TSTP Solution File: LCL485+1 by Prover9---1109a
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : LCL485+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n009.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 13:47:08 EDT 2022
% Result : Theorem 29.36s 29.71s
% Output : Refutation 29.36s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : LCL485+1 : TPTP v8.1.0. Released v3.3.0.
% 0.11/0.12 % Command : tptp2X_and_run_prover9 %d %s
% 0.13/0.33 % Computer : n009.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 600
% 0.13/0.33 % DateTime : Sat Jul 2 15:55:07 EDT 2022
% 0.13/0.33 % CPUTime :
% 0.72/0.98 ============================== Prover9 ===============================
% 0.72/0.98 Prover9 (32) version 2009-11A, November 2009.
% 0.72/0.98 Process 26241 was started by sandbox on n009.cluster.edu,
% 0.72/0.98 Sat Jul 2 15:55:08 2022
% 0.72/0.98 The command was "/export/starexec/sandbox/solver/bin/prover9 -t 300 -f /tmp/Prover9_26088_n009.cluster.edu".
% 0.72/0.98 ============================== end of head ===========================
% 0.72/0.98
% 0.72/0.98 ============================== INPUT =================================
% 0.72/0.98
% 0.72/0.98 % Reading from file /tmp/Prover9_26088_n009.cluster.edu
% 0.72/0.98
% 0.72/0.98 set(prolog_style_variables).
% 0.72/0.98 set(auto2).
% 0.72/0.98 % set(auto2) -> set(auto).
% 0.72/0.98 % set(auto) -> set(auto_inference).
% 0.72/0.98 % set(auto) -> set(auto_setup).
% 0.72/0.98 % set(auto_setup) -> set(predicate_elim).
% 0.72/0.98 % set(auto_setup) -> assign(eq_defs, unfold).
% 0.72/0.98 % set(auto) -> set(auto_limits).
% 0.72/0.98 % set(auto_limits) -> assign(max_weight, "100.000").
% 0.72/0.98 % set(auto_limits) -> assign(sos_limit, 20000).
% 0.72/0.98 % set(auto) -> set(auto_denials).
% 0.72/0.98 % set(auto) -> set(auto_process).
% 0.72/0.98 % set(auto2) -> assign(new_constants, 1).
% 0.72/0.98 % set(auto2) -> assign(fold_denial_max, 3).
% 0.72/0.98 % set(auto2) -> assign(max_weight, "200.000").
% 0.72/0.98 % set(auto2) -> assign(max_hours, 1).
% 0.72/0.98 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 0.72/0.98 % set(auto2) -> assign(max_seconds, 0).
% 0.72/0.98 % set(auto2) -> assign(max_minutes, 5).
% 0.72/0.98 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 0.72/0.98 % set(auto2) -> set(sort_initial_sos).
% 0.72/0.98 % set(auto2) -> assign(sos_limit, -1).
% 0.72/0.98 % set(auto2) -> assign(lrs_ticks, 3000).
% 0.72/0.98 % set(auto2) -> assign(max_megs, 400).
% 0.72/0.98 % set(auto2) -> assign(stats, some).
% 0.72/0.98 % set(auto2) -> clear(echo_input).
% 0.72/0.98 % set(auto2) -> set(quiet).
% 0.72/0.98 % set(auto2) -> clear(print_initial_clauses).
% 0.72/0.98 % set(auto2) -> clear(print_given).
% 0.72/0.98 assign(lrs_ticks,-1).
% 0.72/0.98 assign(sos_limit,10000).
% 0.72/0.98 assign(order,kbo).
% 0.72/0.98 set(lex_order_vars).
% 0.72/0.98 clear(print_given).
% 0.72/0.98
% 0.72/0.98 % formulas(sos). % not echoed (45 formulas)
% 0.72/0.98
% 0.72/0.98 ============================== end of input ==========================
% 0.72/0.98
% 0.72/0.98 % From the command line: assign(max_seconds, 300).
% 0.72/0.98
% 0.72/0.98 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 0.72/0.99
% 0.72/0.99 % Formulas that are not ordinary clauses:
% 0.72/0.99 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].
% 0.72/0.99 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].
% 0.72/0.99 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].
% 0.72/0.99 4 implies_1 <-> (all X all Y is_a_theorem(implies(X,implies(Y,X)))) # label(implies_1) # label(axiom) # label(non_clause). [assumption].
