TSTP Solution File: LCL516+1 by Prover9---1109a
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : LCL516+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 13:47:19 EDT 2022
% Result : Theorem 2.35s 2.67s
% Output : Refutation 2.35s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : LCL516+1 : TPTP v8.1.0. Released v3.3.0.
% 0.06/0.13 % Command : tptp2X_and_run_prover9 %d %s
% 0.12/0.34 % Computer : n023.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 600
% 0.12/0.34 % DateTime : Sun Jul 3 21:01:58 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.43/1.04 ============================== Prover9 ===============================
% 0.43/1.04 Prover9 (32) version 2009-11A, November 2009.
% 0.43/1.04 Process 9905 was started by sandbox on n023.cluster.edu,
% 0.43/1.04 Sun Jul 3 21:01:58 2022
% 0.43/1.04 The command was "/export/starexec/sandbox/solver/bin/prover9 -t 300 -f /tmp/Prover9_9750_n023.cluster.edu".
% 0.43/1.04 ============================== end of head ===========================
% 0.43/1.04
% 0.43/1.04 ============================== INPUT =================================
% 0.43/1.04
% 0.43/1.04 % Reading from file /tmp/Prover9_9750_n023.cluster.edu
% 0.43/1.04
% 0.43/1.04 set(prolog_style_variables).
% 0.43/1.04 set(auto2).
% 0.43/1.04 % set(auto2) -> set(auto).
% 0.43/1.04 % set(auto) -> set(auto_inference).
% 0.43/1.04 % set(auto) -> set(auto_setup).
% 0.43/1.04 % set(auto_setup) -> set(predicate_elim).
% 0.43/1.04 % set(auto_setup) -> assign(eq_defs, unfold).
% 0.43/1.04 % set(auto) -> set(auto_limits).
% 0.43/1.04 % set(auto_limits) -> assign(max_weight, "100.000").
% 0.43/1.04 % set(auto_limits) -> assign(sos_limit, 20000).
% 0.43/1.04 % set(auto) -> set(auto_denials).
% 0.43/1.04 % set(auto) -> set(auto_process).
% 0.43/1.04 % set(auto2) -> assign(new_constants, 1).
% 0.43/1.04 % set(auto2) -> assign(fold_denial_max, 3).
% 0.43/1.04 % set(auto2) -> assign(max_weight, "200.000").
% 0.43/1.04 % set(auto2) -> assign(max_hours, 1).
% 0.43/1.04 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 0.43/1.04 % set(auto2) -> assign(max_seconds, 0).
% 0.43/1.04 % set(auto2) -> assign(max_minutes, 5).
% 0.43/1.04 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 0.43/1.04 % set(auto2) -> set(sort_initial_sos).
% 0.43/1.04 % set(auto2) -> assign(sos_limit, -1).
% 0.43/1.04 % set(auto2) -> assign(lrs_ticks, 3000).
% 0.43/1.04 % set(auto2) -> assign(max_megs, 400).
% 0.43/1.04 % set(auto2) -> assign(stats, some).
% 0.43/1.04 % set(auto2) -> clear(echo_input).
% 0.43/1.04 % set(auto2) -> set(quiet).
% 0.43/1.04 % set(auto2) -> clear(print_initial_clauses).
% 0.43/1.04 % set(auto2) -> clear(print_given).
% 0.43/1.04 assign(lrs_ticks,-1).
% 0.43/1.04 assign(sos_limit,10000).
% 0.43/1.04 assign(order,kbo).
% 0.43/1.04 set(lex_order_vars).
% 0.43/1.04 clear(print_given).
% 0.43/1.04
% 0.43/1.04 % formulas(sos). % not echoed (43 formulas)
% 0.43/1.04
% 0.43/1.04 ============================== end of input ==========================
% 0.43/1.04
% 0.43/1.04 % From the command line: assign(max_seconds, 300).
% 0.43/1.04
% 0.43/1.04 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 0.43/1.04
% 0.43/1.04 % Formulas that are not ordinary clauses:
% 0.43/1.04 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].
% 0.43/1.04 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].
% 0.43/1.04 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].
% 0.43/1.04 4 implies_1 <-> (all X all Y is_a_theorem(implies(X,implies(Y,X)))) # label(implies_1) # label(axiom) # label(non_clause). [assumption].
