TSTP Solution File: LCL493+1 by Prover9---1109a
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : LCL493+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n006.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 13:47:11 EDT 2022
% Result : Theorem 2.14s 2.44s
% Output : Refutation 2.14s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.11 % Problem : LCL493+1 : TPTP v8.1.0. Released v3.3.0.
% 0.06/0.12 % Command : tptp2X_and_run_prover9 %d %s
% 0.12/0.33 % Computer : n006.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 600
% 0.12/0.33 % DateTime : Sat Jul 2 15:17:22 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.39/0.99 ============================== Prover9 ===============================
% 0.39/0.99 Prover9 (32) version 2009-11A, November 2009.
% 0.39/0.99 Process 17939 was started by sandbox on n006.cluster.edu,
% 0.39/0.99 Sat Jul 2 15:17:23 2022
% 0.39/0.99 The command was "/export/starexec/sandbox/solver/bin/prover9 -t 300 -f /tmp/Prover9_17786_n006.cluster.edu".
% 0.39/0.99 ============================== end of head ===========================
% 0.39/0.99
% 0.39/0.99 ============================== INPUT =================================
% 0.39/0.99
% 0.39/0.99 % Reading from file /tmp/Prover9_17786_n006.cluster.edu
% 0.39/0.99
% 0.39/0.99 set(prolog_style_variables).
% 0.39/0.99 set(auto2).
% 0.39/0.99 % set(auto2) -> set(auto).
% 0.39/0.99 % set(auto) -> set(auto_inference).
% 0.39/0.99 % set(auto) -> set(auto_setup).
% 0.39/0.99 % set(auto_setup) -> set(predicate_elim).
% 0.39/0.99 % set(auto_setup) -> assign(eq_defs, unfold).
% 0.39/0.99 % set(auto) -> set(auto_limits).
% 0.39/0.99 % set(auto_limits) -> assign(max_weight, "100.000").
% 0.39/0.99 % set(auto_limits) -> assign(sos_limit, 20000).
% 0.39/0.99 % set(auto) -> set(auto_denials).
% 0.39/0.99 % set(auto) -> set(auto_process).
% 0.39/0.99 % set(auto2) -> assign(new_constants, 1).
% 0.39/0.99 % set(auto2) -> assign(fold_denial_max, 3).
% 0.39/0.99 % set(auto2) -> assign(max_weight, "200.000").
% 0.39/0.99 % set(auto2) -> assign(max_hours, 1).
% 0.39/0.99 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 0.39/0.99 % set(auto2) -> assign(max_seconds, 0).
% 0.39/0.99 % set(auto2) -> assign(max_minutes, 5).
% 0.39/0.99 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 0.39/0.99 % set(auto2) -> set(sort_initial_sos).
% 0.39/0.99 % set(auto2) -> assign(sos_limit, -1).
% 0.39/0.99 % set(auto2) -> assign(lrs_ticks, 3000).
% 0.39/0.99 % set(auto2) -> assign(max_megs, 400).
% 0.39/0.99 % set(auto2) -> assign(stats, some).
% 0.39/0.99 % set(auto2) -> clear(echo_input).
% 0.39/0.99 % set(auto2) -> set(quiet).
% 0.39/0.99 % set(auto2) -> clear(print_initial_clauses).
% 0.39/0.99 % set(auto2) -> clear(print_given).
% 0.39/0.99 assign(lrs_ticks,-1).
% 0.39/0.99 assign(sos_limit,10000).
% 0.39/0.99 assign(order,kbo).
% 0.39/0.99 set(lex_order_vars).
% 0.39/0.99 clear(print_given).
% 0.39/0.99
% 0.39/0.99 % formulas(sos). % not echoed (45 formulas)
% 0.39/0.99
% 0.39/0.99 ============================== end of input ==========================
% 0.39/0.99
% 0.39/0.99 % From the command line: assign(max_seconds, 300).
% 0.39/0.99
% 0.39/0.99 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 0.39/0.99
% 0.39/0.99 % Formulas that are not ordinary clauses:
% 0.39/0.99 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].