% 0.72/0.99 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].
% 0.72/0.99 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].
% 0.72/0.99 7 and_1 <-> (all X all Y is_a_theorem(implies(and(X,Y),X))) # label(and_1) # label(axiom) # label(non_clause). [assumption].
% 0.72/0.99 8 and_2 <-> (all X all Y is_a_theorem(implies(and(X,Y),Y))) # label(and_2) # label(axiom) # label(non_clause). [assumption].
% 0.72/0.99 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].
% 0.72/0.99 10 or_1 <-> (all X all Y is_a_theorem(implies(X,or(X,Y)))) # label(or_1) # label(axiom) # label(non_clause). [assumption].
% 0.72/0.99 11 or_2 <-> (all X all Y is_a_theorem(implies(Y,or(X,Y)))) # label(or_2) # label(axiom) # label(non_clause). [assumption].
% 0.72/0.99 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].
% 0.72/0.99 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].
% 0.72/0.99 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].
% 1.75/2.02 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].
% 1.75/2.02 16 kn1 <-> (all P is_a_theorem(implies(P,and(P,P)))) # label(kn1) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.02 17 kn2 <-> (all P all Q is_a_theorem(implies(and(P,Q),P))) # label(kn2) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.02 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].
% 1.75/2.02 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].
% 1.75/2.02 20 cn2 <-> (all P all Q is_a_theorem(implies(P,implies(not(P),Q)))) # label(cn2) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.02 21 cn3 <-> (all P is_a_theorem(implies(implies(not(P),P),P))) # label(cn3) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.02 22 r1 <-> (all P is_a_theorem(implies(or(P,P),P))) # label(r1) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.02 23 r2 <-> (all P all Q is_a_theorem(implies(Q,or(P,Q)))) # label(r2) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.02 24 r3 <-> (all P all Q is_a_theorem(implies(or(P,Q),or(Q,P)))) # label(r3) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.02 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].
% 1.75/2.02 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].
% 1.75/2.02 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].
% 1.75/2.02 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].
% 1.75/2.02 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].
% 1.75/2.02 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].
% 1.75/2.02 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].
% 1.75/2.02
% 1.75/2.02 ============================== end of process non-clausal formulas ===
% 1.75/2.02
% 1.75/2.02 ============================== PROCESS INITIAL CLAUSES ===============
% 1.75/2.02
% 1.75/2.02 ============================== PREDICATE ELIMINATION =================
% 1.75/2.02
% 1.75/2.02 ============================== end predicate elimination =============
% 1.75/2.02
% 1.75/2.02 Auto_denials: (non-Horn, no changes).
% 1.75/2.02
% 1.75/2.02 Term ordering decisions:
% 1.75/2.02
% 1.75/2.02 % Assigning unary symbol not kb_weight 0 and highest precedence (93).
% 1.75/2.02 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.
% 1.75/2.02
% 1.75/2.02 ============================== end of process initial clauses ========
% 1.75/2.02
% 1.75/2.02 ============================== CLAUSES FOR SEARCH ====================
% 1.75/2.02
% 1.75/2.02 ============================== end of clauses for search =============
% 1.75/2.02
% 1.75/2.02 ============================== SEARCH ================================
% 1.75/2.02
% 1.75/2.02 % Starting search at 0.02 seconds.
% 1.75/2.02
% 1.75/2.02 Low Water (keep): wt=28.000, iters=3467
% 1.75/2.02
% 1.75/2.02 Low Water (keep): wt=26.000, iters=3416
% 1.75/2.02
% 1.75/2.02 Low Water (keep): wt=21.000, iters=3390
% 1.75/2.02
% 1.75/2.02 Low Water (keep): wt=20.000, iters=3369
% 1.75/2.02
% 1.75/2.02 Low Water (keep): wt=19.000, iters=3386
% 1.75/2.02
% 1.75/2.02 Low Water (keep): wt=18.000, iters=3367
% 1.75/2.02
% 1.75/2.02 Low Water (keep): wt=17.000, iters=3360
% 1.75/2.02
% 1.75/2.02 Low Water (keep): wt=16.000, iters=3370
% 1.75/2.02
% 1.75/2.02 Low Water (keep): wt=15.000, iters=3350
% 1.75/2.02
% 1.75/2.02 Low Water (keep): wt=14.000, iters=3360
% 1.75/2.02
% 29.36/29.71 NOTE: Back_subsumption disabled, ratio of kept to back_subsumed is 25 (0.00 of 1.02 sec).
