TSTP Solution File: LCL503+1 by Prover9---1109a
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : LCL503+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n029.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 14.78s 15.06s
% Output : Refutation 14.78s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : LCL503+1 : TPTP v8.1.0. Released v3.3.0.
% 0.07/0.13 % Command : tptp2X_and_run_prover9 %d %s
% 0.12/0.32 % Computer : n029.cluster.edu
% 0.12/0.32 % Model : x86_64 x86_64
% 0.12/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.32 % Memory : 8042.1875MB
% 0.12/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.32 % CPULimit : 300
% 0.12/0.32 % WCLimit : 600
% 0.12/0.32 % DateTime : Sat Jul 2 12:21:10 EDT 2022
% 0.12/0.32 % CPUTime :
% 0.67/0.98 ============================== Prover9 ===============================
% 0.67/0.98 Prover9 (32) version 2009-11A, November 2009.
% 0.67/0.98 Process 25828 was started by sandbox2 on n029.cluster.edu,
% 0.67/0.98 Sat Jul 2 12:21:10 2022
% 0.67/0.98 The command was "/export/starexec/sandbox2/solver/bin/prover9 -t 300 -f /tmp/Prover9_25451_n029.cluster.edu".
% 0.67/0.98 ============================== end of head ===========================
% 0.67/0.98
% 0.67/0.98 ============================== INPUT =================================
% 0.67/0.98
% 0.67/0.98 % Reading from file /tmp/Prover9_25451_n029.cluster.edu
% 0.67/0.98
% 0.67/0.98 set(prolog_style_variables).
% 0.67/0.98 set(auto2).
% 0.67/0.98 % set(auto2) -> set(auto).
% 0.67/0.98 % set(auto) -> set(auto_inference).
% 0.67/0.98 % set(auto) -> set(auto_setup).
% 0.67/0.98 % set(auto_setup) -> set(predicate_elim).
% 0.67/0.98 % set(auto_setup) -> assign(eq_defs, unfold).
% 0.67/0.98 % set(auto) -> set(auto_limits).
% 0.67/0.98 % set(auto_limits) -> assign(max_weight, "100.000").
% 0.67/0.98 % set(auto_limits) -> assign(sos_limit, 20000).
% 0.67/0.98 % set(auto) -> set(auto_denials).
% 0.67/0.98 % set(auto) -> set(auto_process).
% 0.67/0.98 % set(auto2) -> assign(new_constants, 1).
% 0.67/0.98 % set(auto2) -> assign(fold_denial_max, 3).
% 0.67/0.98 % set(auto2) -> assign(max_weight, "200.000").
% 0.67/0.98 % set(auto2) -> assign(max_hours, 1).
% 0.67/0.98 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 0.67/0.98 % set(auto2) -> assign(max_seconds, 0).
% 0.67/0.98 % set(auto2) -> assign(max_minutes, 5).
% 0.67/0.98 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 0.67/0.98 % set(auto2) -> set(sort_initial_sos).
% 0.67/0.98 % set(auto2) -> assign(sos_limit, -1).
% 0.67/0.98 % set(auto2) -> assign(lrs_ticks, 3000).
% 0.67/0.98 % set(auto2) -> assign(max_megs, 400).
% 0.67/0.98 % set(auto2) -> assign(stats, some).
% 0.67/0.98 % set(auto2) -> clear(echo_input).
% 0.67/0.98 % set(auto2) -> set(quiet).
% 0.67/0.98 % set(auto2) -> clear(print_initial_clauses).
% 0.67/0.98 % set(auto2) -> clear(print_given).
% 0.67/0.98 assign(lrs_ticks,-1).
% 0.67/0.98 assign(sos_limit,10000).
% 0.67/0.98 assign(order,kbo).
% 0.67/0.98 set(lex_order_vars).
% 0.67/0.98 clear(print_given).
% 0.67/0.98
% 0.67/0.98 % formulas(sos). % not echoed (43 formulas)
% 0.67/0.98
% 0.67/0.98 ============================== end of input ==========================
% 0.67/0.98
% 0.67/0.98 % From the command line: assign(max_seconds, 300).
% 0.67/0.98
% 0.67/0.98 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 0.67/0.98
% 0.67/0.98 % Formulas that are not ordinary clauses:
% 0.67/0.98 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].
% 0.67/0.98 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].
% 0.67/0.98 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].
