TSTP Solution File: LCL458+1 by Prover9---1109a
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : LCL458+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n013.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 13:46:58 EDT 2022
% Result : Theorem 36.25s 36.52s
% Output : Refutation 36.25s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.11 % Problem : LCL458+1 : TPTP v8.1.0. Released v3.3.0.
% 0.10/0.12 % Command : tptp2X_and_run_prover9 %d %s
% 0.12/0.32 % Computer : n013.cluster.edu
% 0.12/0.32 % Model : x86_64 x86_64
% 0.12/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.32 % Memory : 8042.1875MB
% 0.12/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.32 % CPULimit : 300
% 0.12/0.32 % WCLimit : 600
% 0.12/0.32 % DateTime : Sat Jul 2 19:07:44 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.78/1.07 ============================== Prover9 ===============================
% 0.78/1.07 Prover9 (32) version 2009-11A, November 2009.
% 0.78/1.07 Process 20181 was started by sandbox2 on n013.cluster.edu,
% 0.78/1.07 Sat Jul 2 19:07:45 2022
% 0.78/1.07 The command was "/export/starexec/sandbox2/solver/bin/prover9 -t 300 -f /tmp/Prover9_19780_n013.cluster.edu".
% 0.78/1.07 ============================== end of head ===========================
% 0.78/1.07
% 0.78/1.07 ============================== INPUT =================================
% 0.78/1.07
% 0.78/1.07 % Reading from file /tmp/Prover9_19780_n013.cluster.edu
% 0.78/1.07
% 0.78/1.07 set(prolog_style_variables).
% 0.78/1.07 set(auto2).
% 0.78/1.07 % set(auto2) -> set(auto).
% 0.78/1.07 % set(auto) -> set(auto_inference).
% 0.78/1.07 % set(auto) -> set(auto_setup).
% 0.78/1.07 % set(auto_setup) -> set(predicate_elim).
% 0.78/1.07 % set(auto_setup) -> assign(eq_defs, unfold).
% 0.78/1.07 % set(auto) -> set(auto_limits).
% 0.78/1.07 % set(auto_limits) -> assign(max_weight, "100.000").
% 0.78/1.07 % set(auto_limits) -> assign(sos_limit, 20000).
% 0.78/1.07 % set(auto) -> set(auto_denials).
% 0.78/1.07 % set(auto) -> set(auto_process).
% 0.78/1.07 % set(auto2) -> assign(new_constants, 1).
% 0.78/1.07 % set(auto2) -> assign(fold_denial_max, 3).
% 0.78/1.07 % set(auto2) -> assign(max_weight, "200.000").
% 0.78/1.07 % set(auto2) -> assign(max_hours, 1).
% 0.78/1.07 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 0.78/1.07 % set(auto2) -> assign(max_seconds, 0).
% 0.78/1.07 % set(auto2) -> assign(max_minutes, 5).
% 0.78/1.07 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 0.78/1.07 % set(auto2) -> set(sort_initial_sos).
% 0.78/1.07 % set(auto2) -> assign(sos_limit, -1).
% 0.78/1.07 % set(auto2) -> assign(lrs_ticks, 3000).
% 0.78/1.07 % set(auto2) -> assign(max_megs, 400).
% 0.78/1.07 % set(auto2) -> assign(stats, some).
% 0.78/1.07 % set(auto2) -> clear(echo_input).
% 0.78/1.07 % set(auto2) -> set(quiet).
% 0.78/1.07 % set(auto2) -> clear(print_initial_clauses).
% 0.78/1.07 % set(auto2) -> clear(print_given).
% 0.78/1.07 assign(lrs_ticks,-1).
% 0.78/1.07 assign(sos_limit,10000).
% 0.78/1.07 assign(order,kbo).
% 0.78/1.07 set(lex_order_vars).
% 0.78/1.07 clear(print_given).
% 0.78/1.07
% 0.78/1.07 % formulas(sos). % not echoed (53 formulas)
% 0.78/1.07
% 0.78/1.07 ============================== end of input ==========================
% 0.78/1.07
% 0.78/1.07 % From the command line: assign(max_seconds, 300).
% 0.78/1.07
% 0.78/1.07 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 0.78/1.07
% 0.78/1.07 % Formulas that are not ordinary clauses:
% 0.78/1.07 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].
% 0.78/1.07 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].
% 0.78/1.07 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].
% 0.78/1.07 4 implies_1 <-> (all X all Y is_a_theorem(implies(X,implies(Y,X)))) # label(implies_1) # label(axiom) # label(non_clause). [assumption].
% 0.78/1.07 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].
% 0.78/1.07 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].
% 0.78/1.07 7 and_1 <-> (all X all Y is_a_theorem(implies(and(X,Y),X))) # label(and_1) # label(axiom) # label(non_clause). [assumption].
% 0.78/1.07 8 and_2 <-> (all X all Y is_a_theorem(implies(and(X,Y),Y))) # label(and_2) # label(axiom) # label(non_clause). [assumption].
% 0.78/1.07 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].
% 0.78/1.07 10 or_1 <-> (all X all Y is_a_theorem(implies(X,or(X,Y)))) # label(or_1) # label(axiom) # label(non_clause). [assumption].
% 0.78/1.07 11 or_2 <-> (all X all Y is_a_theorem(implies(Y,or(X,Y)))) # label(or_2) # label(axiom) # label(non_clause). [assumption].
% 0.78/1.07 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].
% 0.78/1.07 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].
% 0.78/1.07 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].
% 1.74/2.01 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].
% 1.74/2.01 16 kn1 <-> (all P is_a_theorem(implies(P,and(P,P)))) # label(kn1) # label(axiom) # label(non_clause). [assumption].
% 1.74/2.01 17 kn2 <-> (all P all Q is_a_theorem(implies(and(P,Q),P))) # label(kn2) # label(axiom) # label(non_clause). [assumption].
% 1.74/2.01 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].
% 1.74/2.01 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].
% 1.74/2.01 20 cn2 <-> (all P all Q is_a_theorem(implies(P,implies(not(P),Q)))) # label(cn2) # label(axiom) # label(non_clause). [assumption].
% 1.74/2.01 21 cn3 <-> (all P is_a_theorem(implies(implies(not(P),P),P))) # label(cn3) # label(axiom) # label(non_clause). [assumption].
% 1.74/2.01 22 r1 <-> (all P is_a_theorem(implies(or(P,P),P))) # label(r1) # label(axiom) # label(non_clause). [assumption].
% 1.74/2.01 23 r2 <-> (all P all Q is_a_theorem(implies(Q,or(P,Q)))) # label(r2) # label(axiom) # label(non_clause). [assumption].