% 29.36/29.71
% 29.36/29.71 Low Water (keep): wt=13.000, iters=3673
% 29.36/29.71
% 29.36/29.71 Low Water (displace): id=8079, wt=38.000
% 29.36/29.71
% 29.36/29.71 Low Water (displace): id=8078, wt=35.000
% 29.36/29.71
% 29.36/29.71 Low Water (displace): id=8077, wt=34.000
% 29.36/29.71
% 29.36/29.71 Low Water (displace): id=14160, wt=32.000
% 29.36/29.71
% 29.36/29.71 Low Water (displace): id=14143, wt=30.000
% 29.36/29.71
% 29.36/29.71 Low Water (displace): id=14493, wt=28.000
% 29.36/29.71
% 29.36/29.71 Low Water (displace): id=15459, wt=12.000
% 29.36/29.71
% 29.36/29.71 Low Water (displace): id=16819, wt=11.000
% 29.36/29.71
% 29.36/29.71 Low Water (displace): id=17017, wt=9.000
% 29.36/29.71
% 29.36/29.71 Low Water (keep): wt=12.000, iters=3397
% 29.36/29.71
% 29.36/29.71 Low Water (keep): wt=11.000, iters=3342
% 29.36/29.71
% 29.36/29.71 ============================== PROOF =================================
% 29.36/29.71 % SZS status Theorem
% 29.36/29.71 % SZS output start Refutation
% 29.36/29.71
% 29.36/29.71 % Proof 1 at 27.06 (+ 1.68) seconds.
% 29.36/29.71 % Length of proof is 105.
% 29.36/29.71 % Level of proof is 21.
% 29.36/29.71 % Maximum clause weight is 20.000.
% 29.36/29.71 % Given clauses 3760.
% 29.36/29.71
% 29.36/29.71 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].
% 29.36/29.71 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].
% 29.36/29.71 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].
% 29.36/29.71 22 r1 <-> (all P is_a_theorem(implies(or(P,P),P))) # label(r1) # label(axiom) # label(non_clause). [assumption].
% 29.36/29.71 23 r2 <-> (all P all Q is_a_theorem(implies(Q,or(P,Q)))) # label(r2) # label(axiom) # label(non_clause). [assumption].
% 29.36/29.71 24 r3 <-> (all P all Q is_a_theorem(implies(or(P,Q),or(Q,P)))) # label(r3) # label(axiom) # label(non_clause). [assumption].
% 29.36/29.71 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].
% 29.36/29.71 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].
% 29.36/29.71 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].
% 29.36/29.71 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].
% 29.36/29.71 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].
% 29.36/29.71 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].
% 29.36/29.71 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].
% 29.36/29.71 32 op_implies_or # label(principia_op_implies_or) # label(axiom). [assumption].
% 29.36/29.71 33 op_and # label(principia_op_and) # label(axiom). [assumption].
% 29.36/29.71 34 op_equiv # label(principia_op_equiv) # label(axiom). [assumption].
% 29.36/29.71 35 modus_ponens # label(principia_modus_ponens) # label(axiom). [assumption].
% 29.36/29.71 36 r1 # label(principia_r1) # label(axiom). [assumption].
% 29.36/29.71 37 r2 # label(principia_r2) # label(axiom). [assumption].
% 29.36/29.71 38 r3 # label(principia_r3) # label(axiom). [assumption].
% 29.36/29.71 39 r4 # label(principia_r4) # label(axiom). [assumption].
% 29.36/29.71 40 r5 # label(principia_r5) # label(axiom). [assumption].
% 29.36/29.71 41 substitution_of_equivalents # label(substitution_of_equivalents) # label(axiom). [assumption].
% 29.36/29.71 42 op_or # label(hilbert_op_or) # label(axiom). [assumption].
% 29.36/29.71 43 op_implies_and # label(hilbert_op_implies_and) # label(axiom). [assumption].
% 29.36/29.71 44 -implies_2 # label(hilbert_implies_2) # label(negated_conjecture). [assumption].
% 29.36/29.71 59 -r1 | is_a_theorem(implies(or(A,A),A)) # label(r1) # label(axiom). [clausify(22)].
