TSTP Solution File: LCL519+1 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : LCL519+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n004.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 13:47:20 EDT 2022
% Result : Theorem 1.95s 2.23s
% Output : Refutation 1.95s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : LCL519+1 : TPTP v8.1.0. Released v3.3.0.
% 0.07/0.13 % Command : tptp2X_and_run_prover9 %d %s
% 0.13/0.33 % Computer : n004.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
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 600
% 0.13/0.34 % DateTime : Sun Jul 3 23:37:23 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.44/1.00 ============================== Prover9 ===============================
% 0.44/1.00 Prover9 (32) version 2009-11A, November 2009.
% 0.44/1.00 Process 24894 was started by sandbox on n004.cluster.edu,
% 0.44/1.00 Sun Jul 3 23:37:23 2022
% 0.44/1.00 The command was "/export/starexec/sandbox/solver/bin/prover9 -t 300 -f /tmp/Prover9_24741_n004.cluster.edu".
% 0.44/1.00 ============================== end of head ===========================
% 0.44/1.00
% 0.44/1.00 ============================== INPUT =================================
% 0.44/1.00
% 0.44/1.00 % Reading from file /tmp/Prover9_24741_n004.cluster.edu
% 0.44/1.00
% 0.44/1.00 set(prolog_style_variables).
% 0.44/1.00 set(auto2).
% 0.44/1.00 % set(auto2) -> set(auto).
% 0.44/1.00 % set(auto) -> set(auto_inference).
% 0.44/1.00 % set(auto) -> set(auto_setup).
% 0.44/1.00 % set(auto_setup) -> set(predicate_elim).
% 0.44/1.00 % set(auto_setup) -> assign(eq_defs, unfold).
% 0.44/1.00 % set(auto) -> set(auto_limits).
% 0.44/1.00 % set(auto_limits) -> assign(max_weight, "100.000").
% 0.44/1.00 % set(auto_limits) -> assign(sos_limit, 20000).
% 0.44/1.00 % set(auto) -> set(auto_denials).
% 0.44/1.00 % set(auto) -> set(auto_process).
% 0.44/1.00 % set(auto2) -> assign(new_constants, 1).
% 0.44/1.00 % set(auto2) -> assign(fold_denial_max, 3).
% 0.44/1.00 % set(auto2) -> assign(max_weight, "200.000").
% 0.44/1.00 % set(auto2) -> assign(max_hours, 1).
% 0.44/1.00 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 0.44/1.00 % set(auto2) -> assign(max_seconds, 0).
% 0.44/1.00 % set(auto2) -> assign(max_minutes, 5).
% 0.44/1.00 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 0.44/1.00 % set(auto2) -> set(sort_initial_sos).
% 0.44/1.00 % set(auto2) -> assign(sos_limit, -1).
% 0.44/1.00 % set(auto2) -> assign(lrs_ticks, 3000).
% 0.44/1.00 % set(auto2) -> assign(max_megs, 400).
% 0.44/1.00 % set(auto2) -> assign(stats, some).
% 0.44/1.00 % set(auto2) -> clear(echo_input).
% 0.44/1.00 % set(auto2) -> set(quiet).
% 0.44/1.00 % set(auto2) -> clear(print_initial_clauses).
% 0.44/1.00 % set(auto2) -> clear(print_given).
% 0.44/1.00 assign(lrs_ticks,-1).
% 0.44/1.00 assign(sos_limit,10000).
% 0.44/1.00 assign(order,kbo).
% 0.44/1.00 set(lex_order_vars).
% 0.44/1.00 clear(print_given).
% 0.44/1.00
% 0.44/1.00 % formulas(sos). % not echoed (43 formulas)
% 0.44/1.00
% 0.44/1.00 ============================== end of input ==========================
% 0.44/1.00
% 0.44/1.00 % From the command line: assign(max_seconds, 300).
% 0.44/1.00
% 0.44/1.00 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 0.44/1.00
% 0.44/1.00 % Formulas that are not ordinary clauses:
% 0.44/1.00 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].