% 0.43/1.04 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].
% 0.43/1.04 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].
% 0.43/1.04 7 and_1 <-> (all X all Y is_a_theorem(implies(and(X,Y),X))) # label(and_1) # label(axiom) # label(non_clause). [assumption].
% 0.43/1.04 8 and_2 <-> (all X all Y is_a_theorem(implies(and(X,Y),Y))) # label(and_2) # label(axiom) # label(non_clause). [assumption].
% 0.43/1.04 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].
% 0.43/1.04 10 or_1 <-> (all X all Y is_a_theorem(implies(X,or(X,Y)))) # label(or_1) # label(axiom) # label(non_clause). [assumption].
% 0.43/1.04 11 or_2 <-> (all X all Y is_a_theorem(implies(Y,or(X,Y)))) # label(or_2) # label(axiom) # label(non_clause). [assumption].
% 0.43/1.04 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].
% 0.43/1.04 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].
% 0.43/1.04 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].
% 1.31/1.59 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].
% 1.31/1.59 16 kn1 <-> (all P is_a_theorem(implies(P,and(P,P)))) # label(kn1) # label(axiom) # label(non_clause). [assumption].
% 1.31/1.59 17 kn2 <-> (all P all Q is_a_theorem(implies(and(P,Q),P))) # label(kn2) # label(axiom) # label(non_clause). [assumption].
% 1.31/1.59 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].
% 1.31/1.59 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].
% 1.31/1.59 20 cn2 <-> (all P all Q is_a_theorem(implies(P,implies(not(P),Q)))) # label(cn2) # label(axiom) # label(non_clause). [assumption].
% 1.31/1.59 21 cn3 <-> (all P is_a_theorem(implies(implies(not(P),P),P))) # label(cn3) # label(axiom) # label(non_clause). [assumption].
% 1.31/1.59 22 r1 <-> (all P is_a_theorem(implies(or(P,P),P))) # label(r1) # label(axiom) # label(non_clause). [assumption].
% 1.31/1.59 23 r2 <-> (all P all Q is_a_theorem(implies(Q,or(P,Q)))) # label(r2) # label(axiom) # label(non_clause). [assumption].
% 1.31/1.59 24 r3 <-> (all P all Q is_a_theorem(implies(or(P,Q),or(Q,P)))) # label(r3) # label(axiom) # label(non_clause). [assumption].
% 1.31/1.59 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].
% 1.31/1.59 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].
% 1.31/1.59 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].
% 1.31/1.59 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].
% 1.31/1.59 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].
% 1.31/1.59 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].
% 1.31/1.59 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].
% 1.31/1.59
% 1.31/1.59 ============================== end of process non-clausal formulas ===
% 1.31/1.59
% 1.31/1.59 ============================== PROCESS INITIAL CLAUSES ===============
% 1.31/1.59
% 1.31/1.59 ============================== PREDICATE ELIMINATION =================
% 1.31/1.59
% 1.31/1.59 ============================== end predicate elimination =============
% 1.31/1.59
% 1.31/1.59 Auto_denials: (non-Horn, no changes).
% 1.31/1.59
% 1.31/1.59 Term ordering decisions:
% 1.31/1.59
% 1.31/1.59 % Assigning unary symbol not kb_weight 0 and highest precedence (94).
% 1.31/1.59 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.
% 1.31/1.59
% 1.31/1.59 ============================== end of process initial clauses ========
% 1.31/1.59
% 1.31/1.59 ============================== CLAUSES FOR SEARCH ====================
% 1.31/1.59
% 1.31/1.59 ============================== end of clauses for search =============
% 1.31/1.59
% 1.31/1.59 ============================== SEARCH ================================
% 1.31/1.59
% 1.31/1.59 % Starting search at 0.02 seconds.
