0.00/0.10 % Problem : theBenchmark.p : TPTP v0.0.0. Released v0.0.0. 0.00/0.10 % Command : tptp2X_and_run_prover9 %d %s 0.10/0.31 % Computer : n027.cluster.edu 0.10/0.31 % Model : x86_64 x86_64 0.10/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz 0.10/0.31 % Memory : 8042.1875MB 0.10/0.31 % OS : Linux 3.10.0-693.el7.x86_64 0.10/0.31 % CPULimit : 1200 0.10/0.31 % DateTime : Tue Jul 13 16:14:25 EDT 2021 0.10/0.31 % CPUTime : 0.71/1.02 ============================== Prover9 =============================== 0.71/1.02 Prover9 (32) version 2009-11A, November 2009. 0.71/1.02 Process 3793 was started by sandbox on n027.cluster.edu, 0.71/1.02 Tue Jul 13 16:14:26 2021 0.71/1.02 The command was "/export/starexec/sandbox/solver/bin/prover9 -t 1200 -f /tmp/Prover9_3638_n027.cluster.edu". 0.71/1.02 ============================== end of head =========================== 0.71/1.02 0.71/1.02 ============================== INPUT ================================= 0.71/1.02 0.71/1.02 % Reading from file /tmp/Prover9_3638_n027.cluster.edu 0.71/1.02 0.71/1.02 set(prolog_style_variables). 0.71/1.02 set(auto2). 0.71/1.02 % set(auto2) -> set(auto). 0.71/1.02 % set(auto) -> set(auto_inference). 0.71/1.02 % set(auto) -> set(auto_setup). 0.71/1.02 % set(auto_setup) -> set(predicate_elim). 0.71/1.02 % set(auto_setup) -> assign(eq_defs, unfold). 0.71/1.02 % set(auto) -> set(auto_limits). 0.71/1.02 % set(auto_limits) -> assign(max_weight, "100.000"). 0.71/1.02 % set(auto_limits) -> assign(sos_limit, 20000). 0.71/1.02 % set(auto) -> set(auto_denials). 0.71/1.02 % set(auto) -> set(auto_process). 0.71/1.02 % set(auto2) -> assign(new_constants, 1). 0.71/1.02 % set(auto2) -> assign(fold_denial_max, 3). 0.71/1.02 % set(auto2) -> assign(max_weight, "200.000"). 0.71/1.02 % set(auto2) -> assign(max_hours, 1). 0.71/1.02 % assign(max_hours, 1) -> assign(max_seconds, 3600). 0.71/1.02 % set(auto2) -> assign(max_seconds, 0). 0.71/1.02 % set(auto2) -> assign(max_minutes, 5). 0.71/1.02 % assign(max_minutes, 5) -> assign(max_seconds, 300). 0.71/1.02 % set(auto2) -> set(sort_initial_sos). 0.71/1.02 % set(auto2) -> assign(sos_limit, -1). 0.71/1.02 % set(auto2) -> assign(lrs_ticks, 3000). 0.71/1.02 % set(auto2) -> assign(max_megs, 400). 0.71/1.02 % set(auto2) -> assign(stats, some). 0.71/1.02 % set(auto2) -> clear(echo_input). 0.71/1.02 % set(auto2) -> set(quiet). 0.71/1.02 % set(auto2) -> clear(print_initial_clauses). 0.71/1.02 % set(auto2) -> clear(print_given). 0.71/1.02 assign(lrs_ticks,-1). 0.71/1.02 assign(sos_limit,10000). 0.71/1.02 assign(order,kbo). 0.71/1.02 set(lex_order_vars). 0.71/1.02 clear(print_given). 0.71/1.02 0.71/1.02 % formulas(sos). % not echoed (45 formulas) 0.71/1.02 0.71/1.02 ============================== end of input ========================== 0.71/1.02 0.71/1.02 % From the command line: assign(max_seconds, 1200). 0.71/1.02 0.71/1.02 ============================== PROCESS NON-CLAUSAL FORMULAS ========== 0.71/1.02 0.71/1.02 % Formulas that are not ordinary clauses: 0.71/1.02 1 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]. 0.71/1.02 2 (all P all Q all R is_a_theorem(implies(implies(P,Q),implies(implies(Q,R),implies(P,R))))) <-> cn1 # label(cn1) # label(axiom) # label(non_clause). [assumption]. 0.71/1.02 3 (all X all Y is_a_theorem(implies(and(X,Y),X))) <-> and_1 # label(and_1) # label(axiom) # label(non_clause). [assumption]. 0.71/1.02 4 (all X all Y is_a_theorem(implies(implies(X,implies(X,Y)),implies(X,Y)))) <-> implies_2 # label(implies_2) # label(axiom) # label(non_clause). [assumption]. 0.71/1.02 5 (all X all Y (is_a_theorem(implies(X,Y)) & is_a_theorem(X) -> is_a_theorem(Y))) <-> modus_ponens # label(modus_ponens) # label(axiom) # label(non_clause). [assumption]. 0.71/1.02 6 (all P all Q is_a_theorem(implies(P,implies(not(P),Q)))) <-> cn2 # label(cn2) # label(axiom) # label(non_clause). [assumption]. 0.71/1.02 7 (all X all Y is_a_theorem(implies(equiv(X,Y),implies(Y,X)))) <-> equivalence_2 # label(equivalence_2) # label(axiom) # label(non_clause). [assumption]. 0.71/1.02 8 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]. 0.71/1.02 9 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]. 