TSTP Solution File: LCL463+1 by Prover9---1109a
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : LCL463+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n019.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 13:47:00 EDT 2022
% Result : Theorem 114.84s 115.17s
% Output : Refutation 114.84s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : LCL463+1 : TPTP v8.1.0. Released v3.3.0.
% 0.03/0.13 % Command : tptp2X_and_run_prover9 %d %s
% 0.13/0.34 % Computer : n019.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 : Mon Jul 4 18:14:38 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.43/1.01 ============================== Prover9 ===============================
% 0.43/1.01 Prover9 (32) version 2009-11A, November 2009.
% 0.43/1.01 Process 31202 was started by sandbox on n019.cluster.edu,
% 0.43/1.01 Mon Jul 4 18:14:39 2022
% 0.43/1.01 The command was "/export/starexec/sandbox/solver/bin/prover9 -t 300 -f /tmp/Prover9_31049_n019.cluster.edu".
% 0.43/1.01 ============================== end of head ===========================
% 0.43/1.01
% 0.43/1.01 ============================== INPUT =================================
% 0.43/1.01
% 0.43/1.01 % Reading from file /tmp/Prover9_31049_n019.cluster.edu
% 0.43/1.01
% 0.43/1.01 set(prolog_style_variables).
% 0.43/1.01 set(auto2).
% 0.43/1.01 % set(auto2) -> set(auto).
% 0.43/1.01 % set(auto) -> set(auto_inference).
% 0.43/1.01 % set(auto) -> set(auto_setup).
% 0.43/1.01 % set(auto_setup) -> set(predicate_elim).
% 0.43/1.01 % set(auto_setup) -> assign(eq_defs, unfold).
% 0.43/1.01 % set(auto) -> set(auto_limits).
% 0.43/1.01 % set(auto_limits) -> assign(max_weight, "100.000").
% 0.43/1.01 % set(auto_limits) -> assign(sos_limit, 20000).
% 0.43/1.01 % set(auto) -> set(auto_denials).
% 0.43/1.01 % set(auto) -> set(auto_process).
% 0.43/1.01 % set(auto2) -> assign(new_constants, 1).
% 0.43/1.01 % set(auto2) -> assign(fold_denial_max, 3).
% 0.43/1.01 % set(auto2) -> assign(max_weight, "200.000").
% 0.43/1.01 % set(auto2) -> assign(max_hours, 1).
% 0.43/1.01 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 0.43/1.01 % set(auto2) -> assign(max_seconds, 0).
% 0.43/1.01 % set(auto2) -> assign(max_minutes, 5).
% 0.43/1.01 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 0.43/1.01 % set(auto2) -> set(sort_initial_sos).
% 0.43/1.01 % set(auto2) -> assign(sos_limit, -1).
% 0.43/1.01 % set(auto2) -> assign(lrs_ticks, 3000).
% 0.43/1.01 % set(auto2) -> assign(max_megs, 400).
% 0.43/1.01 % set(auto2) -> assign(stats, some).
% 0.43/1.01 % set(auto2) -> clear(echo_input).
% 0.43/1.01 % set(auto2) -> set(quiet).
% 0.43/1.01 % set(auto2) -> clear(print_initial_clauses).
% 0.43/1.01 % set(auto2) -> clear(print_given).
% 0.43/1.01 assign(lrs_ticks,-1).
% 0.43/1.01 assign(sos_limit,10000).
% 0.43/1.01 assign(order,kbo).
% 0.43/1.01 set(lex_order_vars).
% 0.43/1.01 clear(print_given).
% 0.43/1.01
% 0.43/1.01 % formulas(sos). % not echoed (43 formulas)
% 0.43/1.01
% 0.43/1.01 ============================== end of input ==========================
% 0.43/1.01
% 0.43/1.01 % From the command line: assign(max_seconds, 300).
% 0.43/1.01
% 0.43/1.01 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 0.43/1.01
% 0.43/1.01 % Formulas that are not ordinary clauses:
% 0.43/1.01 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].
% 0.43/1.01 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].
% 0.43/1.01 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].
% 0.43/1.01 4 implies_1 <-> (all X all Y is_a_theorem(implies(X,implies(Y,X)))) # label(implies_1) # label(axiom) # label(non_clause). [assumption].
% 0.43/1.01 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].
% 0.43/1.01 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].
% 0.43/1.01 7 and_1 <-> (all X all Y is_a_theorem(implies(and(X,Y),X))) # label(and_1) # label(axiom) # label(non_clause). [assumption].
% 0.43/1.01 8 and_2 <-> (all X all Y is_a_theorem(implies(and(X,Y),Y))) # label(and_2) # label(axiom) # label(non_clause). [assumption].
% 0.43/1.01 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].
% 0.43/1.01 10 or_1 <-> (all X all Y is_a_theorem(implies(X,or(X,Y)))) # label(or_1) # label(axiom) # label(non_clause). [assumption].
% 0.43/1.01 11 or_2 <-> (all X all Y is_a_theorem(implies(Y,or(X,Y)))) # label(or_2) # label(axiom) # label(non_clause). [assumption].
% 0.43/1.01 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].
% 0.43/1.01 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].
% 0.43/1.01 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].
% 1.28/1.58 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].
% 1.28/1.58 16 kn1 <-> (all P is_a_theorem(implies(P,and(P,P)))) # label(kn1) # label(axiom) # label(non_clause). [assumption].
% 1.28/1.58 17 kn2 <-> (all P all Q is_a_theorem(implies(and(P,Q),P))) # label(kn2) # label(axiom) # label(non_clause). [assumption].
% 1.28/1.58 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].
% 1.28/1.58 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].
% 1.28/1.58 20 cn2 <-> (all P all Q is_a_theorem(implies(P,implies(not(P),Q)))) # label(cn2) # label(axiom) # label(non_clause). [assumption].
% 1.28/1.58 21 cn3 <-> (all P is_a_theorem(implies(implies(not(P),P),P))) # label(cn3) # label(axiom) # label(non_clause). [assumption].
% 1.28/1.58 22 r1 <-> (all P is_a_theorem(implies(or(P,P),P))) # label(r1) # label(axiom) # label(non_clause). [assumption].
% 1.28/1.58 23 r2 <-> (all P all Q is_a_theorem(implies(Q,or(P,Q)))) # label(r2) # label(axiom) # label(non_clause). [assumption].
% 1.28/1.58 24 r3 <-> (all P all Q is_a_theorem(implies(or(P,Q),or(Q,P)))) # label(r3) # label(axiom) # label(non_clause). [assumption].
