TSTP Solution File: LCL501+1 by Prover9---1109a
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : LCL501+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n008.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 13:47:14 EDT 2022
% Result : Theorem 52.70s 53.04s
% Output : Refutation 52.70s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : LCL501+1 : TPTP v8.1.0. Released v3.3.0.
% 0.07/0.13 % Command : tptp2X_and_run_prover9 %d %s
% 0.13/0.34 % Computer : n008.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 : Sun Jul 3 07:29:38 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.45/1.03 ============================== Prover9 ===============================
% 0.45/1.03 Prover9 (32) version 2009-11A, November 2009.
% 0.45/1.03 Process 13263 was started by sandbox2 on n008.cluster.edu,
% 0.45/1.03 Sun Jul 3 07:29:39 2022
% 0.45/1.03 The command was "/export/starexec/sandbox2/solver/bin/prover9 -t 300 -f /tmp/Prover9_13109_n008.cluster.edu".
% 0.45/1.03 ============================== end of head ===========================
% 0.45/1.03
% 0.45/1.03 ============================== INPUT =================================
% 0.45/1.03
% 0.45/1.03 % Reading from file /tmp/Prover9_13109_n008.cluster.edu
% 0.45/1.03
% 0.45/1.03 set(prolog_style_variables).
% 0.45/1.03 set(auto2).
% 0.45/1.03 % set(auto2) -> set(auto).
% 0.45/1.03 % set(auto) -> set(auto_inference).
% 0.45/1.03 % set(auto) -> set(auto_setup).
% 0.45/1.03 % set(auto_setup) -> set(predicate_elim).
% 0.45/1.03 % set(auto_setup) -> assign(eq_defs, unfold).
% 0.45/1.03 % set(auto) -> set(auto_limits).
% 0.45/1.03 % set(auto_limits) -> assign(max_weight, "100.000").
% 0.45/1.03 % set(auto_limits) -> assign(sos_limit, 20000).
% 0.45/1.03 % set(auto) -> set(auto_denials).
% 0.45/1.03 % set(auto) -> set(auto_process).
% 0.45/1.03 % set(auto2) -> assign(new_constants, 1).
% 0.45/1.03 % set(auto2) -> assign(fold_denial_max, 3).
% 0.45/1.03 % set(auto2) -> assign(max_weight, "200.000").
% 0.45/1.03 % set(auto2) -> assign(max_hours, 1).
% 0.45/1.03 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 0.45/1.03 % set(auto2) -> assign(max_seconds, 0).
% 0.45/1.03 % set(auto2) -> assign(max_minutes, 5).
% 0.45/1.03 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 0.45/1.03 % set(auto2) -> set(sort_initial_sos).
% 0.45/1.03 % set(auto2) -> assign(sos_limit, -1).
% 0.45/1.03 % set(auto2) -> assign(lrs_ticks, 3000).
% 0.45/1.03 % set(auto2) -> assign(max_megs, 400).
% 0.45/1.03 % set(auto2) -> assign(stats, some).
% 0.45/1.03 % set(auto2) -> clear(echo_input).
% 0.45/1.03 % set(auto2) -> set(quiet).
% 0.45/1.03 % set(auto2) -> clear(print_initial_clauses).
% 0.45/1.03 % set(auto2) -> clear(print_given).
% 0.45/1.03 assign(lrs_ticks,-1).
% 0.45/1.03 assign(sos_limit,10000).
% 0.45/1.03 assign(order,kbo).
% 0.45/1.03 set(lex_order_vars).
% 0.45/1.03 clear(print_given).
% 0.45/1.03
% 0.45/1.03 % formulas(sos). % not echoed (45 formulas)
% 0.45/1.03
% 0.45/1.03 ============================== end of input ==========================
% 0.45/1.03
% 0.45/1.03 % From the command line: assign(max_seconds, 300).
% 0.45/1.03
% 0.45/1.03 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 0.45/1.03
% 0.45/1.03 % Formulas that are not ordinary clauses:
% 0.45/1.03 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].
% 0.45/1.03 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].
% 0.45/1.03 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].
% 0.45/1.03 4 implies_1 <-> (all X all Y is_a_theorem(implies(X,implies(Y,X)))) # label(implies_1) # label(axiom) # label(non_clause). [assumption].
% 0.45/1.03 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].
% 0.45/1.03 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].
% 0.45/1.03 7 and_1 <-> (all X all Y is_a_theorem(implies(and(X,Y),X))) # label(and_1) # label(axiom) # label(non_clause). [assumption].
% 0.45/1.03 8 and_2 <-> (all X all Y is_a_theorem(implies(and(X,Y),Y))) # label(and_2) # label(axiom) # label(non_clause). [assumption].
% 0.45/1.03 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].
% 0.45/1.03 10 or_1 <-> (all X all Y is_a_theorem(implies(X,or(X,Y)))) # label(or_1) # label(axiom) # label(non_clause). [assumption].
% 0.45/1.03 11 or_2 <-> (all X all Y is_a_theorem(implies(Y,or(X,Y)))) # label(or_2) # label(axiom) # label(non_clause). [assumption].
% 0.45/1.03 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].
% 0.45/1.03 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].
% 0.45/1.03 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].
% 1.58/1.88 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].
% 1.58/1.88 16 kn1 <-> (all P is_a_theorem(implies(P,and(P,P)))) # label(kn1) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.88 17 kn2 <-> (all P all Q is_a_theorem(implies(and(P,Q),P))) # label(kn2) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.88 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].
% 1.58/1.88 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].
