% 34.23/34.50 54 is_a_theorem(implies(A,implies(B,A))). [copy(53),unit_del(a,37)].
% 34.23/34.50 56 -and_1 | is_a_theorem(implies(and(A,B),A)) # label(and_1) # label(axiom). [clausify(7)].
% 34.23/34.50 57 is_a_theorem(implies(and(A,B),A)). [copy(56),unit_del(a,40)].
% 34.23/34.50 59 -and_2 | is_a_theorem(implies(and(A,B),B)) # label(and_2) # label(axiom). [clausify(8)].
% 34.23/34.50 60 is_a_theorem(implies(and(A,B),B)). [copy(59),unit_del(a,41)].
% 34.23/34.50 62 -or_1 | is_a_theorem(implies(A,or(A,B))) # label(or_1) # label(axiom). [clausify(10)].
% 34.23/34.50 63 is_a_theorem(implies(A,or(A,B))). [copy(62),unit_del(a,43)].
% 34.23/34.50 76 -substitution_of_equivalents | -is_a_theorem(equiv(A,B)) | B = A # label(substitution_of_equivalents) # label(axiom). [clausify(2)].
% 34.23/34.50 77 -is_a_theorem(equiv(A,B)) | B = A. [copy(76),unit_del(a,49)].
% 34.23/34.50 82 -modus_ponens | -is_a_theorem(A) | -is_a_theorem(implies(A,B)) | is_a_theorem(B) # label(modus_ponens) # label(axiom). [clausify(1)].
% 34.23/34.50 83 -is_a_theorem(A) | -is_a_theorem(implies(A,B)) | is_a_theorem(B). [copy(82),unit_del(a,35)].
% 34.23/34.50 84 -and_3 | is_a_theorem(implies(A,implies(B,and(A,B)))) # label(and_3) # label(axiom). [clausify(9)].
% 34.23/34.50 85 is_a_theorem(implies(A,implies(B,and(A,B)))). [copy(84),unit_del(a,42)].
% 34.23/34.50 95 -op_implies_or | or(not(A),B) = implies(A,B) # label(op_implies_or) # label(axiom). [clausify(30)].
% 34.23/34.50 96 or(not(A),B) = implies(A,B). [copy(95),unit_del(a,50)].
% 34.23/34.50 97 -op_implies_and | not(and(A,not(B))) = implies(A,B) # label(op_implies_and) # label(axiom). [clausify(29)].
% 34.23/34.50 98 not(and(A,not(B))) = implies(A,B). [copy(97),unit_del(a,33)].
% 34.23/34.50 99 -modus_tollens | is_a_theorem(implies(implies(not(A),not(B)),implies(B,A))) # label(modus_tollens) # label(axiom). [clausify(3)].
% 34.23/34.50 100 is_a_theorem(implies(implies(not(A),not(B)),implies(B,A))). [copy(99),unit_del(a,36)].
% 34.23/34.50 102 -implies_2 | is_a_theorem(implies(implies(A,implies(A,B)),implies(A,B))) # label(implies_2) # label(axiom). [clausify(5)].
% 34.23/34.50 103 is_a_theorem(implies(implies(A,implies(A,B)),implies(A,B))). [copy(102),unit_del(a,38)].
% 34.23/34.50 105 -op_or | or(A,B) = not(and(not(A),not(B))) # label(op_or) # label(axiom). [clausify(27)].
% 34.23/34.50 106 or(A,B) = implies(not(A),B). [copy(105),rewrite([98(6)]),unit_del(a,32)].
% 34.23/34.50 107 -op_and | and(A,B) = not(or(not(A),not(B))) # label(op_and) # label(axiom). [clausify(28)].
% 34.23/34.50 108 not(implies(not(not(A)),not(B))) = and(A,B). [copy(107),rewrite([106(5)]),flip(b),unit_del(a,51)].
% 34.23/34.50 109 -op_equiv | and(implies(A,B),implies(B,A)) = equiv(A,B) # label(op_equiv) # label(axiom). [clausify(31)].
% 34.23/34.50 110 and(implies(A,B),implies(B,A)) = equiv(A,B). [copy(109),unit_del(a,34)].
% 34.23/34.50 111 -implies_3 | is_a_theorem(implies(implies(A,B),implies(implies(B,C),implies(A,C)))) # label(implies_3) # label(axiom). [clausify(6)].
% 34.23/34.50 112 is_a_theorem(implies(implies(A,B),implies(implies(B,C),implies(A,C)))). [copy(111),unit_del(a,39)].
% 34.23/34.50 114 -equivalence_3 | is_a_theorem(implies(implies(A,B),implies(implies(B,A),equiv(A,B)))) # label(equivalence_3) # label(axiom). [clausify(15)].
