TSTP Solution File: LCL507+1 by Prover9---1109a
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : LCL507+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n013.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 13:47:16 EDT 2022
% Result : Theorem 16.10s 16.38s
% Output : Refutation 16.10s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : LCL507+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 : n013.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 : Mon Jul 4 08:22:44 EDT 2022
% 0.13/0.33 % CPUTime :
% 0.74/1.01 ============================== Prover9 ===============================
% 0.74/1.01 Prover9 (32) version 2009-11A, November 2009.
% 0.74/1.01 Process 29295 was started by sandbox on n013.cluster.edu,
% 0.74/1.01 Mon Jul 4 08:22:45 2022
% 0.74/1.01 The command was "/export/starexec/sandbox/solver/bin/prover9 -t 300 -f /tmp/Prover9_29142_n013.cluster.edu".
% 0.74/1.01 ============================== end of head ===========================
% 0.74/1.01
% 0.74/1.01 ============================== INPUT =================================
% 0.74/1.01
% 0.74/1.01 % Reading from file /tmp/Prover9_29142_n013.cluster.edu
% 0.74/1.01
% 0.74/1.01 set(prolog_style_variables).
% 0.74/1.01 set(auto2).
% 0.74/1.01 % set(auto2) -> set(auto).
% 0.74/1.01 % set(auto) -> set(auto_inference).
% 0.74/1.01 % set(auto) -> set(auto_setup).
% 0.74/1.01 % set(auto_setup) -> set(predicate_elim).
% 0.74/1.01 % set(auto_setup) -> assign(eq_defs, unfold).
% 0.74/1.01 % set(auto) -> set(auto_limits).
% 0.74/1.01 % set(auto_limits) -> assign(max_weight, "100.000").
% 0.74/1.01 % set(auto_limits) -> assign(sos_limit, 20000).
% 0.74/1.01 % set(auto) -> set(auto_denials).
% 0.74/1.01 % set(auto) -> set(auto_process).
% 0.74/1.01 % set(auto2) -> assign(new_constants, 1).
% 0.74/1.01 % set(auto2) -> assign(fold_denial_max, 3).
% 0.74/1.01 % set(auto2) -> assign(max_weight, "200.000").
% 0.74/1.01 % set(auto2) -> assign(max_hours, 1).
% 0.74/1.01 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 0.74/1.01 % set(auto2) -> assign(max_seconds, 0).
% 0.74/1.01 % set(auto2) -> assign(max_minutes, 5).
% 0.74/1.01 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 0.74/1.01 % set(auto2) -> set(sort_initial_sos).
% 0.74/1.01 % set(auto2) -> assign(sos_limit, -1).
% 0.74/1.01 % set(auto2) -> assign(lrs_ticks, 3000).
% 0.74/1.01 % set(auto2) -> assign(max_megs, 400).
% 0.74/1.01 % set(auto2) -> assign(stats, some).
% 0.74/1.01 % set(auto2) -> clear(echo_input).
% 0.74/1.01 % set(auto2) -> set(quiet).
% 0.74/1.01 % set(auto2) -> clear(print_initial_clauses).
% 0.74/1.01 % set(auto2) -> clear(print_given).
% 0.74/1.01 assign(lrs_ticks,-1).
% 0.74/1.01 assign(sos_limit,10000).
% 0.74/1.01 assign(order,kbo).
% 0.74/1.01 set(lex_order_vars).
% 0.74/1.01 clear(print_given).
% 0.74/1.01
% 0.74/1.01 % formulas(sos). % not echoed (43 formulas)
% 0.74/1.01
% 0.74/1.01 ============================== end of input ==========================
% 0.74/1.01
% 0.74/1.01 % From the command line: assign(max_seconds, 300).
% 0.74/1.01
% 0.74/1.01 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 0.74/1.01
% 0.74/1.01 % Formulas that are not ordinary clauses:
% 0.74/1.01 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].
% 0.74/1.01 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].
% 0.74/1.01 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].
% 0.74/1.01 4 implies_1 <-> (all X all Y is_a_theorem(implies(X,implies(Y,X)))) # label(implies_1) # label(axiom) # label(non_clause). [assumption].
% 0.74/1.01 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].
% 0.74/1.01 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].
% 0.74/1.01 7 and_1 <-> (all X all Y is_a_theorem(implies(and(X,Y),X))) # label(and_1) # label(axiom) # label(non_clause). [assumption].