% 1.58/1.88 20 cn2 <-> (all P all Q is_a_theorem(implies(P,implies(not(P),Q)))) # label(cn2) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.88 21 cn3 <-> (all P is_a_theorem(implies(implies(not(P),P),P))) # label(cn3) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.88 22 r1 <-> (all P is_a_theorem(implies(or(P,P),P))) # label(r1) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.88 23 r2 <-> (all P all Q is_a_theorem(implies(Q,or(P,Q)))) # label(r2) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.88 24 r3 <-> (all P all Q is_a_theorem(implies(or(P,Q),or(Q,P)))) # label(r3) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.88 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].
% 1.58/1.88 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].
% 1.58/1.88 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].
% 1.58/1.88 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].
% 1.58/1.88 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].
% 1.58/1.88 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].
% 1.58/1.88 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].
% 1.58/1.88
% 1.58/1.88 ============================== end of process non-clausal formulas ===
% 1.58/1.88
% 1.58/1.88 ============================== PROCESS INITIAL CLAUSES ===============
% 1.58/1.88
% 1.58/1.88 ============================== PREDICATE ELIMINATION =================
% 1.58/1.88
% 1.58/1.88 ============================== end predicate elimination =============
% 1.58/1.88
% 1.58/1.88 Auto_denials: (non-Horn, no changes).
% 1.58/1.88
% 1.58/1.88 Term ordering decisions:
% 1.58/1.88
% 1.58/1.88 % Assigning unary symbol not kb_weight 0 and highest precedence (93).
% 1.58/1.88 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.
% 1.58/1.88
% 1.58/1.88 ============================== end of process initial clauses ========
% 1.58/1.88
% 1.58/1.88 ============================== CLAUSES FOR SEARCH ====================
% 1.58/1.88
% 1.58/1.88 ============================== end of clauses for search =============
% 1.58/1.88
% 1.58/1.88 ============================== SEARCH ================================
% 1.58/1.88
% 1.58/1.88 % Starting search at 0.02 seconds.
% 1.58/1.88
% 1.58/1.88 Low Water (keep): wt=26.000, iters=3421
% 1.58/1.88
% 1.58/1.88 Low Water (keep): wt=24.000, iters=3387
% 1.58/1.88
% 1.58/1.88 Low Water (keep): wt=23.000, iters=3521
% 1.58/1.88
% 1.58/1.88 Low Water (keep): wt=22.000, iters=3354
% 1.58/1.88
% 1.58/1.88 Low Water (keep): wt=21.000, iters=3403
% 1.58/1.88
% 1.58/1.88 Low Water (keep): wt=20.000, iters=3351
% 1.58/1.88
% 1.58/1.88 Low Water (keep): wt=19.000, iters=3340
% 1.58/1.88
% 1.58/1.88 Low Water (keep): wt=18.000, iters=3335
% 1.58/1.88
% 1.58/1.88 Low Water (keep): wt=17.000, iters=3335
% 1.58/1.88
% 1.58/1.88 Low Water (keep): wt=16.000, iters=3411
% 52.70/53.04
% 52.70/53.04 Low Water (keep): wt=15.000, iters=3339
% 52.70/53.04
% 52.70/53.04 Low Water (keep): wt=14.000, iters=3334
% 52.70/53.04
% 52.70/53.04 NOTE: Back_subsumption disabled, ratio of kept to back_subsumed is 23 (0.00 of 1.05 sec).
% 52.70/53.04
% 52.70/53.04 Low Water (keep): wt=13.000, iters=3333
% 52.70/53.04
% 52.70/53.04 Low Water (displace): id=6432, wt=42.000
% 52.70/53.04
% 52.70/53.04 Low Water (displace): id=14820, wt=41.000
% 52.70/53.04
% 52.70/53.04 Low Water (displace): id=12732, wt=40.000
% 52.70/53.04
% 52.70/53.04 Low Water (displace): id=14414, wt=39.000
% 52.70/53.04
% 52.70/53.04 Low Water (displace): id=14838, wt=38.000
% 52.70/53.04
% 52.70/53.04 Low Water (displace): id=14432, wt=36.000
% 52.70/53.04
% 52.70/53.04 Low Water (displace): id=15045, wt=35.000
% 52.70/53.04
% 52.70/53.04 Low Water (displace): id=13481, wt=34.000
% 52.70/53.04
% 52.70/53.04 Low Water (displace): id=15308, wt=33.000
% 52.70/53.04
% 52.70/53.04 Low Water (displace): id=15597, wt=32.000
% 52.70/53.04
% 52.70/53.04 Low Water (displace): id=15382, wt=30.000
% 52.70/53.04
% 52.70/53.04 Low Water (displace): id=15963, wt=29.000
% 52.70/53.04
% 52.70/53.04 Low Water (displace): id=15707, wt=28.000
% 52.70/53.04
% 52.70/53.04 Low Water (displace): id=15964, wt=27.000
% 52.70/53.04
% 52.70/53.04 Low Water (displace): id=15988, wt=26.000
% 52.70/53.04
% 52.70/53.04 Low Water (displace): id=16334, wt=25.000
% 52.70/53.04
% 52.70/53.04 Low Water (displace): id=16197, wt=24.000
% 52.70/53.04
% 52.70/53.04 Low Water (displace): id=16519, wt=23.000
% 52.70/53.04
% 52.70/53.04 Low Water (displace): id=16664, wt=22.000
% 52.70/53.04
% 52.70/53.04 Low Water (displace): id=17072, wt=12.000
% 52.70/53.04
% 52.70/53.04 Low Water (displace): id=18205, wt=11.000
% 52.70/53.04
% 52.70/53.04 Low Water (displace): id=18337, wt=9.000
% 52.70/53.04
% 52.70/53.04 Low Water (keep): wt=12.000, iters=3334
% 52.70/53.04
% 52.70/53.04 Low Water (keep): wt=11.000, iters=3333
% 52.70/53.04
% 52.70/53.04 Low Water (keep): wt=10.000, iters=3337
% 52.70/53.04
% 52.70/53.04 ============================== PROOF =================================
% 52.70/53.04 % SZS status Theorem
% 52.70/53.04 % SZS output start Refutation
% 52.70/53.04
% 52.70/53.04 % Proof 1 at 48.92 (+ 3.10) seconds.