% 0.44/1.00 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].
% 0.44/1.00 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].
% 0.44/1.00 4 implies_1 <-> (all X all Y is_a_theorem(implies(X,implies(Y,X)))) # label(implies_1) # label(axiom) # label(non_clause). [assumption].
% 0.44/1.00 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].
% 0.44/1.00 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].
% 0.44/1.00 7 and_1 <-> (all X all Y is_a_theorem(implies(and(X,Y),X))) # label(and_1) # label(axiom) # label(non_clause). [assumption].
% 0.44/1.00 8 and_2 <-> (all X all Y is_a_theorem(implies(and(X,Y),Y))) # label(and_2) # label(axiom) # label(non_clause). [assumption].
% 0.44/1.00 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].
% 0.44/1.00 10 or_1 <-> (all X all Y is_a_theorem(implies(X,or(X,Y)))) # label(or_1) # label(axiom) # label(non_clause). [assumption].
% 0.44/1.00 11 or_2 <-> (all X all Y is_a_theorem(implies(Y,or(X,Y)))) # label(or_2) # label(axiom) # label(non_clause). [assumption].
% 0.44/1.00 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].
% 0.44/1.00 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].
% 0.44/1.00 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].
% 1.87/2.14 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].
% 1.87/2.14 16 kn1 <-> (all P is_a_theorem(implies(P,and(P,P)))) # label(kn1) # label(axiom) # label(non_clause). [assumption].
% 1.87/2.14 17 kn2 <-> (all P all Q is_a_theorem(implies(and(P,Q),P))) # label(kn2) # label(axiom) # label(non_clause). [assumption].
% 1.87/2.14 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].
% 1.87/2.14 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].
% 1.87/2.14 20 cn2 <-> (all P all Q is_a_theorem(implies(P,implies(not(P),Q)))) # label(cn2) # label(axiom) # label(non_clause). [assumption].
% 1.87/2.14 21 cn3 <-> (all P is_a_theorem(implies(implies(not(P),P),P))) # label(cn3) # label(axiom) # label(non_clause). [assumption].
% 1.87/2.14 22 r1 <-> (all P is_a_theorem(implies(or(P,P),P))) # label(r1) # label(axiom) # label(non_clause). [assumption].
% 1.87/2.14 23 r2 <-> (all P all Q is_a_theorem(implies(Q,or(P,Q)))) # label(r2) # label(axiom) # label(non_clause). [assumption].
% 1.87/2.14 24 r3 <-> (all P all Q is_a_theorem(implies(or(P,Q),or(Q,P)))) # label(r3) # label(axiom) # label(non_clause). [assumption].
% 1.87/2.14 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].
% 1.87/2.14 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].
% 1.87/2.14 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].
% 1.87/2.14 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].
% 1.87/2.14 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].
% 1.87/2.14 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].
% 1.87/2.14 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].
% 1.87/2.14
% 1.87/2.14 ============================== end of process non-clausal formulas ===
% 1.87/2.14
% 1.87/2.14 ============================== PROCESS INITIAL CLAUSES ===============
% 1.87/2.14
% 1.87/2.14 ============================== PREDICATE ELIMINATION =================
% 1.87/2.14
% 1.87/2.14 ============================== end predicate elimination =============
% 1.87/2.14
% 1.87/2.14 Auto_denials: (non-Horn, no changes).
% 1.87/2.14
% 1.87/2.14 Term ordering decisions:
% 1.87/2.14
% 1.87/2.14 % Assigning unary symbol not kb_weight 0 and highest precedence (93).
% 1.87/2.14 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.
% 1.87/2.14
% 1.87/2.14 ============================== end of process initial clauses ========
% 1.87/2.14
% 1.87/2.14 ============================== CLAUSES FOR SEARCH ====================
% 1.87/2.14
% 1.87/2.14 ============================== end of clauses for search =============
% 1.87/2.14
% 1.87/2.14 ============================== SEARCH ================================
% 1.87/2.14
% 1.87/2.14 % Starting search at 0.02 seconds.
