TSTP Solution File: LCL518+1 by Prover9---1109a
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : LCL518+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n023.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 1.47s 1.77s
% Output : Refutation 1.47s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : LCL518+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 : n023.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 : Sun Jul 3 04:59:43 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.44/1.01 ============================== Prover9 ===============================
% 0.44/1.01 Prover9 (32) version 2009-11A, November 2009.
% 0.44/1.01 Process 8882 was started by sandbox on n023.cluster.edu,
% 0.44/1.01 Sun Jul 3 04:59:44 2022
% 0.44/1.01 The command was "/export/starexec/sandbox/solver/bin/prover9 -t 300 -f /tmp/Prover9_8729_n023.cluster.edu".
% 0.44/1.01 ============================== end of head ===========================
% 0.44/1.01
% 0.44/1.01 ============================== INPUT =================================
% 0.44/1.01
% 0.44/1.01 % Reading from file /tmp/Prover9_8729_n023.cluster.edu
% 0.44/1.01
% 0.44/1.01 set(prolog_style_variables).
% 0.44/1.01 set(auto2).
% 0.44/1.01 % set(auto2) -> set(auto).
% 0.44/1.01 % set(auto) -> set(auto_inference).
% 0.44/1.01 % set(auto) -> set(auto_setup).
% 0.44/1.01 % set(auto_setup) -> set(predicate_elim).
% 0.44/1.01 % set(auto_setup) -> assign(eq_defs, unfold).
% 0.44/1.01 % set(auto) -> set(auto_limits).
% 0.44/1.01 % set(auto_limits) -> assign(max_weight, "100.000").
% 0.44/1.01 % set(auto_limits) -> assign(sos_limit, 20000).
% 0.44/1.01 % set(auto) -> set(auto_denials).
% 0.44/1.01 % set(auto) -> set(auto_process).
% 0.44/1.01 % set(auto2) -> assign(new_constants, 1).
% 0.44/1.01 % set(auto2) -> assign(fold_denial_max, 3).
% 0.44/1.01 % set(auto2) -> assign(max_weight, "200.000").
% 0.44/1.01 % set(auto2) -> assign(max_hours, 1).
% 0.44/1.01 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 0.44/1.01 % set(auto2) -> assign(max_seconds, 0).
% 0.44/1.01 % set(auto2) -> assign(max_minutes, 5).
% 0.44/1.01 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 0.44/1.01 % set(auto2) -> set(sort_initial_sos).
% 0.44/1.01 % set(auto2) -> assign(sos_limit, -1).
% 0.44/1.01 % set(auto2) -> assign(lrs_ticks, 3000).
% 0.44/1.01 % set(auto2) -> assign(max_megs, 400).
% 0.44/1.01 % set(auto2) -> assign(stats, some).
% 0.44/1.01 % set(auto2) -> clear(echo_input).
% 0.44/1.01 % set(auto2) -> set(quiet).
% 0.44/1.01 % set(auto2) -> clear(print_initial_clauses).
% 0.44/1.01 % set(auto2) -> clear(print_given).
% 0.44/1.01 assign(lrs_ticks,-1).
% 0.44/1.01 assign(sos_limit,10000).
% 0.44/1.01 assign(order,kbo).
% 0.44/1.01 set(lex_order_vars).
% 0.44/1.01 clear(print_given).
% 0.44/1.01
% 0.44/1.01 % formulas(sos). % not echoed (43 formulas)
% 0.44/1.01
% 0.44/1.01 ============================== end of input ==========================
% 0.44/1.01
% 0.44/1.01 % From the command line: assign(max_seconds, 300).
% 0.44/1.01
% 0.44/1.01 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 0.44/1.01
% 0.44/1.01 % Formulas that are not ordinary clauses:
% 0.44/1.01 1 modus_ponens <-> (all X all Y (is_a_theorem(X) & is_a_theorem(implies(X,Y)) -> is_a_theorem(Y))) # label(modus_ponens) # label(axiom) # label(non_clause). [assumption].
% 0.44/1.01 2 substitution_of_equivalents <-> (all X all Y (is_a_theorem(equiv(X,Y)) -> X = Y)) # label(substitution_of_equivalents) # label(axiom) # label(non_clause). [assumption].