% 29.36/29.71 60 is_a_theorem(implies(or(A,A),A)). [copy(59),unit_del(a,36)].
% 29.36/29.71 62 -r2 | is_a_theorem(implies(A,or(B,A))) # label(r2) # label(axiom). [clausify(23)].
% 29.36/29.71 63 is_a_theorem(implies(A,or(B,A))). [copy(62),unit_del(a,37)].
% 29.36/29.71 65 -substitution_of_equivalents | -is_a_theorem(equiv(A,B)) | B = A # label(substitution_of_equivalents) # label(axiom). [clausify(2)].
% 29.36/29.71 66 -is_a_theorem(equiv(A,B)) | B = A. [copy(65),unit_del(a,41)].
% 29.36/29.71 71 -modus_ponens | -is_a_theorem(A) | -is_a_theorem(implies(A,B)) | is_a_theorem(B) # label(modus_ponens) # label(axiom). [clausify(1)].
% 29.36/29.71 72 -is_a_theorem(A) | -is_a_theorem(implies(A,B)) | is_a_theorem(B). [copy(71),unit_del(a,35)].
% 29.36/29.71 79 -r3 | is_a_theorem(implies(or(A,B),or(B,A))) # label(r3) # label(axiom). [clausify(24)].
% 29.36/29.71 80 is_a_theorem(implies(or(A,B),or(B,A))). [copy(79),unit_del(a,38)].
% 29.36/29.71 82 -op_implies_or | or(not(A),B) = implies(A,B) # label(op_implies_or) # label(axiom). [clausify(30)].
% 29.36/29.71 83 or(not(A),B) = implies(A,B). [copy(82),unit_del(a,32)].
% 29.36/29.71 84 -op_implies_and | not(and(A,not(B))) = implies(A,B) # label(op_implies_and) # label(axiom). [clausify(29)].
% 29.36/29.71 85 not(and(A,not(B))) = implies(A,B). [copy(84),unit_del(a,43)].
% 29.36/29.71 88 implies_2 | -is_a_theorem(implies(implies(c9,implies(c9,c10)),implies(c9,c10))) # label(implies_2) # label(axiom). [clausify(5)].
% 29.36/29.71 89 -is_a_theorem(implies(implies(c9,implies(c9,c10)),implies(c9,c10))). [copy(88),unit_del(a,44)].
% 29.36/29.71 90 -op_or | or(A,B) = not(and(not(A),not(B))) # label(op_or) # label(axiom). [clausify(27)].
% 29.36/29.71 91 or(A,B) = implies(not(A),B). [copy(90),rewrite([85(6)]),unit_del(a,42)].
% 29.36/29.71 92 -op_and | and(A,B) = not(or(not(A),not(B))) # label(op_and) # label(axiom). [clausify(28)].
% 29.36/29.71 93 not(implies(not(not(A)),not(B))) = and(A,B). [copy(92),rewrite([91(5)]),flip(b),unit_del(a,33)].
% 29.36/29.71 94 -op_equiv | and(implies(A,B),implies(B,A)) = equiv(A,B) # label(op_equiv) # label(axiom). [clausify(31)].
% 29.36/29.71 95 and(implies(A,B),implies(B,A)) = equiv(A,B). [copy(94),unit_del(a,34)].
% 29.36/29.71 102 -r4 | is_a_theorem(implies(or(A,or(B,C)),or(B,or(A,C)))) # label(r4) # label(axiom). [clausify(25)].
% 29.36/29.71 103 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)].
% 29.36/29.71 105 -r5 | is_a_theorem(implies(implies(A,B),implies(or(C,A),or(C,B)))) # label(r5) # label(axiom). [clausify(26)].
% 29.36/29.71 106 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)].
% 29.36/29.71 115 implies(not(not(A)),B) = implies(A,B). [back_rewrite(83),rewrite([91(2)])].
% 29.36/29.71 116 is_a_theorem(implies(implies(not(A),B),implies(not(B),A))). [back_rewrite(80),rewrite([91(1),91(3)])].
% 29.36/29.71 117 is_a_theorem(implies(A,implies(not(B),A))). [back_rewrite(63),rewrite([91(1)])].
% 29.36/29.71 118 is_a_theorem(implies(implies(not(A),A),A)). [back_rewrite(60),rewrite([91(1)])].