% 34.23/34.50 115 is_a_theorem(implies(implies(A,B),implies(implies(B,A),equiv(A,B)))). [copy(114),unit_del(a,48)].
% 34.23/34.50 120 r4 | -is_a_theorem(implies(or(c50,or(c51,c52)),or(c51,or(c50,c52)))) # label(r4) # label(axiom). [clausify(25)].
% 34.23/34.50 121 -is_a_theorem(implies(implies(not(c50),implies(not(c51),c52)),implies(not(c51),implies(not(c50),c52)))). [copy(120),rewrite([106(5),106(7),106(12),106(14)]),unit_del(a,52)].
% 34.23/34.50 126 -or_3 | is_a_theorem(implies(implies(A,B),implies(implies(C,B),implies(or(A,C),B)))) # label(or_3) # label(axiom). [clausify(12)].
% 34.23/34.50 127 is_a_theorem(implies(implies(A,B),implies(implies(C,B),implies(implies(not(A),C),B)))). [copy(126),rewrite([106(4)]),unit_del(a,45)].
% 34.23/34.50 131 implies(not(not(A)),B) = implies(A,B). [back_rewrite(96),rewrite([106(2)])].
% 34.23/34.50 136 is_a_theorem(implies(A,implies(not(A),B))). [back_rewrite(63),rewrite([106(1)])].
% 34.23/34.50 137 not(implies(A,not(B))) = and(A,B). [back_rewrite(108),rewrite([131(4)])].
% 34.23/34.50 141 -is_a_theorem(A) | is_a_theorem(implies(B,A)). [resolve(83,b,54,a)].
% 34.23/34.50 142 -is_a_theorem(A) | is_a_theorem(implies(B,and(A,B))). [resolve(85,a,83,b)].
% 34.23/34.50 145 not(and(A,implies(B,C))) = implies(A,and(B,not(C))). [para(98(a,1),98(a,1,1,2))].
% 34.23/34.50 146 -is_a_theorem(implies(not(A),not(B))) | is_a_theorem(implies(B,A)). [resolve(100,a,83,b)].
% 34.23/34.50 149 -is_a_theorem(implies(A,implies(A,B))) | is_a_theorem(implies(A,B)). [resolve(103,a,83,b)].
% 34.23/34.50 150 -is_a_theorem(implies(A,B)) | is_a_theorem(implies(implies(B,C),implies(A,C))). [resolve(112,a,83,b)].
% 34.23/34.50 151 -is_a_theorem(implies(A,B)) | is_a_theorem(implies(implies(B,A),equiv(A,B))). [resolve(115,a,83,b)].
% 34.23/34.50 156 -is_a_theorem(and(A,implies(implies(not(c50),implies(not(c51),c52)),implies(not(c51),implies(not(c50),c52))))). [ur(83,b,60,a,c,121,a)].
% 34.23/34.50 169 -is_a_theorem(implies(A,B)) | is_a_theorem(implies(implies(C,B),implies(implies(not(A),C),B))). [resolve(127,a,83,b)].
% 34.23/34.50 171 is_a_theorem(implies(implies(and(A,not(B)),C),implies(implies(D,C),implies(implies(implies(A,B),D),C)))). [para(98(a,1),127(a,1,2,2,1,1))].
% 34.23/34.50 172 is_a_theorem(implies(A,implies(B,not(not(A))))). [para(131(a,1),54(a,1))].
% 34.23/34.50 179 is_a_theorem(implies(implies(A,not(B)),implies(B,not(A)))). [para(131(a,1),100(a,1,1))].
% 34.23/34.50 182 and(implies(A,not(not(B))),implies(B,A)) = equiv(A,not(not(B))). [para(131(a,1),110(a,1,2))].
% 34.23/34.50 192 is_a_theorem(implies(not(A),implies(A,B))). [para(131(a,1),136(a,1,2))].
% 34.23/34.50 199 and(not(not(A)),B) = and(A,B). [para(131(a,1),137(a,1,1)),rewrite([137(3)]),flip(a)].
% 34.23/34.50 313 is_a_theorem(implies(A,and(implies(and(B,C),C),A))). [resolve(142,a,60,a)].
% 34.23/34.50 314 is_a_theorem(implies(A,and(implies(and(B,C),B),A))). [resolve(142,a,57,a)].
% 34.23/34.51 315 is_a_theorem(implies(A,and(implies(B,implies(C,B)),A))). [resolve(142,a,54,a)].
% 34.23/34.51 402 implies(implies(A,B),and(B,not(A))) = not(equiv(A,B)). [para(110(a,1),145(a,1,1)),flip(a)].
% 34.23/34.51 537 -is_a_theorem(implies(A,not(B))) | is_a_theorem(implies(B,not(A))). [para(131(a,1),146(a,1))].
% 34.23/34.51 1047 is_a_theorem(implies(A,not(not(A)))). [resolve(149,a,172,a)].