% 1.87/2.14
% 1.87/2.14 Low Water (keep): wt=31.000, iters=3409
% 1.87/2.14
% 1.87/2.14 Low Water (keep): wt=29.000, iters=3378
% 1.87/2.14
% 1.87/2.14 Low Water (keep): wt=26.000, iters=3485
% 1.87/2.14
% 1.87/2.14 Low Water (keep): wt=25.000, iters=3378
% 1.87/2.14
% 1.87/2.14 Low Water (keep): wt=24.000, iters=3386
% 1.87/2.14
% 1.87/2.14 Low Water (keep): wt=23.000, iters=3403
% 1.87/2.14
% 1.87/2.14 Low Water (keep): wt=22.000, iters=3438
% 1.87/2.14
% 1.87/2.14 Low Water (keep): wt=21.000, iters=3434
% 1.87/2.14
% 1.87/2.14 Low Water (keep): wt=20.000, iters=3351
% 1.87/2.14
% 1.87/2.14 Low Water (keep): wt=19.000, iters=3357
% 1.87/2.14
% 1.95/2.23 Low Water (keep): wt=18.000, iters=3333
% 1.95/2.23
% 1.95/2.23 Low Water (keep): wt=17.000, iters=3346
% 1.95/2.23
% 1.95/2.23 Low Water (keep): wt=16.000, iters=3350
% 1.95/2.23
% 1.95/2.23 Low Water (keep): wt=15.000, iters=3352
% 1.95/2.23
% 1.95/2.23 ============================== PROOF =================================
% 1.95/2.23 % SZS status Theorem
% 1.95/2.23 % SZS output start Refutation
% 1.95/2.23
% 1.95/2.23 % Proof 1 at 1.21 (+ 0.03) seconds.
% 1.95/2.23 % Length of proof is 91.
% 1.95/2.23 % Level of proof is 19.
% 1.95/2.23 % Maximum clause weight is 15.000.
% 1.95/2.23 % Given clauses 518.
% 1.95/2.23
% 1.95/2.23 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].
% 1.95/2.23 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].
% 1.95/2.23 11 or_2 <-> (all X all Y is_a_theorem(implies(Y,or(X,Y)))) # label(or_2) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.23 16 kn1 <-> (all P is_a_theorem(implies(P,and(P,P)))) # label(kn1) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.23 17 kn2 <-> (all P all Q is_a_theorem(implies(and(P,Q),P))) # label(kn2) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.23 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].
% 1.95/2.23 23 r2 <-> (all P all Q is_a_theorem(implies(Q,or(P,Q)))) # label(r2) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.23 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].
% 1.95/2.23 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].
% 1.95/2.23 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].
% 1.95/2.23 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].
% 1.95/2.23 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].
% 1.95/2.23 32 op_or # label(rosser_op_or) # label(axiom). [assumption].
% 1.95/2.23 33 op_implies_and # label(rosser_op_implies_and) # label(axiom). [assumption].
% 1.95/2.23 34 op_equiv # label(rosser_op_equiv) # label(axiom). [assumption].
% 1.95/2.23 35 modus_ponens # label(rosser_modus_ponens) # label(axiom). [assumption].
% 1.95/2.23 36 kn1 # label(rosser_kn1) # label(axiom). [assumption].
% 1.95/2.23 37 kn2 # label(rosser_kn2) # label(axiom). [assumption].
% 1.95/2.23 38 kn3 # label(rosser_kn3) # label(axiom). [assumption].
% 1.95/2.23 39 substitution_of_equivalents # label(substitution_of_equivalents) # label(axiom). [assumption].
% 1.95/2.23 40 op_implies_or # label(principia_op_implies_or) # label(axiom). [assumption].
% 1.95/2.23 41 op_and # label(principia_op_and) # label(axiom). [assumption].
% 1.95/2.23 42 -r2 # label(principia_r2) # label(negated_conjecture). [assumption].