% 1.28/1.58 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].
% 1.28/1.58 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].
% 1.28/1.58 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].
% 1.28/1.58 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].
% 1.28/1.58 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].
% 1.28/1.58 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].
% 1.28/1.58 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].
% 1.28/1.58
% 1.28/1.58 ============================== end of process non-clausal formulas ===
% 1.28/1.58
% 1.28/1.58 ============================== PROCESS INITIAL CLAUSES ===============
% 1.28/1.58
% 1.28/1.58 ============================== PREDICATE ELIMINATION =================
% 1.28/1.58
% 1.28/1.58 ============================== end predicate elimination =============
% 1.28/1.58
% 1.28/1.58 Auto_denials: (non-Horn, no changes).
% 1.28/1.58
% 1.28/1.58 Term ordering decisions:
% 1.28/1.58
% 1.28/1.58 % Assigning unary symbol not kb_weight 0 and highest precedence (94).
% 1.28/1.58 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.
% 1.28/1.58
% 1.28/1.58 ============================== end of process initial clauses ========
% 1.28/1.58
% 1.28/1.58 ============================== CLAUSES FOR SEARCH ====================
% 1.28/1.58
% 1.28/1.58 ============================== end of clauses for search =============
% 1.28/1.58
% 1.28/1.58 ============================== SEARCH ================================
% 1.28/1.58
% 1.28/1.58 % Starting search at 0.02 seconds.
% 1.28/1.58
% 1.28/1.58 Low Water (keep): wt=36.000, iters=3366
% 1.28/1.58
% 1.28/1.58 Low Water (keep): wt=34.000, iters=3373
% 1.28/1.58
% 1.28/1.58 Low Water (keep): wt=32.000, iters=3403
% 1.28/1.58
% 1.28/1.58 Low Water (keep): wt=31.000, iters=3430
% 1.28/1.58
% 1.28/1.58 Low Water (keep): wt=30.000, iters=3353
% 1.28/1.58
% 1.28/1.58 Low Water (keep): wt=25.000, iters=3366
% 1.28/1.58
% 1.28/1.58 Low Water (keep): wt=24.000, iters=3610
% 1.28/1.58
% 1.28/1.58 Low Water (keep): wt=23.000, iters=3530
% 1.28/1.58
% 1.28/1.58 Low Water (keep): wt=22.000, iters=3385
% 1.28/1.58
% 1.28/1.58 Low Water (keep): wt=21.000, iters=3363
% 1.28/1.58
% 114.84/115.17 Low Water (keep): wt=20.000, iters=3367
% 114.84/115.17
% 114.84/115.17 Low Water (keep): wt=19.000, iters=3352
% 114.84/115.17
% 114.84/115.17 Low Water (keep): wt=18.000, iters=3379
% 114.84/115.17
% 114.84/115.17 Low Water (keep): wt=17.000, iters=3334
% 114.84/115.17
% 114.84/115.17 NOTE: Back_subsumption disabled, ratio of kept to back_subsumed is 97 (0.00 of 1.28 sec).
% 114.84/115.17
% 114.84/115.17 Low Water (displace): id=1643, wt=111.000
% 114.84/115.17
% 114.84/115.17 Low Water (displace): id=2008, wt=103.000
% 114.84/115.17
% 114.84/115.17 Low Water (displace): id=3555, wt=95.000
% 114.84/115.17
% 114.84/115.17 Low Water (displace): id=3117, wt=83.000
% 114.84/115.17
% 114.84/115.17 Low Water (displace): id=1499, wt=75.000
% 114.84/115.17
% 114.84/115.17 Low Water (displace): id=1501, wt=55.000
% 114.84/115.17
% 114.84/115.17 Low Water (displace): id=10292, wt=45.000
% 114.84/115.17
% 114.84/115.17 Low Water (displace): id=10693, wt=16.000
% 114.84/115.17
% 114.84/115.17 Low Water (displace): id=11992, wt=14.000
% 114.84/115.17
% 114.84/115.17 Low Water (displace): id=12322, wt=13.000
% 114.84/115.17
% 114.84/115.17 Low Water (keep): wt=16.000, iters=3342
% 114.84/115.17
% 114.84/115.17 Low Water (displace): id=13214, wt=12.000
% 114.84/115.17
% 114.84/115.17 Low Water (keep): wt=15.000, iters=3335
% 114.84/115.17
% 114.84/115.17 Low Water (keep): wt=14.000, iters=3767
% 114.84/115.17
% 114.84/115.17 Low Water (keep): wt=13.000, iters=3370
% 114.84/115.17
% 114.84/115.17 Low Water (displace): id=149936, wt=11.000
% 114.84/115.17
% 114.84/115.17 Low Water (keep): wt=12.000, iters=3665
% 114.84/115.17
% 114.84/115.17 ============================== PROOF =================================
% 114.84/115.17 % SZS status Theorem
% 114.84/115.17 % SZS output start Refutation
% 114.84/115.17
% 114.84/115.17 % Proof 1 at 107.33 (+ 6.83) seconds.
% 114.84/115.17 % Length of proof is 239.
% 114.84/115.17 % Level of proof is 80.
% 114.84/115.17 % Maximum clause weight is 19.000.
% 114.84/115.17 % Given clauses 8335.
% 114.84/115.17
% 114.84/115.17 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].
% 114.84/115.17 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].
% 114.84/115.17 4 implies_1 <-> (all X all Y is_a_theorem(implies(X,implies(Y,X)))) # label(implies_1) # label(axiom) # label(non_clause). [assumption].
% 114.84/115.17 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].
% 114.84/115.17 20 cn2 <-> (all P all Q is_a_theorem(implies(P,implies(not(P),Q)))) # label(cn2) # label(axiom) # label(non_clause). [assumption].
% 114.84/115.17 21 cn3 <-> (all P is_a_theorem(implies(implies(not(P),P),P))) # label(cn3) # label(axiom) # label(non_clause). [assumption].
% 114.84/115.17 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].
% 114.84/115.17 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].
% 114.84/115.17 34 op_equiv # label(luka_op_equiv) # label(axiom). [assumption].
% 114.84/115.17 35 modus_ponens # label(luka_modus_ponens) # label(axiom). [assumption].
% 114.84/115.17 36 cn1 # label(luka_cn1) # label(axiom). [assumption].
% 114.84/115.17 37 cn2 # label(luka_cn2) # label(axiom). [assumption].