% 1.31/1.59
% 1.31/1.59 Low Water (keep): wt=37.000, iters=3438
% 1.31/1.59
% 1.31/1.59 Low Water (keep): wt=31.000, iters=3353
% 1.31/1.59
% 1.31/1.59 Low Water (keep): wt=30.000, iters=3639
% 1.31/1.59
% 1.31/1.59 Low Water (keep): wt=25.000, iters=3390
% 1.31/1.59
% 1.31/1.59 Low Water (keep): wt=24.000, iters=3402
% 1.31/1.59
% 1.31/1.59 Low Water (keep): wt=23.000, iters=3361
% 1.31/1.59
% 1.31/1.59 Low Water (keep): wt=22.000, iters=3391
% 1.31/1.59
% 1.31/1.59 Low Water (keep): wt=21.000, iters=3427
% 1.31/1.59
% 1.31/1.59 Low Water (keep): wt=20.000, iters=3415
% 1.31/1.59
% 1.31/1.59 Low Water (keep): wt=19.000, iters=3351
% 1.31/1.59
% 1.31/1.59 Low Water (keep): wt=18.000, iters=3498
% 2.35/2.67
% 2.35/2.67 Low Water (keep): wt=17.000, iters=3348
% 2.35/2.67
% 2.35/2.67 Low Water (keep): wt=16.000, iters=3354
% 2.35/2.67
% 2.35/2.67 Low Water (keep): wt=15.000, iters=3436
% 2.35/2.67
% 2.35/2.67 Low Water (displace): id=3270, wt=51.000
% 2.35/2.67
% 2.35/2.67 Low Water (displace): id=3277, wt=49.000
% 2.35/2.67
% 2.35/2.67 Low Water (displace): id=1614, wt=47.000
% 2.35/2.67
% 2.35/2.67 Low Water (displace): id=2744, wt=45.000
% 2.35/2.67
% 2.35/2.67 Low Water (displace): id=3269, wt=43.000
% 2.35/2.67
% 2.35/2.67 Low Water (displace): id=3279, wt=41.000
% 2.35/2.67
% 2.35/2.67 Low Water (displace): id=3465, wt=40.000
% 2.35/2.67
% 2.35/2.67 Low Water (displace): id=3271, wt=39.000
% 2.35/2.67
% 2.35/2.67 Low Water (displace): id=3230, wt=38.000
% 2.35/2.67
% 2.35/2.67 Low Water (displace): id=3280, wt=37.000
% 2.35/2.67
% 2.35/2.67 Low Water (displace): id=3281, wt=35.000
% 2.35/2.67
% 2.35/2.67 Low Water (displace): id=10665, wt=14.000
% 2.35/2.67
% 2.35/2.67 Low Water (displace): id=11359, wt=13.000
% 2.35/2.67
% 2.35/2.67 Low Water (displace): id=11393, wt=12.000
% 2.35/2.67
% 2.35/2.67 Low Water (displace): id=11423, wt=11.000
% 2.35/2.67
% 2.35/2.67 NOTE: Back_subsumption disabled, ratio of kept to back_subsumed is 117 (0.00 of 0.97 sec).
% 2.35/2.67
% 2.35/2.67 Low Water (displace): id=12187, wt=10.000
% 2.35/2.67
% 2.35/2.67 ============================== PROOF =================================
% 2.35/2.67 % SZS status Theorem
% 2.35/2.67 % SZS output start Refutation
% 2.35/2.67
% 2.35/2.67 % Proof 1 at 1.58 (+ 0.07) seconds.
% 2.35/2.67 % Length of proof is 56.
% 2.35/2.67 % Level of proof is 21.
% 2.35/2.67 % Maximum clause weight is 16.000.
% 2.35/2.67 % Given clauses 770.
% 2.35/2.67
% 2.35/2.67 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].
% 2.35/2.67 16 kn1 <-> (all P is_a_theorem(implies(P,and(P,P)))) # label(kn1) # label(axiom) # label(non_clause). [assumption].
% 2.35/2.67 17 kn2 <-> (all P all Q is_a_theorem(implies(and(P,Q),P))) # label(kn2) # label(axiom) # label(non_clause). [assumption].
% 2.35/2.67 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].
% 2.35/2.67 20 cn2 <-> (all P all Q is_a_theorem(implies(P,implies(not(P),Q)))) # label(cn2) # label(axiom) # label(non_clause). [assumption].
% 2.35/2.67 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].
% 2.35/2.67 33 op_implies_and # label(rosser_op_implies_and) # label(axiom). [assumption].
% 2.35/2.67 35 modus_ponens # label(rosser_modus_ponens) # label(axiom). [assumption].
