TSTP Solution File: LCL500+1 by Prover9---1109a
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : LCL500+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n010.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 3.34s 3.62s
% Output : Refutation 3.34s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.11 % Problem : LCL500+1 : TPTP v8.1.0. Released v3.3.0.
% 0.07/0.12 % Command : tptp2X_and_run_prover9 %d %s
% 0.12/0.33 % Computer : n010.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 : Mon Jul 4 06:10:47 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.71/0.98 ============================== Prover9 ===============================
% 0.71/0.98 Prover9 (32) version 2009-11A, November 2009.
% 0.71/0.98 Process 1250 was started by sandbox on n010.cluster.edu,
% 0.71/0.98 Mon Jul 4 06:10:48 2022
% 0.71/0.98 The command was "/export/starexec/sandbox/solver/bin/prover9 -t 300 -f /tmp/Prover9_1083_n010.cluster.edu".
% 0.71/0.98 ============================== end of head ===========================
% 0.71/0.98
% 0.71/0.98 ============================== INPUT =================================
% 0.71/0.98
% 0.71/0.98 % Reading from file /tmp/Prover9_1083_n010.cluster.edu
% 0.71/0.98
% 0.71/0.98 set(prolog_style_variables).
% 0.71/0.98 set(auto2).
% 0.71/0.98 % set(auto2) -> set(auto).
% 0.71/0.98 % set(auto) -> set(auto_inference).
% 0.71/0.98 % set(auto) -> set(auto_setup).
% 0.71/0.98 % set(auto_setup) -> set(predicate_elim).
% 0.71/0.98 % set(auto_setup) -> assign(eq_defs, unfold).
% 0.71/0.98 % set(auto) -> set(auto_limits).
% 0.71/0.98 % set(auto_limits) -> assign(max_weight, "100.000").
% 0.71/0.98 % set(auto_limits) -> assign(sos_limit, 20000).
% 0.71/0.98 % set(auto) -> set(auto_denials).
% 0.71/0.98 % set(auto) -> set(auto_process).
% 0.71/0.98 % set(auto2) -> assign(new_constants, 1).
% 0.71/0.98 % set(auto2) -> assign(fold_denial_max, 3).
% 0.71/0.98 % set(auto2) -> assign(max_weight, "200.000").
% 0.71/0.98 % set(auto2) -> assign(max_hours, 1).
% 0.71/0.98 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 0.71/0.98 % set(auto2) -> assign(max_seconds, 0).
% 0.71/0.98 % set(auto2) -> assign(max_minutes, 5).
% 0.71/0.98 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 0.71/0.98 % set(auto2) -> set(sort_initial_sos).
% 0.71/0.98 % set(auto2) -> assign(sos_limit, -1).
% 0.71/0.98 % set(auto2) -> assign(lrs_ticks, 3000).
% 0.71/0.98 % set(auto2) -> assign(max_megs, 400).
% 0.71/0.98 % set(auto2) -> assign(stats, some).
% 0.71/0.98 % set(auto2) -> clear(echo_input).
% 0.71/0.98 % set(auto2) -> set(quiet).
% 0.71/0.98 % set(auto2) -> clear(print_initial_clauses).
% 0.71/0.98 % set(auto2) -> clear(print_given).
% 0.71/0.98 assign(lrs_ticks,-1).
% 0.71/0.98 assign(sos_limit,10000).
% 0.71/0.98 assign(order,kbo).
% 0.71/0.98 set(lex_order_vars).
% 0.71/0.98 clear(print_given).
% 0.71/0.98
% 0.71/0.98 % formulas(sos). % not echoed (45 formulas)
% 0.71/0.98
% 0.71/0.98 ============================== end of input ==========================
% 0.71/0.98
% 0.71/0.98 % From the command line: assign(max_seconds, 300).
% 0.71/0.98
% 0.71/0.98 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 0.71/0.98
% 0.71/0.98 % Formulas that are not ordinary clauses:
% 0.71/0.98 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].
% 0.71/0.98 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].
% 0.71/0.98 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].