% 114.84/115.17 38 cn3 # label(luka_cn3) # label(axiom). [assumption].
% 114.84/115.17 39 substitution_of_equivalents # label(substitution_of_equivalents) # label(axiom). [assumption].
% 114.84/115.17 40 op_implies_and # label(hilbert_op_implies_and) # label(axiom). [assumption].
% 114.84/115.17 41 -implies_1 # label(hilbert_implies_1) # label(negated_conjecture). [assumption].
% 114.84/115.17 42 implies_1 | -is_a_theorem(implies(c7,implies(c8,c7))) # label(implies_1) # label(axiom). [clausify(4)].
% 114.84/115.18 43 -is_a_theorem(implies(c7,implies(c8,c7))). [copy(42),unit_del(a,41)].
% 114.84/115.18 60 -substitution_of_equivalents | -is_a_theorem(equiv(A,B)) | B = A # label(substitution_of_equivalents) # label(axiom). [clausify(2)].
% 114.84/115.18 61 -is_a_theorem(equiv(A,B)) | B = A. [copy(60),unit_del(a,39)].
% 114.84/115.18 62 -cn2 | is_a_theorem(implies(A,implies(not(A),B))) # label(cn2) # label(axiom). [clausify(20)].
% 114.84/115.18 63 is_a_theorem(implies(A,implies(not(A),B))). [copy(62),unit_del(a,37)].
% 114.84/115.18 65 -cn3 | is_a_theorem(implies(implies(not(A),A),A)) # label(cn3) # label(axiom). [clausify(21)].
% 114.84/115.18 66 is_a_theorem(implies(implies(not(A),A),A)). [copy(65),unit_del(a,38)].
% 114.84/115.18 68 -modus_ponens | -is_a_theorem(A) | -is_a_theorem(implies(A,B)) | is_a_theorem(B) # label(modus_ponens) # label(axiom). [clausify(1)].
% 114.84/115.18 69 -is_a_theorem(A) | -is_a_theorem(implies(A,B)) | is_a_theorem(B). [copy(68),unit_del(a,35)].
% 114.84/115.18 79 -op_implies_and | not(and(A,not(B))) = implies(A,B) # label(op_implies_and) # label(axiom). [clausify(29)].
% 114.84/115.18 80 not(and(A,not(B))) = implies(A,B). [copy(79),unit_del(a,40)].
% 114.84/115.18 89 -op_equiv | and(implies(A,B),implies(B,A)) = equiv(A,B) # label(op_equiv) # label(axiom). [clausify(31)].
% 114.84/115.18 90 and(implies(A,B),implies(B,A)) = equiv(A,B). [copy(89),unit_del(a,34)].
% 114.84/115.18 95 -cn1 | is_a_theorem(implies(implies(A,B),implies(implies(B,C),implies(A,C)))) # label(cn1) # label(axiom). [clausify(19)].
% 114.84/115.18 96 is_a_theorem(implies(implies(A,B),implies(implies(B,C),implies(A,C)))). [copy(95),unit_del(a,36)].
% 114.84/115.18 122 -is_a_theorem(implies(not(A),A)) | is_a_theorem(A). [resolve(69,b,66,a)].
% 114.84/115.18 123 -is_a_theorem(A) | is_a_theorem(implies(not(A),B)). [resolve(69,b,63,a)].
% 114.84/115.18 127 is_a_theorem(implies(and(A,not(B)),implies(implies(A,B),C))). [para(80(a,1),63(a,1,2,1))].
% 114.84/115.18 128 is_a_theorem(implies(implies(implies(A,B),and(A,not(B))),and(A,not(B)))). [para(80(a,1),66(a,1,1,1))].
% 114.84/115.18 129 not(and(A,implies(B,C))) = implies(A,and(B,not(C))). [para(80(a,1),80(a,1,1,2))].
% 114.84/115.18 130 -is_a_theorem(implies(A,B)) | is_a_theorem(implies(implies(B,C),implies(A,C))). [resolve(96,a,69,b)].
% 114.84/115.18 226 is_a_theorem(implies(implies(implies(implies(A,B),C),D),implies(and(A,not(B)),D))). [resolve(130,a,127,a)].
% 114.84/115.18 228 is_a_theorem(implies(implies(A,B),implies(implies(not(A),A),B))). [resolve(130,a,66,a)].
% 114.84/115.18 229 is_a_theorem(implies(implies(implies(not(A),B),C),implies(A,C))). [resolve(130,a,63,a)].
% 114.84/115.18 230 is_a_theorem(implies(implies(implies(implies(not(A),A),B),C),implies(implies(A,B),C))). [resolve(228,a,130,a)].
% 114.84/115.18 232 -is_a_theorem(implies(A,B)) | is_a_theorem(implies(implies(not(A),A),B)). [resolve(228,a,69,b)].
% 114.84/115.18 242 is_a_theorem(implies(implies(implies(A,B),C),implies(implies(implies(not(A),D),B),C))). [resolve(229,a,130,a)].
% 114.84/115.18 244 -is_a_theorem(implies(implies(not(A),B),C)) | is_a_theorem(implies(A,C)). [resolve(229,a,69,b)].
% 114.84/115.18 256 -is_a_theorem(implies(implies(implies(implies(not(A),B),C),implies(A,C)),implies(c7,implies(c8,c7)))). [ur(69,a,229,a,c,43,a)].
% 114.84/115.18 257 implies(implies(A,B),and(B,not(A))) = not(equiv(A,B)). [para(90(a,1),129(a,1,1)),flip(a)].
% 114.84/115.18 258 -is_a_theorem(implies(implies(A,and(B,not(C))),and(A,implies(B,C)))) | is_a_theorem(and(A,implies(B,C))). [para(129(a,1),122(a,1,1))].
% 114.84/115.18 338 is_a_theorem(implies(A,implies(implies(B,C),implies(not(A),C)))). [resolve(244,a,96,a)].
% 114.84/115.18 339 is_a_theorem(implies(A,A)). [resolve(244,a,66,a)].
% 114.84/115.18 341 -is_a_theorem(implies(implies(implies(A,B),C),D)) | is_a_theorem(implies(and(A,not(B)),D)). [para(80(a,1),244(a,1,1,1))].
% 114.84/115.18 403 is_a_theorem(implies(not(implies(A,A)),B)). [resolve(339,a,123,a)].
% 114.84/115.18 422 is_a_theorem(implies(implies(A,B),implies(not(implies(C,C)),B))). [resolve(403,a,130,a)].