% 34.23/34.51 1051 is_a_theorem(implies(A,and(A,A))). [resolve(149,a,85,a)].
% 34.23/34.51 1052 is_a_theorem(implies(A,A)). [resolve(149,a,54,a)].
% 34.23/34.51 1057 is_a_theorem(implies(A,implies(B,B))). [resolve(1052,a,141,a)].
% 34.23/34.51 1121 is_a_theorem(implies(implies(implies(A,B),C),implies(not(A),C))). [resolve(150,a,192,a)].
% 34.23/34.51 1125 is_a_theorem(implies(implies(implies(not(A),B),C),implies(A,C))). [resolve(150,a,136,a)].
% 34.23/34.51 1134 is_a_theorem(implies(implies(A,B),implies(and(C,A),B))). [resolve(150,a,60,a)].
% 34.23/34.51 1135 is_a_theorem(implies(implies(implies(A,B),C),implies(B,C))). [resolve(150,a,54,a)].
% 34.23/34.51 1255 is_a_theorem(implies(A,and(implies(B,and(B,B)),A))). [resolve(1051,a,142,a)].
% 34.23/34.51 1287 is_a_theorem(implies(A,and(A,not(not(A))))). [para(131(a,1),1051(a,1)),rewrite([199(5)])].
% 34.23/34.51 1290 is_a_theorem(implies(implies(implies(A,A),B),implies(C,B))). [resolve(1057,a,150,a)].
% 34.23/34.51 1291 is_a_theorem(implies(A,and(implies(B,implies(C,C)),A))). [resolve(1057,a,142,a)].
% 34.23/34.51 1368 is_a_theorem(implies(implies(implies(A,A),B),equiv(B,implies(A,A)))). [resolve(151,a,1057,a)].
% 34.23/34.51 2626 -is_a_theorem(A) | is_a_theorem(and(A,not(not(A)))). [resolve(1287,a,83,b)].
% 34.23/34.51 4094 is_a_theorem(equiv(A,not(not(A)))). [resolve(2626,a,1047,a),rewrite([137(7),98(6),182(5)])].
% 34.23/34.51 4127 not(not(A)) = A. [resolve(4094,a,77,a)].
% 34.23/34.51 4175 not(and(A,B)) = implies(A,not(B)). [para(4127(a,1),98(a,1,1,2))].
% 34.23/34.51 4176 not(implies(A,B)) = and(A,not(B)). [para(98(a,1),4127(a,1,1))].
% 34.23/34.51 4178 -is_a_theorem(implies(not(A),B)) | is_a_theorem(implies(not(B),A)). [para(4127(a,1),146(a,1,2))].
% 34.23/34.51 6607 -is_a_theorem(implies(A,B)) | is_a_theorem(implies(not(B),not(A))). [para(4127(a,1),537(a,1,2))].
% 34.23/34.51 6643 is_a_theorem(implies(implies(A,B),implies(implies(not(B),A),B))). [resolve(169,a,1052,a)].
% 34.23/34.51 6664 is_a_theorem(implies(implies(A,B),implies(implies(implies(B,not(C)),A),B))). [resolve(169,a,57,a),rewrite([4175(3)])].
% 34.23/34.51 6731 -is_a_theorem(implies(A,B)) | is_a_theorem(implies(and(C,A),B)). [resolve(1134,a,83,b)].
% 34.23/34.51 6750 -is_a_theorem(implies(implies(A,B),C)) | is_a_theorem(implies(B,C)). [resolve(1135,a,83,b)].
% 34.23/34.51 6899 is_a_theorem(implies(implies(implies(A,A),B),B)). [resolve(1290,a,149,a)].
% 34.23/34.51 6920 -is_a_theorem(implies(implies(A,A),B)) | is_a_theorem(B). [resolve(6899,a,83,b)].
% 34.23/34.51 7685 is_a_theorem(implies(implies(implies(A,implies(B,B)),C),C)). [resolve(4178,a,1291,a),rewrite([4175(5),4127(4)])].
% 34.23/34.51 7686 is_a_theorem(implies(implies(implies(A,and(A,A)),B),B)). [resolve(4178,a,1255,a),rewrite([4175(5),4127(4)])].
% 34.23/34.51 7688 is_a_theorem(implies(implies(implies(A,implies(B,A)),C),C)). [resolve(4178,a,315,a),rewrite([4175(5),4127(4)])].
% 34.23/34.51 7689 is_a_theorem(implies(implies(implies(and(A,B),A),C),C)). [resolve(4178,a,314,a),rewrite([4175(5),4127(4)])].
% 34.23/34.51 7690 is_a_theorem(implies(implies(implies(and(A,B),B),C),C)). [resolve(4178,a,313,a),rewrite([4175(5),4127(4)])].