% 0.71/0.98 4 implies_1 <-> (all X all Y is_a_theorem(implies(X,implies(Y,X)))) # label(implies_1) # label(axiom) # label(non_clause). [assumption].
% 0.71/0.98 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].
% 0.71/0.98 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].
% 0.71/0.98 7 and_1 <-> (all X all Y is_a_theorem(implies(and(X,Y),X))) # label(and_1) # label(axiom) # label(non_clause). [assumption].
% 0.71/0.98 8 and_2 <-> (all X all Y is_a_theorem(implies(and(X,Y),Y))) # label(and_2) # label(axiom) # label(non_clause). [assumption].
% 0.71/0.98 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].
% 0.71/0.98 10 or_1 <-> (all X all Y is_a_theorem(implies(X,or(X,Y)))) # label(or_1) # label(axiom) # label(non_clause). [assumption].
% 0.71/0.98 11 or_2 <-> (all X all Y is_a_theorem(implies(Y,or(X,Y)))) # label(or_2) # label(axiom) # label(non_clause). [assumption].
% 0.71/0.98 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].
% 0.71/0.98 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].
% 0.71/0.98 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].
% 1.65/1.95 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].
% 1.65/1.95 16 kn1 <-> (all P is_a_theorem(implies(P,and(P,P)))) # label(kn1) # label(axiom) # label(non_clause). [assumption].
% 1.65/1.95 17 kn2 <-> (all P all Q is_a_theorem(implies(and(P,Q),P))) # label(kn2) # label(axiom) # label(non_clause). [assumption].
% 1.65/1.95 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].
% 1.65/1.95 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].
% 1.65/1.95 20 cn2 <-> (all P all Q is_a_theorem(implies(P,implies(not(P),Q)))) # label(cn2) # label(axiom) # label(non_clause). [assumption].
% 1.65/1.95 21 cn3 <-> (all P is_a_theorem(implies(implies(not(P),P),P))) # label(cn3) # label(axiom) # label(non_clause). [assumption].
% 1.65/1.95 22 r1 <-> (all P is_a_theorem(implies(or(P,P),P))) # label(r1) # label(axiom) # label(non_clause). [assumption].
% 1.65/1.95 23 r2 <-> (all P all Q is_a_theorem(implies(Q,or(P,Q)))) # label(r2) # label(axiom) # label(non_clause). [assumption].
% 1.65/1.95 24 r3 <-> (all P all Q is_a_theorem(implies(or(P,Q),or(Q,P)))) # label(r3) # label(axiom) # label(non_clause). [assumption].
% 1.65/1.95 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].
% 1.65/1.95 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].
% 1.65/1.95 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].
% 1.65/1.95 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].
% 1.65/1.95 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].
% 1.65/1.95 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].
% 1.65/1.95 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].
% 1.65/1.95
% 1.65/1.95 ============================== end of process non-clausal formulas ===
% 1.65/1.95
% 1.65/1.95 ============================== PROCESS INITIAL CLAUSES ===============
% 1.65/1.95
% 1.65/1.95 ============================== PREDICATE ELIMINATION =================
% 1.65/1.95
% 1.65/1.95 ============================== end predicate elimination =============
% 1.65/1.95
% 1.65/1.95 Auto_denials: (non-Horn, no changes).
% 1.65/1.95
% 1.65/1.95 Term ordering decisions:
% 1.65/1.95
% 1.65/1.95 % Assigning unary symbol not kb_weight 0 and highest precedence (93).
% 1.65/1.95 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.
% 1.65/1.95
% 1.65/1.95 ============================== end of process initial clauses ========
% 1.65/1.95
% 1.65/1.95 ============================== CLAUSES FOR SEARCH ====================
% 1.65/1.95
% 1.65/1.95 ============================== end of clauses for search =============
% 1.65/1.95
% 1.65/1.95 ============================== SEARCH ================================
% 1.65/1.95
% 1.65/1.95 % Starting search at 0.02 seconds.