% 114.84/115.18 594 is_a_theorem(implies(implies(not(A),A),implies(implies(B,C),implies(not(A),C)))). [resolve(338,a,232,a)].
% 114.84/115.18 622 is_a_theorem(implies(A,implies(not(implies(B,B)),C))). [resolve(422,a,244,a)].
% 114.84/115.18 734 is_a_theorem(implies(implies(implies(not(implies(A,A)),B),C),implies(D,C))). [resolve(622,a,130,a)].
% 114.84/115.18 999 is_a_theorem(implies(not(equiv(A,A)),and(A,not(A)))). [para(257(a,1),128(a,1,1))].
% 114.84/115.18 1174 is_a_theorem(implies(implies(and(A,not(A)),B),implies(not(equiv(A,A)),B))). [resolve(999,a,130,a)].
% 114.84/115.18 2241 -is_a_theorem(implies(implies(not(implies(A,A)),B),C)) | is_a_theorem(implies(D,C)). [resolve(734,a,69,b)].
% 114.84/115.18 2980 is_a_theorem(implies(A,implies(B,B))). [resolve(2241,a,66,a)].
% 114.84/115.18 2987 is_a_theorem(implies(implies(implies(A,A),B),implies(C,B))). [resolve(2980,a,130,a)].
% 114.84/115.18 3329 is_a_theorem(implies(implies(implies(A,B),C),implies(implies(implies(D,D),B),C))). [resolve(2987,a,130,a)].
% 114.84/115.18 3331 -is_a_theorem(implies(implies(A,A),B)) | is_a_theorem(implies(C,B)). [resolve(2987,a,69,b)].
% 114.84/115.18 3405 is_a_theorem(implies(A,implies(B,implies(not(B),C)))). [resolve(3331,a,229,a)].
% 114.84/115.18 3406 is_a_theorem(implies(A,implies(implies(not(B),B),B))). [resolve(3331,a,228,a)].
% 114.84/115.18 3485 is_a_theorem(implies(implies(implies(A,implies(not(A),B)),C),implies(D,C))). [resolve(3405,a,130,a)].
% 114.84/115.18 3784 is_a_theorem(implies(implies(implies(implies(not(A),A),A),B),implies(C,B))). [resolve(3406,a,130,a)].
% 114.84/115.18 5543 -is_a_theorem(implies(implies(implies(not(A),A),A),B)) | is_a_theorem(implies(C,B)). [resolve(3784,a,69,b)].
% 114.84/115.18 6591 -is_a_theorem(implies(not(A),A)) | is_a_theorem(implies(implies(B,C),implies(not(A),C))). [resolve(594,a,69,b)].
% 114.84/115.18 7095 -is_a_theorem(implies(and(A,not(A)),B)) | is_a_theorem(implies(not(equiv(A,A)),B)). [resolve(1174,a,69,b)].
% 114.84/115.18 7464 is_a_theorem(implies(A,implies(implies(implies(B,B),C),C))). [resolve(3329,a,5543,a)].
% 114.84/115.18 7474 -is_a_theorem(implies(implies(A,B),C)) | is_a_theorem(implies(implies(implies(D,D),B),C)). [resolve(3329,a,69,b)].
% 114.84/115.18 7685 is_a_theorem(implies(implies(implies(implies(implies(A,A),B),B),C),implies(D,C))). [resolve(7464,a,130,a)].
% 114.84/115.18 7687 is_a_theorem(implies(implies(implies(A,A),B),B)). [resolve(7464,a,122,a)].
% 114.84/115.18 7738 is_a_theorem(implies(implies(A,B),implies(implies(implies(C,C),A),B))). [resolve(7687,a,130,a)].
% 114.84/115.18 7739 -is_a_theorem(implies(implies(A,A),B)) | is_a_theorem(B). [resolve(7687,a,69,b)].
% 114.84/115.18 8003 -is_a_theorem(implies(A,B)) | is_a_theorem(implies(implies(implies(C,C),A),B)). [resolve(7738,a,69,b)].
% 114.84/115.18 8582 is_a_theorem(implies(implies(implies(A,A),implies(implies(B,B),C)),implies(D,C))). [resolve(8003,a,2987,a)].
% 114.84/115.18 10337 is_a_theorem(implies(implies(implies(A,A),B),implies(implies(B,C),implies(D,C)))). [resolve(7474,a,96,a)].
% 114.84/115.18 10396 -is_a_theorem(implies(implies(implies(implies(A,A),B),B),C)) | is_a_theorem(implies(D,C)). [resolve(7685,a,69,b)].
% 114.84/115.18 10946 -is_a_theorem(implies(implies(A,A),implies(implies(B,B),C))) | is_a_theorem(implies(D,C)). [resolve(8582,a,69,b)].
% 114.84/115.18 11207 -is_a_theorem(implies(implies(A,A),B)) | is_a_theorem(implies(implies(B,C),implies(D,C))). [resolve(10337,a,69,b)].
% 114.84/115.18 11846 is_a_theorem(implies(A,implies(and(B,not(B)),C))). [resolve(226,a,10396,a)].
% 114.84/115.18 11878 is_a_theorem(implies(and(A,not(A)),B)). [resolve(11846,a,7739,a)].
% 114.84/115.18 11935 is_a_theorem(implies(not(equiv(A,A)),B)). [back_unit_del(7095),unit_del(a,11878)].
% 114.84/115.18 12067 is_a_theorem(implies(implies(A,B),implies(not(equiv(C,C)),B))). [resolve(11935,a,6591,a)].
% 114.84/115.18 13091 is_a_theorem(implies(implies(implies(not(equiv(A,A)),B),C),implies(D,C))). [resolve(12067,a,11207,a)].
% 114.84/115.18 13527 is_a_theorem(implies(A,implies(B,equiv(C,C)))). [resolve(13091,a,5543,a)].
% 114.84/115.18 13562 is_a_theorem(implies(implies(implies(A,equiv(B,B)),C),implies(D,C))). [resolve(13527,a,11207,a)].
% 114.84/115.18 13565 is_a_theorem(implies(A,equiv(B,B))). [resolve(13527,a,10946,a)].
% 114.84/115.18 13633 is_a_theorem(implies(implies(equiv(A,A),B),implies(C,B))). [resolve(13565,a,11207,a)].
% 114.84/115.18 13914 is_a_theorem(implies(implies(implies(A,B),C),implies(implies(equiv(D,D),B),C))). [resolve(13633,a,130,a)].
% 114.84/115.18 14478 -is_a_theorem(implies(implies(implies(not(A),A),B),C)) | is_a_theorem(implies(implies(A,B),C)). [resolve(230,a,69,b)].