0.71/1.02 10 (all P is_a_theorem(implies(or(P,P),P))) <-> r1 # label(r1) # label(axiom) # label(non_clause). [assumption]. 0.71/1.02 11 and_2 <-> (all X all Y is_a_theorem(implies(and(X,Y),Y))) # label(and_2) # label(axiom) # label(non_clause). [assumption]. 0.71/1.02 12 r3 <-> (all P all Q is_a_theorem(implies(or(P,Q),or(Q,P)))) # label(r3) # label(axiom) # label(non_clause). [assumption]. 0.71/1.02 13 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]. 0.71/1.02 14 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]. 2.09/2.39 15 kn1 <-> (all P is_a_theorem(implies(P,and(P,P)))) # label(kn1) # label(axiom) # label(non_clause). [assumption]. 2.09/2.39 16 or_2 <-> (all X all Y is_a_theorem(implies(Y,or(X,Y)))) # label(or_2) # label(axiom) # label(non_clause). [assumption]. 2.09/2.39 17 or_1 <-> (all X all Y is_a_theorem(implies(X,or(X,Y)))) # label(or_1) # label(axiom) # label(non_clause). [assumption]. 2.09/2.39 18 (all P all Q all R is_a_theorem(implies(implies(Q,R),implies(or(P,Q),or(P,R))))) <-> r5 # label(r5) # label(axiom) # label(non_clause). [assumption]. 2.09/2.39 19 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]. 2.09/2.39 20 (all P all Q is_a_theorem(implies(and(P,Q),P))) <-> kn2 # label(kn2) # label(axiom) # label(non_clause). [assumption]. 2.09/2.39 21 (all X all Y is_a_theorem(implies(implies(not(Y),not(X)),implies(X,Y)))) <-> modus_tollens # label(modus_tollens) # label(axiom) # label(non_clause). [assumption]. 2.09/2.39 22 (all X all Y all Z is_a_theorem(implies(implies(X,Z),implies(implies(Y,Z),implies(or(X,Y),Z))))) <-> or_3 # label(or_3) # label(axiom) # label(non_clause). [assumption]. 2.09/2.39 23 implies_1 <-> (all X all Y is_a_theorem(implies(X,implies(Y,X)))) # label(implies_1) # label(axiom) # label(non_clause). [assumption]. 2.09/2.39 24 r2 <-> (all P all Q is_a_theorem(implies(Q,or(P,Q)))) # label(r2) # label(axiom) # label(non_clause). [assumption]. 2.09/2.39 25 cn3 <-> (all P is_a_theorem(implies(implies(not(P),P),P))) # label(cn3) # label(axiom) # label(non_clause). [assumption]. 2.09/2.39 26 (all X all Y (is_a_theorem(equiv(X,Y)) -> X = Y)) <-> substitution_of_equivalents # label(substitution_of_equivalents) # label(axiom) # label(non_clause). [assumption]. 2.09/2.39 27 op_implies_or -> (all X all Y implies(X,Y) = or(not(X),Y)) # label(op_implies_or) # label(axiom) # label(non_clause). [assumption]. 2.09/2.39 28 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]. 2.09/2.39 29 op_or -> (all X all Y or(X,Y) = not(and(not(X),not(Y)))) # label(op_or) # label(axiom) # label(non_clause). [assumption]. 2.09/2.39 30 op_equiv -> (all X all Y and(implies(X,Y),implies(Y,X)) = equiv(X,Y)) # label(op_equiv) # label(axiom) # label(non_clause). [assumption]. 2.09/2.39 31 op_and -> (all X all Y not(or(not(X),not(Y))) = and(X,Y)) # label(op_and) # label(axiom) # label(non_clause). [assumption]. 2.09/2.39 2.09/2.39 ============================== end of process non-clausal formulas === 2.09/2.39 2.09/2.39 ============================== PROCESS INITIAL CLAUSES =============== 2.09/2.39 2.09/2.39 ============================== PREDICATE ELIMINATION ================= 2.09/2.39 2.09/2.39 ============================== end predicate elimination ============= 2.09/2.39 2.09/2.39 Auto_denials: (non-Horn, no changes). 2.09/2.39 2.09/2.39 Term ordering decisions: 2.09/2.39 2.09/2.39 % Assigning unary symbol not kb_weight 0 and highest precedence (93). 2.09/2.39 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. 2.09/2.39 2.09/2.39 ============================== end of process initial clauses ======== 2.09/2.39 2.09/2.39 ============================== CLAUSES FOR SEARCH ==================== 2.09/2.39 2.09/2.39 ============================== end of clauses for search ============= 2.09/2.39 2.09/2.39 ============================== SEARCH ================================ 2.09/2.39 2.09/2.39 % Starting search at 0.01 seconds. 