% 34.23/34.51 8972 is_a_theorem(implies(and(A,B),and(B,A))). [resolve(6607,a,179,a),rewrite([4176(3),4127(2),4176(4),4127(3)])].
% 34.23/34.51 9025 is_a_theorem(implies(equiv(A,B),equiv(B,A))). [para(110(a,1),8972(a,1,1)),rewrite([110(4)])].
% 34.23/34.51 10318 is_a_theorem(implies(and(A,not(B)),implies(B,C))). [resolve(6731,a,192,a)].
% 34.23/34.51 10334 is_a_theorem(implies(and(A,and(B,C)),C)). [resolve(6731,a,60,a)].
% 34.23/34.51 10395 is_a_theorem(implies(A,implies(B,implies(C,A)))). [resolve(10334,a,537,a),rewrite([4175(4),4175(3),4127(2)])].
% 34.23/34.51 13322 -is_a_theorem(implies(implies(A,implies(B,B)),C)) | is_a_theorem(C). [resolve(7685,a,83,b)].
% 34.23/34.51 13345 -is_a_theorem(implies(implies(A,and(A,A)),B)) | is_a_theorem(B). [resolve(7686,a,83,b)].
% 34.23/34.51 13368 -is_a_theorem(implies(implies(A,implies(B,A)),C)) | is_a_theorem(C). [resolve(7688,a,83,b)].
% 34.23/34.51 13391 -is_a_theorem(implies(implies(and(A,B),A),C)) | is_a_theorem(C). [resolve(7689,a,83,b)].
% 34.23/34.51 13435 -is_a_theorem(implies(implies(and(A,B),B),C)) | is_a_theorem(C). [resolve(7690,a,83,b)].
% 34.23/34.51 20199 is_a_theorem(implies(implies(A,B),implies(implies(implies(B,C),A),B))). [resolve(13391,a,171,a)].
% 34.23/34.51 22001 -is_a_theorem(implies(implies(A,B),C)) | is_a_theorem(implies(not(A),C)). [resolve(1121,a,83,b)].
% 34.23/34.51 22056 -is_a_theorem(implies(implies(not(A),B),C)) | is_a_theorem(implies(A,C)). [resolve(1125,a,83,b)].
% 34.23/34.51 23619 is_a_theorem(implies(implies(not(A),and(B,A)),A)). [resolve(6643,a,13435,a)].
% 34.23/34.51 23700 is_a_theorem(implies(A,and(A,implies(B,A)))). [resolve(23619,a,537,a),rewrite([4127(2),4176(4),4175(3),4127(2)])].
% 34.23/34.51 44778 is_a_theorem(implies(not(A),implies(implies(not(B),A),B))). [resolve(22001,a,6643,a)].
% 34.23/34.51 44805 is_a_theorem(implies(not(A),implies(B,and(implies(A,C),B)))). [resolve(22001,a,85,a)].
% 34.23/34.51 44857 is_a_theorem(implies(and(implies(not(A),B),not(A)),B)). [resolve(44778,a,6607,a),rewrite([4176(4),4127(6)])].
% 34.23/34.51 44871 is_a_theorem(implies(A,implies(implies(not(B),not(A)),B))). [para(4127(a,1),44778(a,1,1))].
% 34.23/34.51 45157 is_a_theorem(implies(and(implies(A,B),A),B)). [para(4127(a,1),44857(a,1,1,1,1)),rewrite([4127(3)])].
% 34.23/34.51 45457 is_a_theorem(implies(implies(not(A),and(B,not(B))),A)). [resolve(44871,a,6920,a),rewrite([4176(3)])].
% 34.23/34.51 47588 is_a_theorem(implies(A,and(A,implies(B,B)))). [resolve(45457,a,537,a),rewrite([4127(2),4176(4),4175(3),4127(2)])].
% 34.23/34.51 78893 is_a_theorem(implies(not(A),and(implies(A,B),not(A)))). [resolve(44805,a,149,a)].
% 34.23/34.51 78976 is_a_theorem(implies(implies(implies(A,B),A),A)). [resolve(78893,a,6607,a),rewrite([4175(4),4127(3),4127(4)])].
% 34.23/34.51 98383 is_a_theorem(equiv(implies(A,implies(B,B)),implies(B,B))). [resolve(1368,a,13368,a)].
% 34.23/34.51 98384 is_a_theorem(equiv(equiv(A,A),implies(A,A))). [resolve(1368,a,13345,a),rewrite([110(3)])].
% 34.23/34.51 98385 is_a_theorem(equiv(implies(A,A),implies(B,B))). [resolve(1368,a,13322,a)].
% 34.23/34.51 98387 is_a_theorem(implies(A,equiv(A,implies(B,B)))). [resolve(1368,a,6750,a)].