% 0.67/0.98 4 implies_1 <-> (all X all Y is_a_theorem(implies(X,implies(Y,X)))) # label(implies_1) # label(axiom) # label(non_clause). [assumption].
% 0.67/0.98 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].
% 0.67/0.98 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].
% 0.67/0.98 7 and_1 <-> (all X all Y is_a_theorem(implies(and(X,Y),X))) # label(and_1) # label(axiom) # label(non_clause). [assumption].
% 0.67/0.98 8 and_2 <-> (all X all Y is_a_theorem(implies(and(X,Y),Y))) # label(and_2) # label(axiom) # label(non_clause). [assumption].
% 0.67/0.98 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].
% 0.67/0.98 10 or_1 <-> (all X all Y is_a_theorem(implies(X,or(X,Y)))) # label(or_1) # label(axiom) # label(non_clause). [assumption].
% 0.67/0.98 11 or_2 <-> (all X all Y is_a_theorem(implies(Y,or(X,Y)))) # label(or_2) # label(axiom) # label(non_clause). [assumption].
% 0.67/0.98 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].
% 0.67/0.98 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].
% 0.67/0.98 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].
% 1.11/1.43 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].
% 1.11/1.43 16 kn1 <-> (all P is_a_theorem(implies(P,and(P,P)))) # label(kn1) # label(axiom) # label(non_clause). [assumption].
% 1.11/1.43 17 kn2 <-> (all P all Q is_a_theorem(implies(and(P,Q),P))) # label(kn2) # label(axiom) # label(non_clause). [assumption].
% 1.11/1.43 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].
% 1.11/1.43 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].
% 1.11/1.43 20 cn2 <-> (all P all Q is_a_theorem(implies(P,implies(not(P),Q)))) # label(cn2) # label(axiom) # label(non_clause). [assumption].
% 1.11/1.43 21 cn3 <-> (all P is_a_theorem(implies(implies(not(P),P),P))) # label(cn3) # label(axiom) # label(non_clause). [assumption].
% 1.11/1.43 22 r1 <-> (all P is_a_theorem(implies(or(P,P),P))) # label(r1) # label(axiom) # label(non_clause). [assumption].
% 1.11/1.43 23 r2 <-> (all P all Q is_a_theorem(implies(Q,or(P,Q)))) # label(r2) # label(axiom) # label(non_clause). [assumption].
% 1.11/1.43 24 r3 <-> (all P all Q is_a_theorem(implies(or(P,Q),or(Q,P)))) # label(r3) # label(axiom) # label(non_clause). [assumption].
% 1.11/1.43 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].
% 1.11/1.43 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].
% 1.11/1.43 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].
% 1.11/1.43 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].
% 1.11/1.43 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].
% 1.11/1.43 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].
% 1.11/1.43 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].
% 1.11/1.43
% 1.11/1.43 ============================== end of process non-clausal formulas ===
% 1.11/1.43
% 1.11/1.43 ============================== PROCESS INITIAL CLAUSES ===============
% 1.11/1.43
% 1.11/1.43 ============================== PREDICATE ELIMINATION =================
% 1.11/1.43
% 1.11/1.43 ============================== end predicate elimination =============
% 1.11/1.43
% 1.11/1.43 Auto_denials: (non-Horn, no changes).
% 1.11/1.43
% 1.11/1.43 Term ordering decisions:
% 1.11/1.43
% 1.11/1.43 % Assigning unary symbol not kb_weight 0 and highest precedence (93).
% 1.11/1.43 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.
% 1.11/1.44
% 1.11/1.44 ============================== end of process initial clauses ========
% 1.11/1.44
% 1.11/1.44 ============================== CLAUSES FOR SEARCH ====================
% 1.11/1.44
% 1.11/1.44 ============================== end of clauses for search =============
% 1.11/1.44
% 1.11/1.44 ============================== SEARCH ================================
% 1.11/1.44
% 1.11/1.44 % Starting search at 0.02 seconds.