% 1.74/2.01 24 r3 <-> (all P all Q is_a_theorem(implies(or(P,Q),or(Q,P)))) # label(r3) # label(axiom) # label(non_clause). [assumption].
% 1.74/2.01 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].
% 1.74/2.01 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].
% 1.74/2.01 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].
% 1.74/2.01 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].
% 1.74/2.01 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].
% 1.74/2.01 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].
% 1.74/2.01 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].
% 1.74/2.01
% 1.74/2.01 ============================== end of process non-clausal formulas ===
% 1.74/2.01
% 1.74/2.01 ============================== PROCESS INITIAL CLAUSES ===============
% 1.74/2.01
% 1.74/2.01 ============================== PREDICATE ELIMINATION =================
% 1.74/2.01
% 1.74/2.01 ============================== end predicate elimination =============
% 1.74/2.01
% 1.74/2.01 Auto_denials: (non-Horn, no changes).
% 1.74/2.01
% 1.74/2.01 Term ordering decisions:
% 1.74/2.01
% 1.74/2.01 % Assigning unary symbol not kb_weight 0 and highest precedence (93).
% 1.74/2.01 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.
% 1.74/2.01
% 1.74/2.01 ============================== end of process initial clauses ========
% 1.74/2.01
% 1.74/2.01 ============================== CLAUSES FOR SEARCH ====================
% 1.74/2.01
% 1.74/2.01 ============================== end of clauses for search =============
% 1.74/2.01
% 1.74/2.01 ============================== SEARCH ================================
% 1.74/2.01
% 1.74/2.01 % Starting search at 0.02 seconds.
% 1.74/2.01
% 1.74/2.01 Low Water (keep): wt=34.000, iters=3336
% 1.74/2.01
% 1.74/2.01 Low Water (keep): wt=28.000, iters=3350
% 1.74/2.01
% 1.74/2.01 Low Water (keep): wt=22.000, iters=3353
% 1.74/2.01
% 1.74/2.01 Low Water (keep): wt=21.000, iters=3352
% 1.74/2.01
% 1.74/2.01 Low Water (keep): wt=19.000, iters=3357
% 1.74/2.01
% 1.74/2.01 Low Water (keep): wt=17.000, iters=3344
% 1.74/2.01
% 1.74/2.01 Low Water (keep): wt=16.000, iters=3345
% 1.74/2.01
% 1.74/2.01 Low Water (keep): wt=15.000, iters=3333
% 1.74/2.01
% 1.74/2.01 Low Water (keep): wt=14.000, iters=3389
% 1.74/2.01
% 1.74/2.01 Low Water (keep): wt=13.000, iters=3354
% 36.25/36.52
% 36.25/36.52 NOTE: Back_subsumption disabled, ratio of kept to back_subsumed is 40 (0.00 of 1.03 sec).
% 36.25/36.52
% 36.25/36.52 Low Water (displace): id=3496, wt=41.000
% 36.25/36.52
% 36.25/36.52 Low Water (displace): id=3494, wt=40.000
% 36.25/36.52
% 36.25/36.52 Low Water (displace): id=4692, wt=39.000
% 36.25/36.52
% 36.25/36.52 Low Water (displace): id=4690, wt=38.000
% 36.25/36.52
% 36.25/36.52 Low Water (displace): id=5197, wt=37.000
% 36.25/36.52
% 36.25/36.52 Low Water (displace): id=5195, wt=36.000
% 36.25/36.52
% 36.25/36.52 Low Water (displace): id=5150, wt=35.000
% 36.25/36.52
% 36.25/36.52 Low Water (displace): id=5199, wt=34.000
% 36.25/36.52
% 36.25/36.52 Low Water (displace): id=5148, wt=33.000
% 36.25/36.52
% 36.25/36.52 Low Water (displace): id=5201, wt=32.000
% 36.25/36.52
% 36.25/36.52 Low Water (displace): id=5192, wt=31.000
% 36.25/36.52
% 36.25/36.52 Low Water (displace): id=5204, wt=30.000
% 36.25/36.52
% 36.25/36.52 Low Water (displace): id=5196, wt=29.000
% 36.25/36.52
% 36.25/36.52 Low Water (displace): id=5207, wt=28.000
% 36.25/36.52
% 36.25/36.52 Low Water (displace): id=12619, wt=21.000
% 36.25/36.52
% 36.25/36.52 Low Water (displace): id=12622, wt=20.000
% 36.25/36.52
% 36.25/36.52 Low Water (displace): id=12753, wt=12.000
% 36.25/36.52
% 36.25/36.52 Low Water (displace): id=12755, wt=11.000
% 36.25/36.52
% 36.25/36.52 Low Water (displace): id=13077, wt=10.000
% 36.25/36.52
% 36.25/36.52 Low Water (keep): wt=12.000, iters=3449
% 36.25/36.52
% 36.25/36.52 Low Water (displace): id=18783, wt=9.000
% 36.25/36.52
% 36.25/36.52 Low Water (keep): wt=11.000, iters=3334
% 36.25/36.52
% 36.25/36.52 Low Water (keep): wt=10.000, iters=3333
% 36.25/36.52
% 36.25/36.52 ============================== PROOF =================================
% 36.25/36.52 % SZS status Theorem
% 36.25/36.52 % SZS output start Refutation
% 36.25/36.52
% 36.25/36.52 % Proof 1 at 33.34 (+ 2.12) seconds.
% 36.25/36.52 % Length of proof is 262.
% 36.25/36.52 % Level of proof is 43.
% 36.25/36.52 % Maximum clause weight is 20.000.
% 36.25/36.52 % Given clauses 5295.
% 36.25/36.52
% 36.25/36.52 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].
% 36.25/36.52 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].
% 36.25/36.52 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].
% 36.25/36.52 4 implies_1 <-> (all X all Y is_a_theorem(implies(X,implies(Y,X)))) # label(implies_1) # label(axiom) # label(non_clause). [assumption].
% 36.25/36.52 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].
% 36.25/36.52 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].
% 36.25/36.52 7 and_1 <-> (all X all Y is_a_theorem(implies(and(X,Y),X))) # label(and_1) # label(axiom) # label(non_clause). [assumption].
% 36.25/36.52 8 and_2 <-> (all X all Y is_a_theorem(implies(and(X,Y),Y))) # label(and_2) # label(axiom) # label(non_clause). [assumption].
% 36.25/36.52 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].
% 36.25/36.52 10 or_1 <-> (all X all Y is_a_theorem(implies(X,or(X,Y)))) # label(or_1) # label(axiom) # label(non_clause). [assumption].