% 0.39/0.99 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].
% 0.39/0.99 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].
% 0.39/0.99 4 implies_1 <-> (all X all Y is_a_theorem(implies(X,implies(Y,X)))) # label(implies_1) # label(axiom) # label(non_clause). [assumption].
% 0.39/0.99 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].
% 0.39/0.99 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].
% 0.39/0.99 7 and_1 <-> (all X all Y is_a_theorem(implies(and(X,Y),X))) # label(and_1) # label(axiom) # label(non_clause). [assumption].
% 0.39/0.99 8 and_2 <-> (all X all Y is_a_theorem(implies(and(X,Y),Y))) # label(and_2) # label(axiom) # label(non_clause). [assumption].
% 0.39/0.99 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].
% 0.39/0.99 10 or_1 <-> (all X all Y is_a_theorem(implies(X,or(X,Y)))) # label(or_1) # label(axiom) # label(non_clause). [assumption].
% 0.39/0.99 11 or_2 <-> (all X all Y is_a_theorem(implies(Y,or(X,Y)))) # label(or_2) # label(axiom) # label(non_clause). [assumption].
% 0.39/0.99 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].
% 0.39/0.99 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].
% 0.39/0.99 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].
% 1.71/1.99 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].
% 1.71/1.99 16 kn1 <-> (all P is_a_theorem(implies(P,and(P,P)))) # label(kn1) # label(axiom) # label(non_clause). [assumption].
% 1.71/1.99 17 kn2 <-> (all P all Q is_a_theorem(implies(and(P,Q),P))) # label(kn2) # label(axiom) # label(non_clause). [assumption].
% 1.71/1.99 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].
% 1.71/1.99 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].
% 1.71/1.99 20 cn2 <-> (all P all Q is_a_theorem(implies(P,implies(not(P),Q)))) # label(cn2) # label(axiom) # label(non_clause). [assumption].
% 1.71/1.99 21 cn3 <-> (all P is_a_theorem(implies(implies(not(P),P),P))) # label(cn3) # label(axiom) # label(non_clause). [assumption].
% 1.71/1.99 22 r1 <-> (all P is_a_theorem(implies(or(P,P),P))) # label(r1) # label(axiom) # label(non_clause). [assumption].
% 1.71/1.99 23 r2 <-> (all P all Q is_a_theorem(implies(Q,or(P,Q)))) # label(r2) # label(axiom) # label(non_clause). [assumption].
% 1.71/1.99 24 r3 <-> (all P all Q is_a_theorem(implies(or(P,Q),or(Q,P)))) # label(r3) # label(axiom) # label(non_clause). [assumption].
% 1.71/1.99 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].
% 1.71/1.99 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].
% 1.71/1.99 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].
% 1.71/1.99 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].
% 1.71/1.99 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].
% 1.71/1.99 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].
% 1.71/1.99 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].
% 1.71/1.99
% 1.71/1.99 ============================== end of process non-clausal formulas ===
% 1.71/1.99
% 1.71/1.99 ============================== PROCESS INITIAL CLAUSES ===============
% 1.71/1.99
% 1.71/1.99 ============================== PREDICATE ELIMINATION =================
% 1.71/1.99
% 1.71/1.99 ============================== end predicate elimination =============
% 1.71/1.99
% 1.71/1.99 Auto_denials: (non-Horn, no changes).
% 1.71/1.99
% 1.71/1.99 Term ordering decisions:
% 1.71/1.99
% 1.71/1.99 % Assigning unary symbol not kb_weight 0 and highest precedence (93).
% 1.71/1.99 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.
% 1.71/1.99
% 1.71/1.99 ============================== end of process initial clauses ========
% 1.71/1.99
% 1.71/1.99 ============================== CLAUSES FOR SEARCH ====================
% 1.71/1.99
% 1.71/1.99 ============================== end of clauses for search =============
% 1.71/1.99
% 1.71/1.99 ============================== SEARCH ================================
% 1.71/1.99
% 1.71/1.99 % Starting search at 0.02 seconds.