2.09/2.39 2.09/2.39 Low Water (keep): wt=26.000, iters=3429 2.09/2.39 2.09/2.39 Low Water (keep): wt=24.000, iters=3395 2.09/2.39 2.09/2.39 Low Water (keep): wt=23.000, iters=3529 2.09/2.39 2.09/2.39 Low Water (keep): wt=22.000, iters=3354 2.09/2.39 2.09/2.39 Low Water (keep): wt=21.000, iters=3403 2.09/2.39 2.09/2.39 Low Water (keep): wt=20.000, iters=3351 2.09/2.39 2.09/2.39 Low Water (keep): wt=19.000, iters=3340 2.09/2.39 2.09/2.39 Low Water (keep): wt=18.000, iters=3335 2.09/2.39 2.09/2.39 Low Water (keep): wt=17.000, iters=3349 2.09/2.39 2.09/2.39 Low Water (keep): wt=16.000, iters=3334 2.09/2.39 2.09/2.39 Low Water (keep): wt=15.000, iters=3467 59.52/59.90 59.52/59.90 Low Water (keep): wt=14.000, iters=3334 59.52/59.90 59.52/59.90 NOTE: Back_subsumption disabled, ratio of kept to back_subsumed is 31 (0.00 of 1.62 sec). 59.52/59.90 59.52/59.90 Low Water (keep): wt=13.000, iters=3333 59.52/59.90 59.52/59.90 Low Water (displace): id=6436, wt=42.000 59.52/59.90 59.52/59.90 Low Water (displace): id=14952, wt=41.000 59.52/59.90 59.52/59.90 Low Water (displace): id=12801, wt=40.000 59.52/59.90 59.52/59.90 Low Water (displace): id=14521, wt=39.000 59.52/59.90 59.52/59.90 Low Water (displace): id=14970, wt=38.000 59.52/59.90 59.52/59.90 Low Water (displace): id=14539, wt=36.000 59.52/59.90 59.52/59.90 Low Water (displace): id=15119, wt=35.000 59.52/59.90 59.52/59.90 Low Water (displace): id=13727, wt=34.000 59.52/59.90 59.52/59.90 Low Water (displace): id=15179, wt=33.000 59.52/59.90 59.52/59.90 Low Water (displace): id=15230, wt=32.000 59.52/59.90 59.52/59.90 Low Water (displace): id=15432, wt=30.000 59.52/59.90 59.52/59.90 Low Water (displace): id=15724, wt=29.000 59.52/59.90 59.52/59.90 Low Water (displace): id=13628, wt=28.000 59.52/59.90 59.52/59.90 Low Water (displace): id=15448, wt=27.000 59.52/59.90 59.52/59.90 Low Water (displace): id=15813, wt=26.000 59.52/59.90 59.52/59.90 Low Water (displace): id=16163, wt=24.000 59.52/59.90 59.52/59.90 Low Water (displace): id=16562, wt=23.000 59.52/59.90 59.52/59.90 Low Water (displace): id=16437, wt=22.000 59.52/59.90 59.52/59.90 Low Water (displace): id=17031, wt=11.000 59.52/59.90 59.52/59.90 Low Water (displace): id=18150, wt=10.000 59.52/59.90 59.52/59.90 Low Water (displace): id=19115, wt=9.000 59.52/59.90 59.52/59.90 Low Water (keep): wt=12.000, iters=3336 59.52/59.90 59.52/59.90 Low Water (keep): wt=11.000, iters=3342 59.52/59.90 59.52/59.90 Low Water (keep): wt=10.000, iters=3340 59.52/59.90 59.52/59.90 ============================== PROOF ================================= 59.52/59.90 % SZS status Theorem 59.52/59.90 % SZS output start Refutation 59.52/59.90 59.52/59.90 % Proof 1 at 55.21 (+ 3.61) seconds. 59.52/59.90 % Length of proof is 204. 59.52/59.90 % Level of proof is 38. 59.52/59.90 % Maximum clause weight is 16.000. 59.52/59.90 % Given clauses 5028. 59.52/59.90 59.52/59.90 5 (all X all Y (is_a_theorem(implies(X,Y)) & is_a_theorem(X) -> is_a_theorem(Y))) <-> modus_ponens # label(modus_ponens) # label(axiom) # label(non_clause). [assumption]. 59.52/59.90 10 (all P is_a_theorem(implies(or(P,P),P))) <-> r1 # label(r1) # label(axiom) # label(non_clause). [assumption]. 59.52/59.90 12 r3 <-> (all P all Q is_a_theorem(implies(or(P,Q),or(Q,P)))) # label(r3) # label(axiom) # label(non_clause). [assumption]. 59.52/59.90 14 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]. 59.52/59.90 18 (all P all Q all R is_a_theorem(implies(implies(Q,R),implies(or(P,Q),or(P,R))))) <-> r5 # label(r5) # label(axiom) # label(non_clause). [assumption]. 59.52/59.90 19 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]. 59.52/59.90 24 r2 <-> (all P all Q is_a_theorem(implies(Q,or(P,Q)))) # label(r2) # label(axiom) # label(non_clause). [assumption]. 59.52/59.90 26 (all X all Y (is_a_theorem(equiv(X,Y)) -> X = Y)) <-> substitution_of_equivalents # label(substitution_of_equivalents) # label(axiom) # label(non_clause). [assumption]. 59.52/59.90 27 op_implies_or -> (all X all Y implies(X,Y) = or(not(X),Y)) # label(op_implies_or) # label(axiom) # label(non_clause). [assumption]. 59.52/59.90 28 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]. 59.52/59.90 29 op_or -> (all X all Y or(X,Y) = not(and(not(X),not(Y)))) # label(op_or) # label(axiom) # label(non_clause). [assumption]. 59.52/59.90 30 op_equiv -> (all X all Y and(implies(X,Y),implies(Y,X)) = equiv(X,Y)) # label(op_equiv) # label(axiom) # label(non_clause). [assumption]. 