% 36.25/36.52 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].
% 36.25/36.52 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].
% 36.25/36.52 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].
% 36.25/36.52 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].
% 36.25/36.52 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].
% 36.25/36.52 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].
% 36.25/36.52 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].
% 36.25/36.52 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].
% 36.25/36.52 32 op_or # label(hilbert_op_or) # label(axiom). [assumption].
% 36.25/36.52 33 op_implies_and # label(hilbert_op_implies_and) # label(axiom). [assumption].
% 36.25/36.52 34 op_equiv # label(hilbert_op_equiv) # label(axiom). [assumption].
% 36.25/36.52 35 modus_ponens # label(hilbert_modus_ponens) # label(axiom). [assumption].
% 36.25/36.52 36 modus_tollens # label(hilbert_modus_tollens) # label(axiom). [assumption].
% 36.25/36.52 37 implies_1 # label(hilbert_implies_1) # label(axiom). [assumption].
% 36.25/36.52 38 implies_2 # label(hilbert_implies_2) # label(axiom). [assumption].
% 36.25/36.52 39 implies_3 # label(hilbert_implies_3) # label(axiom). [assumption].
% 36.25/36.52 40 and_1 # label(hilbert_and_1) # label(axiom). [assumption].
% 36.25/36.52 41 and_2 # label(hilbert_and_2) # label(axiom). [assumption].
% 36.25/36.52 42 and_3 # label(hilbert_and_3) # label(axiom). [assumption].
% 36.25/36.52 43 or_1 # label(hilbert_or_1) # label(axiom). [assumption].
% 36.25/36.52 45 or_3 # label(hilbert_or_3) # label(axiom). [assumption].
% 36.25/36.52 48 equivalence_3 # label(hilbert_equivalence_3) # label(axiom). [assumption].
% 36.25/36.52 49 substitution_of_equivalents # label(substitution_of_equivalents) # label(axiom). [assumption].
% 36.25/36.52 50 op_implies_or # label(principia_op_implies_or) # label(axiom). [assumption].
% 36.25/36.52 51 op_and # label(principia_op_and) # label(axiom). [assumption].
% 36.25/36.52 52 -r5 # label(principia_r5) # label(negated_conjecture). [assumption].
% 36.25/36.52 53 -implies_1 | is_a_theorem(implies(A,implies(B,A))) # label(implies_1) # label(axiom). [clausify(4)].
% 36.25/36.52 54 is_a_theorem(implies(A,implies(B,A))). [copy(53),unit_del(a,37)].
% 36.25/36.52 56 -and_1 | is_a_theorem(implies(and(A,B),A)) # label(and_1) # label(axiom). [clausify(7)].
% 36.25/36.52 57 is_a_theorem(implies(and(A,B),A)). [copy(56),unit_del(a,40)].
% 36.25/36.52 59 -and_2 | is_a_theorem(implies(and(A,B),B)) # label(and_2) # label(axiom). [clausify(8)].
% 36.25/36.52 60 is_a_theorem(implies(and(A,B),B)). [copy(59),unit_del(a,41)].
% 36.25/36.52 62 -or_1 | is_a_theorem(implies(A,or(A,B))) # label(or_1) # label(axiom). [clausify(10)].
% 36.25/36.52 63 is_a_theorem(implies(A,or(A,B))). [copy(62),unit_del(a,43)].
% 36.25/36.52 76 -substitution_of_equivalents | -is_a_theorem(equiv(A,B)) | B = A # label(substitution_of_equivalents) # label(axiom). [clausify(2)].
% 36.25/36.52 77 -is_a_theorem(equiv(A,B)) | B = A. [copy(76),unit_del(a,49)].
% 36.25/36.52 82 -modus_ponens | -is_a_theorem(A) | -is_a_theorem(implies(A,B)) | is_a_theorem(B) # label(modus_ponens) # label(axiom). [clausify(1)].
% 36.25/36.52 83 -is_a_theorem(A) | -is_a_theorem(implies(A,B)) | is_a_theorem(B). [copy(82),unit_del(a,35)].
% 36.25/36.52 84 -and_3 | is_a_theorem(implies(A,implies(B,and(A,B)))) # label(and_3) # label(axiom). [clausify(9)].
% 36.25/36.52 85 is_a_theorem(implies(A,implies(B,and(A,B)))). [copy(84),unit_del(a,42)].
% 36.25/36.52 95 -op_implies_or | or(not(A),B) = implies(A,B) # label(op_implies_or) # label(axiom). [clausify(30)].
% 36.25/36.52 96 or(not(A),B) = implies(A,B). [copy(95),unit_del(a,50)].
% 36.25/36.52 97 -op_implies_and | not(and(A,not(B))) = implies(A,B) # label(op_implies_and) # label(axiom). [clausify(29)].
% 36.25/36.52 98 not(and(A,not(B))) = implies(A,B). [copy(97),unit_del(a,33)].
% 36.25/36.52 99 -modus_tollens | is_a_theorem(implies(implies(not(A),not(B)),implies(B,A))) # label(modus_tollens) # label(axiom). [clausify(3)].
% 36.25/36.52 100 is_a_theorem(implies(implies(not(A),not(B)),implies(B,A))). [copy(99),unit_del(a,36)].
% 36.25/36.52 102 -implies_2 | is_a_theorem(implies(implies(A,implies(A,B)),implies(A,B))) # label(implies_2) # label(axiom). [clausify(5)].
% 36.25/36.52 103 is_a_theorem(implies(implies(A,implies(A,B)),implies(A,B))). [copy(102),unit_del(a,38)].
% 36.25/36.52 105 -op_or | or(A,B) = not(and(not(A),not(B))) # label(op_or) # label(axiom). [clausify(27)].
% 36.25/36.52 106 or(A,B) = implies(not(A),B). [copy(105),rewrite([98(6)]),unit_del(a,32)].
% 36.25/36.52 107 -op_and | and(A,B) = not(or(not(A),not(B))) # label(op_and) # label(axiom). [clausify(28)].
% 36.25/36.52 108 not(implies(not(not(A)),not(B))) = and(A,B). [copy(107),rewrite([106(5)]),flip(b),unit_del(a,51)].
% 36.25/36.52 109 -op_equiv | and(implies(A,B),implies(B,A)) = equiv(A,B) # label(op_equiv) # label(axiom). [clausify(31)].
% 36.25/36.52 110 and(implies(A,B),implies(B,A)) = equiv(A,B). [copy(109),unit_del(a,34)].