% 1.65/1.95
% 1.65/1.95 Low Water (keep): wt=26.000, iters=3405
% 1.65/1.95
% 1.65/1.95 Low Water (keep): wt=22.000, iters=3353
% 1.65/1.95
% 1.65/1.95 Low Water (keep): wt=20.000, iters=3390
% 1.65/1.95
% 1.65/1.95 Low Water (keep): wt=19.000, iters=3362
% 1.65/1.95
% 1.65/1.95 Low Water (keep): wt=18.000, iters=3337
% 1.65/1.95
% 1.65/1.95 Low Water (keep): wt=17.000, iters=3353
% 1.65/1.95
% 1.65/1.95 Low Water (keep): wt=16.000, iters=3483
% 1.65/1.95
% 1.65/1.95 Low Water (keep): wt=15.000, iters=3337
% 1.65/1.95
% 1.65/1.95 Low Water (keep): wt=14.000, iters=3343
% 1.65/1.95
% 1.65/1.95 NOTE: Back_subsumption disabled, ratio of kept to back_subsumed is 23 (0.00 of 0.94 sec).
% 3.34/3.62
% 3.34/3.62 Low Water (keep): wt=13.000, iters=3335
% 3.34/3.62
% 3.34/3.62 Low Water (displace): id=14146, wt=44.000
% 3.34/3.62
% 3.34/3.62 Low Water (displace): id=14149, wt=42.000
% 3.34/3.62
% 3.34/3.62 Low Water (displace): id=14152, wt=40.000
% 3.34/3.62
% 3.34/3.62 Low Water (displace): id=12812, wt=38.000
% 3.34/3.62
% 3.34/3.62 Low Water (displace): id=11256, wt=36.000
% 3.34/3.62
% 3.34/3.62 Low Water (displace): id=14140, wt=32.000
% 3.34/3.62
% 3.34/3.62 Low Water (displace): id=14141, wt=30.000
% 3.34/3.62
% 3.34/3.62 Low Water (displace): id=15266, wt=12.000
% 3.34/3.62
% 3.34/3.62 Low Water (displace): id=15445, wt=11.000
% 3.34/3.62
% 3.34/3.62 Low Water (keep): wt=12.000, iters=3340
% 3.34/3.62
% 3.34/3.62 Low Water (displace): id=16957, wt=10.000
% 3.34/3.62
% 3.34/3.62 Low Water (displace): id=16964, wt=9.000
% 3.34/3.62
% 3.34/3.62 ============================== PROOF =================================
% 3.34/3.62 % SZS status Theorem
% 3.34/3.62 % SZS output start Refutation
% 3.34/3.62
% 3.34/3.62 % Proof 1 at 2.53 (+ 0.12) seconds.
% 3.34/3.62 % Length of proof is 95.
% 3.34/3.62 % Level of proof is 18.
% 3.34/3.62 % Maximum clause weight is 16.000.
% 3.34/3.62 % Given clauses 1040.
% 3.34/3.62
% 3.34/3.62 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].
% 3.34/3.62 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].
% 3.34/3.62 17 kn2 <-> (all P all Q is_a_theorem(implies(and(P,Q),P))) # label(kn2) # label(axiom) # label(non_clause). [assumption].
% 3.34/3.62 22 r1 <-> (all P is_a_theorem(implies(or(P,P),P))) # label(r1) # label(axiom) # label(non_clause). [assumption].
% 3.34/3.62 23 r2 <-> (all P all Q is_a_theorem(implies(Q,or(P,Q)))) # label(r2) # label(axiom) # label(non_clause). [assumption].
% 3.34/3.62 24 r3 <-> (all P all Q is_a_theorem(implies(or(P,Q),or(Q,P)))) # label(r3) # label(axiom) # label(non_clause). [assumption].
% 3.34/3.62 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].
% 3.34/3.62 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].
% 3.34/3.62 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].
% 3.34/3.62 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].
% 3.34/3.62 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].
% 3.34/3.62 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].
% 3.34/3.62 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].
% 3.34/3.62 32 op_implies_or # label(principia_op_implies_or) # label(axiom). [assumption].
% 3.34/3.62 33 op_and # label(principia_op_and) # label(axiom). [assumption].
% 3.34/3.62 34 op_equiv # label(principia_op_equiv) # label(axiom). [assumption].