% 52.70/53.04 % Length of proof is 209.
% 52.70/53.04 % Level of proof is 38.
% 52.70/53.04 % Maximum clause weight is 16.000.
% 52.70/53.04 % Given clauses 5359.
% 52.70/53.04
% 52.70/53.04 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].
% 52.70/53.04 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].
% 52.70/53.04 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].
% 52.70/53.04 22 r1 <-> (all P is_a_theorem(implies(or(P,P),P))) # label(r1) # label(axiom) # label(non_clause). [assumption].
% 52.70/53.04 23 r2 <-> (all P all Q is_a_theorem(implies(Q,or(P,Q)))) # label(r2) # label(axiom) # label(non_clause). [assumption].
% 52.70/53.04 24 r3 <-> (all P all Q is_a_theorem(implies(or(P,Q),or(Q,P)))) # label(r3) # label(axiom) # label(non_clause). [assumption].
% 52.70/53.04 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].
% 52.70/53.04 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].
% 52.70/53.04 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].
% 52.70/53.04 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].
% 52.70/53.04 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].
% 52.70/53.04 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].
% 52.70/53.04 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].
% 52.70/53.04 32 op_implies_or # label(principia_op_implies_or) # label(axiom). [assumption].
% 52.70/53.04 33 op_and # label(principia_op_and) # label(axiom). [assumption].
% 52.70/53.04 34 op_equiv # label(principia_op_equiv) # label(axiom). [assumption].
% 52.70/53.04 35 modus_ponens # label(principia_modus_ponens) # label(axiom). [assumption].
% 52.70/53.04 36 r1 # label(principia_r1) # label(axiom). [assumption].
% 52.70/53.04 37 r2 # label(principia_r2) # label(axiom). [assumption].
% 52.70/53.04 38 r3 # label(principia_r3) # label(axiom). [assumption].
% 52.70/53.04 39 r4 # label(principia_r4) # label(axiom). [assumption].
% 52.70/53.04 40 r5 # label(principia_r5) # label(axiom). [assumption].
% 52.70/53.04 41 substitution_of_equivalents # label(substitution_of_equivalents) # label(axiom). [assumption].
% 52.70/53.04 42 op_or # label(rosser_op_or) # label(axiom). [assumption].
% 52.70/53.04 43 op_implies_and # label(rosser_op_implies_and) # label(axiom). [assumption].
% 52.70/53.04 44 -kn3 # label(rosser_kn3) # label(negated_conjecture). [assumption].
% 52.70/53.04 59 -r1 | is_a_theorem(implies(or(A,A),A)) # label(r1) # label(axiom). [clausify(22)].
% 52.70/53.04 60 is_a_theorem(implies(or(A,A),A)). [copy(59),unit_del(a,36)].
% 52.70/53.04 62 -r2 | is_a_theorem(implies(A,or(B,A))) # label(r2) # label(axiom). [clausify(23)].
% 52.70/53.04 63 is_a_theorem(implies(A,or(B,A))). [copy(62),unit_del(a,37)].
% 52.70/53.04 65 -substitution_of_equivalents | -is_a_theorem(equiv(A,B)) | B = A # label(substitution_of_equivalents) # label(axiom). [clausify(2)].
% 52.70/53.04 66 -is_a_theorem(equiv(A,B)) | B = A. [copy(65),unit_del(a,41)].
% 52.70/53.04 71 -modus_ponens | -is_a_theorem(A) | -is_a_theorem(implies(A,B)) | is_a_theorem(B) # label(modus_ponens) # label(axiom). [clausify(1)].
% 52.70/53.04 72 -is_a_theorem(A) | -is_a_theorem(implies(A,B)) | is_a_theorem(B). [copy(71),unit_del(a,35)].
% 52.70/53.04 79 -r3 | is_a_theorem(implies(or(A,B),or(B,A))) # label(r3) # label(axiom). [clausify(24)].
% 52.70/53.04 80 is_a_theorem(implies(or(A,B),or(B,A))). [copy(79),unit_del(a,38)].
% 52.70/53.04 82 -op_implies_or | or(not(A),B) = implies(A,B) # label(op_implies_or) # label(axiom). [clausify(30)].
% 52.70/53.04 83 or(not(A),B) = implies(A,B). [copy(82),unit_del(a,32)].
% 52.70/53.04 84 -op_implies_and | not(and(A,not(B))) = implies(A,B) # label(op_implies_and) # label(axiom). [clausify(29)].
% 52.70/53.04 85 not(and(A,not(B))) = implies(A,B). [copy(84),unit_del(a,43)].
% 52.70/53.04 90 -op_or | or(A,B) = not(and(not(A),not(B))) # label(op_or) # label(axiom). [clausify(27)].
% 52.70/53.04 91 or(A,B) = implies(not(A),B). [copy(90),rewrite([85(6)]),unit_del(a,42)].
% 52.70/53.04 92 -op_and | and(A,B) = not(or(not(A),not(B))) # label(op_and) # label(axiom). [clausify(28)].