% 1.71/1.99
% 1.71/1.99 Low Water (keep): wt=26.000, iters=3466
% 1.71/1.99
% 1.71/1.99 Low Water (keep): wt=24.000, iters=3375
% 1.71/1.99
% 1.71/1.99 Low Water (keep): wt=21.000, iters=3404
% 1.71/1.99
% 1.71/1.99 Low Water (keep): wt=20.000, iters=3373
% 1.71/1.99
% 1.71/1.99 Low Water (keep): wt=19.000, iters=3340
% 1.71/1.99
% 1.71/1.99 Low Water (keep): wt=18.000, iters=3540
% 1.71/1.99
% 1.71/1.99 Low Water (keep): wt=17.000, iters=3421
% 1.71/1.99
% 1.71/1.99 Low Water (keep): wt=16.000, iters=3359
% 1.71/1.99
% 1.71/1.99 Low Water (keep): wt=15.000, iters=3335
% 1.71/1.99
% 1.71/1.99 Low Water (keep): wt=14.000, iters=3340
% 1.71/1.99
% 2.14/2.44 NOTE: Back_subsumption disabled, ratio of kept to back_subsumed is 25 (0.00 of 0.99 sec).
% 2.14/2.44
% 2.14/2.44 ============================== PROOF =================================
% 2.14/2.44 % SZS status Theorem
% 2.14/2.44 % SZS output start Refutation
% 2.14/2.44
% 2.14/2.44 % Proof 1 at 1.41 (+ 0.06) seconds.
% 2.14/2.44 % Length of proof is 92.
% 2.14/2.44 % Level of proof is 17.
% 2.14/2.44 % Maximum clause weight is 16.000.
% 2.14/2.44 % Given clauses 788.
% 2.14/2.44
% 2.14/2.44 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].
% 2.14/2.44 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].
% 2.14/2.44 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].
% 2.14/2.44 22 r1 <-> (all P is_a_theorem(implies(or(P,P),P))) # label(r1) # label(axiom) # label(non_clause). [assumption].
% 2.14/2.44 23 r2 <-> (all P all Q is_a_theorem(implies(Q,or(P,Q)))) # label(r2) # label(axiom) # label(non_clause). [assumption].
% 2.14/2.44 24 r3 <-> (all P all Q is_a_theorem(implies(or(P,Q),or(Q,P)))) # label(r3) # label(axiom) # label(non_clause). [assumption].
% 2.14/2.44 25 r4 <-> (all P all Q all R is_a_theorem(implies(or(P,or(Q,R)),or(Q,or(P,R))))) # label(r4) # label(axiom) # label(non_clause). [assumption].
% 2.14/2.44 26 r5 <-> (all P all Q all R is_a_theorem(implies(implies(Q,R),implies(or(P,Q),or(P,R))))) # label(r5) # label(axiom) # label(non_clause). [assumption].
% 2.14/2.44 27 op_or -> (all X all Y or(X,Y) = not(and(not(X),not(Y)))) # label(op_or) # label(axiom) # label(non_clause). [assumption].
% 2.14/2.44 28 op_and -> (all X all Y and(X,Y) = not(or(not(X),not(Y)))) # label(op_and) # label(axiom) # label(non_clause). [assumption].
% 2.14/2.44 29 op_implies_and -> (all X all Y implies(X,Y) = not(and(X,not(Y)))) # label(op_implies_and) # label(axiom) # label(non_clause). [assumption].
% 2.14/2.44 30 op_implies_or -> (all X all Y implies(X,Y) = or(not(X),Y)) # label(op_implies_or) # label(axiom) # label(non_clause). [assumption].
% 2.14/2.44 31 op_equiv -> (all X all Y equiv(X,Y) = and(implies(X,Y),implies(Y,X))) # label(op_equiv) # label(axiom) # label(non_clause). [assumption].
% 2.14/2.44 32 op_implies_or # label(principia_op_implies_or) # label(axiom). [assumption].
% 2.14/2.44 33 op_and # label(principia_op_and) # label(axiom). [assumption].
% 2.14/2.44 34 op_equiv # label(principia_op_equiv) # label(axiom). [assumption].