% 3.34/3.62 35 modus_ponens # label(principia_modus_ponens) # label(axiom). [assumption].
% 3.34/3.62 36 r1 # label(principia_r1) # label(axiom). [assumption].
% 3.34/3.62 37 r2 # label(principia_r2) # label(axiom). [assumption].
% 3.34/3.62 38 r3 # label(principia_r3) # label(axiom). [assumption].
% 3.34/3.62 39 r4 # label(principia_r4) # label(axiom). [assumption].
% 3.34/3.62 40 r5 # label(principia_r5) # label(axiom). [assumption].
% 3.34/3.62 41 substitution_of_equivalents # label(substitution_of_equivalents) # label(axiom). [assumption].
% 3.34/3.62 42 op_or # label(rosser_op_or) # label(axiom). [assumption].
% 3.34/3.62 43 op_implies_and # label(rosser_op_implies_and) # label(axiom). [assumption].
% 3.34/3.62 44 -kn2 # label(rosser_kn2) # label(negated_conjecture). [assumption].
% 3.34/3.62 57 kn2 | -is_a_theorem(implies(and(c34,c35),c34)) # label(kn2) # label(axiom). [clausify(17)].
% 3.34/3.62 58 -is_a_theorem(implies(and(c34,c35),c34)). [copy(57),unit_del(a,44)].
% 3.34/3.62 59 -r1 | is_a_theorem(implies(or(A,A),A)) # label(r1) # label(axiom). [clausify(22)].
% 3.34/3.62 60 is_a_theorem(implies(or(A,A),A)). [copy(59),unit_del(a,36)].
% 3.34/3.62 62 -r2 | is_a_theorem(implies(A,or(B,A))) # label(r2) # label(axiom). [clausify(23)].
% 3.34/3.62 63 is_a_theorem(implies(A,or(B,A))). [copy(62),unit_del(a,37)].
% 3.34/3.62 65 -substitution_of_equivalents | -is_a_theorem(equiv(A,B)) | B = A # label(substitution_of_equivalents) # label(axiom). [clausify(2)].
% 3.34/3.62 66 -is_a_theorem(equiv(A,B)) | B = A. [copy(65),unit_del(a,41)].
% 3.34/3.62 71 -modus_ponens | -is_a_theorem(A) | -is_a_theorem(implies(A,B)) | is_a_theorem(B) # label(modus_ponens) # label(axiom). [clausify(1)].
% 3.34/3.62 72 -is_a_theorem(A) | -is_a_theorem(implies(A,B)) | is_a_theorem(B). [copy(71),unit_del(a,35)].
% 3.34/3.62 79 -r3 | is_a_theorem(implies(or(A,B),or(B,A))) # label(r3) # label(axiom). [clausify(24)].
% 3.34/3.62 80 is_a_theorem(implies(or(A,B),or(B,A))). [copy(79),unit_del(a,38)].
% 3.34/3.62 82 -op_implies_or | or(not(A),B) = implies(A,B) # label(op_implies_or) # label(axiom). [clausify(30)].
% 3.34/3.62 83 or(not(A),B) = implies(A,B). [copy(82),unit_del(a,32)].
% 3.34/3.62 84 -op_implies_and | not(and(A,not(B))) = implies(A,B) # label(op_implies_and) # label(axiom). [clausify(29)].
% 3.34/3.62 85 not(and(A,not(B))) = implies(A,B). [copy(84),unit_del(a,43)].
% 3.34/3.62 90 -op_or | or(A,B) = not(and(not(A),not(B))) # label(op_or) # label(axiom). [clausify(27)].
% 3.34/3.62 91 or(A,B) = implies(not(A),B). [copy(90),rewrite([85(6)]),unit_del(a,42)].
% 3.34/3.62 92 -op_and | and(A,B) = not(or(not(A),not(B))) # label(op_and) # label(axiom). [clausify(28)].
% 3.34/3.62 93 not(implies(not(not(A)),not(B))) = and(A,B). [copy(92),rewrite([91(5)]),flip(b),unit_del(a,33)].