% 52.70/53.04 93 not(implies(not(not(A)),not(B))) = and(A,B). [copy(92),rewrite([91(5)]),flip(b),unit_del(a,33)].
% 52.70/53.04 94 -op_equiv | and(implies(A,B),implies(B,A)) = equiv(A,B) # label(op_equiv) # label(axiom). [clausify(31)].
% 52.70/53.04 95 and(implies(A,B),implies(B,A)) = equiv(A,B). [copy(94),unit_del(a,34)].
% 52.70/53.04 102 -r4 | is_a_theorem(implies(or(A,or(B,C)),or(B,or(A,C)))) # label(r4) # label(axiom). [clausify(25)].
% 52.70/53.04 103 is_a_theorem(implies(implies(not(A),implies(not(B),C)),implies(not(B),implies(not(A),C)))). [copy(102),rewrite([91(2),91(4),91(6),91(8)]),unit_del(a,39)].
% 52.70/53.04 105 -r5 | is_a_theorem(implies(implies(A,B),implies(or(C,A),or(C,B)))) # label(r5) # label(axiom). [clausify(26)].
% 52.70/53.04 106 is_a_theorem(implies(implies(A,B),implies(implies(not(C),A),implies(not(C),B)))). [copy(105),rewrite([91(3),91(5)]),unit_del(a,40)].
% 52.70/53.04 112 kn3 | -is_a_theorem(implies(implies(c36,c37),implies(not(and(c37,c38)),not(and(c38,c36))))) # label(kn3) # label(axiom). [clausify(18)].
% 52.70/53.04 113 -is_a_theorem(implies(implies(c36,c37),implies(not(and(c37,c38)),not(and(c38,c36))))). [copy(112),unit_del(a,44)].
% 52.70/53.04 115 implies(not(not(A)),B) = implies(A,B). [back_rewrite(83),rewrite([91(2)])].
% 52.70/53.04 116 is_a_theorem(implies(implies(not(A),B),implies(not(B),A))). [back_rewrite(80),rewrite([91(1),91(3)])].
% 52.70/53.04 117 is_a_theorem(implies(A,implies(not(B),A))). [back_rewrite(63),rewrite([91(1)])].
% 52.70/53.04 118 is_a_theorem(implies(implies(not(A),A),A)). [back_rewrite(60),rewrite([91(1)])].
% 52.70/53.04 121 not(implies(A,not(B))) = and(A,B). [back_rewrite(93),rewrite([115(4)])].
% 52.70/53.04 124 not(and(A,implies(B,C))) = implies(A,and(B,not(C))). [para(85(a,1),85(a,1,1,2))].
% 52.70/53.04 125 -is_a_theorem(implies(not(A),implies(not(B),C))) | is_a_theorem(implies(not(B),implies(not(A),C))). [resolve(103,a,72,b)].
% 52.70/53.04 128 -is_a_theorem(implies(A,B)) | is_a_theorem(implies(implies(not(C),A),implies(not(C),B))). [resolve(106,a,72,b)].
% 52.70/53.04 133 implies(not(implies(A,B)),C) = implies(and(A,not(B)),C). [para(85(a,1),115(a,1,1,1))].
% 52.70/53.04 135 and(implies(A,not(not(B))),implies(B,A)) = equiv(A,not(not(B))). [para(115(a,1),95(a,1,2))].
% 52.70/53.04 139 is_a_theorem(implies(implies(A,B),implies(implies(C,A),implies(C,B)))). [para(115(a,1),106(a,1,2,1)),rewrite([115(5)])].
% 52.70/53.04 140 -is_a_theorem(implies(not(A),B)) | is_a_theorem(implies(not(B),A)). [resolve(116,a,72,b)].
% 52.70/53.04 144 is_a_theorem(implies(implies(A,B),implies(not(B),not(A)))). [para(115(a,1),116(a,1,1))].
% 52.70/53.04 145 is_a_theorem(implies(implies(not(A),not(B)),implies(B,A))). [para(115(a,1),116(a,1,2))].
% 52.70/53.04 150 is_a_theorem(implies(A,implies(B,A))). [para(115(a,1),117(a,1,2))].
% 52.70/53.04 153 -is_a_theorem(implies(not(A),A)) | is_a_theorem(A). [resolve(118,a,72,b)].
% 52.70/53.04 157 is_a_theorem(implies(implies(A,not(A)),not(A))). [para(115(a,1),118(a,1,1))].
% 52.70/53.04 160 implies(not(and(A,B)),C) = implies(implies(A,not(B)),C). [para(121(a,1),115(a,1,1,1))].
% 52.70/53.04 161 and(not(not(A)),B) = and(A,B). [para(115(a,1),121(a,1,1)),rewrite([121(3)]),flip(a)].
% 52.70/53.04 172 -is_a_theorem(implies(implies(c36,c37),implies(implies(c37,not(c38)),not(and(c38,c36))))). [back_rewrite(113),rewrite([160(12)])].
% 52.70/53.04 173 implies(implies(A,B),and(B,not(A))) = not(equiv(A,B)). [para(95(a,1),124(a,1,1)),flip(a)].
% 52.70/53.04 196 -is_a_theorem(A) | is_a_theorem(implies(B,A)). [resolve(150,a,72,b)].
% 52.70/53.04 200 is_a_theorem(implies(A,implies(B,not(not(A))))). [para(115(a,1),150(a,1))].
% 52.70/53.04 204 is_a_theorem(implies(not(A),implies(not(B),not(B)))). [resolve(125,a,150,a)].
% 52.70/53.04 207 -is_a_theorem(implies(not(A),implies(B,C))) | is_a_theorem(implies(B,implies(not(A),C))). [para(115(a,1),125(a,1,2)),rewrite([115(9)])].