% 36.25/36.52 111 -implies_3 | is_a_theorem(implies(implies(A,B),implies(implies(B,C),implies(A,C)))) # label(implies_3) # label(axiom). [clausify(6)].
% 36.25/36.52 112 is_a_theorem(implies(implies(A,B),implies(implies(B,C),implies(A,C)))). [copy(111),unit_del(a,39)].
% 36.25/36.52 114 -equivalence_3 | is_a_theorem(implies(implies(A,B),implies(implies(B,A),equiv(A,B)))) # label(equivalence_3) # label(axiom). [clausify(15)].
% 36.25/36.52 115 is_a_theorem(implies(implies(A,B),implies(implies(B,A),equiv(A,B)))). [copy(114),unit_del(a,48)].
% 36.25/36.52 124 r5 | -is_a_theorem(implies(implies(c54,c55),implies(or(c53,c54),or(c53,c55)))) # label(r5) # label(axiom). [clausify(26)].
% 36.25/36.52 125 -is_a_theorem(implies(implies(c54,c55),implies(implies(not(c53),c54),implies(not(c53),c55)))). [copy(124),rewrite([106(7),106(11)]),unit_del(a,52)].
% 36.25/36.52 126 -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)].
% 36.25/36.52 127 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)].
% 36.25/36.52 131 implies(not(not(A)),B) = implies(A,B). [back_rewrite(96),rewrite([106(2)])].
% 36.25/36.52 136 is_a_theorem(implies(A,implies(not(A),B))). [back_rewrite(63),rewrite([106(1)])].
% 36.25/36.52 137 not(implies(A,not(B))) = and(A,B). [back_rewrite(108),rewrite([131(4)])].
% 36.25/36.52 141 -is_a_theorem(A) | is_a_theorem(implies(B,A)). [resolve(83,b,54,a)].
% 36.25/36.52 142 -is_a_theorem(A) | is_a_theorem(implies(B,and(A,B))). [resolve(85,a,83,b)].
% 36.25/36.52 145 not(and(A,implies(B,C))) = implies(A,and(B,not(C))). [para(98(a,1),98(a,1,1,2))].
% 36.25/36.52 146 -is_a_theorem(implies(not(A),not(B))) | is_a_theorem(implies(B,A)). [resolve(100,a,83,b)].
% 36.25/36.52 149 -is_a_theorem(implies(A,implies(A,B))) | is_a_theorem(implies(A,B)). [resolve(103,a,83,b)].
% 36.25/36.52 150 -is_a_theorem(implies(A,B)) | is_a_theorem(implies(implies(B,C),implies(A,C))). [resolve(112,a,83,b)].
% 36.25/36.52 151 -is_a_theorem(implies(A,B)) | is_a_theorem(implies(implies(B,A),equiv(A,B))). [resolve(115,a,83,b)].
% 36.25/36.52 152 -is_a_theorem(implies(implies(c54,c55),implies(implies(c54,c55),implies(implies(not(c53),c54),implies(not(c53),c55))))). [ur(83,b,103,a,c,125,a)].
% 36.25/36.52 169 -is_a_theorem(implies(A,B)) | is_a_theorem(implies(implies(C,B),implies(implies(not(A),C),B))). [resolve(127,a,83,b)].
% 36.25/36.52 171 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))].
% 36.25/36.52 172 is_a_theorem(implies(A,implies(B,not(not(A))))). [para(131(a,1),54(a,1))].
% 36.25/36.52 179 is_a_theorem(implies(implies(A,not(B)),implies(B,not(A)))). [para(131(a,1),100(a,1,1))].
% 36.25/36.52 182 and(implies(A,not(not(B))),implies(B,A)) = equiv(A,not(not(B))). [para(131(a,1),110(a,1,2))].
% 36.25/36.52 187 is_a_theorem(implies(implies(not(A),B),implies(implies(C,B),implies(implies(A,C),B)))). [para(131(a,1),127(a,1,2,2,1))].
% 36.25/36.52 192 is_a_theorem(implies(not(A),implies(A,B))). [para(131(a,1),136(a,1,2))].
% 36.25/36.52 199 and(not(not(A)),B) = and(A,B). [para(131(a,1),137(a,1,1)),rewrite([137(3)]),flip(a)].
% 36.25/36.52 318 is_a_theorem(implies(A,and(implies(and(B,C),C),A))). [resolve(142,a,60,a)].
% 36.25/36.52 319 is_a_theorem(implies(A,and(implies(and(B,C),B),A))). [resolve(142,a,57,a)].
% 36.25/36.52 320 is_a_theorem(implies(A,and(implies(B,implies(C,B)),A))). [resolve(142,a,54,a)].
% 36.25/36.52 401 implies(implies(A,B),and(B,not(A))) = not(equiv(A,B)). [para(110(a,1),145(a,1,1)),flip(a)].
% 36.25/36.52 536 -is_a_theorem(implies(A,not(B))) | is_a_theorem(implies(B,not(A))). [para(131(a,1),146(a,1))].
% 36.25/36.52 617 is_a_theorem(implies(and(A,B),not(not(A)))). [para(199(a,1),57(a,1,1))].
% 36.25/36.52 1053 is_a_theorem(implies(A,not(not(A)))). [resolve(149,a,172,a)].
% 36.25/36.52 1057 is_a_theorem(implies(A,and(A,A))). [resolve(149,a,85,a)].
% 36.25/36.52 1058 is_a_theorem(implies(A,A)). [resolve(149,a,54,a)].
% 36.25/36.52 1062 is_a_theorem(implies(A,and(implies(B,B),A))). [resolve(1058,a,142,a)].
% 36.25/36.52 1063 is_a_theorem(implies(A,implies(B,B))). [resolve(1058,a,141,a)].
% 36.25/36.52 1121 is_a_theorem(implies(implies(A,B),implies(and(A,C),B))). [resolve(150,a,617,a),rewrite([131(3)])].
% 36.25/36.52 1127 is_a_theorem(implies(implies(implies(A,B),C),implies(not(A),C))). [resolve(150,a,192,a)].
% 36.25/36.52 1140 is_a_theorem(implies(implies(A,B),implies(and(C,A),B))). [resolve(150,a,60,a)].
% 36.25/36.52 1141 is_a_theorem(implies(implies(implies(A,B),C),implies(B,C))). [resolve(150,a,54,a)].
% 36.25/36.52 1270 is_a_theorem(implies(A,and(implies(B,and(B,B)),A))). [resolve(1057,a,142,a)].
% 36.25/36.52 1302 is_a_theorem(implies(A,and(A,not(not(A))))). [para(131(a,1),1057(a,1)),rewrite([199(5)])].