% 114.84/115.18 15148 is_a_theorem(implies(A,implies(implies(equiv(B,B),C),C))). [resolve(13914,a,10396,a)].
% 114.84/115.18 15164 -is_a_theorem(implies(implies(A,B),C)) | is_a_theorem(implies(implies(equiv(D,D),B),C)). [resolve(13914,a,69,b)].
% 114.84/115.18 15172 is_a_theorem(implies(implies(implies(implies(equiv(A,A),B),B),C),implies(D,C))). [resolve(15148,a,11207,a)].
% 114.84/115.18 15184 is_a_theorem(implies(implies(equiv(A,A),B),B)). [resolve(15148,a,7739,a)].
% 114.84/115.18 15262 is_a_theorem(implies(implies(A,B),implies(implies(equiv(C,C),A),B))). [resolve(15184,a,130,a)].
% 114.84/115.18 15263 -is_a_theorem(implies(equiv(A,A),B)) | is_a_theorem(B). [resolve(15184,a,69,b)].
% 114.84/115.18 15514 -is_a_theorem(implies(A,B)) | is_a_theorem(implies(implies(equiv(C,C),A),B)). [resolve(15262,a,69,b)].
% 114.84/115.18 15624 is_a_theorem(implies(A,implies(implies(implies(not(implies(B,B)),C),D),D))). [resolve(242,a,10396,a)].
% 114.84/115.18 15631 is_a_theorem(implies(A,implies(implies(implies(not(not(B)),C),B),B))). [resolve(242,a,5543,a)].
% 114.84/115.18 15641 -is_a_theorem(implies(implies(A,B),C)) | is_a_theorem(implies(implies(implies(not(A),D),B),C)). [resolve(242,a,69,b)].
% 114.84/115.18 16721 is_a_theorem(implies(implies(implies(not(not(A)),B),A),A)). [resolve(15631,a,15263,a)].
% 114.84/115.18 16767 is_a_theorem(implies(implies(A,B),implies(implies(implies(not(not(A)),C),A),B))). [resolve(16721,a,130,a)].
% 114.84/115.18 16768 -is_a_theorem(implies(implies(not(not(A)),B),A)) | is_a_theorem(A). [resolve(16721,a,69,b)].
% 114.84/115.18 17262 is_a_theorem(implies(implies(implies(not(implies(A,A)),B),C),C)). [resolve(15624,a,16768,a)].
% 114.84/115.18 17312 -is_a_theorem(implies(implies(not(implies(A,A)),B),C)) | is_a_theorem(C). [resolve(17262,a,69,b)].
% 114.84/115.18 17381 -is_a_theorem(implies(c7,implies(implies(not(c8),A),c7))). [ur(130,b,256,a)].
% 114.84/115.18 17387 -is_a_theorem(implies(implies(not(c7),A),implies(implies(not(c8),B),c7))). [ur(244,b,17381,a)].
% 114.84/115.18 18316 is_a_theorem(implies(implies(equiv(A,A),B),implies(implies(B,C),implies(D,C)))). [resolve(15164,a,10337,a)].
% 114.84/115.18 18389 -is_a_theorem(implies(implies(implies(equiv(A,A),B),B),C)) | is_a_theorem(implies(D,C)). [resolve(15172,a,69,b)].
% 114.84/115.18 20148 -is_a_theorem(implies(A,B)) | is_a_theorem(implies(implies(implies(not(not(A)),C),A),B)). [resolve(16767,a,69,b)].
% 114.84/115.18 20303 -is_a_theorem(implies(equiv(A,A),B)) | is_a_theorem(implies(implies(B,C),implies(D,C))). [resolve(18316,a,69,b)].
% 114.84/115.18 20360 is_a_theorem(implies(A,implies(implies(implies(not(equiv(B,B)),C),D),D))). [resolve(18389,a,242,a)].
% 114.84/115.18 20405 is_a_theorem(implies(implies(implies(not(equiv(A,A)),B),C),C)). [resolve(20360,a,17312,a)].
% 114.84/115.18 20449 is_a_theorem(implies(implies(A,B),implies(implies(implies(not(equiv(C,C)),D),A),B))). [resolve(20405,a,130,a)].
% 114.84/115.18 20450 -is_a_theorem(implies(implies(not(equiv(A,A)),B),C)) | is_a_theorem(C). [resolve(20405,a,69,b)].
% 114.84/115.18 22481 is_a_theorem(implies(implies(implies(not(implies(A,A)),B),and(A,not(A))),C)). [resolve(20148,a,11878,a),rewrite([80(3)])].
% 114.84/115.18 23513 is_a_theorem(implies(and(not(implies(A,A)),not(B)),C)). [resolve(341,a,22481,a)].
% 114.84/115.18 23516 is_a_theorem(implies(and(not(equiv(A,A)),not(B)),C)). [resolve(341,a,20405,a)].
% 114.84/115.18 23519 is_a_theorem(implies(and(not(not(A)),not(B)),A)). [resolve(341,a,16721,a)].
% 114.84/115.18 23526 is_a_theorem(implies(and(A,not(equiv(B,B))),implies(C,D))). [resolve(341,a,13562,a)].
% 114.84/115.18 23535 is_a_theorem(implies(and(implies(not(A),A),not(A)),implies(B,C))). [resolve(341,a,3784,a)].
% 114.84/115.18 23536 is_a_theorem(implies(and(A,not(implies(not(A),B))),implies(C,D))). [resolve(341,a,3485,a)].
% 114.84/115.18 23545 is_a_theorem(implies(and(A,not(B)),implies(implies(implies(not(A),C),B),D))). [resolve(341,a,242,a)].
% 114.84/115.18 23559 is_a_theorem(implies(implies(equiv(A,A),and(not(not(B)),not(C))),B)). [resolve(23519,a,15514,a)].
% 114.84/115.18 23573 is_a_theorem(implies(implies(implies(not(not(A)),B),and(not(not(A)),not(B))),A)). [resolve(23519,a,232,a),rewrite([80(5)])].
% 114.84/115.18 23574 is_a_theorem(implies(implies(A,B),implies(and(not(not(A)),not(C)),B))). [resolve(23519,a,130,a)].
% 114.84/115.18 23897 is_a_theorem(implies(implies(equiv(A,A),and(not(implies(B,B)),not(C))),D)). [resolve(23513,a,15514,a)].