% 29.36/29.71 121 not(implies(A,not(B))) = and(A,B). [back_rewrite(93),rewrite([115(4)])].
% 29.36/29.71 125 -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)].
% 29.36/29.71 129 -is_a_theorem(implies(A,B)) | is_a_theorem(implies(implies(not(C),A),implies(not(C),B))). [resolve(106,a,72,b)].
% 29.36/29.71 133 implies(not(implies(A,B)),C) = implies(and(A,not(B)),C). [para(85(a,1),115(a,1,1,1))].
% 29.36/29.71 135 and(implies(A,not(not(B))),implies(B,A)) = equiv(A,not(not(B))). [para(115(a,1),95(a,1,2))].
% 29.36/29.71 139 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)])].
% 29.36/29.71 140 -is_a_theorem(implies(not(A),B)) | is_a_theorem(implies(not(B),A)). [resolve(116,a,72,b)].
% 29.36/29.71 141 -is_a_theorem(implies(implies(implies(not(A),B),implies(not(B),A)),implies(implies(c9,implies(c9,c10)),implies(c9,c10)))). [ur(72,a,116,a,c,89,a)].
% 29.36/29.71 144 is_a_theorem(implies(implies(A,B),implies(not(B),not(A)))). [para(115(a,1),116(a,1,1))].
% 29.36/29.71 150 is_a_theorem(implies(A,implies(B,A))). [para(115(a,1),117(a,1,2))].
% 29.36/29.71 153 -is_a_theorem(implies(not(A),A)) | is_a_theorem(A). [resolve(118,a,72,b)].
% 29.36/29.71 157 is_a_theorem(implies(implies(A,not(A)),not(A))). [para(115(a,1),118(a,1,1))].
% 29.36/29.71 161 and(not(not(A)),B) = and(A,B). [para(115(a,1),121(a,1,1)),rewrite([121(3)]),flip(a)].
% 29.36/29.71 202 is_a_theorem(implies(A,implies(B,not(not(A))))). [para(115(a,1),150(a,1))].
% 29.36/29.71 206 is_a_theorem(implies(not(A),implies(not(B),not(B)))). [resolve(125,a,150,a)].
% 29.36/29.71 247 -is_a_theorem(A) | is_a_theorem(implies(B,not(not(A)))). [resolve(202,a,72,b)].
% 29.36/29.71 345 is_a_theorem(implies(implies(not(A),implies(not(B),B)),implies(not(A),B))). [resolve(129,a,118,a)].
% 29.36/29.71 390 is_a_theorem(implies(not(A),not(A))). [resolve(206,a,153,a)].
% 29.36/29.71 431 is_a_theorem(implies(A,not(not(A)))). [para(115(a,1),390(a,1))].
% 29.36/29.71 433 is_a_theorem(implies(A,implies(B,B))). [resolve(431,a,247,a),rewrite([121(4),85(3)])].
% 29.36/29.71 459 is_a_theorem(implies(A,A)). [resolve(433,a,153,a)].
% 29.36/29.71 747 implies(and(A,not(not(B))),C) = implies(and(A,B),C). [para(121(a,1),133(a,1,1)),flip(a)].
% 29.36/29.71 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)].
% 29.36/29.71 1302 -is_a_theorem(equiv(A,B)) | not(not(B)) = A. [para(1000(a,1),66(a,1))].
% 29.36/29.71 1322 is_a_theorem(implies(and(A,B),B)). [resolve(140,a,202,a),rewrite([121(5),747(4)])].
% 29.36/29.71 1324 -is_a_theorem(implies(A,B)) | is_a_theorem(implies(not(B),not(A))). [para(115(a,1),140(a,1))].
% 29.36/29.71 1465 is_a_theorem(implies(implies(not(A),and(B,C)),implies(not(A),C))). [resolve(1322,a,129,a)].
% 29.36/29.71 1587 -is_a_theorem(implies(A,B)) | is_a_theorem(implies(implies(C,A),implies(C,B))). [resolve(139,a,72,b)].
% 29.36/29.71 1935 -is_a_theorem(implies(implies(implies(A,B),implies(not(B),not(A))),implies(implies(c9,implies(c9,c10)),implies(c9,c10)))). [para(115(a,1),141(a,1,1,1))].