% 1.95/2.23 51 -or_2 | is_a_theorem(implies(A,or(B,A))) # label(or_2) # label(axiom). [clausify(11)].
% 1.95/2.23 52 or_2 | -is_a_theorem(implies(c23,or(c22,c23))) # label(or_2) # label(axiom). [clausify(11)].
% 1.95/2.23 53 -kn1 | is_a_theorem(implies(A,and(A,A))) # label(kn1) # label(axiom). [clausify(16)].
% 1.95/2.23 54 is_a_theorem(implies(A,and(A,A))). [copy(53),unit_del(a,36)].
% 1.95/2.23 56 -kn2 | is_a_theorem(implies(and(A,B),A)) # label(kn2) # label(axiom). [clausify(17)].
% 1.95/2.23 57 is_a_theorem(implies(and(A,B),A)). [copy(56),unit_del(a,37)].
% 1.95/2.23 61 r2 | -is_a_theorem(implies(c47,or(c46,c47))) # label(r2) # label(axiom). [clausify(23)].
% 1.95/2.23 62 -is_a_theorem(implies(c47,or(c46,c47))). [copy(61),unit_del(a,42)].
% 1.95/2.23 63 -substitution_of_equivalents | -is_a_theorem(equiv(A,B)) | B = A # label(substitution_of_equivalents) # label(axiom). [clausify(2)].
% 1.95/2.23 64 -is_a_theorem(equiv(A,B)) | B = A. [copy(63),unit_del(a,39)].
% 1.95/2.23 69 -modus_ponens | -is_a_theorem(A) | -is_a_theorem(implies(A,B)) | is_a_theorem(B) # label(modus_ponens) # label(axiom). [clausify(1)].
% 1.95/2.23 70 -is_a_theorem(A) | -is_a_theorem(implies(A,B)) | is_a_theorem(B). [copy(69),unit_del(a,35)].
% 1.95/2.23 79 -op_implies_or | or(not(A),B) = implies(A,B) # label(op_implies_or) # label(axiom). [clausify(30)].
% 1.95/2.23 80 or(not(A),B) = implies(A,B). [copy(79),unit_del(a,40)].
% 1.95/2.23 81 -op_implies_and | not(and(A,not(B))) = implies(A,B) # label(op_implies_and) # label(axiom). [clausify(29)].
% 1.95/2.23 82 not(and(A,not(B))) = implies(A,B). [copy(81),unit_del(a,33)].
% 1.95/2.23 87 -op_or | or(A,B) = not(and(not(A),not(B))) # label(op_or) # label(axiom). [clausify(27)].
% 1.95/2.23 88 or(A,B) = implies(not(A),B). [copy(87),rewrite([82(6)]),unit_del(a,32)].
% 1.95/2.23 89 -op_and | and(A,B) = not(or(not(A),not(B))) # label(op_and) # label(axiom). [clausify(28)].
% 1.95/2.23 90 not(implies(not(not(A)),not(B))) = and(A,B). [copy(89),rewrite([88(5)]),flip(b),unit_del(a,41)].
% 1.95/2.23 91 -op_equiv | and(implies(A,B),implies(B,A)) = equiv(A,B) # label(op_equiv) # label(axiom). [clausify(31)].
% 1.95/2.23 92 and(implies(A,B),implies(B,A)) = equiv(A,B). [copy(91),unit_del(a,34)].
% 1.95/2.23 111 -kn3 | is_a_theorem(implies(implies(A,B),implies(not(and(B,C)),not(and(C,A))))) # label(kn3) # label(axiom). [clausify(18)].
% 1.95/2.23 112 is_a_theorem(implies(implies(A,B),implies(not(and(B,C)),not(and(C,A))))). [copy(111),unit_del(a,38)].
% 1.95/2.23 115 implies(not(not(A)),B) = implies(A,B). [back_rewrite(80),rewrite([88(2)])].
% 1.95/2.23 118 -is_a_theorem(implies(c47,implies(not(c46),c47))). [back_rewrite(62),rewrite([88(4)])].