% 34.23/34.51 98431 equiv(A,A) = implies(A,A). [resolve(98384,a,77,a),flip(a)].
% 34.23/34.51 98534 implies(A,A) = implies(B,B). [resolve(98385,a,77,a)].
% 34.23/34.51 98538 implies(A,A) = c_0. [new_symbol(98534)].
% 34.23/34.51 98629 equiv(A,A) = c_0. [back_rewrite(98431),rewrite([98538(2)])].
% 34.23/34.51 98635 is_a_theorem(implies(A,equiv(A,c_0))). [back_rewrite(98387),rewrite([98538(1)])].
% 34.23/34.51 98636 is_a_theorem(c_0). [back_rewrite(98385),rewrite([98538(1),98538(2),98629(3)])].
% 34.23/34.51 98637 is_a_theorem(equiv(implies(A,c_0),c_0)). [back_rewrite(98383),rewrite([98538(1),98538(3)])].
% 34.23/34.51 99012 is_a_theorem(implies(A,and(A,c_0))). [back_rewrite(47588),rewrite([98538(1)])].
% 34.23/34.51 100049 is_a_theorem(implies(implies(c_0,A),A)). [back_rewrite(6899),rewrite([98538(1)])].
% 34.23/34.51 100572 and(c_0,c_0) = c_0. [para(98538(a,1),110(a,1,1)),rewrite([98538(2),98629(4)])].
% 34.23/34.51 101139 is_a_theorem(equiv(implies(and(A,B),B),c_0)). [resolve(98635,a,13435,a)].
% 34.23/34.51 101140 is_a_theorem(equiv(implies(and(A,B),A),c_0)). [resolve(98635,a,13391,a)].
% 34.23/34.51 101141 is_a_theorem(equiv(implies(A,implies(B,A)),c_0)). [resolve(98635,a,13368,a)].
% 34.23/34.51 101142 is_a_theorem(equiv(implies(A,and(A,A)),c_0)). [resolve(98635,a,13345,a)].
% 34.23/34.51 101164 -is_a_theorem(A) | is_a_theorem(equiv(A,c_0)). [resolve(98635,a,83,b)].
% 34.23/34.51 101229 implies(A,c_0) = c_0. [resolve(98637,a,77,a),flip(a)].
% 34.23/34.51 101270 and(implies(c_0,A),c_0) = equiv(c_0,A). [para(101229(a,1),110(a,1,2))].
% 34.23/34.51 101776 is_a_theorem(implies(implies(and(A,c_0),A),equiv(A,and(A,c_0)))). [resolve(99012,a,151,a)].
% 34.23/34.51 102663 is_a_theorem(equiv(implies(implies(c_0,A),A),c_0)). [resolve(101164,a,100049,a)].
% 34.23/34.51 104676 implies(and(A,B),B) = c_0. [resolve(101139,a,77,a),flip(a)].
% 34.23/34.51 104683 is_a_theorem(implies(implies(A,and(B,C)),implies(c_0,implies(A,C)))). [para(104676(a,1),112(a,1,2,1))].
% 34.23/34.51 104706 implies(and(A,B),A) = c_0. [resolve(101140,a,77,a),flip(a)].
% 34.23/34.51 104707 is_a_theorem(implies(c_0,equiv(A,and(A,c_0)))). [back_rewrite(101776),rewrite([104706(3)])].
% 34.23/34.51 104748 implies(A,implies(B,A)) = c_0. [resolve(101141,a,77,a),flip(a)].
% 34.23/34.51 104769 implies(A,and(A,A)) = c_0. [resolve(101142,a,77,a),flip(a)].
% 34.23/34.51 104770 equiv(A,and(A,A)) = c_0. [para(104769(a,1),110(a,1,1)),rewrite([104706(3),100572(3)]),flip(a)].
% 34.23/34.51 104791 and(A,A) = A. [para(104770(a,1),77(a,1)),unit_del(a,98636)].
% 34.23/34.51 104794 implies(A,not(A)) = not(A). [para(104791(a,1),4175(a,1,1)),flip(a)].
% 34.23/34.51 104807 is_a_theorem(implies(implies(A,B),implies(implies(B,not(A)),not(A)))). [para(104794(a,1),112(a,1,2,2))].
% 34.23/34.51 105448 implies(implies(c_0,A),A) = c_0. [resolve(102663,a,77,a),flip(a)].
% 34.23/34.51 105449 equiv(implies(c_0,A),A) = c_0. [para(105448(a,1),110(a,1,1)),rewrite([104748(4),104791(3)]),flip(a)].
% 34.23/34.51 105498 implies(c_0,A) = A. [para(105449(a,1),77(a,1)),flip(b),unit_del(a,98636)].
% 34.23/34.51 105560 is_a_theorem(equiv(A,and(A,c_0))). [back_rewrite(104707),rewrite([105498(5)])].