% 2.14/2.44 35 modus_ponens # label(principia_modus_ponens) # label(axiom). [assumption].
% 2.14/2.44 36 r1 # label(principia_r1) # label(axiom). [assumption].
% 2.14/2.44 37 r2 # label(principia_r2) # label(axiom). [assumption].
% 2.14/2.44 38 r3 # label(principia_r3) # label(axiom). [assumption].
% 2.14/2.44 39 r4 # label(principia_r4) # label(axiom). [assumption].
% 2.14/2.44 40 r5 # label(principia_r5) # label(axiom). [assumption].
% 2.14/2.44 41 substitution_of_equivalents # label(substitution_of_equivalents) # label(axiom). [assumption].
% 2.14/2.44 42 op_or # label(hilbert_op_or) # label(axiom). [assumption].
% 2.14/2.44 43 op_implies_and # label(hilbert_op_implies_and) # label(axiom). [assumption].
% 2.14/2.44 44 -equivalence_1 # label(hilbert_equivalence_1) # label(negated_conjecture). [assumption].
% 2.14/2.44 59 -r1 | is_a_theorem(implies(or(A,A),A)) # label(r1) # label(axiom). [clausify(22)].
% 2.14/2.44 60 is_a_theorem(implies(or(A,A),A)). [copy(59),unit_del(a,36)].
% 2.14/2.44 62 -r2 | is_a_theorem(implies(A,or(B,A))) # label(r2) # label(axiom). [clausify(23)].
% 2.14/2.44 63 is_a_theorem(implies(A,or(B,A))). [copy(62),unit_del(a,37)].
% 2.14/2.44 65 -substitution_of_equivalents | -is_a_theorem(equiv(A,B)) | B = A # label(substitution_of_equivalents) # label(axiom). [clausify(2)].
% 2.14/2.44 66 -is_a_theorem(equiv(A,B)) | B = A. [copy(65),unit_del(a,41)].
% 2.14/2.44 71 -modus_ponens | -is_a_theorem(A) | -is_a_theorem(implies(A,B)) | is_a_theorem(B) # label(modus_ponens) # label(axiom). [clausify(1)].
% 2.14/2.44 72 -is_a_theorem(A) | -is_a_theorem(implies(A,B)) | is_a_theorem(B). [copy(71),unit_del(a,35)].
% 2.14/2.44 75 equivalence_1 | -is_a_theorem(implies(equiv(c27,c28),implies(c27,c28))) # label(equivalence_1) # label(axiom). [clausify(13)].
% 2.14/2.44 76 -is_a_theorem(implies(equiv(c27,c28),implies(c27,c28))). [copy(75),unit_del(a,44)].
% 2.14/2.44 79 -r3 | is_a_theorem(implies(or(A,B),or(B,A))) # label(r3) # label(axiom). [clausify(24)].
% 2.14/2.44 80 is_a_theorem(implies(or(A,B),or(B,A))). [copy(79),unit_del(a,38)].
% 2.14/2.44 82 -op_implies_or | or(not(A),B) = implies(A,B) # label(op_implies_or) # label(axiom). [clausify(30)].
% 2.14/2.44 83 or(not(A),B) = implies(A,B). [copy(82),unit_del(a,32)].
% 2.14/2.44 84 -op_implies_and | not(and(A,not(B))) = implies(A,B) # label(op_implies_and) # label(axiom). [clausify(29)].
% 2.14/2.44 85 not(and(A,not(B))) = implies(A,B). [copy(84),unit_del(a,43)].
% 2.14/2.44 90 -op_or | or(A,B) = not(and(not(A),not(B))) # label(op_or) # label(axiom). [clausify(27)].
% 2.14/2.44 91 or(A,B) = implies(not(A),B). [copy(90),rewrite([85(6)]),unit_del(a,42)].
% 2.14/2.44 92 -op_and | and(A,B) = not(or(not(A),not(B))) # label(op_and) # label(axiom). [clausify(28)].