% 52.70/53.04 243 -is_a_theorem(A) | is_a_theorem(implies(B,not(not(A)))). [resolve(200,a,72,b)].
% 52.70/53.04 264 is_a_theorem(implies(implies(not(A),implies(not(B),B)),implies(not(A),B))). [resolve(128,a,118,a)].
% 52.70/53.04 401 is_a_theorem(implies(not(A),not(A))). [resolve(204,a,153,a)].
% 52.70/53.04 422 is_a_theorem(implies(A,not(and(not(B),B)))). [resolve(401,a,243,a),rewrite([121(4)])].
% 52.70/53.04 442 is_a_theorem(implies(A,not(not(A)))). [para(115(a,1),401(a,1))].
% 52.70/53.04 449 implies(and(A,not(not(B))),C) = implies(and(A,B),C). [para(121(a,1),133(a,1,1)),flip(a)].
% 52.70/53.04 506 is_a_theorem(implies(A,implies(B,B))). [resolve(442,a,243,a),rewrite([121(4),85(3)])].
% 52.70/53.04 535 is_a_theorem(implies(A,A)). [resolve(506,a,153,a)].
% 52.70/53.04 556 is_a_theorem(implies(A,not(not(implies(B,B))))). [resolve(535,a,243,a)].
% 52.70/53.04 686 equiv(A,not(not(B))) = equiv(A,B). [para(135(a,1),161(a,2)),rewrite([121(4),85(3),95(3)]),flip(a)].
% 52.70/53.04 1132 -is_a_theorem(equiv(A,B)) | not(not(B)) = A. [para(686(a,1),66(a,1))].
% 52.70/53.04 1144 is_a_theorem(implies(A,implies(implies(B,C),implies(implies(D,B),implies(D,C))))). [resolve(139,a,196,a)].
% 52.70/53.04 1147 -is_a_theorem(implies(A,B)) | is_a_theorem(implies(implies(C,A),implies(C,B))). [resolve(139,a,72,b)].
% 52.70/53.04 1339 is_a_theorem(implies(and(A,not(A)),B)). [resolve(140,a,556,a),rewrite([115(5),133(3)])].
% 52.70/53.04 1341 is_a_theorem(implies(and(not(A),A),B)). [resolve(140,a,422,a),rewrite([115(5)])].
% 52.70/53.04 1344 is_a_theorem(implies(and(A,B),B)). [resolve(140,a,200,a),rewrite([121(5),449(4)])].
% 52.70/53.04 1346 -is_a_theorem(implies(A,B)) | is_a_theorem(implies(not(B),not(A))). [para(115(a,1),140(a,1))].
% 52.70/53.04 2023 is_a_theorem(implies(implies(A,not(B)),implies(B,not(A)))). [para(115(a,1),144(a,1,2))].
% 52.70/53.04 2271 -is_a_theorem(implies(not(A),not(B))) | is_a_theorem(implies(B,A)). [resolve(145,a,72,b)].
% 52.70/53.04 5706 is_a_theorem(implies(A,and(A,A))). [resolve(1346,a,157,a),rewrite([121(5),115(4)])].
% 52.70/53.04 5896 -is_a_theorem(A) | is_a_theorem(and(A,A)). [resolve(5706,a,72,b)].
% 52.70/53.04 6035 is_a_theorem(equiv(A,A)). [resolve(5896,a,535,a),rewrite([95(3)])].
% 52.70/53.04 6068 not(not(A)) = A. [resolve(6035,a,1132,a)].
% 52.70/53.04 6415 not(and(A,B)) = implies(A,not(B)). [para(6068(a,1),85(a,1,1,2))].
% 52.70/53.04 6416 not(implies(A,B)) = and(A,not(B)). [para(85(a,1),6068(a,1,1))].
% 52.70/53.04 6694 -is_a_theorem(implies(implies(c36,c37),implies(implies(c37,not(c38)),implies(c38,not(c36))))). [back_rewrite(172),rewrite([6415(11)])].
% 52.70/53.04 8073 is_a_theorem(implies(and(A,B),and(B,A))). [resolve(2023,a,1346,a),rewrite([6416(3),6068(2),6416(4),6068(3)])].
% 52.70/53.04 8075 -is_a_theorem(implies(A,not(B))) | is_a_theorem(implies(B,not(A))). [resolve(2023,a,72,b)].
% 52.70/53.04 8138 -is_a_theorem(implies(A,implies(B,C))) | is_a_theorem(implies(B,implies(A,C))). [para(6068(a,1),207(a,1,1)),rewrite([6068(5)])].
% 52.70/53.04 8338 is_a_theorem(implies(A,implies(and(B,C),and(C,B)))). [resolve(8073,a,196,a)].
% 52.70/53.04 10734 is_a_theorem(implies(implies(A,implies(not(B),B)),implies(A,B))). [para(6068(a,1),264(a,1,1,1)),rewrite([6068(5)])].
% 52.70/53.04 13529 -is_a_theorem(implies(A,implies(not(B),B))) | is_a_theorem(implies(A,B)). [resolve(10734,a,72,b)].
% 52.70/53.04 15830 is_a_theorem(implies(implies(A,B),implies(A,and(B,B)))). [resolve(1147,a,5706,a)].
% 52.70/53.04 15844 is_a_theorem(implies(implies(A,and(B,C)),implies(A,C))). [resolve(1147,a,1344,a)].
% 52.70/53.04 15847 is_a_theorem(implies(implies(A,and(not(B),B)),implies(A,C))). [resolve(1147,a,1341,a)].