59.52/59.90 31 op_and -> (all X all Y not(or(not(X),not(Y))) = and(X,Y)) # label(op_and) # label(axiom) # label(non_clause). [assumption]. 59.52/59.90 32 r3 # label(principia_r3) # label(axiom). [assumption]. 59.52/59.90 33 substitution_of_equivalents # label(substitution_of_equivalents) # label(axiom). [assumption]. 59.52/59.90 34 r5 # label(principia_r5) # label(axiom). [assumption]. 59.52/59.90 35 op_equiv # label(principia_op_equiv) # label(axiom). [assumption]. 59.52/59.90 36 r1 # label(principia_r1) # label(axiom). [assumption]. 59.52/59.90 37 r2 # label(principia_r2) # label(axiom). [assumption]. 59.52/59.90 38 modus_ponens # label(principia_modus_ponens) # label(axiom). [assumption]. 59.52/59.90 39 op_and # label(principia_op_and) # label(axiom). [assumption]. 59.52/59.90 40 op_implies_or # label(principia_op_implies_or) # label(axiom). [assumption]. 59.52/59.90 41 r4 # label(principia_r4) # label(axiom). [assumption]. 59.52/59.90 42 op_implies_and # label(rosser_op_implies_and) # label(axiom). [assumption]. 59.52/59.91 43 op_or # label(rosser_op_or) # label(axiom). [assumption]. 59.52/59.91 44 -kn3 # label(rosser_kn3) # label(negated_conjecture). [assumption]. 59.52/59.91 47 is_a_theorem(implies(or(A,A),A)) | -r1 # label(r1) # label(axiom). [clausify(10)]. 59.52/59.91 48 is_a_theorem(implies(or(A,A),A)). [copy(47),unit_del(b,36)]. 59.52/59.91 61 -r2 | is_a_theorem(implies(A,or(B,A))) # label(r2) # label(axiom). [clausify(24)]. 59.52/59.91 62 is_a_theorem(implies(A,or(B,A))). [copy(61),unit_del(a,37)]. 59.52/59.91 68 -is_a_theorem(equiv(A,B)) | B = A | -substitution_of_equivalents # label(substitution_of_equivalents) # label(axiom). [clausify(26)]. 59.52/59.91 69 -is_a_theorem(equiv(A,B)) | B = A. [copy(68),unit_del(c,33)]. 59.52/59.91 70 -is_a_theorem(implies(A,B)) | -is_a_theorem(A) | is_a_theorem(B) | -modus_ponens # label(modus_ponens) # label(axiom). [clausify(5)]. 59.52/59.91 71 -is_a_theorem(implies(A,B)) | -is_a_theorem(A) | is_a_theorem(B). [copy(70),unit_del(d,38)]. 59.52/59.91 76 -r3 | is_a_theorem(implies(or(A,B),or(B,A))) # label(r3) # label(axiom). [clausify(12)]. 59.52/59.91 77 is_a_theorem(implies(or(A,B),or(B,A))). [copy(76),unit_del(a,32)]. 59.52/59.91 81 -op_implies_or | or(not(A),B) = implies(A,B) # label(op_implies_or) # label(axiom). [clausify(27)]. 59.52/59.91 82 or(not(A),B) = implies(A,B). [copy(81),unit_del(a,40)]. 59.52/59.91 83 -op_implies_and | not(and(A,not(B))) = implies(A,B) # label(op_implies_and) # label(axiom). [clausify(28)]. 59.52/59.91 84 not(and(A,not(B))) = implies(A,B). [copy(83),unit_del(a,42)]. 59.52/59.91 89 -op_or | or(A,B) = not(and(not(A),not(B))) # label(op_or) # label(axiom). [clausify(29)]. 59.52/59.91 90 or(A,B) = implies(not(A),B). [copy(89),rewrite([84(6)]),unit_del(a,43)]. 59.52/59.91 91 -op_and | not(or(not(A),not(B))) = and(A,B) # label(op_and) # label(axiom). [clausify(31)]. 59.52/59.91 92 not(implies(not(not(A)),not(B))) = and(A,B). [copy(91),rewrite([90(4)]),unit_del(a,39)]. 59.52/59.91 93 -op_equiv | equiv(A,B) = and(implies(A,B),implies(B,A)) # label(op_equiv) # label(axiom). [clausify(30)]. 59.52/59.91 94 and(implies(A,B),implies(B,A)) = equiv(A,B). [copy(93),flip(b),unit_del(a,35)]. 59.52/59.91 102 is_a_theorem(implies(implies(A,B),implies(or(C,A),or(C,B)))) | -r5 # label(r5) # label(axiom). [clausify(18)]. 59.52/59.91 103 is_a_theorem(implies(implies(A,B),implies(implies(not(C),A),implies(not(C),B)))). [copy(102),rewrite([90(2),90(4)]),unit_del(b,34)]. 59.52/59.91 104 -r4 | is_a_theorem(implies(or(A,or(B,C)),or(B,or(A,C)))) # label(r4) # label(axiom). [clausify(19)]. 59.52/59.91 105 is_a_theorem(implies(implies(not(A),implies(not(B),C)),implies(not(B),implies(not(A),C)))). [copy(104),rewrite([90(2),90(4),90(6),90(8)]),unit_del(a,41)]. 59.52/59.91 107 kn3 | -is_a_theorem(implies(implies(c28,c29),implies(not(and(c29,c30)),not(and(c30,c28))))) # label(kn3) # label(axiom). [clausify(14)]. 59.52/59.91 108 -is_a_theorem(implies(implies(c28,c29),implies(not(and(c29,c30)),not(and(c30,c28))))). [copy(107),unit_del(a,44)]. 59.52/59.91 114 implies(not(not(A)),B) = implies(A,B). [back_rewrite(82),rewrite([90(2)])]. 