% 114.84/115.18 23945 is_a_theorem(implies(implies(implies(A,A),and(not(equiv(B,B)),not(C))),D)). [resolve(23516,a,8003,a)].
% 114.84/115.18 24218 is_a_theorem(implies(implies(implies(A,B),C),implies(and(D,not(equiv(E,E))),C))). [resolve(23526,a,130,a)].
% 114.84/115.18 24459 is_a_theorem(implies(and(implies(not(A),A),not(A)),not(equiv(B,C)))). [para(257(a,1),23535(a,1,2))].
% 114.84/115.18 24505 is_a_theorem(implies(and(A,not(implies(not(A),B))),not(equiv(C,D)))). [para(257(a,1),23536(a,1,2))].
% 114.84/115.18 25019 is_a_theorem(implies(and(not(not(not(equiv(A,A)))),not(B)),C)). [resolve(23574,a,20450,a)].
% 114.84/115.18 25107 is_a_theorem(implies(implies(implies(A,A),and(not(not(not(equiv(B,B)))),not(C))),D)). [resolve(25019,a,8003,a)].
% 114.84/115.18 27358 is_a_theorem(implies(and(A,implies(B,not(A))),implies(not(equiv(not(A),B)),C))). [para(257(a,1),23545(a,1,2,1)),rewrite([80(4)])].
% 114.84/115.18 27652 is_a_theorem(and(equiv(A,A),implies(not(implies(B,B)),C))). [resolve(23897,a,258,a)].
% 114.84/115.18 27972 is_a_theorem(and(implies(A,A),implies(not(equiv(B,B)),C))). [resolve(23945,a,258,a)].
% 114.84/115.18 44334 is_a_theorem(implies(implies(implies(not(equiv(A,A)),B),and(not(not(C)),not(D))),C)). [resolve(15641,a,23559,a)].
% 114.84/115.18 52593 -is_a_theorem(implies(A,B)) | is_a_theorem(implies(implies(implies(not(equiv(C,C)),D),A),B)). [resolve(20449,a,69,b)].
% 114.84/115.18 54938 is_a_theorem(implies(implies(not(A),and(not(not(A)),not(not(A)))),A)). [resolve(23573,a,14478,a)].
% 114.84/115.18 55003 -is_a_theorem(implies(not(A),and(not(not(A)),not(not(A))))) | is_a_theorem(A). [resolve(54938,a,69,b)].
% 114.84/115.18 55232 is_a_theorem(implies(A,implies(and(B,not(equiv(C,C))),D))). [resolve(24218,a,18389,a)].
% 114.84/115.18 55275 is_a_theorem(implies(implies(implies(and(A,not(equiv(B,B))),C),D),implies(E,D))). [resolve(55232,a,20303,a)].
% 114.84/115.18 60385 -is_a_theorem(and(A,implies(B,not(A)))) | is_a_theorem(implies(not(equiv(not(A),B)),C)). [resolve(27358,a,69,b)].
% 114.84/115.18 111532 is_a_theorem(implies(implies(implies(not(equiv(A,A)),B),and(not(implies(C,C)),not(D))),E)). [resolve(52593,a,23513,a)].
% 114.84/115.18 112436 is_a_theorem(implies(and(and(A,not(equiv(B,B))),not(C)),implies(D,E))). [resolve(55275,a,341,a)].
% 114.84/115.18 112583 is_a_theorem(implies(and(and(A,not(equiv(B,B))),not(C)),not(equiv(D,E)))). [para(257(a,1),112436(a,1,2))].
% 114.84/115.18 116051 is_a_theorem(implies(not(equiv(not(implies(A,A)),not(equiv(B,B)))),C)). [resolve(60385,a,27972,a)].
% 114.84/115.18 116054 is_a_theorem(implies(not(equiv(not(equiv(A,A)),not(implies(B,B)))),C)). [resolve(60385,a,27652,a)].
% 114.84/115.18 116089 is_a_theorem(equiv(not(implies(A,A)),not(equiv(B,B)))). [resolve(116051,a,55003,a)].
% 114.84/115.18 116183 not(equiv(A,A)) = not(implies(B,B)). [resolve(116089,a,61,a)].
% 114.84/115.18 116191 not(equiv(A,A)) = c_0. [new_symbol(116183)].
% 114.84/115.18 116198 not(implies(A,A)) = c_0. [back_rewrite(116183),rewrite([116191(2)]),flip(a)].
% 114.84/115.18 116212 is_a_theorem(implies(c_0,A)). [back_rewrite(116054),rewrite([116191(2),116198(3),116191(4)])].
% 114.84/115.18 116271 is_a_theorem(implies(and(and(A,c_0),not(B)),not(equiv(C,D)))). [back_rewrite(112583),rewrite([116191(2)])].
% 114.84/115.18 116330 is_a_theorem(implies(implies(implies(c_0,A),and(c_0,not(B))),C)). [back_rewrite(111532),rewrite([116191(2),116198(4)])].
% 114.84/115.18 116603 is_a_theorem(implies(implies(implies(c_0,A),and(not(not(B)),not(C))),B)). [back_rewrite(44334),rewrite([116191(2)])].
% 114.84/115.18 116739 is_a_theorem(implies(implies(implies(A,A),and(not(not(c_0)),not(B))),C)). [back_rewrite(25107),rewrite([116191(3)])].
% 114.84/115.18 116805 -is_a_theorem(implies(implies(c_0,A),B)) | is_a_theorem(B). [back_rewrite(20450),rewrite([116191(2)])].
% 114.84/115.18 118563 implies(A,equiv(B,B)) = not(and(A,c_0)). [para(116191(a,1),80(a,1,1,2)),flip(a)].
% 114.84/115.18 118668 is_a_theorem(implies(and(implies(not(A),A),not(A)),c_0)). [para(116191(a,1),24459(a,1,2))].
% 114.84/115.18 118669 is_a_theorem(implies(and(A,not(implies(not(A),B))),c_0)). [para(116191(a,1),24505(a,1,2))].
% 114.84/115.18 119470 implies(A,implies(B,B)) = not(and(A,c_0)). [para(116198(a,1),80(a,1,1,2)),flip(a)].
% 114.84/115.18 127908 -is_a_theorem(implies(not(and(equiv(A,A),c_0)),B)) | is_a_theorem(B). [para(118563(a,1),7739(a,1,1))].
% 114.84/115.18 129025 is_a_theorem(implies(implies(c_0,A),implies(and(implies(not(B),B),not(B)),A))). [resolve(118668,a,130,a)].