% 52.70/53.04 15883 -is_a_theorem(implies(A,B)) | is_a_theorem(implies(A,and(B,B))). [resolve(15830,a,72,b)].
% 52.70/53.04 15914 is_a_theorem(implies(implies(not(A),and(B,A)),A)). [resolve(15844,a,13529,a)].
% 52.70/53.04 15926 -is_a_theorem(implies(A,and(B,C))) | is_a_theorem(implies(A,C)). [resolve(15844,a,72,b)].
% 52.70/53.04 15973 is_a_theorem(implies(A,and(A,implies(B,A)))). [resolve(15914,a,8075,a),rewrite([6068(2),6416(4),6415(3),6068(2)])].
% 52.70/53.04 16340 is_a_theorem(not(equiv(A,not(A)))). [resolve(15883,a,157,a),rewrite([173(6)])].
% 52.70/53.04 16362 is_a_theorem(implies(A,not(equiv(B,not(B))))). [resolve(16340,a,196,a)].
% 52.70/53.04 16465 is_a_theorem(implies(equiv(A,not(A)),B)). [resolve(16362,a,2271,a)].
% 52.70/53.04 16483 is_a_theorem(implies(implies(A,equiv(B,not(B))),implies(A,C))). [resolve(16465,a,1147,a)].
% 52.70/53.04 16510 is_a_theorem(implies(equiv(not(A),A),B)). [para(6068(a,1),16465(a,1,1,2))].
% 52.70/53.04 16681 is_a_theorem(implies(and(A,B),A)). [resolve(15926,a,8073,a)].
% 52.70/53.04 16714 is_a_theorem(implies(A,implies(not(A),not(B)))). [resolve(16681,a,8075,a),rewrite([6415(3)])].
% 52.70/53.04 16717 is_a_theorem(implies(implies(A,and(B,C)),implies(A,B))). [resolve(16681,a,1147,a)].
% 52.70/53.04 17224 is_a_theorem(implies(A,implies(not(A),B))). [para(6068(a,1),16714(a,1,2,2))].
% 52.70/53.04 17265 is_a_theorem(implies(implies(A,B),implies(A,implies(not(B),C)))). [resolve(17224,a,1147,a)].
% 52.70/53.04 19115 is_a_theorem(implies(not(equiv(A,B)),implies(implies(A,B),B))). [para(173(a,1),16717(a,1,1))].
% 52.70/53.04 26850 is_a_theorem(implies(implies(not(A),and(not(B),B)),A)). [resolve(15847,a,13529,a)].
% 52.70/53.04 26893 is_a_theorem(implies(A,and(A,implies(not(B),not(B))))). [resolve(26850,a,8075,a),rewrite([6068(2),6416(4),6415(3)])].
% 52.70/53.04 26984 is_a_theorem(implies(A,and(A,implies(B,B)))). [para(6068(a,1),26893(a,1,2,2,1)),rewrite([6068(2)])].
% 52.70/53.04 27011 is_a_theorem(implies(implies(A,and(B,not(B))),not(A))). [resolve(26984,a,1346,a),rewrite([6415(3),6416(2)])].
% 52.70/53.04 27689 -is_a_theorem(implies(A,and(B,not(B)))) | is_a_theorem(not(A)). [resolve(27011,a,72,b)].
% 52.70/53.04 29912 is_a_theorem(implies(implies(not(A),equiv(B,not(B))),A)). [resolve(16483,a,13529,a)].
% 52.70/53.04 30027 is_a_theorem(implies(A,and(A,not(equiv(B,not(B)))))). [resolve(29912,a,8075,a),rewrite([6068(2),6416(4)])].
% 52.70/53.04 30031 -is_a_theorem(implies(not(A),equiv(B,not(B)))) | is_a_theorem(A). [resolve(29912,a,72,b)].
% 52.70/53.04 30125 is_a_theorem(implies(A,and(A,not(equiv(not(B),B))))). [para(6068(a,1),30027(a,1,2,2,1,2))].
% 52.70/53.04 30180 -is_a_theorem(implies(A,equiv(B,not(B)))) | is_a_theorem(not(A)). [para(6068(a,1),30031(a,1,1))].
% 52.70/53.04 30768 -is_a_theorem(implies(A,equiv(not(B),B))) | is_a_theorem(not(A)). [para(6068(a,1),30180(a,1,2,2))].
% 52.70/53.04 31702 -is_a_theorem(implies(A,B)) | is_a_theorem(implies(A,implies(not(B),C))). [resolve(17265,a,72,b)].
% 52.70/53.04 40539 is_a_theorem(implies(A,implies(implies(A,equiv(not(B),B)),C))). [resolve(31702,a,30125,a),rewrite([6415(5),6068(4)])].
% 52.70/53.04 47978 is_a_theorem(implies(A,not(equiv(A,equiv(not(B),B))))). [para(173(a,1),40539(a,1,2))].
% 52.70/53.04 48109 is_a_theorem(implies(equiv(not(A),equiv(not(B),B)),A)). [resolve(47978,a,2271,a)].
% 52.70/53.04 48182 is_a_theorem(not(equiv(not(equiv(not(A),A)),equiv(not(B),B)))). [resolve(48109,a,30768,a)].
% 52.70/53.04 84132 is_a_theorem(implies(implies(A,B),implies(not(equiv(A,B)),B))). [resolve(8138,a,19115,a)].
% 52.70/53.04 84180 is_a_theorem(implies(A,implies(implies(A,B),B))). [resolve(8138,a,535,a)].
% 52.70/53.04 84451 -is_a_theorem(A) | is_a_theorem(implies(implies(A,B),B)). [resolve(84180,a,72,b)].