59.52/59.91 115 is_a_theorem(implies(implies(not(A),B),implies(not(B),A))). [back_rewrite(77),rewrite([90(1),90(3)])]. 59.52/59.91 116 is_a_theorem(implies(A,implies(not(B),A))). [back_rewrite(62),rewrite([90(1)])]. 59.52/59.91 119 is_a_theorem(implies(implies(not(A),A),A)). [back_rewrite(48),rewrite([90(1)])]. 59.52/59.91 120 not(implies(A,not(B))) = and(A,B). [back_rewrite(92),rewrite([114(4)])]. 59.52/59.91 123 not(and(A,implies(B,C))) = implies(A,and(B,not(C))). [para(84(a,1),84(a,1,1,2))]. 59.52/59.91 124 -is_a_theorem(implies(A,B)) | is_a_theorem(implies(implies(not(C),A),implies(not(C),B))). [resolve(103,a,71,a)]. 59.52/59.91 126 -is_a_theorem(implies(not(A),implies(not(B),C))) | is_a_theorem(implies(not(B),implies(not(A),C))). [resolve(105,a,71,a)]. 59.52/59.91 132 implies(not(implies(A,B)),C) = implies(and(A,not(B)),C). [para(84(a,1),114(a,1,1,1))]. 59.52/59.91 134 and(implies(A,not(not(B))),implies(B,A)) = equiv(A,not(not(B))). [para(114(a,1),94(a,1,2))]. 59.52/59.91 136 is_a_theorem(implies(implies(A,B),implies(implies(C,A),implies(C,B)))). [para(114(a,1),103(a,1,2,1)),rewrite([114(5)])]. 59.52/59.91 139 -is_a_theorem(implies(not(A),B)) | is_a_theorem(implies(not(B),A)). [resolve(115,a,71,a)]. 59.52/59.91 143 is_a_theorem(implies(implies(A,B),implies(not(B),not(A)))). [para(114(a,1),115(a,1,1))]. 59.52/59.91 144 is_a_theorem(implies(implies(not(A),not(B)),implies(B,A))). [para(114(a,1),115(a,1,2))]. 59.52/59.91 149 is_a_theorem(implies(A,implies(B,A))). [para(114(a,1),116(a,1,2))]. 59.52/59.91 152 -is_a_theorem(implies(not(A),A)) | is_a_theorem(A). [resolve(119,a,71,a)]. 59.52/59.91 156 is_a_theorem(implies(implies(A,not(A)),not(A))). [para(114(a,1),119(a,1,1))]. 59.52/59.91 159 implies(not(and(A,B)),C) = implies(implies(A,not(B)),C). [para(120(a,1),114(a,1,1,1))]. 59.52/59.91 160 and(not(not(A)),B) = and(A,B). [para(114(a,1),120(a,1,1)),rewrite([120(3)]),flip(a)]. 59.52/59.91 171 -is_a_theorem(implies(implies(c28,c29),implies(implies(c29,not(c30)),not(and(c30,c28))))). [back_rewrite(108),rewrite([159(12)])]. 59.52/59.91 172 implies(implies(A,B),and(B,not(A))) = not(equiv(A,B)). [para(94(a,1),123(a,1,1)),flip(a)]. 59.52/59.91 195 -is_a_theorem(A) | is_a_theorem(implies(B,A)). [resolve(149,a,71,a)]. 59.52/59.91 199 is_a_theorem(implies(A,implies(B,not(not(A))))). [para(114(a,1),149(a,1))]. 59.52/59.91 204 is_a_theorem(implies(implies(not(A),implies(not(B),B)),implies(not(A),B))). [resolve(124,a,119,a)]. 59.52/59.91 243 -is_a_theorem(A) | is_a_theorem(implies(B,not(not(A)))). [resolve(199,a,71,a)]. 59.52/59.91 263 is_a_theorem(implies(not(A),implies(not(B),not(B)))). [resolve(126,a,149,a)]. 59.52/59.91 266 -is_a_theorem(implies(not(A),implies(B,C))) | is_a_theorem(implies(B,implies(not(A),C))). [para(114(a,1),126(a,1,2)),rewrite([114(9)])]. 59.52/59.91 402 is_a_theorem(implies(not(A),not(A))). [resolve(263,a,152,a)]. 59.52/59.91 423 is_a_theorem(implies(A,not(and(not(B),B)))). [resolve(402,a,243,a),rewrite([120(4)])]. 59.52/59.91 443 is_a_theorem(implies(A,not(not(A)))). [para(114(a,1),402(a,1))]. 59.52/59.91 450 implies(and(A,not(not(B))),C) = implies(and(A,B),C). [para(120(a,1),132(a,1,1)),flip(a)]. 59.52/59.91 507 is_a_theorem(implies(A,implies(B,B))). [resolve(443,a,243,a),rewrite([120(4),84(3)])]. 59.52/59.91 536 is_a_theorem(implies(A,A)). [resolve(507,a,152,a)]. 59.52/59.91 557 is_a_theorem(implies(A,not(not(implies(B,B))))). [resolve(536,a,243,a)]. 59.52/59.91 687 equiv(A,not(not(B))) = equiv(A,B). [para(134(a,1),160(a,2)),rewrite([120(4),84(3),94(3)]),flip(a)]. 59.52/59.91 1015 -is_a_theorem(implies(A,B)) | is_a_theorem(implies(implies(C,A),implies(C,B))). [resolve(136,a,71,a)]. 59.52/59.91 1139 -is_a_theorem(equiv(A,B)) | not(not(B)) = A. [para(687(a,1),69(a,1))]. 59.52/59.91 1343 is_a_theorem(implies(and(A,not(A)),B)). [resolve(139,a,557,a),rewrite([114(5),132(3)])]. 59.52/59.91 1345 is_a_theorem(implies(and(not(A),A),B)). [resolve(139,a,423,a),rewrite([114(5)])]. 59.52/59.91 1348 is_a_theorem(implies(and(A,B),B)). [resolve(139,a,199,a),rewrite([120(5),450(4)])]. 59.52/59.91 1350 -is_a_theorem(implies(A,B)) | is_a_theorem(implies(not(B),not(A))). [para(114(a,1),139(a,1))]. 