% 2.14/2.44 93 not(implies(not(not(A)),not(B))) = and(A,B). [copy(92),rewrite([91(5)]),flip(b),unit_del(a,33)].
% 2.14/2.44 94 -op_equiv | and(implies(A,B),implies(B,A)) = equiv(A,B) # label(op_equiv) # label(axiom). [clausify(31)].
% 2.14/2.44 95 and(implies(A,B),implies(B,A)) = equiv(A,B). [copy(94),unit_del(a,34)].
% 2.14/2.44 102 -r4 | is_a_theorem(implies(or(A,or(B,C)),or(B,or(A,C)))) # label(r4) # label(axiom). [clausify(25)].
% 2.14/2.44 103 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)].
% 2.14/2.44 105 -r5 | is_a_theorem(implies(implies(A,B),implies(or(C,A),or(C,B)))) # label(r5) # label(axiom). [clausify(26)].
% 2.14/2.44 106 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)].
% 2.14/2.44 115 implies(not(not(A)),B) = implies(A,B). [back_rewrite(83),rewrite([91(2)])].
% 2.14/2.44 116 is_a_theorem(implies(implies(not(A),B),implies(not(B),A))). [back_rewrite(80),rewrite([91(1),91(3)])].
% 2.14/2.44 117 is_a_theorem(implies(A,implies(not(B),A))). [back_rewrite(63),rewrite([91(1)])].
% 2.14/2.44 118 is_a_theorem(implies(implies(not(A),A),A)). [back_rewrite(60),rewrite([91(1)])].
% 2.14/2.44 121 not(implies(A,not(B))) = and(A,B). [back_rewrite(93),rewrite([115(4)])].
% 2.14/2.44 125 -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)].
% 2.14/2.44 129 -is_a_theorem(implies(A,B)) | is_a_theorem(implies(implies(not(C),A),implies(not(C),B))). [resolve(106,a,72,b)].
% 2.14/2.44 133 implies(not(implies(A,B)),C) = implies(and(A,not(B)),C). [para(85(a,1),115(a,1,1,1))].
% 2.14/2.44 135 and(implies(A,not(not(B))),implies(B,A)) = equiv(A,not(not(B))). [para(115(a,1),95(a,1,2))].
% 2.14/2.44 140 -is_a_theorem(implies(not(A),B)) | is_a_theorem(implies(not(B),A)). [resolve(116,a,72,b)].
% 2.14/2.44 144 is_a_theorem(implies(implies(A,B),implies(not(B),not(A)))). [para(115(a,1),116(a,1,1))].
% 2.14/2.44 150 is_a_theorem(implies(A,implies(B,A))). [para(115(a,1),117(a,1,2))].
% 2.14/2.44 153 -is_a_theorem(implies(not(A),A)) | is_a_theorem(A). [resolve(118,a,72,b)].
% 2.14/2.44 157 is_a_theorem(implies(implies(A,not(A)),not(A))). [para(115(a,1),118(a,1,1))].
% 2.14/2.44 161 and(not(not(A)),B) = and(A,B). [para(115(a,1),121(a,1,1)),rewrite([121(3)]),flip(a)].
% 2.14/2.44 202 is_a_theorem(implies(A,implies(B,not(not(A))))). [para(115(a,1),150(a,1))].
% 2.14/2.44 206 is_a_theorem(implies(not(A),implies(not(B),not(B)))). [resolve(125,a,150,a)].
% 2.14/2.44 247 -is_a_theorem(A) | is_a_theorem(implies(B,not(not(A)))). [resolve(202,a,72,b)].
% 2.14/2.44 390 is_a_theorem(implies(not(A),not(A))). [resolve(206,a,153,a)].
% 2.14/2.44 431 is_a_theorem(implies(A,not(not(A)))). [para(115(a,1),390(a,1))].
% 2.14/2.44 433 is_a_theorem(implies(A,implies(B,B))). [resolve(431,a,247,a),rewrite([121(4),85(3)])].
% 2.14/2.44 459 is_a_theorem(implies(A,A)). [resolve(433,a,153,a)].