% 36.25/36.52 1305 is_a_theorem(implies(implies(implies(A,A),B),implies(C,B))). [resolve(1063,a,150,a)].
% 36.25/36.52 1306 is_a_theorem(implies(A,and(implies(B,implies(C,C)),A))). [resolve(1063,a,142,a)].
% 36.25/36.52 1383 is_a_theorem(implies(implies(implies(A,A),B),equiv(B,implies(A,A)))). [resolve(151,a,1063,a)].
% 36.25/36.52 1384 is_a_theorem(implies(implies(and(A,A),A),equiv(A,and(A,A)))). [resolve(151,a,1057,a)].
% 36.25/36.52 2206 -is_a_theorem(A) | is_a_theorem(and(implies(B,B),A)). [resolve(1062,a,83,b)].
% 36.25/36.52 2621 -is_a_theorem(A) | is_a_theorem(and(A,not(not(A)))). [resolve(1302,a,83,b)].
% 36.25/36.52 4106 is_a_theorem(equiv(A,not(not(A)))). [resolve(2621,a,1053,a),rewrite([137(7),98(6),182(5)])].
% 36.25/36.52 4139 not(not(A)) = A. [resolve(4106,a,77,a)].
% 36.25/36.52 4266 not(and(A,B)) = implies(A,not(B)). [para(4139(a,1),98(a,1,1,2))].
% 36.25/36.52 4267 not(implies(A,B)) = and(A,not(B)). [para(98(a,1),4139(a,1,1))].
% 36.25/36.52 4268 is_a_theorem(implies(implies(not(A),B),implies(not(B),A))). [para(4139(a,1),100(a,1,1,2))].
% 36.25/36.52 4269 -is_a_theorem(implies(not(A),B)) | is_a_theorem(implies(not(B),A)). [para(4139(a,1),146(a,1,2))].
% 36.25/36.52 6815 -is_a_theorem(implies(A,B)) | is_a_theorem(implies(not(B),not(A))). [para(4139(a,1),536(a,1,2))].
% 36.25/36.52 6826 -is_a_theorem(implies(A,B)) | is_a_theorem(implies(and(A,C),B)). [resolve(1121,a,83,b)].
% 36.25/36.52 6848 is_a_theorem(implies(implies(A,B),implies(implies(not(B),A),B))). [resolve(169,a,1058,a)].
% 36.25/36.52 6920 -is_a_theorem(implies(A,B)) | is_a_theorem(implies(and(C,A),B)). [resolve(1140,a,83,b)].
% 36.25/36.52 6936 -is_a_theorem(implies(implies(A,B),C)) | is_a_theorem(implies(B,C)). [resolve(1141,a,83,b)].
% 36.25/36.52 7072 is_a_theorem(implies(implies(implies(A,A),B),B)). [resolve(1305,a,149,a)].
% 36.25/36.52 7083 is_a_theorem(and(implies(A,A),implies(implies(implies(B,B),C),C))). [resolve(7072,a,2206,a)].
% 36.25/36.52 7090 -is_a_theorem(implies(implies(A,A),B)) | is_a_theorem(B). [resolve(7072,a,83,b)].
% 36.25/36.52 7887 is_a_theorem(implies(implies(implies(A,implies(B,B)),C),C)). [resolve(4269,a,1306,a),rewrite([4266(5),4139(4)])].
% 36.25/36.52 7888 is_a_theorem(implies(implies(implies(A,and(A,A)),B),B)). [resolve(4269,a,1270,a),rewrite([4266(5),4139(4)])].
% 36.25/36.52 7890 is_a_theorem(implies(implies(implies(A,implies(B,A)),C),C)). [resolve(4269,a,320,a),rewrite([4266(5),4139(4)])].
% 36.25/36.52 7891 is_a_theorem(implies(implies(implies(and(A,B),A),C),C)). [resolve(4269,a,319,a),rewrite([4266(5),4139(4)])].
% 36.25/36.52 7892 is_a_theorem(implies(implies(implies(and(A,B),B),C),C)). [resolve(4269,a,318,a),rewrite([4266(5),4139(4)])].
% 36.25/36.52 9060 is_a_theorem(implies(and(A,B),and(B,A))). [resolve(6815,a,179,a),rewrite([4267(3),4139(2),4267(4),4139(3)])].
% 36.25/36.52 9106 is_a_theorem(implies(equiv(A,B),equiv(B,A))). [para(110(a,1),9060(a,1,1)),rewrite([110(4)])].
% 36.25/36.52 9284 is_a_theorem(implies(and(A,B),implies(C,A))). [resolve(6826,a,54,a)].
% 36.25/36.52 10543 is_a_theorem(implies(and(A,not(B)),implies(B,C))). [resolve(6920,a,192,a)].
% 36.25/36.52 10559 is_a_theorem(implies(and(A,and(B,C)),C)). [resolve(6920,a,60,a)].
% 36.25/36.52 10622 is_a_theorem(implies(A,implies(B,implies(C,A)))). [resolve(10559,a,536,a),rewrite([4266(4),4266(3),4139(2)])].
% 36.25/36.52 12060 is_a_theorem(implies(A,implies(implies(A,B),implies(C,B)))). [resolve(6936,a,112,a)].
% 36.25/36.52 12061 is_a_theorem(implies(A,implies(B,and(implies(C,A),B)))). [resolve(6936,a,85,a)].
% 36.25/36.52 13429 -is_a_theorem(implies(implies(A,implies(B,B)),C)) | is_a_theorem(C). [resolve(7887,a,83,b)].
% 36.25/36.52 13476 -is_a_theorem(implies(implies(A,and(A,A)),B)) | is_a_theorem(B). [resolve(7888,a,83,b)].
% 36.25/36.52 13495 -is_a_theorem(implies(implies(A,implies(B,A)),C)) | is_a_theorem(C). [resolve(7890,a,83,b)].
% 36.25/36.52 13514 -is_a_theorem(implies(implies(and(A,B),A),C)) | is_a_theorem(C). [resolve(7891,a,83,b)].
% 36.25/36.52 13534 -is_a_theorem(implies(implies(and(A,B),B),C)) | is_a_theorem(C). [resolve(7892,a,83,b)].
% 36.25/36.52 18030 is_a_theorem(implies(A,and(implies(B,A),A))). [resolve(12061,a,149,a)].
% 36.25/36.52 18049 is_a_theorem(implies(implies(implies(A,not(B)),B),B)). [resolve(18030,a,4269,a),rewrite([4266(5),4139(4)])].