% 29.36/29.71 2872 is_a_theorem(implies(implies(A,not(B)),implies(B,not(A)))). [para(115(a,1),144(a,1,2))].
% 29.36/29.71 6630 is_a_theorem(implies(A,and(A,A))). [resolve(1324,a,157,a),rewrite([121(5),115(4)])].
% 29.36/29.71 6647 -is_a_theorem(A) | is_a_theorem(and(A,A)). [resolve(6630,a,72,b)].
% 29.36/29.71 6782 is_a_theorem(equiv(A,A)). [resolve(6647,a,459,a),rewrite([95(3)])].
% 29.36/29.71 6971 not(not(A)) = A. [resolve(6782,a,1302,a)].
% 29.36/29.71 7043 not(and(A,B)) = implies(A,not(B)). [para(6971(a,1),85(a,1,1,2))].
% 29.36/29.71 7044 not(implies(A,B)) = and(A,not(B)). [para(85(a,1),6971(a,1,1))].
% 29.36/29.71 8929 is_a_theorem(implies(and(A,B),and(B,A))). [resolve(2872,a,1324,a),rewrite([7044(3),6971(2),7044(4),6971(3)])].
% 29.36/29.71 8931 -is_a_theorem(implies(A,not(B))) | is_a_theorem(implies(B,not(A))). [resolve(2872,a,72,b)].
% 29.36/29.71 14511 is_a_theorem(implies(implies(A,and(B,C)),implies(A,C))). [para(6971(a,1),1465(a,1,1,1)),rewrite([6971(4)])].
% 29.36/29.71 14522 -is_a_theorem(implies(A,and(B,C))) | is_a_theorem(implies(A,C)). [resolve(14511,a,72,b)].
% 29.36/29.71 14552 is_a_theorem(implies(and(A,B),A)). [resolve(14522,a,8929,a)].
% 29.36/29.71 14639 is_a_theorem(implies(A,implies(not(A),not(B)))). [resolve(14552,a,8931,a),rewrite([7043(3)])].
% 29.36/29.71 15274 is_a_theorem(implies(A,implies(not(A),B))). [para(6971(a,1),14639(a,1,2,2))].
% 29.36/29.71 15333 is_a_theorem(implies(not(A),implies(A,B))). [para(6971(a,1),15274(a,1,2,1))].
% 29.36/29.71 18460 is_a_theorem(implies(implies(A,implies(not(B),B)),implies(A,B))). [para(6971(a,1),345(a,1,1,1)),rewrite([6971(5)])].
% 29.36/29.71 19654 -is_a_theorem(implies(A,implies(not(B),B))) | is_a_theorem(implies(A,B)). [resolve(18460,a,72,b)].
% 29.36/29.71 29508 is_a_theorem(implies(implies(A,not(B)),implies(A,implies(B,C)))). [resolve(1587,a,15333,a)].
% 29.36/29.71 34947 is_a_theorem(implies(implies(and(A,not(B)),not(A)),implies(A,B))). [resolve(29508,a,19654,a),rewrite([7044(2)])].
% 29.36/29.71 112399 $F. [ur(1587,b,1935,a),rewrite([7044(4)]),unit_del(a,34947)].
% 29.36/29.71
% 29.36/29.71 % SZS output end Refutation
% 29.36/29.71 ============================== end of proof ==========================
% 29.36/29.71
% 29.36/29.71 ============================== STATISTICS ============================
% 29.36/29.71
% 29.36/29.71 Given=3760. Generated=3480095. Kept=112347. proofs=1.
% 29.36/29.71 Usable=3592. Sos=9999. Demods=6. Limbo=0, Disabled=98830. Hints=0.
% 29.36/29.71 Megabytes=74.55.
% 29.36/29.71 User_CPU=27.06, System_CPU=1.68, Wall_clock=28.
% 29.36/29.71
% 29.36/29.71 ============================== end of statistics =====================
% 29.36/29.71
% 29.36/29.71 ============================== end of search =========================
% 29.36/29.71
% 29.36/29.71 THEOREM PROVED
% 29.36/29.71 % SZS status Theorem
% 29.36/29.71
% 29.36/29.71 Exiting with 1 proof.
% 29.36/29.71
% 29.36/29.71 Process 26241 exit (max_proofs) Sat Jul 2 15:55:36 2022
% 29.36/29.71 Prover9 interrupted
%------------------------------------------------------------------------------