% 0.74/1.01 8 and_2 <-> (all X all Y is_a_theorem(implies(and(X,Y),Y))) # label(and_2) # label(axiom) # label(non_clause). [assumption].
% 0.74/1.01 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].
% 0.74/1.01 10 or_1 <-> (all X all Y is_a_theorem(implies(X,or(X,Y)))) # label(or_1) # label(axiom) # label(non_clause). [assumption].
% 0.74/1.01 11 or_2 <-> (all X all Y is_a_theorem(implies(Y,or(X,Y)))) # label(or_2) # label(axiom) # label(non_clause). [assumption].
% 0.74/1.01 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].
% 0.74/1.01 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].
% 0.74/1.01 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].
% 1.13/1.43 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].
% 1.13/1.43 16 kn1 <-> (all P is_a_theorem(implies(P,and(P,P)))) # label(kn1) # label(axiom) # label(non_clause). [assumption].
% 1.13/1.43 17 kn2 <-> (all P all Q is_a_theorem(implies(and(P,Q),P))) # label(kn2) # label(axiom) # label(non_clause). [assumption].
% 1.13/1.43 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].
% 1.13/1.43 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].
% 1.13/1.43 20 cn2 <-> (all P all Q is_a_theorem(implies(P,implies(not(P),Q)))) # label(cn2) # label(axiom) # label(non_clause). [assumption].
% 1.13/1.43 21 cn3 <-> (all P is_a_theorem(implies(implies(not(P),P),P))) # label(cn3) # label(axiom) # label(non_clause). [assumption].
% 1.13/1.43 22 r1 <-> (all P is_a_theorem(implies(or(P,P),P))) # label(r1) # label(axiom) # label(non_clause). [assumption].
% 1.13/1.43 23 r2 <-> (all P all Q is_a_theorem(implies(Q,or(P,Q)))) # label(r2) # label(axiom) # label(non_clause). [assumption].
% 1.13/1.43 24 r3 <-> (all P all Q is_a_theorem(implies(or(P,Q),or(Q,P)))) # label(r3) # label(axiom) # label(non_clause). [assumption].
% 1.13/1.43 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].
% 1.13/1.43 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].
% 1.13/1.43 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].
% 1.13/1.43 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].
% 1.13/1.43 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].
% 1.13/1.43 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].
% 1.13/1.43 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].
% 1.13/1.43
% 1.13/1.43 ============================== end of process non-clausal formulas ===
% 1.13/1.43
% 1.13/1.43 ============================== PROCESS INITIAL CLAUSES ===============
% 1.13/1.43
% 1.13/1.43 ============================== PREDICATE ELIMINATION =================
% 1.13/1.43
% 1.13/1.43 ============================== end predicate elimination =============
% 1.13/1.43
% 1.13/1.43 Auto_denials: (non-Horn, no changes).
% 1.13/1.43
% 1.13/1.43 Term ordering decisions:
% 1.13/1.43
% 1.13/1.43 % Assigning unary symbol not kb_weight 0 and highest precedence (93).
% 1.13/1.43 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.
% 1.13/1.43
% 1.13/1.43 ============================== end of process initial clauses ========
% 1.13/1.43
% 1.13/1.43 ============================== CLAUSES FOR SEARCH ====================
% 1.13/1.43
% 1.13/1.43 ============================== end of clauses for search =============
% 1.13/1.43
% 1.13/1.43 ============================== SEARCH ================================
% 1.13/1.43
% 1.13/1.43 % Starting search at 0.02 seconds.