% 36.25/36.52 18251 is_a_theorem(implies(implies(A,B),implies(implies(implies(B,C),A),B))). [resolve(13514,a,171,a)].
% 36.25/36.52 29085 -is_a_theorem(implies(implies(A,B),C)) | is_a_theorem(implies(not(A),C)). [resolve(1127,a,83,b)].
% 36.25/36.52 31861 is_a_theorem(implies(implies(not(A),and(B,A)),A)). [resolve(6848,a,13534,a)].
% 36.25/36.52 31941 is_a_theorem(implies(A,and(A,implies(B,A)))). [resolve(31861,a,536,a),rewrite([4139(2),4267(4),4266(3),4139(2)])].
% 36.25/36.52 43873 is_a_theorem(implies(not(A),implies(implies(not(B),A),B))). [resolve(29085,a,6848,a)].
% 36.25/36.52 43887 is_a_theorem(implies(A,implies(implies(B,C),implies(implies(A,B),C)))). [resolve(29085,a,187,a),rewrite([4139(2)])].
% 36.25/36.52 43889 is_a_theorem(implies(not(A),implies(B,and(implies(A,C),B)))). [resolve(29085,a,85,a)].
% 36.25/36.52 43901 is_a_theorem(implies(A,implies(implies(not(B),not(A)),B))). [para(4139(a,1),43873(a,1,1))].
% 36.25/36.52 44340 is_a_theorem(implies(implies(not(A),and(B,not(B))),A)). [resolve(43901,a,7090,a),rewrite([4267(3)])].
% 36.25/36.52 46524 is_a_theorem(implies(A,and(A,implies(B,B)))). [resolve(44340,a,536,a),rewrite([4139(2),4267(4),4266(3),4139(2)])].
% 36.25/36.52 78324 is_a_theorem(implies(not(A),and(implies(A,B),not(A)))). [resolve(43889,a,149,a)].
% 36.25/36.52 78407 is_a_theorem(implies(implies(implies(A,B),A),A)). [resolve(78324,a,6815,a),rewrite([4266(4),4139(3),4139(4)])].
% 36.25/36.52 104705 is_a_theorem(equiv(implies(A,implies(B,B)),implies(B,B))). [resolve(1383,a,13495,a)].
% 36.25/36.52 104706 is_a_theorem(equiv(equiv(A,A),implies(A,A))). [resolve(1383,a,13476,a),rewrite([110(3)])].
% 36.25/36.52 104707 is_a_theorem(equiv(implies(A,A),implies(B,B))). [resolve(1383,a,13429,a)].
% 36.25/36.52 104716 is_a_theorem(implies(A,equiv(A,implies(B,B)))). [resolve(1383,a,6936,a)].
% 36.25/36.52 104839 equiv(A,A) = implies(A,A). [resolve(104706,a,77,a),flip(a)].
% 36.25/36.52 104927 is_a_theorem(implies(A,and(equiv(implies(B,B),implies(C,C)),A))). [resolve(104707,a,142,a)].
% 36.25/36.52 104929 implies(A,A) = implies(B,B). [resolve(104707,a,77,a)].
% 36.25/36.52 104933 implies(A,A) = c_0. [new_symbol(104929)].
% 36.25/36.52 104938 is_a_theorem(implies(A,and(c_0,A))). [back_rewrite(104927),rewrite([104933(1),104933(2),104839(3),104933(3)])].
% 36.25/36.52 105011 equiv(A,A) = c_0. [back_rewrite(104839),rewrite([104933(2)])].
% 36.25/36.52 105013 is_a_theorem(implies(A,equiv(A,c_0))). [back_rewrite(104716),rewrite([104933(1)])].
% 36.25/36.52 105014 is_a_theorem(c_0). [back_rewrite(104707),rewrite([104933(1),104933(2),105011(3)])].
% 36.25/36.52 105015 is_a_theorem(equiv(implies(A,c_0),c_0)). [back_rewrite(104705),rewrite([104933(1),104933(3)])].
% 36.25/36.52 105151 is_a_theorem(implies(A,and(A,c_0))). [back_rewrite(46524),rewrite([104933(1)])].
% 36.25/36.52 106484 is_a_theorem(and(c_0,implies(implies(c_0,A),A))). [back_rewrite(7083),rewrite([104933(1),104933(2)])].
% 36.25/36.52 107104 and(A,not(A)) = not(c_0). [para(104933(a,1),4267(a,1,1)),flip(a)].
% 36.25/36.52 107452 is_a_theorem(implies(implies(and(c_0,A),A),equiv(A,and(c_0,A)))). [resolve(104938,a,151,a)].
% 36.25/36.52 107745 is_a_theorem(equiv(implies(and(A,B),B),c_0)). [resolve(105013,a,13534,a)].
% 36.25/36.52 107746 is_a_theorem(equiv(implies(and(A,B),A),c_0)). [resolve(105013,a,13514,a)].
% 36.25/36.52 107747 is_a_theorem(equiv(implies(A,implies(B,A)),c_0)). [resolve(105013,a,13495,a)].
% 36.25/36.52 107841 implies(A,c_0) = c_0. [resolve(105015,a,77,a),flip(a)].
% 36.25/36.52 107902 and(implies(c_0,A),c_0) = equiv(c_0,A). [para(107841(a,1),110(a,1,2))].
% 36.25/36.52 108520 is_a_theorem(implies(implies(and(A,c_0),A),equiv(A,and(A,c_0)))). [resolve(105151,a,151,a)].
% 36.25/36.52 109410 and(implies(A,B),and(A,not(B))) = not(c_0). [para(4267(a,1),107104(a,1,2))].
% 36.25/36.52 110053 is_a_theorem(equiv(A,and(A,A))). [resolve(1384,a,13534,a)].
% 36.25/36.52 110093 and(A,A) = A. [resolve(110053,a,77,a)].
% 36.25/36.52 110100 implies(A,not(A)) = not(A). [para(110093(a,1),4266(a,1,1)),flip(a)].
% 36.25/36.52 110111 is_a_theorem(implies(implies(A,B),implies(implies(B,not(A)),not(A)))). [para(110100(a,1),112(a,1,2,2))].
% 36.25/36.52 112188 implies(and(A,B),B) = c_0. [resolve(107745,a,77,a),flip(a)].
% 36.25/36.52 112189 is_a_theorem(implies(c_0,equiv(A,and(c_0,A)))). [back_rewrite(107452),rewrite([112188(3)])].
% 36.25/36.52 112191 is_a_theorem(implies(implies(A,and(B,C)),implies(c_0,implies(A,C)))). [para(112188(a,1),112(a,1,2,1))].