% 0.44/1.01 3 modus_tollens <-> (all X all Y is_a_theorem(implies(implies(not(Y),not(X)),implies(X,Y)))) # label(modus_tollens) # label(axiom) # label(non_clause). [assumption].
% 0.44/1.01 4 implies_1 <-> (all X all Y is_a_theorem(implies(X,implies(Y,X)))) # label(implies_1) # label(axiom) # label(non_clause). [assumption].
% 0.44/1.01 5 implies_2 <-> (all X all Y is_a_theorem(implies(implies(X,implies(X,Y)),implies(X,Y)))) # label(implies_2) # label(axiom) # label(non_clause). [assumption].
% 0.44/1.01 6 implies_3 <-> (all X all Y all Z is_a_theorem(implies(implies(X,Y),implies(implies(Y,Z),implies(X,Z))))) # label(implies_3) # label(axiom) # label(non_clause). [assumption].
% 0.44/1.01 7 and_1 <-> (all X all Y is_a_theorem(implies(and(X,Y),X))) # label(and_1) # label(axiom) # label(non_clause). [assumption].
% 0.44/1.01 8 and_2 <-> (all X all Y is_a_theorem(implies(and(X,Y),Y))) # label(and_2) # label(axiom) # label(non_clause). [assumption].
% 0.44/1.01 9 and_3 <-> (all X all Y is_a_theorem(implies(X,implies(Y,and(X,Y))))) # label(and_3) # label(axiom) # label(non_clause). [assumption].
% 0.44/1.01 10 or_1 <-> (all X all Y is_a_theorem(implies(X,or(X,Y)))) # label(or_1) # label(axiom) # label(non_clause). [assumption].
% 0.44/1.01 11 or_2 <-> (all X all Y is_a_theorem(implies(Y,or(X,Y)))) # label(or_2) # label(axiom) # label(non_clause). [assumption].
% 0.44/1.01 12 or_3 <-> (all X all Y all Z is_a_theorem(implies(implies(X,Z),implies(implies(Y,Z),implies(or(X,Y),Z))))) # label(or_3) # label(axiom) # label(non_clause). [assumption].
% 0.44/1.01 13 equivalence_1 <-> (all X all Y is_a_theorem(implies(equiv(X,Y),implies(X,Y)))) # label(equivalence_1) # label(axiom) # label(non_clause). [assumption].
% 0.44/1.01 14 equivalence_2 <-> (all X all Y is_a_theorem(implies(equiv(X,Y),implies(Y,X)))) # label(equivalence_2) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.77 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].
% 1.47/1.77 16 kn1 <-> (all P is_a_theorem(implies(P,and(P,P)))) # label(kn1) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.77 17 kn2 <-> (all P all Q is_a_theorem(implies(and(P,Q),P))) # label(kn2) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.77 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].
% 1.47/1.77 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].
% 1.47/1.77 20 cn2 <-> (all P all Q is_a_theorem(implies(P,implies(not(P),Q)))) # label(cn2) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.77 21 cn3 <-> (all P is_a_theorem(implies(implies(not(P),P),P))) # label(cn3) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.77 22 r1 <-> (all P is_a_theorem(implies(or(P,P),P))) # label(r1) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.77 23 r2 <-> (all P all Q is_a_theorem(implies(Q,or(P,Q)))) # label(r2) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.77 24 r3 <-> (all P all Q is_a_theorem(implies(or(P,Q),or(Q,P)))) # label(r3) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.77 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].
% 1.47/1.77 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].
% 1.47/1.77 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].
% 1.47/1.77 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].
% 1.47/1.77 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].
% 1.47/1.77 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].
% 1.47/1.77 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].
% 1.47/1.77
% 1.47/1.77 ============================== end of process non-clausal formulas ===
% 1.47/1.77
% 1.47/1.77 ============================== PROCESS INITIAL CLAUSES ===============
% 1.47/1.77
% 1.47/1.77 ============================== PREDICATE ELIMINATION =================
% 1.47/1.77
% 1.47/1.77 ============================== end predicate elimination =============
% 1.47/1.77
% 1.47/1.77 Auto_denials: (non-Horn, no changes).
% 1.47/1.77
% 1.47/1.77 Term ordering decisions:
% 1.47/1.77
% 1.47/1.77 % Assigning unary symbol not kb_weight 0 and highest precedence (93).