% 2.35/2.67 36 kn1 # label(rosser_kn1) # label(axiom). [assumption].
% 2.35/2.67 37 kn2 # label(rosser_kn2) # label(axiom). [assumption].
% 2.35/2.67 38 kn3 # label(rosser_kn3) # label(axiom). [assumption].
% 2.35/2.67 41 -cn2 # label(luka_cn2) # label(negated_conjecture). [assumption].
% 2.35/2.67 52 -kn1 | is_a_theorem(implies(A,and(A,A))) # label(kn1) # label(axiom). [clausify(16)].
% 2.35/2.67 53 is_a_theorem(implies(A,and(A,A))). [copy(52),unit_del(a,36)].
% 2.35/2.67 55 -kn2 | is_a_theorem(implies(and(A,B),A)) # label(kn2) # label(axiom). [clausify(17)].
% 2.35/2.67 56 is_a_theorem(implies(and(A,B),A)). [copy(55),unit_del(a,37)].
% 2.35/2.67 64 cn2 | -is_a_theorem(implies(c42,implies(not(c42),c43))) # label(cn2) # label(axiom). [clausify(20)].
% 2.35/2.67 65 -is_a_theorem(implies(c42,implies(not(c42),c43))). [copy(64),unit_del(a,41)].
% 2.35/2.67 68 -modus_ponens | -is_a_theorem(A) | -is_a_theorem(implies(A,B)) | is_a_theorem(B) # label(modus_ponens) # label(axiom). [clausify(1)].
% 2.35/2.67 69 -is_a_theorem(A) | -is_a_theorem(implies(A,B)) | is_a_theorem(B). [copy(68),unit_del(a,35)].
% 2.35/2.67 79 -op_implies_and | not(and(A,not(B))) = implies(A,B) # label(op_implies_and) # label(axiom). [clausify(29)].
% 2.35/2.67 80 not(and(A,not(B))) = implies(A,B). [copy(79),unit_del(a,33)].
% 2.35/2.67 109 -kn3 | is_a_theorem(implies(implies(A,B),implies(not(and(B,C)),not(and(C,A))))) # label(kn3) # label(axiom). [clausify(18)].
% 2.35/2.67 110 is_a_theorem(implies(implies(A,B),implies(not(and(B,C)),not(and(C,A))))). [copy(109),unit_del(a,38)].
% 2.35/2.67 133 -is_a_theorem(implies(A,B)) | is_a_theorem(implies(not(and(B,C)),not(and(C,A)))). [resolve(110,a,69,b)].
% 2.35/2.67 276 is_a_theorem(implies(not(and(A,B)),not(and(B,and(A,C))))). [resolve(133,a,56,a)].
% 2.35/2.67 277 is_a_theorem(implies(not(and(and(A,A),B)),not(and(B,A)))). [resolve(133,a,53,a)].
% 2.35/2.67 281 -is_a_theorem(not(and(A,B))) | is_a_theorem(not(and(B,and(A,C)))). [resolve(276,a,69,b)].
% 2.35/2.67 358 -is_a_theorem(not(and(and(A,A),B))) | is_a_theorem(not(and(B,A))). [resolve(277,a,69,b)].
% 2.35/2.67 408 -is_a_theorem(implies(and(A,A),B)) | is_a_theorem(not(and(not(B),A))). [para(80(a,1),358(a,1))].
% 2.35/2.67 704 is_a_theorem(not(and(not(A),A))). [resolve(408,a,56,a)].
% 2.35/2.67 707 is_a_theorem(not(and(A,and(not(A),B)))). [resolve(704,a,281,a)].
% 2.35/2.67 737 is_a_theorem(implies(not(not(A)),A)). [para(80(a,1),704(a,1))].
% 2.35/2.67 740 is_a_theorem(implies(not(and(A,B)),implies(B,not(A)))). [resolve(737,a,133,a),rewrite([80(6)])].
% 2.35/2.67 742 -is_a_theorem(not(not(A))) | is_a_theorem(A). [resolve(737,a,69,b)].
% 2.35/2.67 919 is_a_theorem(not(and(and(not(A),B),and(A,C)))). [resolve(707,a,281,a)].