% 114.84/115.18 129119 is_a_theorem(implies(implies(c_0,A),implies(and(B,not(implies(not(B),C))),A))). [resolve(118669,a,130,a)].
% 114.84/115.18 131041 is_a_theorem(and(implies(c_0,A),implies(c_0,B))). [resolve(116330,a,258,a)].
% 114.84/115.18 131076 is_a_theorem(implies(not(equiv(not(implies(c_0,A)),c_0)),B)). [resolve(131041,a,60385,a)].
% 114.84/115.18 131274 is_a_theorem(equiv(not(implies(c_0,A)),c_0)). [resolve(131076,a,55003,a)].
% 114.84/115.18 131368 not(implies(c_0,A)) = c_0. [resolve(131274,a,61,a),flip(a)].
% 114.84/115.18 131409 implies(A,implies(c_0,B)) = not(and(A,c_0)). [para(131368(a,1),80(a,1,1,2)),flip(a)].
% 114.84/115.18 142775 is_a_theorem(implies(and(and(A,c_0),not(B)),c_0)). [para(116191(a,1),116271(a,1,2))].
% 114.84/115.18 142846 is_a_theorem(implies(implies(c_0,A),implies(and(and(B,c_0),not(C)),A))). [resolve(142775,a,130,a)].
% 114.84/115.18 167897 is_a_theorem(implies(not(equiv(c_0,not(not(A)))),A)). [para(257(a,1),116603(a,1,1))].
% 114.84/115.18 168306 is_a_theorem(implies(implies(A,B),implies(not(equiv(c_0,not(not(A)))),B))). [resolve(167897,a,130,a)].
% 114.84/115.18 170581 is_a_theorem(and(implies(A,A),implies(not(not(c_0)),B))). [resolve(116739,a,258,a)].
% 114.84/115.18 170658 is_a_theorem(implies(not(equiv(c_0,not(not(c_0)))),A)). [resolve(170581,a,60385,a),rewrite([116198(2)])].
% 114.84/115.18 170731 is_a_theorem(equiv(c_0,not(not(c_0)))). [resolve(170658,a,55003,a)].
% 114.84/115.18 170838 not(not(c_0)) = c_0. [resolve(170731,a,61,a)].
% 114.84/115.18 170842 not(and(A,c_0)) = implies(A,not(c_0)). [para(170838(a,1),80(a,1,1,2))].
% 114.84/115.18 170843 is_a_theorem(not(c_0)). [para(170838(a,1),122(a,1,1)),unit_del(a,116212)].
% 114.84/115.18 170851 implies(implies(not(c_0),A),and(A,c_0)) = not(equiv(not(c_0),A)). [para(170838(a,1),257(a,1,2,2))].
% 114.84/115.18 170853 is_a_theorem(implies(A,not(c_0))). [para(170838(a,1),3405(a,1,2,2,1)),rewrite([131409(5),170842(5),119470(6),170842(3)])].
% 114.84/115.18 171495 implies(A,implies(c_0,B)) = implies(A,not(c_0)). [back_rewrite(131409),rewrite([170842(6)])].
% 114.84/115.18 171653 -is_a_theorem(implies(implies(equiv(A,A),not(c_0)),B)) | is_a_theorem(B). [back_rewrite(127908),rewrite([170842(4)])].
% 114.84/115.18 171731 implies(A,implies(B,B)) = implies(A,not(c_0)). [back_rewrite(119470),rewrite([170842(5)])].
% 114.84/115.18 172041 implies(A,equiv(B,B)) = implies(A,not(c_0)). [back_rewrite(118563),rewrite([170842(5)])].
% 114.84/115.18 172534 is_a_theorem(implies(implies(not(c_0),A),implies(B,A))). [resolve(170853,a,20303,a)].
% 114.84/115.18 173681 is_a_theorem(implies(implies(implies(A,B),C),implies(implies(not(c_0),B),C))). [resolve(172534,a,130,a)].
% 114.84/115.18 192318 is_a_theorem(implies(and(and(A,c_0),not(B)),C)). [resolve(142846,a,116805,a)].
% 114.84/115.18 202535 -is_a_theorem(implies(A,B)) | is_a_theorem(implies(not(equiv(c_0,not(not(A)))),B)). [resolve(168306,a,69,b)].
% 114.84/115.18 215920 is_a_theorem(implies(A,implies(implies(not(c_0),B),B))). [resolve(173681,a,18389,a)].
% 114.84/115.18 215926 is_a_theorem(implies(implies(A,B),implies(implies(not(c_0),A),B))). [resolve(173681,a,14478,a)].
% 114.84/115.18 215950 is_a_theorem(implies(implies(not(c_0),A),A)). [resolve(215920,a,171653,a)].
% 114.84/115.18 216087 -is_a_theorem(implies(not(c_0),A)) | is_a_theorem(A). [resolve(215950,a,69,b)].
% 114.84/115.18 219912 -is_a_theorem(implies(A,B)) | is_a_theorem(implies(implies(not(c_0),A),B)). [resolve(215926,a,69,b)].
% 114.84/115.18 221382 is_a_theorem(implies(implies(not(c_0),and(and(A,c_0),not(B))),C)). [resolve(219912,a,192318,a)].
% 114.84/115.18 228841 is_a_theorem(and(not(c_0),implies(and(A,c_0),B))). [resolve(221382,a,258,a)].
% 114.84/115.18 228877 is_a_theorem(implies(not(equiv(c_0,and(A,c_0))),B)). [resolve(228841,a,60385,a),rewrite([170838(3)])].
% 114.84/115.18 228949 is_a_theorem(equiv(c_0,and(A,c_0))). [resolve(228877,a,55003,a)].
% 114.84/115.18 229047 and(A,c_0) = c_0. [resolve(228949,a,61,a)].
% 114.84/115.18 229090 implies(implies(not(c_0),A),c_0) = not(equiv(not(c_0),A)). [back_rewrite(170851),rewrite([229047(5)])].
% 114.84/115.18 229091 implies(A,not(c_0)) = not(c_0). [back_rewrite(170842),rewrite([229047(2)]),flip(a)].
% 114.84/115.18 229111 implies(A,equiv(B,B)) = not(c_0). [back_rewrite(172041),rewrite([229091(5)])].
% 114.84/115.18 229114 implies(A,implies(B,B)) = not(c_0). [back_rewrite(171731),rewrite([229091(5)])].
% 114.84/115.18 229130 implies(A,implies(c_0,B)) = not(c_0). [back_rewrite(171495),rewrite([229091(6)])].