% 1.47/1.77 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.
% 1.47/1.77
% 1.47/1.77 ============================== end of process initial clauses ========
% 1.47/1.77
% 1.47/1.77 ============================== CLAUSES FOR SEARCH ====================
% 1.47/1.77
% 1.47/1.77 ============================== end of clauses for search =============
% 1.47/1.77
% 1.47/1.77 ============================== SEARCH ================================
% 1.47/1.77
% 1.47/1.77 % Starting search at 0.02 seconds.
% 1.47/1.77
% 1.47/1.77 Low Water (keep): wt=33.000, iters=3370
% 1.47/1.77
% 1.47/1.77 Low Water (keep): wt=31.000, iters=3346
% 1.47/1.77
% 1.47/1.77 Low Water (keep): wt=29.000, iters=3343
% 1.47/1.77
% 1.47/1.77 Low Water (keep): wt=27.000, iters=3333
% 1.47/1.77
% 1.47/1.77 Low Water (keep): wt=26.000, iters=3543
% 1.47/1.77
% 1.47/1.77 Low Water (keep): wt=25.000, iters=3352
% 1.47/1.77
% 1.47/1.77 Low Water (keep): wt=24.000, iters=3378
% 1.47/1.77
% 1.47/1.77 Low Water (keep): wt=23.000, iters=3357
% 1.47/1.77
% 1.47/1.77 ============================== PROOF =================================
% 1.47/1.77 % SZS status Theorem
% 1.47/1.77 % SZS output start Refutation
% 1.47/1.77
% 1.47/1.77 % Proof 1 at 0.75 (+ 0.02) seconds.
% 1.47/1.77 % Length of proof is 99.
% 1.47/1.77 % Level of proof is 19.
% 1.47/1.77 % Maximum clause weight is 20.000.
% 1.47/1.77 % Given clauses 393.
% 1.47/1.77
% 1.47/1.77 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].
% 1.47/1.77 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].
% 1.47/1.77 16 kn1 <-> (all P is_a_theorem(implies(P,and(P,P)))) # label(kn1) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.77 17 kn2 <-> (all P all Q is_a_theorem(implies(and(P,Q),P))) # label(kn2) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.77 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].
% 1.47/1.77 21 cn3 <-> (all P is_a_theorem(implies(implies(not(P),P),P))) # label(cn3) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.77 22 r1 <-> (all P is_a_theorem(implies(or(P,P),P))) # label(r1) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.77 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].
% 1.47/1.77 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].
% 1.47/1.77 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].
% 1.47/1.77 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].
% 1.47/1.77 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].
% 1.47/1.77 32 op_or # label(rosser_op_or) # label(axiom). [assumption].
% 1.47/1.77 33 op_implies_and # label(rosser_op_implies_and) # label(axiom). [assumption].
% 1.47/1.77 34 op_equiv # label(rosser_op_equiv) # label(axiom). [assumption].
% 1.47/1.77 35 modus_ponens # label(rosser_modus_ponens) # label(axiom). [assumption].
% 1.47/1.77 36 kn1 # label(rosser_kn1) # label(axiom). [assumption].
% 1.47/1.77 37 kn2 # label(rosser_kn2) # label(axiom). [assumption].
% 1.47/1.77 38 kn3 # label(rosser_kn3) # label(axiom). [assumption].
% 1.47/1.77 39 substitution_of_equivalents # label(substitution_of_equivalents) # label(axiom). [assumption].
% 1.47/1.77 40 op_implies_or # label(principia_op_implies_or) # label(axiom). [assumption].
% 1.47/1.77 41 op_and # label(principia_op_and) # label(axiom). [assumption].
% 1.47/1.77 42 -r1 # label(principia_r1) # label(negated_conjecture). [assumption].
% 1.47/1.77 53 -kn1 | is_a_theorem(implies(A,and(A,A))) # label(kn1) # label(axiom). [clausify(16)].
% 1.47/1.77 54 is_a_theorem(implies(A,and(A,A))). [copy(53),unit_del(a,36)].
% 1.47/1.77 56 -kn2 | is_a_theorem(implies(and(A,B),A)) # label(kn2) # label(axiom). [clausify(17)].
% 1.47/1.77 57 is_a_theorem(implies(and(A,B),A)). [copy(56),unit_del(a,37)].