% 1.11/1.44
% 1.11/1.44 Low Water (keep): wt=34.000, iters=3476
% 1.11/1.44
% 1.11/1.44 Low Water (keep): wt=32.000, iters=3427
% 1.11/1.44
% 1.11/1.44 Low Water (keep): wt=31.000, iters=3651
% 1.11/1.44
% 1.11/1.44 Low Water (keep): wt=29.000, iters=3538
% 1.11/1.44
% 1.11/1.44 Low Water (keep): wt=26.000, iters=3431
% 1.11/1.44
% 1.11/1.44 Low Water (keep): wt=25.000, iters=3337
% 1.11/1.44
% 1.11/1.44 Low Water (keep): wt=24.000, iters=3349
% 1.11/1.44
% 1.11/1.44 Low Water (keep): wt=23.000, iters=3449
% 1.11/1.44
% 1.11/1.44 Low Water (keep): wt=22.000, iters=3343
% 1.11/1.44
% 1.11/1.44 Low Water (keep): wt=21.000, iters=3348
% 14.78/15.06
% 14.78/15.06 Low Water (keep): wt=20.000, iters=3605
% 14.78/15.06
% 14.78/15.06 Low Water (keep): wt=19.000, iters=3433
% 14.78/15.06
% 14.78/15.06 Low Water (keep): wt=18.000, iters=3345
% 14.78/15.06
% 14.78/15.06 Low Water (keep): wt=17.000, iters=3385
% 14.78/15.06
% 14.78/15.06 Low Water (keep): wt=16.000, iters=3377
% 14.78/15.06
% 14.78/15.06 Low Water (keep): wt=15.000, iters=3343
% 14.78/15.06
% 14.78/15.06 Low Water (displace): id=2363, wt=51.000
% 14.78/15.06
% 14.78/15.06 Low Water (displace): id=2362, wt=49.000
% 14.78/15.06
% 14.78/15.06 Low Water (displace): id=1968, wt=47.000
% 14.78/15.06
% 14.78/15.06 Low Water (displace): id=1967, wt=45.000
% 14.78/15.06
% 14.78/15.06 Low Water (displace): id=1626, wt=43.000
% 14.78/15.06
% 14.78/15.06 Low Water (displace): id=2394, wt=42.000
% 14.78/15.06
% 14.78/15.06 Low Water (displace): id=1625, wt=41.000
% 14.78/15.06
% 14.78/15.06 Low Water (displace): id=1995, wt=40.000
% 14.78/15.06
% 14.78/15.06 Low Water (displace): id=2399, wt=38.000
% 14.78/15.06
% 14.78/15.06 Low Water (displace): id=2392, wt=36.000
% 14.78/15.06
% 14.78/15.06 Low Water (displace): id=3300, wt=35.000
% 14.78/15.06
% 14.78/15.06 Low Water (displace): id=3339, wt=34.000
% 14.78/15.06
% 14.78/15.06 Low Water (displace): id=10689, wt=14.000
% 14.78/15.06
% 14.78/15.06 Low Water (displace): id=10746, wt=13.000
% 14.78/15.06
% 14.78/15.06 NOTE: Back_subsumption disabled, ratio of kept to back_subsumed is 155 (0.00 of 1.01 sec).
% 14.78/15.06
% 14.78/15.06 Low Water (displace): id=11468, wt=12.000
% 14.78/15.06
% 14.78/15.06 Low Water (displace): id=11515, wt=11.000
% 14.78/15.06
% 14.78/15.06 Low Water (displace): id=11754, wt=10.000
% 14.78/15.06
% 14.78/15.06 Low Water (keep): wt=14.000, iters=3354
% 14.78/15.06
% 14.78/15.06 Low Water (displace): id=16297, wt=9.000
% 14.78/15.06
% 14.78/15.06 Low Water (keep): wt=13.000, iters=3339
% 14.78/15.06
% 14.78/15.06 Low Water (keep): wt=12.000, iters=3344
% 14.78/15.06
% 14.78/15.06 ============================== PROOF =================================
% 14.78/15.06 % SZS status Theorem
% 14.78/15.06 % SZS output start Refutation
% 14.78/15.06
% 14.78/15.06 % Proof 1 at 12.99 (+ 1.10) seconds.
% 14.78/15.06 % Length of proof is 53.
% 14.78/15.06 % Level of proof is 21.
% 14.78/15.06 % Maximum clause weight is 14.000.
% 14.78/15.06 % Given clauses 2875.
% 14.78/15.06
% 14.78/15.06 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].
% 14.78/15.06 4 implies_1 <-> (all X all Y is_a_theorem(implies(X,implies(Y,X)))) # label(implies_1) # label(axiom) # label(non_clause). [assumption].