% 3.34/3.62 94 -op_equiv | and(implies(A,B),implies(B,A)) = equiv(A,B) # label(op_equiv) # label(axiom). [clausify(31)].
% 3.34/3.62 95 and(implies(A,B),implies(B,A)) = equiv(A,B). [copy(94),unit_del(a,34)].
% 3.34/3.62 102 -r4 | is_a_theorem(implies(or(A,or(B,C)),or(B,or(A,C)))) # label(r4) # label(axiom). [clausify(25)].
% 3.34/3.62 103 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)].
% 3.34/3.62 105 -r5 | is_a_theorem(implies(implies(A,B),implies(or(C,A),or(C,B)))) # label(r5) # label(axiom). [clausify(26)].
% 3.34/3.62 106 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)].
% 3.34/3.62 115 implies(not(not(A)),B) = implies(A,B). [back_rewrite(83),rewrite([91(2)])].
% 3.34/3.62 116 is_a_theorem(implies(implies(not(A),B),implies(not(B),A))). [back_rewrite(80),rewrite([91(1),91(3)])].
% 3.34/3.62 117 is_a_theorem(implies(A,implies(not(B),A))). [back_rewrite(63),rewrite([91(1)])].
% 3.34/3.62 118 is_a_theorem(implies(implies(not(A),A),A)). [back_rewrite(60),rewrite([91(1)])].
% 3.34/3.62 121 not(implies(A,not(B))) = and(A,B). [back_rewrite(93),rewrite([115(4)])].
% 3.34/3.62 127 -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)].
% 3.34/3.62 135 implies(not(implies(A,B)),C) = implies(and(A,not(B)),C). [para(85(a,1),115(a,1,1,1))].
% 3.34/3.62 137 and(implies(A,not(not(B))),implies(B,A)) = equiv(A,not(not(B))). [para(115(a,1),95(a,1,2))].
% 3.34/3.62 141 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)])].
% 3.34/3.62 142 -is_a_theorem(implies(not(A),B)) | is_a_theorem(implies(not(B),A)). [resolve(116,a,72,b)].
% 3.34/3.62 146 is_a_theorem(implies(implies(A,B),implies(not(B),not(A)))). [para(115(a,1),116(a,1,1))].
% 3.34/3.62 152 is_a_theorem(implies(A,implies(B,A))). [para(115(a,1),117(a,1,2))].
% 3.34/3.62 155 -is_a_theorem(implies(not(A),A)) | is_a_theorem(A). [resolve(118,a,72,b)].
% 3.34/3.62 159 is_a_theorem(implies(implies(A,not(A)),not(A))). [para(115(a,1),118(a,1,1))].
% 3.34/3.62 163 and(not(not(A)),B) = and(A,B). [para(115(a,1),121(a,1,1)),rewrite([121(3)]),flip(a)].
% 3.34/3.62 192 is_a_theorem(implies(A,implies(B,not(not(A))))). [para(115(a,1),152(a,1))].
% 3.34/3.62 235 -is_a_theorem(A) | is_a_theorem(implies(B,not(not(A)))). [resolve(192,a,72,b)].
% 3.34/3.62 258 is_a_theorem(implies(not(A),implies(not(B),not(B)))). [resolve(127,a,152,a)].
% 3.34/3.62 262 -is_a_theorem(implies(A,implies(not(B),C))) | is_a_theorem(implies(not(B),implies(A,C))). [para(115(a,1),127(a,1)),rewrite([115(8)])].
% 3.34/3.62 388 is_a_theorem(implies(not(A),not(A))). [resolve(258,a,155,a)].
% 3.34/3.62 428 is_a_theorem(implies(A,not(not(A)))). [para(115(a,1),388(a,1))].
% 3.34/3.62 430 is_a_theorem(implies(A,implies(B,B))). [resolve(428,a,235,a),rewrite([121(4),85(3)])].
% 3.34/3.62 455 is_a_theorem(implies(A,A)). [resolve(430,a,155,a)].
% 3.34/3.62 887 implies(and(A,not(not(B))),C) = implies(and(A,B),C). [para(121(a,1),135(a,1,1)),flip(a)].