% 1.47/1.77 59 r1 | -is_a_theorem(implies(or(c45,c45),c45)) # label(r1) # label(axiom). [clausify(22)].
% 1.47/1.77 60 -is_a_theorem(implies(or(c45,c45),c45)). [copy(59),unit_del(a,42)].
% 1.47/1.77 63 -substitution_of_equivalents | -is_a_theorem(equiv(A,B)) | B = A # label(substitution_of_equivalents) # label(axiom). [clausify(2)].
% 1.47/1.77 64 -is_a_theorem(equiv(A,B)) | B = A. [copy(63),unit_del(a,39)].
% 1.47/1.77 67 -cn3 | is_a_theorem(implies(implies(not(A),A),A)) # label(cn3) # label(axiom). [clausify(21)].
% 1.47/1.77 68 cn3 | -is_a_theorem(implies(implies(not(c44),c44),c44)) # label(cn3) # label(axiom). [clausify(21)].
% 1.47/1.77 69 -modus_ponens | -is_a_theorem(A) | -is_a_theorem(implies(A,B)) | is_a_theorem(B) # label(modus_ponens) # label(axiom). [clausify(1)].
% 1.47/1.77 70 -is_a_theorem(A) | -is_a_theorem(implies(A,B)) | is_a_theorem(B). [copy(69),unit_del(a,35)].
% 1.47/1.77 79 -op_implies_or | or(not(A),B) = implies(A,B) # label(op_implies_or) # label(axiom). [clausify(30)].
% 1.47/1.77 80 or(not(A),B) = implies(A,B). [copy(79),unit_del(a,40)].
% 1.47/1.77 81 -op_implies_and | not(and(A,not(B))) = implies(A,B) # label(op_implies_and) # label(axiom). [clausify(29)].
% 1.47/1.77 82 not(and(A,not(B))) = implies(A,B). [copy(81),unit_del(a,33)].
% 1.47/1.77 87 -op_or | or(A,B) = not(and(not(A),not(B))) # label(op_or) # label(axiom). [clausify(27)].
% 1.47/1.77 88 or(A,B) = implies(not(A),B). [copy(87),rewrite([82(6)]),unit_del(a,32)].
% 1.47/1.77 89 -op_and | and(A,B) = not(or(not(A),not(B))) # label(op_and) # label(axiom). [clausify(28)].
% 1.47/1.77 90 not(implies(not(not(A)),not(B))) = and(A,B). [copy(89),rewrite([88(5)]),flip(b),unit_del(a,41)].
% 1.47/1.77 91 -op_equiv | and(implies(A,B),implies(B,A)) = equiv(A,B) # label(op_equiv) # label(axiom). [clausify(31)].
% 1.47/1.77 92 and(implies(A,B),implies(B,A)) = equiv(A,B). [copy(91),unit_del(a,34)].
% 1.47/1.77 111 -kn3 | is_a_theorem(implies(implies(A,B),implies(not(and(B,C)),not(and(C,A))))) # label(kn3) # label(axiom). [clausify(18)].
% 1.47/1.77 112 is_a_theorem(implies(implies(A,B),implies(not(and(B,C)),not(and(C,A))))). [copy(111),unit_del(a,38)].
% 1.47/1.77 115 implies(not(not(A)),B) = implies(A,B). [back_rewrite(80),rewrite([88(2)])].
% 1.47/1.77 120 -is_a_theorem(implies(implies(not(c45),c45),c45)). [back_rewrite(60),rewrite([88(3)])].
% 1.47/1.77 125 not(implies(A,not(B))) = and(A,B). [back_rewrite(90),rewrite([115(4)])].
% 1.47/1.77 126 -is_a_theorem(and(A,B)) | is_a_theorem(A). [resolve(70,b,57,a)].
% 1.47/1.77 127 -is_a_theorem(A) | is_a_theorem(and(A,A)). [resolve(70,b,54,a)].
% 1.47/1.77 129 is_a_theorem(implies(implies(A,A),equiv(A,A))). [para(92(a,1),54(a,1,2))].
% 1.47/1.77 132 -is_a_theorem(implies(A,B)) | is_a_theorem(implies(not(and(B,C)),not(and(C,A)))). [resolve(112,a,70,b)].
% 1.47/1.77 134 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))].