% 52.70/53.04 86669 is_a_theorem(implies(implies(implies(and(A,B),A),C),C)). [resolve(84451,a,16681,a)].
% 52.70/53.04 86817 is_a_theorem(implies(implies(implies(A,and(A,A)),B),B)). [resolve(84451,a,5706,a)].
% 52.70/53.04 86856 is_a_theorem(implies(implies(implies(and(A,B),B),C),C)). [resolve(84451,a,1344,a)].
% 52.70/53.04 86867 is_a_theorem(implies(implies(implies(A,A),B),B)). [resolve(84451,a,535,a)].
% 52.70/53.04 86893 is_a_theorem(implies(implies(implies(A,implies(B,A)),C),C)). [resolve(84451,a,150,a)].
% 52.70/53.04 87525 is_a_theorem(implies(A,and(implies(B,B),A))). [resolve(86867,a,8075,a),rewrite([6416(4),6068(3)])].
% 52.70/53.04 87783 -is_a_theorem(A) | is_a_theorem(and(implies(B,B),A)). [resolve(87525,a,72,b)].
% 52.70/53.04 89121 is_a_theorem(and(implies(A,A),implies(B,and(B,implies(C,B))))). [resolve(87783,a,15973,a)].
% 52.70/53.04 94745 -is_a_theorem(implies(implies(and(A,B),A),C)) | is_a_theorem(C). [resolve(86669,a,72,b)].
% 52.70/53.04 95142 -is_a_theorem(implies(implies(A,and(A,A)),B)) | is_a_theorem(B). [resolve(86817,a,72,b)].
% 52.70/53.04 95237 -is_a_theorem(implies(implies(and(A,B),B),C)) | is_a_theorem(C). [resolve(86856,a,72,b)].
% 52.70/53.04 95443 -is_a_theorem(implies(implies(A,implies(B,A)),C)) | is_a_theorem(C). [resolve(86893,a,72,b)].
% 52.70/53.04 140704 is_a_theorem(implies(not(equiv(A,implies(B,A))),implies(B,A))). [resolve(84132,a,95443,a)].
% 52.70/53.04 140705 is_a_theorem(implies(not(equiv(and(A,B),B)),B)). [resolve(84132,a,95237,a)].
% 52.70/53.04 140810 -is_a_theorem(implies(A,B)) | is_a_theorem(implies(not(equiv(A,B)),B)). [resolve(84132,a,72,b)].
% 52.70/53.04 140901 is_a_theorem(equiv(and(A,equiv(not(B),B)),equiv(not(B),B))). [resolve(140705,a,30768,a),rewrite([6068(8)])].
% 52.70/53.04 174076 is_a_theorem(implies(not(equiv(A,implies(not(A),A))),A)). [resolve(140704,a,13529,a)].
% 52.70/53.04 174202 is_a_theorem(equiv(and(A,not(A)),not(equiv(A,A)))). [resolve(174076,a,27689,a),rewrite([6415(5),6068(4),173(6),6068(7)])].
% 52.70/53.04 174368 not(equiv(A,A)) = and(A,not(A)). [resolve(174202,a,66,a)].
% 52.70/53.04 174382 equiv(A,A) = implies(A,A). [para(174368(a,1),6068(a,1,1)),rewrite([6415(3),6068(2)]),flip(a)].
% 52.70/53.04 176999 is_a_theorem(implies(not(equiv(equiv(not(A),A),B)),B)). [resolve(140810,a,16510,a)].
% 52.70/53.04 177111 is_a_theorem(implies(not(equiv(and(A,not(A)),B)),B)). [resolve(140810,a,1339,a)].
% 52.70/53.04 177139 is_a_theorem(equiv(equiv(not(A),A),equiv(not(B),B))). [resolve(176999,a,30768,a),rewrite([6068(7)])].
% 52.70/53.04 177155 is_a_theorem(implies(A,equiv(equiv(not(B),B),not(A)))). [resolve(176999,a,8075,a),rewrite([6068(6)])].
% 52.70/53.04 177251 is_a_theorem(equiv(and(A,not(A)),equiv(not(B),B))). [resolve(177111,a,30768,a),rewrite([6068(7)])].
% 52.70/53.04 177315 equiv(not(A),A) = equiv(not(B),B). [resolve(177139,a,66,a)].
% 52.70/53.04 177320 equiv(not(A),A) = c_0. [new_symbol(177315)].
% 52.70/53.04 177328 is_a_theorem(equiv(and(A,not(A)),c_0)). [back_rewrite(177251),rewrite([177320(4)])].
% 52.70/53.04 177344 is_a_theorem(implies(A,equiv(c_0,not(A)))). [back_rewrite(177155),rewrite([177320(2)])].
% 52.70/53.04 177502 is_a_theorem(equiv(and(A,c_0),c_0)). [back_rewrite(140901),rewrite([177320(2),177320(4)])].
% 52.70/53.04 177676 is_a_theorem(not(c_0)). [back_rewrite(48182),rewrite([177320(2),177320(4),177320(4)])].
% 52.70/53.04 179297 and(A,c_0) = c_0. [resolve(177502,a,66,a),flip(a)].
% 52.70/53.04 179306 implies(A,not(c_0)) = not(c_0). [para(179297(a,1),6415(a,1,1)),flip(a)].
% 52.70/53.04 179561 and(A,not(A)) = c_0. [resolve(177328,a,66,a),flip(a)].
% 52.70/53.04 179816 implies(A,A) = not(c_0). [para(179561(a,1),6415(a,1,1)),rewrite([6068(4)]),flip(a)].
% 52.70/53.04 180085 equiv(A,A) = not(c_0). [back_rewrite(174382),rewrite([179816(2)])].