% 36.25/36.52 112192 and(and(A,B),not(B)) = not(c_0). [para(112188(a,1),4267(a,1,1)),flip(a)].
% 36.25/36.52 112214 implies(and(A,B),A) = c_0. [resolve(107746,a,77,a),flip(a)].
% 36.25/36.52 112215 is_a_theorem(implies(c_0,equiv(A,and(A,c_0)))). [back_rewrite(108520),rewrite([112214(3)])].
% 36.25/36.52 112237 is_a_theorem(implies(implies(A,and(B,C)),implies(c_0,implies(A,B)))). [para(112214(a,1),112(a,1,2,1))].
% 36.25/36.52 112267 implies(A,implies(B,A)) = c_0. [resolve(107747,a,77,a),flip(a)].
% 36.25/36.52 112269 and(c_0,implies(implies(A,B),B)) = equiv(B,implies(A,B)). [para(112267(a,1),110(a,1,1))].
% 36.25/36.52 112272 and(A,and(B,not(A))) = not(c_0). [para(112267(a,1),4267(a,1,1)),rewrite([4267(4)]),flip(a)].
% 36.25/36.52 112311 is_a_theorem(equiv(A,implies(c_0,A))). [back_rewrite(106484),rewrite([112269(5)])].
% 36.25/36.52 112351 implies(c_0,A) = A. [resolve(112311,a,77,a)].
% 36.25/36.52 112357 is_a_theorem(implies(implies(A,and(B,C)),implies(A,B))). [back_rewrite(112237),rewrite([112351(5)])].
% 36.25/36.52 112358 is_a_theorem(equiv(A,and(A,c_0))). [back_rewrite(112215),rewrite([112351(5)])].
% 36.25/36.52 112361 is_a_theorem(implies(implies(A,and(B,C)),implies(A,C))). [back_rewrite(112191),rewrite([112351(5)])].
% 36.25/36.52 112362 is_a_theorem(equiv(A,and(c_0,A))). [back_rewrite(112189),rewrite([112351(5)])].
% 36.25/36.52 112372 equiv(c_0,A) = and(A,c_0). [back_rewrite(107902),rewrite([112351(2)]),flip(a)].
% 36.25/36.52 114361 and(A,c_0) = A. [resolve(112358,a,77,a)].
% 36.25/36.52 114362 equiv(c_0,A) = A. [back_rewrite(112372),rewrite([114361(4)])].
% 36.25/36.52 114811 -is_a_theorem(A) | c_0 = A. [para(114362(a,1),77(a,1)),flip(b)].
% 36.25/36.52 115247 implies(implies(implies(A,B),A),A) = c_0. [resolve(114811,a,78407,a),flip(a)].
% 36.25/36.52 115358 implies(A,and(A,implies(B,A))) = c_0. [resolve(114811,a,31941,a),flip(a)].
% 36.25/36.52 115379 implies(implies(implies(A,not(B)),B),B) = c_0. [resolve(114811,a,18049,a),flip(a)].
% 36.25/36.52 115429 implies(A,implies(implies(A,B),implies(C,B))) = c_0. [resolve(114811,a,12060,a),flip(a)].
% 36.25/36.52 115456 implies(A,implies(B,implies(C,A))) = c_0. [resolve(114811,a,10622,a),flip(a)].
% 36.25/36.52 115466 implies(and(A,not(B)),implies(B,C)) = c_0. [resolve(114811,a,10543,a),flip(a)].
% 36.25/36.52 115494 implies(and(A,B),implies(C,A)) = c_0. [resolve(114811,a,9284,a),flip(a)].
% 36.25/36.52 115512 implies(equiv(A,B),equiv(B,A)) = c_0. [resolve(114811,a,9106,a),flip(a)].
% 36.25/36.52 115517 implies(and(A,B),and(B,A)) = c_0. [resolve(114811,a,9060,a),flip(a)].
% 36.25/36.52 115536 implies(implies(not(A),B),implies(not(B),A)) = c_0. [resolve(114811,a,4268,a),flip(a)].
% 36.25/36.52 115540 implies(implies(implies(A,B),C),implies(B,C)) = c_0. [resolve(114811,a,1141,a),flip(a)].
% 36.25/36.52 115667 and(c_0,A) = A. [resolve(112362,a,77,a)].
% 36.25/36.52 115706 equiv(A,implies(B,A)) = implies(implies(B,A),A). [back_rewrite(112269),rewrite([115667(4)]),flip(a)].
% 36.25/36.52 117878 equiv(A,and(A,implies(B,A))) = c_0. [para(115358(a,1),110(a,1,1)),rewrite([112214(4),110093(3)]),flip(a)].
% 36.25/36.52 118154 equiv(implies(A,B),and(B,C)) = implies(implies(A,B),and(B,C)). [para(115494(a,1),110(a,1,2)),rewrite([114361(5)]),flip(a)].
% 36.25/36.52 118347 equiv(equiv(A,B),equiv(B,A)) = c_0. [para(115512(a,1),110(a,1,1)),rewrite([115512(4),110093(3)]),flip(a)].
% 36.25/36.52 118355 equiv(and(A,B),and(B,A)) = c_0. [para(115517(a,1),110(a,1,1)),rewrite([115517(4),110093(3)]),flip(a)].
% 36.25/36.52 119071 and(A,implies(B,A)) = A. [para(117878(a,1),77(a,1)),unit_del(a,105014)].
% 36.25/36.52 119158 equiv(A,B) = equiv(B,A). [para(118347(a,1),77(a,1)),unit_del(a,105014)].
% 36.25/36.52 119485 -is_a_theorem(equiv(A,B)) | A = B. [para(119158(a,1),77(a,1))].
% 36.25/36.52 119752 and(A,B) = and(B,A). [para(118355(a,1),77(a,1)),unit_del(a,105014)].
% 36.25/36.52 120271 and(not(A),and(B,A)) = not(c_0). [back_rewrite(112192),rewrite([119752(3)])].
% 36.25/36.52 120421 implies(A,not(B)) = implies(B,not(A)). [para(119752(a,1),4266(a,1,1)),rewrite([4266(2)])].
% 36.25/36.52 120526 is_a_theorem(implies(implies(A,B),implies(A,and(A,B)))). [back_rewrite(110111),rewrite([120421(3),120421(5),4267(4),4139(3)])].
% 36.25/36.52 121016 and(not(c_0),implies(A,B)) = not(c_0). [para(112272(a,1),120271(a,1,2)),rewrite([4266(3),4139(2),119752(4)])].