% 1.13/1.43
% 1.13/1.43 Low Water (keep): wt=34.000, iters=3468
% 1.13/1.43
% 1.13/1.43 Low Water (keep): wt=32.000, iters=3420
% 1.13/1.43
% 1.13/1.43 Low Water (keep): wt=30.000, iters=3391
% 1.13/1.43
% 1.13/1.43 Low Water (keep): wt=29.000, iters=3535
% 1.13/1.43
% 1.13/1.43 Low Water (keep): wt=26.000, iters=3429
% 1.13/1.43
% 1.13/1.43 Low Water (keep): wt=25.000, iters=3334
% 1.13/1.43
% 1.13/1.43 Low Water (keep): wt=24.000, iters=3352
% 1.13/1.43
% 1.13/1.43 Low Water (keep): wt=23.000, iters=3444
% 1.13/1.43
% 1.13/1.43 Low Water (keep): wt=22.000, iters=3457
% 1.13/1.43
% 1.13/1.43 Low Water (keep): wt=21.000, iters=3357
% 1.13/1.43
% 16.10/16.38 Low Water (keep): wt=20.000, iters=3416
% 16.10/16.38
% 16.10/16.38 Low Water (keep): wt=19.000, iters=3393
% 16.10/16.38
% 16.10/16.38 Low Water (keep): wt=18.000, iters=3583
% 16.10/16.38
% 16.10/16.38 Low Water (keep): wt=17.000, iters=3353
% 16.10/16.38
% 16.10/16.38 Low Water (keep): wt=16.000, iters=3353
% 16.10/16.38
% 16.10/16.38 Low Water (keep): wt=15.000, iters=3389
% 16.10/16.38
% 16.10/16.38 Low Water (displace): id=2363, wt=51.000
% 16.10/16.38
% 16.10/16.38 Low Water (displace): id=2362, wt=49.000
% 16.10/16.38
% 16.10/16.38 Low Water (displace): id=1968, wt=47.000
% 16.10/16.38
% 16.10/16.38 Low Water (displace): id=1967, wt=45.000
% 16.10/16.38
% 16.10/16.38 Low Water (displace): id=1626, wt=43.000
% 16.10/16.38
% 16.10/16.38 Low Water (displace): id=2394, wt=42.000
% 16.10/16.38
% 16.10/16.38 Low Water (displace): id=1625, wt=41.000
% 16.10/16.38
% 16.10/16.38 Low Water (displace): id=1995, wt=40.000
% 16.10/16.38
% 16.10/16.38 Low Water (displace): id=2399, wt=38.000
% 16.10/16.38
% 16.10/16.38 Low Water (displace): id=2392, wt=36.000
% 16.10/16.38
% 16.10/16.38 Low Water (displace): id=3299, wt=35.000
% 16.10/16.38
% 16.10/16.38 Low Water (displace): id=3338, wt=34.000
% 16.10/16.38
% 16.10/16.38 Low Water (displace): id=10640, wt=14.000
% 16.10/16.38
% 16.10/16.38 Low Water (displace): id=10673, wt=13.000
% 16.10/16.38
% 16.10/16.38 Low Water (keep): wt=14.000, iters=3400
% 16.10/16.38
% 16.10/16.38 NOTE: Back_subsumption disabled, ratio of kept to back_subsumed is 139 (0.00 of 0.97 sec).
% 16.10/16.38
% 16.10/16.38 Low Water (displace): id=11354, wt=12.000
% 16.10/16.38
% 16.10/16.38 Low Water (displace): id=11414, wt=11.000
% 16.10/16.38
% 16.10/16.38 Low Water (displace): id=13342, wt=10.000
% 16.10/16.38
% 16.10/16.38 Low Water (displace): id=16581, wt=9.000
% 16.10/16.38
% 16.10/16.38 Low Water (keep): wt=13.000, iters=3375
% 16.10/16.38
% 16.10/16.38 Low Water (keep): wt=12.000, iters=3335
% 16.10/16.38
% 16.10/16.38 ============================== PROOF =================================
% 16.10/16.38 % SZS status Theorem
% 16.10/16.38 % SZS output start Refutation
% 16.10/16.38
% 16.10/16.38 % Proof 1 at 14.23 (+ 1.15) seconds.
% 16.10/16.38 % Length of proof is 57.
% 16.10/16.38 % Level of proof is 24.
% 16.10/16.38 % Maximum clause weight is 14.000.
% 16.10/16.38 % Given clauses 2911.
% 16.10/16.38
% 16.10/16.38 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].
% 16.10/16.38 8 and_2 <-> (all X all Y is_a_theorem(implies(and(X,Y),Y))) # label(and_2) # label(axiom) # label(non_clause). [assumption].
% 16.10/16.38 16 kn1 <-> (all P is_a_theorem(implies(P,and(P,P)))) # label(kn1) # label(axiom) # label(non_clause). [assumption].
% 16.10/16.38 17 kn2 <-> (all P all Q is_a_theorem(implies(and(P,Q),P))) # label(kn2) # label(axiom) # label(non_clause). [assumption].
% 16.10/16.38 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].
% 16.10/16.38 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].
% 16.10/16.38 33 op_implies_and # label(rosser_op_implies_and) # label(axiom). [assumption].