% 34.23/34.51 105563 is_a_theorem(implies(implies(A,and(B,C)),implies(A,C))). [back_rewrite(104683),rewrite([105498(5)])].
% 34.23/34.51 105572 equiv(c_0,A) = and(A,c_0). [back_rewrite(101270),rewrite([105498(2)]),flip(a)].
% 34.23/34.51 107722 and(A,c_0) = A. [resolve(105560,a,77,a)].
% 34.23/34.51 107727 equiv(c_0,A) = A. [back_rewrite(105572),rewrite([107722(4)])].
% 34.23/34.51 107730 implies(A,not(c_0)) = not(A). [para(107722(a,1),4175(a,1,1)),flip(a)].
% 34.23/34.51 107815 -is_a_theorem(A) | c_0 = A. [para(107727(a,1),77(a,1)),flip(b)].
% 34.23/34.51 108260 implies(implies(implies(A,B),A),A) = c_0. [resolve(107815,a,78976,a),flip(a)].
% 34.23/34.51 108316 implies(and(implies(A,B),A),B) = c_0. [resolve(107815,a,45157,a),flip(a)].
% 34.23/34.51 108321 implies(not(A),implies(implies(not(B),A),B)) = c_0. [resolve(107815,a,44778,a),flip(a)].
% 34.23/34.51 108370 implies(A,and(A,implies(B,A))) = c_0. [resolve(107815,a,23700,a),flip(a)].
% 34.23/34.51 108468 implies(A,implies(B,implies(C,A))) = c_0. [resolve(107815,a,10395,a),flip(a)].
% 34.23/34.51 108478 implies(and(A,not(B)),implies(B,C)) = c_0. [resolve(107815,a,10318,a),flip(a)].
% 34.23/34.51 108524 implies(equiv(A,B),equiv(B,A)) = c_0. [resolve(107815,a,9025,a),flip(a)].
% 34.23/34.51 108529 implies(and(A,B),and(B,A)) = c_0. [resolve(107815,a,8972,a),flip(a)].
% 34.23/34.51 108549 implies(implies(implies(A,B),C),implies(B,C)) = c_0. [resolve(107815,a,1135,a),flip(a)].
% 34.23/34.51 108607 implies(A,implies(not(A),B)) = c_0. [resolve(107815,a,136,a),flip(a)].
% 34.23/34.51 110750 equiv(implies(implies(A,B),A),A) = c_0. [para(108260(a,1),110(a,1,1)),rewrite([104748(4),104791(3)]),flip(a)].
% 34.23/34.51 110764 and(and(implies(A,B),A),not(B)) = not(c_0). [para(108316(a,1),4176(a,1,1)),flip(a)].
% 34.23/34.51 110773 equiv(A,and(A,implies(B,A))) = c_0. [para(108370(a,1),110(a,1,1)),rewrite([104706(4),104791(3)]),flip(a)].
% 34.23/34.51 111170 equiv(equiv(A,B),equiv(B,A)) = c_0. [para(108524(a,1),110(a,1,1)),rewrite([108524(4),104791(3)]),flip(a)].
% 34.23/34.51 111304 equiv(and(A,B),and(B,A)) = c_0. [para(108529(a,1),110(a,1,1)),rewrite([108529(4),104791(3)]),flip(a)].
% 34.23/34.51 111788 implies(implies(A,B),A) = A. [para(110750(a,1),77(a,1)),flip(b),unit_del(a,98636)].
% 34.23/34.51 111790 and(A,implies(A,implies(A,B))) = equiv(implies(A,B),A). [para(111788(a,1),110(a,1,1))].
% 34.23/34.51 111791 and(implies(A,implies(A,B)),A) = equiv(A,implies(A,B)). [para(111788(a,1),110(a,1,2))].
% 34.23/34.51 111792 and(implies(A,B),not(A)) = not(A). [para(111788(a,1),4176(a,1,1)),flip(a)].
% 34.23/34.51 111807 implies(A,implies(A,B)) = implies(A,B). [para(111788(a,1),111788(a,1,1))].
% 34.23/34.51 111808 equiv(A,implies(A,B)) = and(implies(A,B),A). [back_rewrite(111791),rewrite([111807(2)]),flip(a)].
% 34.23/34.51 111809 equiv(implies(A,B),A) = and(A,implies(A,B)). [back_rewrite(111790),rewrite([111807(2)]),flip(a)].
% 34.23/34.51 111818 and(A,implies(B,A)) = A. [para(110773(a,1),77(a,1)),unit_del(a,98636)].
% 34.23/34.51 111820 implies(A,and(B,not(A))) = not(A). [para(111818(a,1),4175(a,1,1)),rewrite([4176(3)]),flip(a)].