% 2.14/2.44 747 implies(and(A,not(not(B))),C) = implies(and(A,B),C). [para(121(a,1),133(a,1,1)),flip(a)].
% 2.14/2.44 1000 equiv(A,not(not(B))) = equiv(A,B). [para(135(a,1),161(a,2)),rewrite([121(4),85(3),95(3)]),flip(a)].
% 2.14/2.44 1302 -is_a_theorem(equiv(A,B)) | not(not(B)) = A. [para(1000(a,1),66(a,1))].
% 2.14/2.44 1322 is_a_theorem(implies(and(A,B),B)). [resolve(140,a,202,a),rewrite([121(5),747(4)])].
% 2.14/2.44 1324 -is_a_theorem(implies(A,B)) | is_a_theorem(implies(not(B),not(A))). [para(115(a,1),140(a,1))].
% 2.14/2.44 1466 is_a_theorem(implies(implies(not(A),and(B,C)),implies(not(A),C))). [resolve(1322,a,129,a)].
% 2.14/2.44 2856 is_a_theorem(implies(implies(A,not(B)),implies(B,not(A)))). [para(115(a,1),144(a,1,2))].
% 2.14/2.44 6607 is_a_theorem(implies(A,and(A,A))). [resolve(1324,a,157,a),rewrite([121(5),115(4)])].
% 2.14/2.44 6624 -is_a_theorem(A) | is_a_theorem(and(A,A)). [resolve(6607,a,72,b)].
% 2.14/2.44 6759 is_a_theorem(equiv(A,A)). [resolve(6624,a,459,a),rewrite([95(3)])].
% 2.14/2.44 6953 not(not(A)) = A. [resolve(6759,a,1302,a)].
% 2.14/2.44 7026 not(implies(A,B)) = and(A,not(B)). [para(85(a,1),6953(a,1,1))].
% 2.14/2.44 8902 is_a_theorem(implies(and(A,B),and(B,A))). [resolve(2856,a,1324,a),rewrite([7026(3),6953(2),7026(4),6953(3)])].
% 2.14/2.44 9205 is_a_theorem(implies(equiv(A,B),equiv(B,A))). [para(95(a,1),8902(a,1,1)),rewrite([95(4)])].
% 2.14/2.44 9283 -is_a_theorem(implies(implies(equiv(A,B),equiv(B,A)),implies(equiv(c27,c28),implies(c27,c28)))). [ur(72,a,9205,a,c,76,a)].
% 2.14/2.44 14633 is_a_theorem(implies(implies(A,and(B,C)),implies(A,C))). [para(6953(a,1),1466(a,1,1,1)),rewrite([6953(4)])].
% 2.14/2.44 14664 is_a_theorem(implies(implies(A,equiv(B,C)),implies(A,implies(C,B)))). [para(95(a,1),14633(a,1,1,2))].
% 2.14/2.44 14665 $F. [resolve(14664,a,9283,a)].
% 2.14/2.44
% 2.14/2.44 % SZS output end Refutation
% 2.14/2.44 ============================== end of proof ==========================
% 2.14/2.44
% 2.14/2.44 ============================== STATISTICS ============================
% 2.14/2.44
% 2.14/2.44 Given=788. Generated=112400. Kept=14613. proofs=1.
% 2.14/2.44 Usable=633. Sos=9242. Demods=12. Limbo=30, Disabled=4781. Hints=0.
% 2.14/2.44 Megabytes=10.49.
% 2.14/2.44 User_CPU=1.41, System_CPU=0.06, Wall_clock=1.
% 2.14/2.44
% 2.14/2.44 ============================== end of statistics =====================
% 2.14/2.44
% 2.14/2.44 ============================== end of search =========================
% 2.14/2.44
% 2.14/2.44 THEOREM PROVED
% 2.14/2.44 % SZS status Theorem
% 2.14/2.44
% 2.14/2.44 Exiting with 1 proof.
% 2.14/2.44
% 2.14/2.44 Process 17939 exit (max_proofs) Sat Jul 2 15:17:24 2022
% 2.14/2.44 Prover9 interrupted
%------------------------------------------------------------------------------