% 1.95/2.23 121 or_2 | -is_a_theorem(implies(c23,implies(not(c22),c23))). [back_rewrite(52),rewrite([88(5)])].
% 1.95/2.23 122 -or_2 | is_a_theorem(implies(A,implies(not(B),A))). [back_rewrite(51),rewrite([88(2)])].
% 1.95/2.23 125 not(implies(A,not(B))) = and(A,B). [back_rewrite(90),rewrite([115(4)])].
% 1.95/2.23 126 -is_a_theorem(and(A,B)) | is_a_theorem(A). [resolve(70,b,57,a)].
% 1.95/2.23 127 -is_a_theorem(A) | is_a_theorem(and(A,A)). [resolve(70,b,54,a)].
% 1.95/2.23 129 is_a_theorem(implies(implies(A,A),equiv(A,A))). [para(92(a,1),54(a,1,2))].
% 1.95/2.23 132 -is_a_theorem(implies(A,B)) | is_a_theorem(implies(not(and(B,C)),not(and(C,A)))). [resolve(112,a,70,b)].
% 1.95/2.23 134 is_a_theorem(implies(implies(not(A),B),implies(not(and(B,C)),implies(C,A)))). [para(82(a,1),112(a,1,2,2))].
% 1.95/2.23 137 is_a_theorem(implies(A,and(not(not(A)),not(not(A))))). [para(115(a,1),54(a,1))].
% 1.95/2.23 138 -is_a_theorem(not(not(A))) | -is_a_theorem(implies(A,B)) | is_a_theorem(B). [para(115(a,1),70(b,1))].
% 1.95/2.23 139 implies(not(implies(A,B)),C) = implies(and(A,not(B)),C). [para(82(a,1),115(a,1,1,1))].
% 1.95/2.23 141 and(implies(A,not(not(B))),implies(B,A)) = equiv(A,not(not(B))). [para(115(a,1),92(a,1,2))].
% 1.95/2.23 149 -or_2. [ur(122,b,118,a)].
% 1.95/2.23 150 -is_a_theorem(implies(c23,implies(not(c22),c23))). [back_unit_del(121),unit_del(a,149)].
% 1.95/2.23 153 implies(not(and(A,B)),C) = implies(implies(A,not(B)),C). [para(125(a,1),115(a,1,1,1))].
% 1.95/2.23 154 and(not(not(A)),B) = and(A,B). [para(115(a,1),125(a,1,1)),rewrite([125(3)]),flip(a)].
% 1.95/2.23 158 is_a_theorem(implies(implies(not(A),B),implies(implies(B,not(C)),implies(C,A)))). [back_rewrite(134),rewrite([153(6)])].
% 1.95/2.23 159 -is_a_theorem(implies(A,B)) | is_a_theorem(implies(implies(B,not(C)),not(and(C,A)))). [back_rewrite(132),rewrite([153(7)])].
% 1.95/2.23 161 is_a_theorem(implies(A,and(A,not(not(A))))). [back_rewrite(137),rewrite([154(5)])].
% 1.95/2.23 167 -is_a_theorem(implies(implies(and(A,B),A),implies(c23,implies(not(c22),c23)))). [ur(70,a,57,a,c,150,a)].
% 1.95/2.23 169 is_a_theorem(and(implies(and(A,B),A),implies(and(A,B),A))). [resolve(127,a,57,a)].
% 1.95/2.23 172 -is_a_theorem(implies(A,A)) | is_a_theorem(equiv(A,A)). [resolve(129,a,70,b)].
% 1.95/2.23 217 is_a_theorem(implies(A,and(A,not(not(not(not(A))))))). [para(115(a,1),161(a,1)),rewrite([154(7)])].
% 1.95/2.23 274 -is_a_theorem(and(A,B)) | is_a_theorem(not(not(A))). [para(154(a,1),126(a,1))].
% 1.95/2.23 536 is_a_theorem(implies(A,and(A,not(not(not(not(not(not(A))))))))). [para(115(a,1),217(a,1)),rewrite([154(9)])].