% 34.23/34.51 111967 equiv(A,B) = equiv(B,A). [para(111170(a,1),77(a,1)),unit_del(a,98636)].
% 34.23/34.51 111987 and(implies(A,B),A) = and(A,implies(A,B)). [back_rewrite(111809),rewrite([111967(2),111808(2)])].
% 34.23/34.51 112294 and(and(A,implies(A,B)),not(B)) = not(c_0). [back_rewrite(110764),rewrite([111987(2)])].
% 34.23/34.51 112409 -is_a_theorem(equiv(A,B)) | A = B. [para(111967(a,1),77(a,1))].
% 34.23/34.51 113122 and(A,B) = and(B,A). [para(111304(a,1),77(a,1)),unit_del(a,98636)].
% 34.23/34.51 113150 and(not(A),and(B,implies(B,A))) = not(c_0). [back_rewrite(112294),rewrite([113122(4)])].
% 34.23/34.51 113197 and(not(A),implies(A,B)) = not(A). [back_rewrite(111792),rewrite([113122(3)])].
% 34.23/34.51 113625 implies(A,not(B)) = implies(B,not(A)). [para(113122(a,1),4175(a,1,1)),rewrite([4175(2)])].
% 34.23/34.51 113785 is_a_theorem(implies(implies(A,B),implies(A,and(A,B)))). [back_rewrite(104807),rewrite([113625(3),113625(5),4176(4),4127(3)])].
% 34.23/34.51 113874 and(not(A),implies(and(B,not(A)),A)) = equiv(A,and(B,not(A))). [para(111820(a,1),110(a,1,1))].
% 34.23/34.51 113965 and(A,implies(not(A),B)) = A. [para(4127(a,1),113197(a,1,1)),rewrite([4127(5)])].
% 34.23/34.51 114101 is_a_theorem(implies(A,implies(implies(A,and(B,C)),B))). [resolve(6664,a,22056,a),rewrite([113625(4),4176(3),4127(2)])].
% 34.23/34.51 114115 is_a_theorem(implies(implies(implies(and(A,B),C),A),A)). [para(108607(a,1),6664(a,1,2,1)),rewrite([4176(3),4127(2),105498(5)])].
% 34.23/34.51 114295 implies(implies(A,and(B,C)),implies(A,C)) = c_0. [resolve(105563,a,107815,a),flip(a)].
% 34.23/34.51 114297 -is_a_theorem(implies(A,and(B,C))) | is_a_theorem(implies(A,C)). [resolve(105563,a,83,b)].
% 34.23/34.51 114897 and(c_0,implies(A,B)) = implies(A,B). [para(108478(a,1),111818(a,1,2)),rewrite([113122(3)])].
% 34.23/34.51 115671 is_a_theorem(equiv(implies(A,B),implies(A,and(A,B)))). [resolve(113785,a,151,a),rewrite([114295(4),105498(6)])].
% 34.23/34.51 116140 is_a_theorem(implies(A,implies(implies(A,and(B,C)),C))). [para(113122(a,1),114101(a,1,2,1,2))].
% 34.23/34.51 116156 is_a_theorem(equiv(A,implies(implies(and(A,B),C),A))). [resolve(114115,a,151,a),rewrite([104748(4),111967(5),105498(6)])].
% 34.23/34.51 116908 -is_a_theorem(implies(A,B)) | is_a_theorem(implies(A,implies(not(B),C))). [para(113965(a,1),114297(a,1,2))].
% 34.23/34.51 117294 implies(A,and(A,B)) = implies(A,B). [resolve(115671,a,112409,a),flip(a)].
% 34.23/34.51 117341 implies(not(A),and(B,not(A))) = implies(not(A),B). [para(117294(a,1),106(a,2)),rewrite([113122(2),106(3)])].
% 34.23/34.51 117342 equiv(A,and(A,B)) = implies(A,B). [para(117294(a,1),110(a,1,1)),rewrite([104706(3),113122(3),114897(3)]),flip(a)].
% 34.23/34.51 117467 -is_a_theorem(implies(A,B)) | and(A,B) = A. [para(117342(a,1),77(a,1))].
% 34.23/34.51 117474 equiv(c_0,implies(A,B)) = implies(A,B). [para(114897(a,1),117342(a,1,2)),rewrite([105498(6)])].
% 34.23/34.51 117553 -is_a_theorem(implies(A,B)) | implies(A,B) = c_0. [para(117474(a,1),77(a,1))].
% 34.23/34.51 117917 is_a_theorem(implies(implies(A,B),implies(A,equiv(A,B)))). [para(402(a,1),116140(a,1,2,1)),rewrite([113625(5),4127(4)])].
% 34.23/34.51 117943 implies(implies(and(A,B),C),A) = A. [resolve(116156,a,112409,a),flip(a)].