% 52.70/53.04 180330 is_a_theorem(and(not(c_0),implies(A,and(A,implies(B,A))))). [back_rewrite(89121),rewrite([179816(1)])].
% 52.70/53.04 180675 and(not(c_0),not(c_0)) = not(c_0). [para(179816(a,1),95(a,1,1)),rewrite([179816(3),180085(6)])].
% 52.70/53.04 181101 is_a_theorem(equiv(c_0,and(and(A,B),not(B)))). [resolve(177344,a,95237,a),rewrite([6416(4)])].
% 52.70/53.04 181102 is_a_theorem(equiv(c_0,and(A,implies(A,not(A))))). [resolve(177344,a,95142,a),rewrite([6416(4),6415(3)])].
% 52.70/53.04 181103 is_a_theorem(equiv(c_0,and(and(A,B),not(A)))). [resolve(177344,a,94745,a),rewrite([6416(4)])].
% 52.70/53.04 183584 and(implies(not(c_0),A),not(c_0)) = equiv(not(c_0),A). [para(179306(a,1),95(a,1,2))].
% 52.70/53.04 185588 and(and(A,B),not(B)) = c_0. [resolve(181101,a,66,a)].
% 52.70/53.04 185592 implies(and(A,B),B) = not(c_0). [para(185588(a,1),6415(a,1,1)),rewrite([6068(5)]),flip(a)].
% 52.70/53.04 185612 and(A,implies(A,not(A))) = c_0. [resolve(181102,a,66,a)].
% 52.70/53.04 185615 implies(A,and(A,A)) = not(c_0). [para(185612(a,1),6415(a,1,1)),rewrite([6416(5),6068(4)]),flip(a)].
% 52.70/53.04 185619 equiv(A,and(A,A)) = not(c_0). [para(185615(a,1),95(a,1,1)),rewrite([185592(4),180675(5)]),flip(a)].
% 52.70/53.04 185621 and(A,A) = A. [para(185619(a,1),66(a,1)),unit_del(a,177676)].
% 52.70/53.04 185665 and(and(A,B),not(A)) = c_0. [resolve(181103,a,66,a)].
% 52.70/53.04 185670 implies(and(A,B),A) = not(c_0). [para(185665(a,1),6415(a,1,1)),rewrite([6068(5)]),flip(a)].
% 52.70/53.04 185691 and(not(c_0),implies(A,and(A,B))) = equiv(and(A,B),A). [para(185670(a,1),95(a,1,1))].
% 52.70/53.04 185705 is_a_theorem(equiv(and(A,implies(B,A)),A)). [back_rewrite(180330),rewrite([185691(6)])].
% 52.70/53.04 185777 and(A,implies(B,A)) = A. [resolve(185705,a,66,a),flip(a)].
% 52.70/53.04 185860 and(A,not(c_0)) = A. [para(179816(a,1),185777(a,1,2))].
% 52.70/53.04 185862 equiv(not(c_0),A) = implies(not(c_0),A). [back_rewrite(183584),rewrite([185860(6)]),flip(a)].
% 52.70/53.04 190854 -is_a_theorem(implies(not(c_0),A)) | not(c_0) = A. [para(185862(a,1),66(a,1)),flip(b)].
% 52.70/53.04 191913 implies(and(A,B),and(B,A)) = not(c_0). [resolve(190854,a,8338,a),flip(a)].
% 52.70/53.04 191917 implies(implies(A,B),implies(implies(C,A),implies(C,B))) = not(c_0). [resolve(190854,a,1144,a),flip(a)].
% 52.70/53.04 196661 -is_a_theorem(implies(implies(c37,not(c38)),implies(implies(c36,c37),implies(c38,not(c36))))). [ur(8138,b,6694,a)].
% 52.70/53.04 198422 equiv(and(A,B),and(B,A)) = not(c_0). [para(191913(a,1),95(a,1,1)),rewrite([191913(5),185621(5)]),flip(a)].
% 52.70/53.04 199739 and(A,B) = and(B,A). [para(198422(a,1),66(a,1)),unit_del(a,177676)].
% 52.70/53.04 201009 implies(A,not(B)) = implies(B,not(A)). [para(199739(a,1),6415(a,1,1)),rewrite([6415(2)])].
% 52.70/53.04 201178 $F. [back_rewrite(196661),rewrite([201009(11),191917(13)]),unit_del(a,177676)].
% 52.70/53.04
% 52.70/53.04 % SZS output end Refutation
% 52.70/53.04 ============================== end of proof ==========================
% 52.70/53.04
% 52.70/53.04 ============================== STATISTICS ============================
% 52.70/53.04
% 52.70/53.04 Given=5359. Generated=5689963. Kept=201126. proofs=1.
% 52.70/53.04 Usable=512. Sos=2212. Demods=429. Limbo=169, Disabled=198307. Hints=0.
% 52.70/53.04 Megabytes=120.48.
% 52.70/53.04 User_CPU=48.92, System_CPU=3.10, Wall_clock=52.
% 52.70/53.04
% 52.70/53.04 ============================== end of statistics =====================
% 52.70/53.04
% 52.70/53.04 ============================== end of search =========================
% 52.70/53.04
% 52.70/53.04 THEOREM PROVED
% 52.70/53.04 % SZS status Theorem
% 52.70/53.04
% 52.70/53.04 Exiting with 1 proof.
% 52.70/53.04
% 52.70/53.04 Process 13263 exit (max_proofs) Sun Jul 3 07:30:31 2022
% 52.70/53.04 Prover9 interrupted
%------------------------------------------------------------------------------