% 14.78/15.06 16 kn1 <-> (all P is_a_theorem(implies(P,and(P,P)))) # label(kn1) # label(axiom) # label(non_clause). [assumption].
% 14.78/15.06 17 kn2 <-> (all P all Q is_a_theorem(implies(and(P,Q),P))) # label(kn2) # label(axiom) # label(non_clause). [assumption].
% 14.78/15.06 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].
% 14.78/15.07 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].
% 14.78/15.07 33 op_implies_and # label(rosser_op_implies_and) # label(axiom). [assumption].
% 14.78/15.07 35 modus_ponens # label(rosser_modus_ponens) # label(axiom). [assumption].
% 14.78/15.07 36 kn1 # label(rosser_kn1) # label(axiom). [assumption].
% 14.78/15.07 37 kn2 # label(rosser_kn2) # label(axiom). [assumption].
% 14.78/15.07 38 kn3 # label(rosser_kn3) # label(axiom). [assumption].
% 14.78/15.07 40 -implies_1 # label(hilbert_implies_1) # label(negated_conjecture). [assumption].
% 14.78/15.07 41 implies_1 | -is_a_theorem(implies(c7,implies(c8,c7))) # label(implies_1) # label(axiom). [clausify(4)].
% 14.78/15.07 42 -is_a_theorem(implies(c7,implies(c8,c7))). [copy(41),unit_del(a,40)].
% 14.78/15.07 51 -kn1 | is_a_theorem(implies(A,and(A,A))) # label(kn1) # label(axiom). [clausify(16)].
% 14.78/15.07 52 is_a_theorem(implies(A,and(A,A))). [copy(51),unit_del(a,36)].
% 14.78/15.07 54 -kn2 | is_a_theorem(implies(and(A,B),A)) # label(kn2) # label(axiom). [clausify(17)].
% 14.78/15.07 55 is_a_theorem(implies(and(A,B),A)). [copy(54),unit_del(a,37)].
% 14.78/15.07 67 -modus_ponens | -is_a_theorem(A) | -is_a_theorem(implies(A,B)) | is_a_theorem(B) # label(modus_ponens) # label(axiom). [clausify(1)].
% 14.78/15.07 68 -is_a_theorem(A) | -is_a_theorem(implies(A,B)) | is_a_theorem(B). [copy(67),unit_del(a,35)].
% 14.78/15.07 78 -op_implies_and | not(and(A,not(B))) = implies(A,B) # label(op_implies_and) # label(axiom). [clausify(29)].
% 14.78/15.07 79 not(and(A,not(B))) = implies(A,B). [copy(78),unit_del(a,33)].
% 14.78/15.07 108 -kn3 | is_a_theorem(implies(implies(A,B),implies(not(and(B,C)),not(and(C,A))))) # label(kn3) # label(axiom). [clausify(18)].
% 14.78/15.07 109 is_a_theorem(implies(implies(A,B),implies(not(and(B,C)),not(and(C,A))))). [copy(108),unit_del(a,38)].
% 14.78/15.07 132 -is_a_theorem(implies(A,B)) | is_a_theorem(implies(not(and(B,C)),not(and(C,A)))). [resolve(109,a,68,b)].
% 14.78/15.07 135 is_a_theorem(implies(implies(not(A),B),implies(not(and(B,C)),implies(C,A)))). [para(79(a,1),109(a,1,2,2))].
% 14.78/15.07 277 is_a_theorem(implies(not(and(and(A,A),B)),not(and(B,A)))). [resolve(132,a,52,a)].
% 14.78/15.07 301 -is_a_theorem(not(and(and(A,A),B))) | is_a_theorem(not(and(B,A))). [resolve(277,a,68,b)].
% 14.78/15.07 409 -is_a_theorem(implies(and(A,A),B)) | is_a_theorem(not(and(not(B),A))). [para(79(a,1),301(a,1))].
% 14.78/15.07 706 is_a_theorem(not(and(not(A),A))). [resolve(409,a,55,a)].
% 14.78/15.07 737 -is_a_theorem(implies(not(and(not(A),A)),implies(c7,implies(c8,c7)))). [ur(68,a,706,a,c,42,a)].
% 14.78/15.07 739 is_a_theorem(implies(not(not(A)),A)). [para(79(a,1),706(a,1))].
% 14.78/15.07 742 is_a_theorem(implies(not(and(A,B)),implies(B,not(A)))). [resolve(739,a,132,a),rewrite([79(6)])].