% 34.23/34.51 117996 implies(implies(A,implies(B,not(C))),B) = B. [para(113625(a,1),117943(a,1,1)),rewrite([4175(2)])].
% 34.23/34.51 118593 implies(implies(A,B),implies(A,equiv(A,B))) = c_0. [resolve(117917,a,117553,a)].
% 34.23/34.51 118747 implies(implies(A,implies(B,C)),B) = B. [para(4127(a,1),117996(a,1,1,2,2))].
% 34.23/34.51 121676 implies(not(A),and(B,implies(B,A))) = A. [para(113150(a,1),117294(a,1,2)),rewrite([107730(4),4127(2)]),flip(a)].
% 34.23/34.51 121690 implies(and(A,not(B)),B) = implies(A,B). [para(104748(a,1),121676(a,1,2,2)),rewrite([4176(2),107722(4)])].
% 34.23/34.51 121714 implies(implies(not(A),B),A) = implies(B,A). [para(108321(a,1),121676(a,1,2,2)),rewrite([4176(4),113122(4),107722(7),113625(6),4175(5),4176(4),117294(5),113625(3),4127(2),111807(2)]),flip(a)].
% 34.23/34.51 121730 implies(and(A,not(B)),implies(implies(C,A),B)) = implies(A,B). [para(108549(a,1),121676(a,1,2,2)),rewrite([4176(2),113122(6),114897(6)])].
% 34.23/34.51 121740 equiv(A,and(B,not(A))) = and(not(A),implies(B,A)). [back_rewrite(113874),rewrite([121690(4)]),flip(a)].
% 34.23/34.51 121926 implies(implies(A,B),B) = implies(not(B),A). [para(121690(a,1),402(a,1,1)),rewrite([4175(4),4127(3),111818(3),111967(5),121740(5),4175(6),4176(5),117341(6)])].
% 34.23/34.51 121996 implies(not(A),B) = implies(not(B),A). [para(113625(a,1),121714(a,1,1)),rewrite([4127(2),121926(2)])].
% 34.23/34.51 122001 -is_a_theorem(implies(A,B)) | implies(not(A),B) = B. [para(121714(a,1),117467(a,1)),rewrite([121996(4),113122(5),111818(5),121996(4)]),flip(b)].
% 34.23/34.51 124218 implies(implies(implies(A,B),C),A) = implies(C,A). [resolve(20199,a,122001,a),rewrite([4176(2),121730(6)]),flip(a)].
% 34.23/34.51 125155 is_a_theorem(implies(implies(A,B),implies(and(A,not(equiv(A,B))),C))). [para(118593(a,1),116908(a,1)),rewrite([4176(6)]),unit_del(a,98636)].
% 34.23/34.51 126701 implies(implies(A,B),implies(A,C)) = implies(B,implies(A,C)). [para(111788(a,1),124218(a,1,1,1))].
% 34.23/34.51 126708 implies(implies(A,B),implies(and(A,C),D)) = implies(B,implies(and(A,C),D)). [para(117943(a,1),124218(a,1,1,1))].
% 34.23/34.51 126710 implies(implies(A,B),implies(C,implies(A,D))) = implies(B,implies(C,implies(A,D))). [para(118747(a,1),124218(a,1,1,1))].
% 34.23/34.51 126780 is_a_theorem(implies(A,implies(and(B,not(equiv(B,A))),C))). [back_rewrite(125155),rewrite([126708(6)])].
% 34.23/34.51 126782 -is_a_theorem(A). [back_rewrite(156),rewrite([126710(15),126701(12),108468(9),107722(2)])].
% 34.23/34.51 126783 $F. [resolve(126782,a,126780,a)].
% 34.23/34.51
% 34.23/34.51 % SZS output end Refutation
% 34.23/34.51 ============================== end of proof ==========================
% 34.23/34.51
% 34.23/34.51 ============================== STATISTICS ============================
% 34.23/34.51
% 34.23/34.51 Given=5186. Generated=4365882. Kept=126711. proofs=1.
% 34.23/34.51 Usable=1084. Sos=6667. Demods=1566. Limbo=72, Disabled=118969. Hints=0.
% 34.23/34.51 Megabytes=70.79.
% 34.23/34.51 User_CPU=31.39, System_CPU=2.12, Wall_clock=33.
% 34.23/34.51
% 34.23/34.51 ============================== end of statistics =====================
% 34.23/34.51
% 34.23/34.51 ============================== end of search =========================
% 34.23/34.51
% 34.23/34.51 THEOREM PROVED
% 34.23/34.51 % SZS status Theorem
% 34.23/34.51
% 34.23/34.51 Exiting with 1 proof.
% 34.23/34.51
% 34.23/34.51 Process 9939 exit (max_proofs) Sun Jul 3 16:30:20 2022
% 34.23/34.51 Prover9 interrupted
%------------------------------------------------------------------------------