% 1.47/1.77 137 is_a_theorem(implies(A,and(not(not(A)),not(not(A))))). [para(115(a,1),54(a,1))].
% 1.47/1.77 138 -is_a_theorem(not(not(A))) | -is_a_theorem(implies(A,B)) | is_a_theorem(B). [para(115(a,1),70(b,1))].
% 1.47/1.77 139 implies(not(implies(A,B)),C) = implies(and(A,not(B)),C). [para(82(a,1),115(a,1,1,1))].
% 1.47/1.77 141 and(implies(A,not(not(B))),implies(B,A)) = equiv(A,not(not(B))). [para(115(a,1),92(a,1,2))].
% 1.47/1.77 147 -cn3. [ur(67,b,120,a)].
% 1.47/1.77 148 -is_a_theorem(implies(implies(not(c44),c44),c44)). [back_unit_del(68),unit_del(a,147)].
% 1.47/1.77 149 not(and(A,and(B,C))) = implies(A,implies(B,not(C))). [para(125(a,1),82(a,1,1,2))].
% 1.47/1.77 151 implies(not(and(A,B)),C) = implies(implies(A,not(B)),C). [para(125(a,1),115(a,1,1,1))].
% 1.47/1.77 152 and(not(not(A)),B) = and(A,B). [para(115(a,1),125(a,1,1)),rewrite([125(3)]),flip(a)].
% 1.47/1.77 156 is_a_theorem(implies(implies(not(A),B),implies(implies(B,not(C)),implies(C,A)))). [back_rewrite(134),rewrite([151(6)])].
% 1.47/1.77 157 -is_a_theorem(implies(A,B)) | is_a_theorem(implies(implies(B,not(C)),not(and(C,A)))). [back_rewrite(132),rewrite([151(7)])].
% 1.47/1.77 159 is_a_theorem(implies(A,and(A,not(not(A))))). [back_rewrite(137),rewrite([152(5)])].
% 1.47/1.77 163 -is_a_theorem(implies(implies(A,and(A,A)),implies(implies(not(c44),c44),c44))). [ur(70,a,54,a,c,148,a)].
% 1.47/1.77 171 is_a_theorem(and(implies(and(A,B),A),implies(and(A,B),A))). [resolve(127,a,57,a)].
% 1.47/1.77 172 is_a_theorem(and(implies(A,and(A,A)),implies(A,and(A,A)))). [resolve(127,a,54,a)].
% 1.47/1.77 220 is_a_theorem(implies(A,and(A,not(not(not(not(A))))))). [para(115(a,1),159(a,1)),rewrite([152(7)])].
% 1.47/1.77 275 is_a_theorem(implies(and(A,B),not(not(A)))). [para(152(a,1),57(a,1,1))].
% 1.47/1.77 278 -is_a_theorem(and(A,B)) | is_a_theorem(not(not(A))). [para(152(a,1),126(a,1))].
% 1.47/1.77 298 is_a_theorem(implies(and(A,B),not(not(not(not(A)))))). [para(152(a,1),275(a,1,1))].
% 1.47/1.77 305 -is_a_theorem(not(not(implies(A,A)))) | is_a_theorem(equiv(A,A)). [resolve(138,b,129,a)].
% 1.47/1.77 516 is_a_theorem(implies(A,and(A,not(not(not(not(not(not(A))))))))). [para(115(a,1),220(a,1)),rewrite([152(9)])].
% 1.47/1.77 571 is_a_theorem(implies(and(A,B),not(not(not(not(not(not(A)))))))). [para(152(a,1),298(a,1,1))].
% 1.47/1.77 575 implies(and(A,not(not(B))),C) = implies(and(A,B),C). [para(125(a,1),139(a,1,1)),flip(a)].
% 1.47/1.77 731 -is_a_theorem(implies(A,A)) | is_a_theorem(equiv(not(not(A)),not(not(A)))). [para(115(a,1),305(a,1,1,1)),rewrite([125(4),82(3)])].
% 1.47/1.77 793 equiv(A,not(not(B))) = equiv(A,B). [para(141(a,1),152(a,2)),rewrite([125(4),82(3),92(3)]),flip(a)].
% 1.47/1.77 801 -is_a_theorem(implies(A,A)) | is_a_theorem(equiv(not(not(A)),A)). [back_rewrite(731),rewrite([793(7)])].