% 3.34/3.62 1160 equiv(A,not(not(B))) = equiv(A,B). [para(137(a,1),163(a,2)),rewrite([121(4),85(3),95(3)]),flip(a)].
% 3.34/3.62 1248 -is_a_theorem(equiv(A,B)) | not(not(B)) = A. [para(1160(a,1),66(a,1))].
% 3.34/3.62 1263 is_a_theorem(implies(and(A,B),B)). [resolve(142,a,192,a),rewrite([121(5),887(4)])].
% 3.34/3.62 1265 -is_a_theorem(implies(A,B)) | is_a_theorem(implies(not(B),not(A))). [para(115(a,1),142(a,1))].
% 3.34/3.62 3119 is_a_theorem(implies(implies(A,not(B)),implies(B,not(A)))). [para(115(a,1),146(a,1,2))].
% 3.34/3.62 6432 is_a_theorem(implies(A,and(A,A))). [resolve(1265,a,159,a),rewrite([121(5),115(4)])].
% 3.34/3.62 6653 -is_a_theorem(A) | is_a_theorem(and(A,A)). [resolve(6432,a,72,b)].
% 3.34/3.62 6796 is_a_theorem(equiv(A,A)). [resolve(6653,a,455,a),rewrite([95(3)])].
% 3.34/3.62 6829 not(not(A)) = A. [resolve(6796,a,1248,a)].
% 3.34/3.62 6898 not(implies(A,B)) = and(A,not(B)). [para(85(a,1),6829(a,1,1))].
% 3.34/3.62 8884 is_a_theorem(implies(and(A,B),and(B,A))). [resolve(3119,a,1265,a),rewrite([6898(3),6829(2),6898(4),6829(3)])].
% 3.34/3.62 9005 -is_a_theorem(implies(implies(and(A,B),and(B,A)),implies(and(c34,c35),c34))). [ur(72,a,8884,a,c,58,a)].
% 3.34/3.62 15005 is_a_theorem(implies(not(A),implies(implies(not(A),B),B))). [resolve(262,a,455,a)].
% 3.34/3.62 16939 is_a_theorem(implies(A,implies(implies(A,B),B))). [para(6829(a,1),15005(a,1,1)),rewrite([6829(2)])].
% 3.34/3.62 16951 -is_a_theorem(A) | is_a_theorem(implies(implies(A,B),B)). [resolve(16939,a,72,b)].
% 3.34/3.62 17143 is_a_theorem(implies(implies(implies(and(A,B),B),C),C)). [resolve(16951,a,1263,a)].
% 3.34/3.62 19181 -is_a_theorem(implies(implies(and(A,B),B),C)) | is_a_theorem(C). [resolve(17143,a,72,b)].
% 3.34/3.62 23370 is_a_theorem(implies(implies(A,and(B,C)),implies(A,C))). [resolve(19181,a,141,a)].
% 3.34/3.62 23371 $F. [resolve(23370,a,9005,a)].
% 3.34/3.62
% 3.34/3.62 % SZS output end Refutation
% 3.34/3.62 ============================== end of proof ==========================
% 3.34/3.62
% 3.34/3.62 ============================== STATISTICS ============================
% 3.34/3.62
% 3.34/3.62 Given=1040. Generated=212651. Kept=23319. proofs=1.
% 3.34/3.62 Usable=888. Sos=9999. Demods=7. Limbo=6, Disabled=12499. Hints=0.
% 3.34/3.62 Megabytes=13.65.
% 3.34/3.62 User_CPU=2.53, System_CPU=0.12, Wall_clock=3.
% 3.34/3.62
% 3.34/3.62 ============================== end of statistics =====================
% 3.34/3.62
% 3.34/3.62 ============================== end of search =========================
% 3.34/3.62
% 3.34/3.62 THEOREM PROVED
% 3.34/3.62 % SZS status Theorem
% 3.34/3.62
% 3.34/3.62 Exiting with 1 proof.
% 3.34/3.62
% 3.34/3.62 Process 1250 exit (max_proofs) Mon Jul 4 06:10:51 2022
% 3.34/3.62 Prover9 interrupted
%------------------------------------------------------------------------------