59.52/59.91 2027 is_a_theorem(implies(implies(A,not(B)),implies(B,not(A)))). [para(114(a,1),143(a,1,2))]. 59.52/59.91 2275 -is_a_theorem(implies(not(A),not(B))) | is_a_theorem(implies(B,A)). [resolve(144,a,71,a)]. 59.52/59.91 5710 is_a_theorem(implies(A,and(A,A))). [resolve(1350,a,156,a),rewrite([120(5),114(4)])]. 59.52/59.91 5900 -is_a_theorem(A) | is_a_theorem(and(A,A)). [resolve(5710,a,71,a)]. 59.52/59.91 6039 is_a_theorem(equiv(A,A)). [resolve(5900,a,536,a),rewrite([94(3)])]. 59.52/59.91 6072 not(not(A)) = A. [resolve(6039,a,1139,a)]. 59.52/59.91 6419 not(and(A,B)) = implies(A,not(B)). [para(6072(a,1),84(a,1,1,2))]. 59.52/59.91 6420 not(implies(A,B)) = and(A,not(B)). [para(84(a,1),6072(a,1,1))]. 59.52/59.91 6427 implies(implies(not(A),B),and(B,A)) = not(equiv(not(A),B)). [para(6072(a,1),172(a,1,2,2))]. 59.52/59.91 6698 -is_a_theorem(implies(implies(c28,c29),implies(implies(c29,not(c30)),implies(c30,not(c28))))). [back_rewrite(171),rewrite([6419(11)])]. 59.52/59.91 8077 is_a_theorem(implies(and(A,B),and(B,A))). [resolve(2027,a,1350,a),rewrite([6420(3),6072(2),6420(4),6072(3)])]. 59.52/59.91 8079 -is_a_theorem(implies(A,not(B))) | is_a_theorem(implies(B,not(A))). [resolve(2027,a,71,a)]. 59.52/59.91 8387 is_a_theorem(implies(A,implies(and(B,C),and(C,B)))). [resolve(8077,a,195,a)]. 59.52/59.91 8554 is_a_theorem(implies(implies(A,implies(not(B),B)),implies(A,B))). [para(6072(a,1),204(a,1,1,1)),rewrite([6072(5)])]. 59.52/59.91 11058 -is_a_theorem(implies(A,implies(B,C))) | is_a_theorem(implies(B,implies(A,C))). [para(6072(a,1),266(a,1,1)),rewrite([6072(5)])]. 59.52/59.91 13454 -is_a_theorem(implies(A,implies(not(B),B))) | is_a_theorem(implies(A,B)). [resolve(8554,a,71,a)]. 59.52/59.91 15929 is_a_theorem(implies(implies(A,B),implies(A,and(B,B)))). [resolve(1015,a,5710,a)]. 59.52/59.91 15943 is_a_theorem(implies(implies(A,and(B,C)),implies(A,C))). [resolve(1015,a,1348,a)]. 59.52/59.91 15946 is_a_theorem(implies(implies(A,and(not(B),B)),implies(A,C))). [resolve(1015,a,1345,a)]. 59.52/59.91 15981 -is_a_theorem(implies(A,B)) | is_a_theorem(implies(A,and(B,B))). [resolve(15929,a,71,a)]. 59.52/59.91 15989 is_a_theorem(implies(implies(not(A),and(B,A)),A)). [resolve(15943,a,13454,a)]. 59.52/59.91 16001 -is_a_theorem(implies(A,and(B,C))) | is_a_theorem(implies(A,C)). [resolve(15943,a,71,a)]. 59.52/59.91 16080 is_a_theorem(implies(A,and(A,implies(B,A)))). [resolve(15989,a,8079,a),rewrite([6072(2),6420(4),6419(3),6072(2)])]. 59.52/59.91 16431 is_a_theorem(not(equiv(A,not(A)))). [resolve(15981,a,156,a),rewrite([172(6)])]. 59.52/59.91 16439 is_a_theorem(not(equiv(not(A),A))). [resolve(15981,a,119,a),rewrite([6427(4)])]. 59.52/59.91 16453 is_a_theorem(implies(A,not(equiv(B,not(B))))). [resolve(16431,a,195,a)]. 59.52/59.91 16536 is_a_theorem(implies(equiv(A,not(A)),B)). [resolve(16453,a,2275,a)]. 59.52/59.91 16570 is_a_theorem(implies(implies(A,equiv(B,not(B))),implies(A,C))). [resolve(16536,a,1015,a)]. 59.52/59.91 16597 is_a_theorem(implies(equiv(not(A),A),B)). [para(6072(a,1),16536(a,1,1,2))]. 59.52/59.91 16779 is_a_theorem(implies(and(A,B),A)). [resolve(16001,a,8077,a)]. 59.52/59.91 16813 is_a_theorem(implies(implies(A,and(B,C)),implies(A,B))). [resolve(16779,a,1015,a)]. 59.52/59.91 17067 is_a_theorem(implies(equiv(A,B),implies(A,B))). [para(94(a,1),16779(a,1,1))]. 59.52/59.91 19040 is_a_theorem(implies(not(equiv(A,B)),implies(implies(A,B),B))). [para(172(a,1),16813(a,1,1))]. 59.52/59.91 26982 is_a_theorem(implies(implies(not(A),and(not(B),B)),A)). [resolve(15946,a,13454,a)]. 59.52/59.91 27028 is_a_theorem(implies(A,and(A,implies(not(B),not(B))))). [resolve(26982,a,8079,a),rewrite([6072(2),6420(4),6419(3)])]. 59.52/59.91 27121 is_a_theorem(implies(A,and(A,implies(B,B)))). [para(6072(a,1),27028(a,1,2,2,1)),rewrite([6072(2)])]. 59.52/59.91 27148 is_a_theorem(implies(implies(A,and(B,not(B))),not(A))). [resolve(27121,a,1350,a),rewrite([6419(3),6420(2)])]. 59.52/59.91 27792 -is_a_theorem(implies(A,and(B,not(B)))) | is_a_theorem(not(A)). [resolve(27148,a,71,a)]. 59.52/59.91 30108 is_a_theorem(implies(implies(not(A),equiv(B,not(B))),A)). [resolve(16570,a,13454,a)]. 