% 114.84/115.18 229143 and(not(c_0),implies(not(c_0),A)) = equiv(A,not(c_0)). [para(229091(a,1),90(a,1,1))].
% 114.84/115.18 238976 implies(not(c_0),c_0) = c_0. [para(116191(a,1),229090(a,2)),rewrite([229091(5)])].
% 114.84/115.18 239005 not(equiv(not(c_0),equiv(A,A))) = c_0. [para(229111(a,1),229090(a,1,1)),rewrite([238976(4)]),flip(a)].
% 114.84/115.18 239006 not(equiv(not(c_0),implies(A,A))) = c_0. [para(229114(a,1),229090(a,1,1)),rewrite([238976(4)]),flip(a)].
% 114.84/115.18 239007 not(equiv(not(c_0),implies(c_0,A))) = c_0. [para(229130(a,1),229090(a,1,1)),rewrite([238976(4)]),flip(a)].
% 114.84/115.18 239076 implies(A,equiv(not(c_0),equiv(B,B))) = not(c_0). [para(239005(a,1),80(a,1,1,2)),rewrite([229047(2)]),flip(a)].
% 114.84/115.18 239077 is_a_theorem(equiv(not(c_0),equiv(A,A))). [para(239005(a,1),122(a,1,1)),rewrite([239076(6)]),unit_del(a,170843)].
% 114.84/115.18 239123 equiv(A,A) = not(c_0). [resolve(239077,a,61,a)].
% 114.84/115.18 239857 implies(A,equiv(not(c_0),implies(B,B))) = not(c_0). [para(239006(a,1),80(a,1,1,2)),rewrite([229047(2)]),flip(a)].
% 114.84/115.18 239858 is_a_theorem(equiv(not(c_0),implies(A,A))). [para(239006(a,1),122(a,1,1)),rewrite([239857(6)]),unit_del(a,170843)].
% 114.84/115.18 239900 implies(A,A) = not(c_0). [resolve(239858,a,61,a)].
% 114.84/115.18 240509 and(not(c_0),not(c_0)) = not(c_0). [para(239900(a,1),90(a,1,1)),rewrite([239900(3),239123(6)])].
% 114.84/115.18 240577 implies(A,equiv(not(c_0),implies(c_0,B))) = not(c_0). [para(239007(a,1),80(a,1,1,2)),rewrite([229047(2)]),flip(a)].
% 114.84/115.18 240578 is_a_theorem(equiv(not(c_0),implies(c_0,A))). [para(239007(a,1),122(a,1,1)),rewrite([240577(7)]),unit_del(a,170843)].
% 114.84/115.18 240615 implies(c_0,A) = not(c_0). [resolve(240578,a,61,a)].
% 114.84/115.18 240801 is_a_theorem(implies(not(c_0),implies(and(A,not(implies(not(A),B))),C))). [back_rewrite(129119),rewrite([240615(2)])].
% 114.84/115.18 240802 is_a_theorem(implies(not(c_0),implies(and(implies(not(A),A),not(A)),B))). [back_rewrite(129025),rewrite([240615(2)])].
% 114.84/115.18 249144 is_a_theorem(implies(and(A,not(implies(not(A),B))),C)). [resolve(240801,a,216087,a)].
% 114.84/115.18 249152 is_a_theorem(implies(not(equiv(c_0,not(implies(A,implies(not(A),B))))),C)). [resolve(249144,a,202535,a),rewrite([80(6)])].
% 114.84/115.18 249197 is_a_theorem(implies(and(implies(not(A),A),not(A)),B)). [resolve(240802,a,216087,a)].
% 114.84/115.18 249203 is_a_theorem(implies(implies(not(c_0),and(implies(not(A),A),not(A))),B)). [resolve(249197,a,219912,a)].
% 114.84/115.18 250221 is_a_theorem(equiv(c_0,not(implies(A,implies(not(A),B))))). [resolve(249152,a,55003,a)].
% 114.84/115.18 250227 not(implies(A,implies(not(A),B))) = c_0. [resolve(250221,a,61,a)].
% 114.84/115.18 250232 implies(A,implies(B,implies(not(B),C))) = not(c_0). [para(250227(a,1),80(a,1,1,2)),rewrite([229047(2)]),flip(a)].
% 114.84/115.18 250245 equiv(implies(A,implies(not(A),B)),not(c_0)) = not(c_0). [para(250232(a,1),229143(a,1,2)),rewrite([240509(5)]),flip(a)].
% 114.84/115.18 250249 implies(A,implies(not(A),B)) = not(c_0). [para(250245(a,1),61(a,1)),flip(b),unit_del(a,170843)].
% 114.84/115.18 250252 and(not(c_0),implies(implies(not(A),B),A)) = equiv(A,implies(not(A),B)). [para(250249(a,1),90(a,1,1))].
% 114.84/115.18 250311 is_a_theorem(equiv(A,implies(not(A),A))). [resolve(249203,a,258,a),rewrite([250252(6)])].
% 114.84/115.18 250344 implies(not(A),A) = A. [resolve(250311,a,61,a)].
% 114.84/115.18 250413 is_a_theorem(implies(implies(not(A),B),implies(implies(B,A),A))). [para(250344(a,1),96(a,1,2,2))].
% 114.84/115.18 250414 $F. [resolve(250413,a,17387,a)].
% 114.84/115.18
% 114.84/115.18 % SZS output end Refutation
% 114.84/115.18 ============================== end of proof ==========================
% 114.84/115.18
% 114.84/115.18 ============================== STATISTICS ============================
% 114.84/115.18
% 114.84/115.18 Given=8335. Generated=13914884. Kept=250363. proofs=1.
% 114.84/115.18 Usable=1828. Sos=6468. Demods=56. Limbo=4, Disabled=242134. Hints=0.
% 114.84/115.18 Megabytes=178.33.
% 114.84/115.18 User_CPU=107.33, System_CPU=6.83, Wall_clock=114.
% 114.84/115.18
% 114.84/115.18 ============================== end of statistics =====================
% 114.84/115.18
% 114.84/115.18 ============================== end of search =========================
% 114.84/115.18
% 114.84/115.18 THEOREM PROVED
% 114.84/115.18 % SZS status Theorem
% 114.84/115.18
% 114.84/115.18 Exiting with 1 proof.
% 114.84/115.18
% 114.84/115.18 Process 31202 exit (max_proofs) Mon Jul 4 18:16:33 2022
% 114.84/115.18 Prover9 interrupted
%------------------------------------------------------------------------------