% 16.10/16.38 35 modus_ponens # label(rosser_modus_ponens) # label(axiom). [assumption].
% 16.10/16.38 36 kn1 # label(rosser_kn1) # label(axiom). [assumption].
% 16.10/16.38 37 kn2 # label(rosser_kn2) # label(axiom). [assumption].
% 16.10/16.38 38 kn3 # label(rosser_kn3) # label(axiom). [assumption].
% 16.10/16.38 40 -and_2 # label(hilbert_and_2) # label(negated_conjecture). [assumption].
% 16.10/16.38 45 and_2 | -is_a_theorem(implies(and(c16,c17),c17)) # label(and_2) # label(axiom). [clausify(8)].
% 16.10/16.38 46 -is_a_theorem(implies(and(c16,c17),c17)). [copy(45),unit_del(a,40)].
% 16.10/16.38 51 -kn1 | is_a_theorem(implies(A,and(A,A))) # label(kn1) # label(axiom). [clausify(16)].
% 16.10/16.38 52 is_a_theorem(implies(A,and(A,A))). [copy(51),unit_del(a,36)].
% 16.10/16.38 54 -kn2 | is_a_theorem(implies(and(A,B),A)) # label(kn2) # label(axiom). [clausify(17)].
% 16.10/16.38 55 is_a_theorem(implies(and(A,B),A)). [copy(54),unit_del(a,37)].
% 16.10/16.38 67 -modus_ponens | -is_a_theorem(A) | -is_a_theorem(implies(A,B)) | is_a_theorem(B) # label(modus_ponens) # label(axiom). [clausify(1)].
% 16.10/16.38 68 -is_a_theorem(A) | -is_a_theorem(implies(A,B)) | is_a_theorem(B). [copy(67),unit_del(a,35)].
% 16.10/16.38 78 -op_implies_and | not(and(A,not(B))) = implies(A,B) # label(op_implies_and) # label(axiom). [clausify(29)].
% 16.10/16.38 79 not(and(A,not(B))) = implies(A,B). [copy(78),unit_del(a,33)].
% 16.10/16.38 108 -kn3 | is_a_theorem(implies(implies(A,B),implies(not(and(B,C)),not(and(C,A))))) # label(kn3) # label(axiom). [clausify(18)].
% 16.10/16.38 109 is_a_theorem(implies(implies(A,B),implies(not(and(B,C)),not(and(C,A))))). [copy(108),unit_del(a,38)].
% 16.10/16.38 132 -is_a_theorem(implies(A,B)) | is_a_theorem(implies(not(and(B,C)),not(and(C,A)))). [resolve(109,a,68,b)].
% 16.10/16.38 135 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))].
% 16.10/16.38 277 is_a_theorem(implies(not(and(and(A,A),B)),not(and(B,A)))). [resolve(132,a,52,a)].
% 16.10/16.38 301 -is_a_theorem(not(and(and(A,A),B))) | is_a_theorem(not(and(B,A))). [resolve(277,a,68,b)].
% 16.10/16.38 409 -is_a_theorem(implies(and(A,A),B)) | is_a_theorem(not(and(not(B),A))). [para(79(a,1),301(a,1))].
% 16.10/16.38 706 is_a_theorem(not(and(not(A),A))). [resolve(409,a,55,a)].
% 16.10/16.38 737 -is_a_theorem(implies(not(and(not(A),A)),implies(and(c16,c17),c17))). [ur(68,a,706,a,c,46,a)].
% 16.10/16.38 739 is_a_theorem(implies(not(not(A)),A)). [para(79(a,1),706(a,1))].
% 16.10/16.38 742 is_a_theorem(implies(not(and(A,B)),implies(B,not(A)))). [resolve(739,a,132,a),rewrite([79(6)])].
% 16.10/16.38 744 -is_a_theorem(not(not(A))) | is_a_theorem(A). [resolve(739,a,68,b)].
% 16.10/16.38 1034 -is_a_theorem(not(and(A,B))) | is_a_theorem(implies(B,not(A))). [resolve(742,a,68,b)].
% 16.10/16.38 1622 -is_a_theorem(implies(A,B)) | is_a_theorem(implies(not(B),not(A))). [para(79(a,1),1034(a,1))].
% 16.10/16.38 2118 -is_a_theorem(implies(not(c17),not(and(c16,c17)))). [ur(68,b,135,a,c,737,a)].