% 36.25/36.52 121156 and(not(c_0),not(equiv(A,B))) = not(c_0). [para(401(a,1),121016(a,1,2))].
% 36.25/36.52 121258 -is_a_theorem(implies(implies(c54,c55),and(A,implies(implies(c54,c55),implies(implies(not(c53),c54),implies(not(c53),c55)))))). [ur(83,b,112357,a,c,152,a),rewrite([119752(17)])].
% 36.25/36.52 121362 implies(implies(A,and(B,C)),implies(A,C)) = c_0. [resolve(112361,a,114811,a),flip(a)].
% 36.25/36.52 122156 and(c_0,implies(A,B)) = implies(A,B). [para(115466(a,1),119071(a,1,2)),rewrite([119752(3)])].
% 36.25/36.52 122998 is_a_theorem(equiv(implies(A,B),implies(A,and(A,B)))). [resolve(120526,a,151,a),rewrite([121362(4),112351(6)])].
% 36.25/36.52 123462 not(equiv(not(c_0),equiv(A,B))) = equiv(A,B). [para(121156(a,1),401(a,1,2)),rewrite([120421(4),112351(4),120421(5),4139(4),112351(3),119158(5)]),flip(a)].
% 36.25/36.52 124219 implies(A,and(A,B)) = implies(A,B). [resolve(122998,a,119485,a),flip(a)].
% 36.25/36.52 124254 implies(not(A),and(B,not(A))) = implies(not(A),B). [para(124219(a,1),106(a,2)),rewrite([119752(2),106(3)])].
% 36.25/36.52 124255 equiv(A,and(A,B)) = implies(A,B). [para(124219(a,1),110(a,1,1)),rewrite([112214(3),119752(3),122156(3)]),flip(a)].
% 36.25/36.52 124370 -is_a_theorem(implies(A,B)) | and(A,B) = A. [para(124255(a,1),77(a,1))].
% 36.25/36.52 124433 implies(implies(A,B),A) = A. [para(115247(a,1),124370(a,1)),rewrite([119752(5),119071(5)]),flip(b),unit_del(a,105014)].
% 36.25/36.52 124442 implies(implies(A,not(B)),B) = B. [para(115379(a,1),124370(a,1)),rewrite([119752(6),119071(6)]),flip(b),unit_del(a,105014)].
% 36.25/36.52 131215 implies(implies(A,B),and(A,not(B))) = and(A,not(B)). [para(109410(a,1),124219(a,1,2)),rewrite([120421(4),4267(3),112351(4)]),flip(a)].
% 36.25/36.52 131216 equiv(not(c_0),implies(A,B)) = and(A,not(B)). [para(109410(a,1),124255(a,1,2)),rewrite([119158(4),131215(8)])].
% 36.25/36.52 131681 and(A,implies(implies(A,B),implies(C,B))) = A. [para(115429(a,1),124370(a,1)),unit_del(a,105014)].
% 36.25/36.52 131881 and(implies(not(A),B),implies(not(B),A)) = implies(not(A),B). [para(115536(a,1),124370(a,1)),unit_del(a,105014)].
% 36.25/36.52 131900 and(implies(A,B),implies(implies(C,A),B)) = implies(implies(C,A),B). [para(115540(a,1),124370(a,1)),rewrite([119752(6)]),unit_del(a,105014)].
% 36.25/36.52 132951 implies(implies(implies(A,B),C),A) = implies(C,A). [resolve(18251,a,124370,a),rewrite([131900(5)])].
% 36.25/36.52 133093 implies(implies(A,B),B) = implies(not(B),A). [para(115706(a,1),123462(a,1,1,2)),rewrite([131216(5),119752(3),4266(4),4267(3),124254(4),115706(4)]),flip(a)].
% 36.25/36.52 133136 equiv(A,implies(B,A)) = implies(not(A),B). [back_rewrite(115706),rewrite([133093(4)])].
% 36.25/36.52 133139 implies(A,and(B,A)) = implies(A,B). [para(4139(a,1),133093(a,2,1)),rewrite([120421(4),4267(3),4139(2)])].
% 36.25/36.52 133353 implies(implies(A,B),and(B,A)) = A. [para(133139(a,1),133136(a,1,2)),rewrite([119158(3),118154(3),4266(5),124442(6)])].
% 36.25/36.52 133365 implies(not(A),B) = implies(not(B),A). [para(115536(a,1),133353(a,1,1)),rewrite([131881(6),112351(4)])].
% 36.25/36.52 133385 implies(implies(A,B),B) = implies(not(A),B). [back_rewrite(133093),rewrite([133365(4)])].
% 36.25/36.52 136829 implies(implies(A,B),implies(C,B)) = implies(and(C,not(B)),A). [para(131681(a,1),133353(a,1,2)),rewrite([132951(4),133385(3),4267(2)]),flip(a)].
% 36.25/36.52 136999 is_a_theorem(implies(A,implies(and(implies(A,B),not(C)),B))). [back_rewrite(43887),rewrite([136829(4)])].
% 36.25/36.52 137111 implies(implies(A,B),implies(A,C)) = implies(B,implies(A,C)). [para(124433(a,1),132951(a,1,1,1))].
% 36.25/36.52 137160 -is_a_theorem(implies(implies(c54,c55),A)). [back_rewrite(121258),rewrite([137111(15),137111(13),115456(11),114361(5)])].
% 36.25/36.52 137161 $F. [resolve(137160,a,136999,a)].
% 36.25/36.52
% 36.25/36.52 % SZS output end Refutation
% 36.25/36.52 ============================== end of proof ==========================
% 36.25/36.52
% 36.25/36.52 ============================== STATISTICS ============================
% 36.25/36.52
% 36.25/36.52 Given=5295. Generated=4296671. Kept=137089. proofs=1.
% 36.25/36.52 Usable=1220. Sos=8093. Demods=1920. Limbo=49, Disabled=127808. Hints=0.
% 36.25/36.52 Megabytes=76.90.
% 36.25/36.52 User_CPU=33.35, System_CPU=2.12, Wall_clock=36.
% 36.25/36.52
% 36.25/36.52 ============================== end of statistics =====================
% 36.25/36.52
% 36.25/36.52 ============================== end of search =========================
% 36.25/36.52
% 36.25/36.52 THEOREM PROVED
% 36.25/36.52 % SZS status Theorem
% 36.25/36.52
% 36.25/36.52 Exiting with 1 proof.
% 36.25/36.52
% 36.25/36.52 Process 20181 exit (max_proofs) Sat Jul 2 19:08:21 2022
% 36.25/36.52 Prover9 interrupted
%------------------------------------------------------------------------------