% 1.95/2.23 593 implies(and(A,not(not(B))),C) = implies(and(A,B),C). [para(125(a,1),139(a,1,1)),flip(a)].
% 1.95/2.23 819 equiv(A,not(not(B))) = equiv(A,B). [para(141(a,1),154(a,2)),rewrite([125(4),82(3),92(3)]),flip(a)].
% 1.95/2.23 897 -is_a_theorem(equiv(A,B)) | not(not(B)) = A. [para(819(a,1),64(a,1))].
% 1.95/2.23 1162 is_a_theorem(not(not(implies(and(A,B),A)))). [resolve(169,a,274,a)].
% 1.95/2.23 1204 is_a_theorem(not(and(and(not(A),B),A))). [para(125(a,1),1162(a,1,1))].
% 1.95/2.23 2266 is_a_theorem(implies(implies(and(A,A),not(B)),not(and(B,A)))). [resolve(159,a,536,a),rewrite([593(9),593(7),593(5)])].
% 1.95/2.23 2587 -is_a_theorem(implies(and(not(c22),not(c23)),and(not(c23),A))). [ur(70,b,158,a,c,167,a),rewrite([139(9)])].
% 1.95/2.23 3252 -is_a_theorem(not(and(and(A,A),B))) | is_a_theorem(not(and(B,A))). [resolve(2266,a,138,b),rewrite([125(4)])].
% 1.95/2.23 8327 is_a_theorem(implies(A,A)). [resolve(3252,a,1204,a),rewrite([82(3)])].
% 1.95/2.23 8341 is_a_theorem(equiv(A,A)). [back_unit_del(172),unit_del(a,8327)].
% 1.95/2.23 8348 is_a_theorem(implies(implies(A,not(B)),not(and(B,A)))). [resolve(8327,a,159,a)].
% 1.95/2.23 8603 not(not(A)) = A. [resolve(8341,a,897,a)].
% 1.95/2.23 8915 not(and(A,B)) = implies(A,not(B)). [para(8603(a,1),82(a,1,1,2))].
% 1.95/2.23 8926 is_a_theorem(implies(implies(A,not(B)),implies(B,not(A)))). [back_rewrite(8348),rewrite([8915(4)])].
% 1.95/2.23 11754 is_a_theorem(implies(implies(not(A),not(B)),implies(B,A))). [para(8603(a,1),8926(a,1,2,2))].
% 1.95/2.23 14092 -is_a_theorem(implies(implies(not(c23),not(A)),implies(not(c22),c23))). [ur(70,b,11754,a,c,2587,a),rewrite([8915(4),8915(10),8603(9)])].
% 1.95/2.23 14093 $F. [resolve(14092,a,11754,a)].
% 1.95/2.23
% 1.95/2.23 % SZS output end Refutation
% 1.95/2.23 ============================== end of proof ==========================
% 1.95/2.23
% 1.95/2.23 ============================== STATISTICS ============================
% 1.95/2.23
% 1.95/2.23 Given=518. Generated=36319. Kept=14041. proofs=1.
% 1.95/2.23 Usable=255. Sos=6213. Demods=18. Limbo=11, Disabled=7633. Hints=0.
% 1.95/2.23 Megabytes=10.38.
% 1.95/2.23 User_CPU=1.21, System_CPU=0.03, Wall_clock=1.
% 1.95/2.23
% 1.95/2.23 ============================== end of statistics =====================
% 1.95/2.23
% 1.95/2.23 ============================== end of search =========================
% 1.95/2.23
% 1.95/2.23 THEOREM PROVED
% 1.95/2.23 % SZS status Theorem
% 1.95/2.23
% 1.95/2.23 Exiting with 1 proof.
% 1.95/2.23
% 1.95/2.23 Process 24894 exit (max_proofs) Sun Jul 3 23:37:24 2022
% 1.95/2.23 Prover9 interrupted
%------------------------------------------------------------------------------