59.52/59.91 30169 -is_a_theorem(implies(not(A),equiv(B,not(B)))) | is_a_theorem(A). [resolve(30108,a,71,a)]. 59.52/59.91 30335 -is_a_theorem(implies(A,equiv(B,not(B)))) | is_a_theorem(not(A)). [para(6072(a,1),30169(a,1,1))]. 59.52/59.91 30925 -is_a_theorem(implies(A,equiv(not(B),B))) | is_a_theorem(not(A)). [para(6072(a,1),30335(a,1,2,2))]. 59.52/59.91 41319 is_a_theorem(implies(implies(A,B),implies(not(equiv(A,B)),B))). [resolve(11058,a,19040,a)]. 59.52/59.91 41325 is_a_theorem(implies(A,implies(equiv(A,B),B))). [resolve(11058,a,17067,a)]. 59.52/59.91 41350 is_a_theorem(implies(A,implies(implies(A,B),B))). [resolve(11058,a,536,a)]. 59.52/59.91 41354 is_a_theorem(implies(implies(A,B),implies(implies(B,C),implies(A,C)))). [resolve(11058,a,136,a)]. 59.52/59.91 41390 -is_a_theorem(A) | is_a_theorem(implies(equiv(A,B),B)). [resolve(41325,a,71,a)]. 59.52/59.91 41418 -is_a_theorem(A) | is_a_theorem(implies(implies(A,B),B)). [resolve(41350,a,71,a)]. 59.52/59.91 41610 is_a_theorem(implies(equiv(not(equiv(not(A),A)),B),B)). [resolve(41390,a,16439,a)]. 59.52/59.91 41807 is_a_theorem(implies(implies(implies(and(A,B),A),C),C)). [resolve(41418,a,16779,a)]. 59.52/59.91 41842 is_a_theorem(implies(implies(implies(A,and(A,A)),B),B)). [resolve(41418,a,5710,a)]. 59.52/59.91 41850 is_a_theorem(implies(implies(implies(and(A,B),B),C),C)). [resolve(41418,a,1348,a)]. 59.52/59.91 41855 is_a_theorem(implies(implies(implies(A,A),B),B)). [resolve(41418,a,536,a)]. 59.52/59.91 41861 is_a_theorem(implies(implies(implies(A,implies(B,A)),C),C)). [resolve(41418,a,149,a)]. 59.52/59.91 42150 is_a_theorem(implies(A,and(implies(B,B),A))). [resolve(41855,a,8079,a),rewrite([6420(4),6072(3)])]. 59.52/59.91 42222 -is_a_theorem(A) | is_a_theorem(and(implies(B,B),A)). [resolve(42150,a,71,a)]. 59.52/59.91 42442 is_a_theorem(and(implies(A,A),implies(B,and(B,implies(C,B))))). [resolve(42222,a,16080,a)]. 59.52/59.91 43530 is_a_theorem(not(equiv(not(equiv(not(A),A)),equiv(not(B),B)))). [resolve(41610,a,30925,a)]. 59.52/59.91 44638 -is_a_theorem(implies(implies(and(A,B),A),C)) | is_a_theorem(C). [resolve(41807,a,71,a)]. 59.52/59.91 44932 -is_a_theorem(implies(implies(A,and(A,A)),B)) | is_a_theorem(B). [resolve(41842,a,71,a)]. 59.52/59.91 44985 -is_a_theorem(implies(implies(and(A,B),B),C)) | is_a_theorem(C). [resolve(41850,a,71,a)]. 59.52/59.91 45091 -is_a_theorem(implies(implies(A,implies(B,A)),C)) | is_a_theorem(C). [resolve(41861,a,71,a)]. 59.52/59.91 89762 is_a_theorem(implies(not(equiv(A,implies(B,A))),implies(B,A))). [resolve(41319,a,45091,a)]. 59.52/59.91 89763 is_a_theorem(implies(not(equiv(and(A,B),B)),B)). [resolve(41319,a,44985,a)]. 59.52/59.91 89828 -is_a_theorem(implies(A,B)) | is_a_theorem(implies(not(equiv(A,B)),B)). [resolve(41319,a,71,a)]. 59.52/59.91 89895 is_a_theorem(equiv(and(A,equiv(not(B),B)),equiv(not(B),B))). [resolve(89763,a,30925,a),rewrite([6072(8)])]. 59.52/59.91 138637 is_a_theorem(implies(not(equiv(A,implies(not(A),A))),A)). [resolve(89762,a,13454,a)]. 59.52/59.91 138746 is_a_theorem(equiv(and(A,not(A)),not(equiv(A,A)))). [resolve(138637,a,27792,a),rewrite([6419(5),6072(4),172(6),6072(7)])]. 59.52/59.91 138901 not(equiv(A,A)) = and(A,not(A)). [resolve(138746,a,69,a)]. 59.52/59.91 138912 equiv(A,A) = implies(A,A). [para(138901(a,1),6072(a,1,1)),rewrite([6419(3),6072(2)]),flip(a)]. 59.52/59.91 141330 is_a_theorem(implies(not(equiv(equiv(not(A),A),B)),B)). [resolve(89828,a,16597,a)]. 59.52/59.91 141458 is_a_theorem(implies(not(equiv(and(A,not(A)),B)),B)). [resolve(89828,a,1343,a)]. 59.52/59.91 141490 is_a_theorem(equiv(equiv(not(A),A),equiv(not(B),B))). [resolve(141330,a,30925,a),rewrite([6072(7)])]. 59.52/59.91 141508 is_a_theorem(implies(A,equiv(equiv(not(B),B),not(A)))). [resolve(141330,a,8079,a),rewrite([6072(6)])]. 59.52/59.91 141614 is_a_theorem(equiv(and(A,not(A)),equiv(not(B),B))). [resolve(141458,a,30925,a),rewrite([6072(7)])]. 59.52/59.91 141671 equiv(not(A),A) = equiv(not(B),B). [resolve(141490,a,69,a)]. 59.52/59.91 141676 equiv(not(A),A) = c_0. [new_symbol(141671)]. 59.52/59.91 141681 is_a_theorem(equiv(and(A,not(A)),c_0)). [back_rewrite(141614),rewrite([141676(4)])]. 