% 14.78/15.07 744 -is_a_theorem(not(not(A))) | is_a_theorem(A). [resolve(739,a,68,b)].
% 14.78/15.07 1034 -is_a_theorem(not(and(A,B))) | is_a_theorem(implies(B,not(A))). [resolve(742,a,68,b)].
% 14.78/15.07 1622 -is_a_theorem(implies(A,B)) | is_a_theorem(implies(not(B),not(A))). [para(79(a,1),1034(a,1))].
% 14.78/15.07 2118 -is_a_theorem(implies(not(implies(c8,c7)),not(c7))). [ur(68,b,135,a,c,737,a)].
% 14.78/15.07 4624 is_a_theorem(implies(not(A),not(and(A,B)))). [resolve(1622,a,55,a)].
% 14.78/15.07 4625 is_a_theorem(implies(not(and(A,A)),not(A))). [resolve(1622,a,52,a)].
% 14.78/15.07 4847 is_a_theorem(implies(not(and(not(and(A,B)),C)),implies(C,A))). [resolve(4624,a,132,a),rewrite([79(7)])].
% 14.78/15.07 4911 is_a_theorem(implies(not(A),implies(A,B))). [para(79(a,1),4624(a,1,2))].
% 14.78/15.07 4918 is_a_theorem(implies(not(and(implies(A,B),C)),implies(C,A))). [resolve(4911,a,132,a),rewrite([79(6)])].
% 14.78/15.07 5329 -is_a_theorem(not(and(A,A))) | is_a_theorem(not(A)). [resolve(4625,a,68,b)].
% 14.78/15.07 5435 -is_a_theorem(implies(not(A),A)) | is_a_theorem(not(not(A))). [para(79(a,1),5329(a,1))].
% 14.78/15.07 10814 -is_a_theorem(not(and(implies(A,B),C))) | is_a_theorem(implies(C,A)). [resolve(4918,a,68,b)].
% 14.78/15.07 10838 is_a_theorem(implies(implies(implies(A,B),C),implies(not(C),A))). [para(79(a,1),4918(a,1,1))].
% 14.78/15.07 13131 -is_a_theorem(implies(implies(A,B),C)) | is_a_theorem(implies(not(C),A)). [para(79(a,1),10814(a,1))].
% 14.78/15.07 13882 is_a_theorem(implies(not(implies(not(A),B)),implies(B,C))). [resolve(13131,a,10838,a)].
% 14.78/15.07 14335 is_a_theorem(not(not(implies(not(A),not(A))))). [resolve(13882,a,5435,a)].
% 14.78/15.07 14453 is_a_theorem(implies(not(A),not(A))). [resolve(14335,a,744,a)].
% 14.78/15.07 14483 is_a_theorem(implies(not(and(not(A),B)),implies(B,A))). [resolve(14453,a,132,a),rewrite([79(6)])].
% 14.78/15.07 62862 -is_a_theorem(implies(not(and(not(c7),A)),implies(c8,c7))). [ur(68,b,4847,a,c,2118,a),rewrite([79(10)])].
% 14.78/15.07 62863 $F. [resolve(62862,a,14483,a)].
% 14.78/15.07
% 14.78/15.07 % SZS output end Refutation
% 14.78/15.07 ============================== end of proof ==========================
% 14.78/15.07
% 14.78/15.07 ============================== STATISTICS ============================
% 14.78/15.07
% 14.78/15.07 Given=2875. Generated=2134220. Kept=62812. proofs=1.
% 14.78/15.07 Usable=2858. Sos=9999. Demods=5. Limbo=101, Disabled=49925. Hints=0.
% 14.78/15.07 Megabytes=41.72.
% 14.78/15.07 User_CPU=12.99, System_CPU=1.10, Wall_clock=15.
% 14.78/15.07
% 14.78/15.07 ============================== end of statistics =====================
% 14.78/15.07
% 14.78/15.07 ============================== end of search =========================
% 14.78/15.07
% 14.78/15.07 THEOREM PROVED
% 14.78/15.07 % SZS status Theorem
% 14.78/15.07
% 14.78/15.07 Exiting with 1 proof.
% 14.78/15.07
% 14.78/15.07 Process 25828 exit (max_proofs) Sat Jul 2 12:21:25 2022
% 14.78/15.07 Prover9 interrupted
%------------------------------------------------------------------------------