% 1.47/1.77 1151 is_a_theorem(not(not(implies(and(A,B),A)))). [resolve(171,a,278,a)].
% 1.47/1.77 1191 is_a_theorem(not(and(and(not(A),B),A))). [para(125(a,1),1151(a,1,1))].
% 1.47/1.77 1195 is_a_theorem(implies(and(implies(A,B),C),implies(A,not(not(B))))). [para(82(a,1),1191(a,1,1,1,1)),rewrite([149(6)])].
% 1.47/1.77 2294 is_a_theorem(implies(implies(A,not(B)),implies(B,implies(A,not(C))))). [resolve(157,a,571,a),rewrite([115(8),115(6),115(4),149(5)])].
% 1.47/1.77 2295 is_a_theorem(implies(implies(and(A,A),not(B)),not(and(B,A)))). [resolve(157,a,516,a),rewrite([575(9),575(7),575(5)])].
% 1.47/1.77 2410 -is_a_theorem(and(implies(A,B),C)) | is_a_theorem(implies(A,not(not(B)))). [resolve(1195,a,70,b)].
% 1.47/1.77 3121 -is_a_theorem(implies(A,not(B))) | is_a_theorem(implies(B,implies(A,not(C)))). [resolve(2294,a,70,b)].
% 1.47/1.77 3219 -is_a_theorem(not(and(and(A,A),B))) | is_a_theorem(not(and(B,A))). [resolve(2295,a,138,b),rewrite([125(4)])].
% 1.47/1.77 3425 is_a_theorem(implies(A,not(not(and(A,A))))). [resolve(2410,a,172,a)].
% 1.47/1.77 5857 is_a_theorem(implies(implies(A,not(A)),implies(A,not(B)))). [resolve(3121,a,3425,a),rewrite([151(5)])].
% 1.47/1.77 5874 is_a_theorem(equiv(not(and(A,A)),implies(A,not(A)))). [resolve(5857,a,801,a),rewrite([125(3)])].
% 1.47/1.77 6031 not(and(A,A)) = implies(A,not(A)). [resolve(5874,a,64,a),flip(a)].
% 1.47/1.77 6179 implies(not(A),not(not(A))) = implies(not(A),A). [para(6031(a,1),82(a,1))].
% 1.47/1.77 7392 not(implies(not(A),A)) = and(not(A),not(A)). [para(6179(a,1),125(a,1,1))].
% 1.47/1.77 7907 is_a_theorem(implies(implies(not(A),B),implies(implies(B,and(not(C),not(C))),implies(implies(not(C),C),A)))). [para(7392(a,1),156(a,1,2,1,2))].
% 1.47/1.77 8267 is_a_theorem(implies(A,A)). [resolve(3219,a,1191,a),rewrite([82(3)])].
% 1.47/1.77 8512 -is_a_theorem(implies(implies(A,A),implies(implies(B,and(B,B)),implies(implies(not(c44),c44),c44)))). [ur(70,a,8267,a,c,163,a)].
% 1.47/1.77 8513 $F. [resolve(8512,a,7907,a)].
% 1.47/1.77
% 1.47/1.77 % SZS output end Refutation
% 1.47/1.77 ============================== end of proof ==========================
% 1.47/1.77
% 1.47/1.77 ============================== STATISTICS ============================
% 1.47/1.77
% 1.47/1.77 Given=393. Generated=22200. Kept=8461. proofs=1.
% 1.47/1.77 Usable=343. Sos=6377. Demods=184. Limbo=230, Disabled=1582. Hints=0.
% 1.47/1.77 Megabytes=9.30.
% 1.47/1.77 User_CPU=0.75, System_CPU=0.02, Wall_clock=0.
% 1.47/1.77
% 1.47/1.77 ============================== end of statistics =====================
% 1.47/1.77
% 1.47/1.77 ============================== end of search =========================
% 1.47/1.77
% 1.47/1.77 THEOREM PROVED
% 1.47/1.77 % SZS status Theorem
% 1.47/1.77
% 1.47/1.77 Exiting with 1 proof.
% 1.47/1.77
% 1.47/1.77 Process 8882 exit (max_proofs) Sun Jul 3 04:59:44 2022
% 1.47/1.77 Prover9 interrupted
%------------------------------------------------------------------------------