% 2.35/2.67 1174 -is_a_theorem(not(and(A,B))) | is_a_theorem(implies(B,not(A))). [resolve(740,a,69,b)].
% 2.35/2.67 1780 is_a_theorem(implies(and(A,B),not(and(not(A),C)))). [resolve(1174,a,919,a)].
% 2.35/2.67 1787 -is_a_theorem(implies(A,B)) | is_a_theorem(implies(not(B),not(A))). [para(80(a,1),1174(a,1))].
% 2.35/2.67 2676 is_a_theorem(implies(and(A,B),implies(not(A),C))). [para(80(a,1),1780(a,1,2))].
% 2.35/2.67 2680 is_a_theorem(not(and(not(implies(not(A),B)),A))). [resolve(2676,a,408,a)].
% 2.35/2.67 3022 -is_a_theorem(implies(not(and(not(implies(not(A),B)),A)),implies(c42,implies(not(c42),c43)))). [ur(69,a,2680,a,c,65,a)].
% 2.35/2.67 4885 is_a_theorem(implies(not(A),not(and(A,B)))). [resolve(1787,a,56,a)].
% 2.35/2.67 4886 is_a_theorem(implies(not(and(A,A)),not(A))). [resolve(1787,a,53,a)].
% 2.35/2.67 4966 is_a_theorem(implies(not(A),implies(A,B))). [para(80(a,1),4885(a,1,2))].
% 2.35/2.67 4973 is_a_theorem(implies(not(and(implies(A,B),C)),implies(C,A))). [resolve(4966,a,133,a),rewrite([80(6)])].
% 2.35/2.67 5390 -is_a_theorem(not(and(A,A))) | is_a_theorem(not(A)). [resolve(4886,a,69,b)].
% 2.35/2.67 5493 -is_a_theorem(implies(not(A),A)) | is_a_theorem(not(not(A))). [para(80(a,1),5390(a,1))].
% 2.35/2.67 11509 -is_a_theorem(not(and(implies(A,B),C))) | is_a_theorem(implies(C,A)). [resolve(4973,a,69,b)].
% 2.35/2.67 11528 is_a_theorem(implies(implies(implies(A,B),C),implies(not(C),A))). [para(80(a,1),4973(a,1,1))].
% 2.35/2.67 13743 -is_a_theorem(implies(implies(A,B),C)) | is_a_theorem(implies(not(C),A)). [para(80(a,1),11509(a,1))].
% 2.35/2.67 14776 is_a_theorem(implies(not(implies(not(A),B)),implies(B,C))). [resolve(13743,a,11528,a)].
% 2.35/2.67 15561 is_a_theorem(not(not(implies(not(A),not(A))))). [resolve(14776,a,5493,a)].
% 2.35/2.67 15592 is_a_theorem(implies(not(A),not(A))). [resolve(15561,a,742,a)].
% 2.35/2.67 15619 is_a_theorem(implies(not(and(not(A),B)),implies(B,A))). [resolve(15592,a,133,a),rewrite([80(6)])].
% 2.35/2.67 15620 $F. [resolve(15619,a,3022,a)].
% 2.35/2.67
% 2.35/2.67 % SZS output end Refutation
% 2.35/2.67 ============================== end of proof ==========================
% 2.35/2.67
% 2.35/2.67 ============================== STATISTICS ============================
% 2.35/2.67
% 2.35/2.67 Given=770. Generated=140501. Kept=15569. proofs=1.
% 2.35/2.67 Usable=765. Sos=9999. Demods=5. Limbo=9, Disabled=4867. Hints=0.
% 2.35/2.67 Megabytes=13.71.
% 2.35/2.67 User_CPU=1.58, System_CPU=0.07, Wall_clock=2.
% 2.35/2.67
% 2.35/2.67 ============================== end of statistics =====================
% 2.35/2.67
% 2.35/2.67 ============================== end of search =========================
% 2.35/2.67
% 2.35/2.67 THEOREM PROVED
% 2.35/2.67 % SZS status Theorem
% 2.35/2.67
% 2.35/2.67 Exiting with 1 proof.
% 2.35/2.67
% 2.35/2.67 Process 9905 exit (max_proofs) Sun Jul 3 21:02:00 2022
% 2.35/2.67 Prover9 interrupted
%------------------------------------------------------------------------------