59.52/59.91 141702 is_a_theorem(implies(A,equiv(c_0,not(A)))). [back_rewrite(141508),rewrite([141676(2)])]. 59.52/59.91 141842 is_a_theorem(equiv(and(A,c_0),c_0)). [back_rewrite(89895),rewrite([141676(2),141676(4)])]. 59.52/59.91 141964 is_a_theorem(not(c_0)). [back_rewrite(43530),rewrite([141676(2),141676(4),141676(4)])]. 59.52/59.91 143470 and(A,c_0) = c_0. [resolve(141842,a,69,a),flip(a)]. 59.52/59.91 143553 implies(A,not(c_0)) = not(c_0). [para(143470(a,1),6419(a,1,1)),flip(a)]. 59.52/59.91 143797 and(A,not(A)) = c_0. [resolve(141681,a,69,a),flip(a)]. 59.52/59.91 143957 implies(A,A) = not(c_0). [para(143797(a,1),6419(a,1,1)),rewrite([6072(4)]),flip(a)]. 59.52/59.91 144159 equiv(A,A) = not(c_0). [back_rewrite(138912),rewrite([143957(2)])]. 59.52/59.91 144396 is_a_theorem(and(not(c_0),implies(A,and(A,implies(B,A))))). [back_rewrite(42442),rewrite([143957(1)])]. 59.52/59.91 144725 and(not(c_0),not(c_0)) = not(c_0). [para(143957(a,1),94(a,1,1)),rewrite([143957(3),144159(6)])]. 59.52/59.91 145194 is_a_theorem(equiv(c_0,and(and(A,B),not(B)))). [resolve(141702,a,44985,a),rewrite([6420(4)])]. 59.52/59.91 145195 is_a_theorem(equiv(c_0,and(A,implies(A,not(A))))). [resolve(141702,a,44932,a),rewrite([6420(4),6419(3)])]. 59.52/59.91 145196 is_a_theorem(equiv(c_0,and(and(A,B),not(A)))). [resolve(141702,a,44638,a),rewrite([6420(4)])]. 59.52/59.91 147817 and(implies(not(c_0),A),not(c_0)) = equiv(not(c_0),A). [para(143553(a,1),94(a,1,2))]. 59.52/59.91 149857 and(and(A,B),not(B)) = c_0. [resolve(145194,a,69,a)]. 59.52/59.91 149861 implies(and(A,B),B) = not(c_0). [para(149857(a,1),6419(a,1,1)),rewrite([6072(5)]),flip(a)]. 59.52/59.91 149884 and(A,implies(A,not(A))) = c_0. [resolve(145195,a,69,a)]. 59.52/59.91 149887 implies(A,and(A,A)) = not(c_0). [para(149884(a,1),6419(a,1,1)),rewrite([6420(5),6072(4)]),flip(a)]. 59.52/59.91 149891 equiv(A,and(A,A)) = not(c_0). [para(149887(a,1),94(a,1,1)),rewrite([149861(4),144725(5)]),flip(a)]. 59.52/59.91 149895 and(A,A) = A. [para(149891(a,1),69(a,1)),unit_del(a,141964)]. 59.52/59.91 149989 and(and(A,B),not(A)) = c_0. [resolve(145196,a,69,a)]. 59.52/59.91 149998 implies(and(A,B),A) = not(c_0). [para(149989(a,1),6419(a,1,1)),rewrite([6072(5)]),flip(a)]. 59.52/59.91 150018 and(not(c_0),implies(A,and(A,B))) = equiv(and(A,B),A). [para(149998(a,1),94(a,1,1))]. 59.52/59.91 150034 is_a_theorem(equiv(and(A,implies(B,A)),A)). [back_rewrite(144396),rewrite([150018(6)])]. 59.52/59.91 150124 and(A,implies(B,A)) = A. [resolve(150034,a,69,a),flip(a)]. 59.52/59.91 150193 and(A,not(c_0)) = A. [para(143957(a,1),150124(a,1,2))]. 59.52/59.91 150195 equiv(not(c_0),A) = implies(not(c_0),A). [back_rewrite(147817),rewrite([150193(6)]),flip(a)]. 59.52/59.91 154278 -is_a_theorem(implies(not(c_0),A)) | not(c_0) = A. [para(150195(a,1),69(a,1)),flip(b)]. 59.52/59.91 155165 implies(and(A,B),and(B,A)) = not(c_0). [resolve(154278,a,8387,a),flip(a)]. 59.52/59.91 159662 equiv(and(A,B),and(B,A)) = not(c_0). [para(155165(a,1),94(a,1,1)),rewrite([155165(5),149895(5)]),flip(a)]. 59.52/59.91 161573 and(A,B) = and(B,A). [para(159662(a,1),69(a,1)),unit_del(a,141964)]. 59.52/59.91 162622 implies(A,not(B)) = implies(B,not(A)). [para(161573(a,1),6419(a,1,1)),rewrite([6419(2)])]. 59.52/59.91 162785 $F. [back_rewrite(6698),rewrite([162622(11)]),unit_del(a,41354)]. 59.52/59.91 59.52/59.91 % SZS output end Refutation 59.52/59.91 ============================== end of proof ========================== 59.52/59.91 59.52/59.91 ============================== STATISTICS ============================ 59.52/59.91 59.52/59.91 Given=5028. Generated=5073233. Kept=162734. proofs=1. 59.52/59.91 Usable=439. Sos=1913. Demods=418. Limbo=163, Disabled=160293. Hints=0. 59.52/59.91 Megabytes=95.10. 59.52/59.91 User_CPU=55.21, System_CPU=3.61, Wall_clock=58. 59.52/59.91 59.52/59.91 ============================== end of statistics ===================== 59.52/59.91 59.52/59.91 ============================== end of search ========================= 59.52/59.91 59.52/59.91 THEOREM PROVED 59.52/59.91 % SZS status Theorem 59.52/59.91 59.52/59.91 Exiting with 1 proof. 59.52/59.91 59.52/59.91 Process 3793 exit (max_proofs) Tue Jul 13 16:15:24 2021 59.52/59.91 Prover9 interrupted 59.52/59.91 EOF