% 16.10/16.38 4614 is_a_theorem(implies(not(A),not(and(A,B)))). [resolve(1622,a,55,a)].
% 16.10/16.38 4615 is_a_theorem(implies(not(and(A,A)),not(A))). [resolve(1622,a,52,a)].
% 16.10/16.38 4845 is_a_theorem(implies(not(and(not(and(A,B)),C)),implies(C,A))). [resolve(4614,a,132,a),rewrite([79(7)])].
% 16.10/16.38 4909 is_a_theorem(implies(not(A),implies(A,B))). [para(79(a,1),4614(a,1,2))].
% 16.10/16.38 4916 is_a_theorem(implies(not(and(implies(A,B),C)),implies(C,A))). [resolve(4909,a,132,a),rewrite([79(6)])].
% 16.10/16.38 5327 -is_a_theorem(not(and(A,A))) | is_a_theorem(not(A)). [resolve(4615,a,68,b)].
% 16.10/16.38 5435 -is_a_theorem(implies(not(A),A)) | is_a_theorem(not(not(A))). [para(79(a,1),5327(a,1))].
% 16.10/16.38 11097 -is_a_theorem(not(and(implies(A,B),C))) | is_a_theorem(implies(C,A)). [resolve(4916,a,68,b)].
% 16.10/16.38 11113 is_a_theorem(implies(implies(implies(A,B),C),implies(not(C),A))). [para(79(a,1),4916(a,1,1))].
% 16.10/16.38 13032 -is_a_theorem(implies(implies(A,B),C)) | is_a_theorem(implies(not(C),A)). [para(79(a,1),11097(a,1))].
% 16.10/16.38 13908 is_a_theorem(implies(not(implies(not(A),B)),implies(B,C))). [resolve(13032,a,11113,a)].
% 16.10/16.38 14428 is_a_theorem(not(not(implies(not(A),not(A))))). [resolve(13908,a,5435,a)].
% 16.10/16.38 14550 is_a_theorem(implies(not(A),not(A))). [resolve(14428,a,744,a)].
% 16.10/16.38 14583 is_a_theorem(implies(not(and(not(A),B)),implies(B,A))). [resolve(14550,a,132,a),rewrite([79(6)])].
% 16.10/16.38 15986 -is_a_theorem(not(and(not(A),B))) | is_a_theorem(implies(B,A)). [resolve(14583,a,68,b)].
% 16.10/16.38 16013 -is_a_theorem(implies(not(not(and(c16,c17))),c17)). [ur(68,b,14583,a,c,2118,a),rewrite([79(9)])].
% 16.10/16.38 17136 is_a_theorem(implies(A,A)). [resolve(15986,a,706,a)].
% 16.10/16.38 17240 is_a_theorem(implies(not(and(A,B)),not(and(B,A)))). [resolve(17136,a,132,a)].
% 16.10/16.38 63953 -is_a_theorem(implies(not(and(c17,A)),not(and(c16,c17)))). [ur(68,b,4845,a,c,16013,a),rewrite([79(10)])].
% 16.10/16.38 63954 $F. [resolve(63953,a,17240,a)].
% 16.10/16.38
% 16.10/16.38 % SZS output end Refutation
% 16.10/16.38 ============================== end of proof ==========================
% 16.10/16.38
% 16.10/16.38 ============================== STATISTICS ============================
% 16.10/16.38
% 16.10/16.38 Given=2911. Generated=2268494. Kept=63903. proofs=1.
% 16.10/16.38 Usable=2895. Sos=9999. Demods=5. Limbo=81, Disabled=50999. Hints=0.
% 16.10/16.38 Megabytes=42.25.
% 16.10/16.38 User_CPU=14.23, System_CPU=1.15, Wall_clock=15.
% 16.10/16.38
% 16.10/16.38 ============================== end of statistics =====================
% 16.10/16.38
% 16.10/16.38 ============================== end of search =========================
% 16.10/16.38
% 16.10/16.38 THEOREM PROVED
% 16.10/16.38 % SZS status Theorem
% 16.10/16.38
% 16.10/16.38 Exiting with 1 proof.
% 16.10/16.38
% 16.10/16.38 Process 29295 exit (max_proofs) Mon Jul 4 08:23:00 2022
% 16.10/16.38 Prover9 interrupted
%------------------------------------------------------------------------------