0.09/0.11 % Problem : theBenchmark.p : TPTP v0.0.0. Released v0.0.0. 0.09/0.11 % Command : tptp2X_and_run_prover9 %d %s 0.10/0.31 % Computer : n018.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 : 960 0.10/0.31 % WCLimit : 120 0.10/0.31 % DateTime : Tue Aug 9 05:12:15 EDT 2022 0.10/0.32 % CPUTime : 0.71/1.09 ============================== Prover9 =============================== 0.71/1.09 Prover9 (32) version 2009-11A, November 2009. 0.71/1.09 Process 31202 was started by sandbox2 on n018.cluster.edu, 0.71/1.09 Tue Aug 9 05:12:16 2022 0.71/1.09 The command was "/export/starexec/sandbox2/solver/bin/prover9 -t 960 -f /tmp/Prover9_31049_n018.cluster.edu". 0.71/1.09 ============================== end of head =========================== 0.71/1.09 0.71/1.09 ============================== INPUT ================================= 0.71/1.09 0.71/1.09 % Reading from file /tmp/Prover9_31049_n018.cluster.edu 0.71/1.09 0.71/1.09 set(prolog_style_variables). 0.71/1.09 set(auto2). 0.71/1.09 % set(auto2) -> set(auto). 0.71/1.09 % set(auto) -> set(auto_inference). 0.71/1.09 % set(auto) -> set(auto_setup). 0.71/1.09 % set(auto_setup) -> set(predicate_elim). 0.71/1.09 % set(auto_setup) -> assign(eq_defs, unfold). 0.71/1.09 % set(auto) -> set(auto_limits). 0.71/1.09 % set(auto_limits) -> assign(max_weight, "100.000"). 0.71/1.09 % set(auto_limits) -> assign(sos_limit, 20000). 0.71/1.09 % set(auto) -> set(auto_denials). 0.71/1.09 % set(auto) -> set(auto_process). 0.71/1.09 % set(auto2) -> assign(new_constants, 1). 0.71/1.09 % set(auto2) -> assign(fold_denial_max, 3). 0.71/1.09 % set(auto2) -> assign(max_weight, "200.000"). 0.71/1.09 % set(auto2) -> assign(max_hours, 1). 0.71/1.09 % assign(max_hours, 1) -> assign(max_seconds, 3600). 0.71/1.09 % set(auto2) -> assign(max_seconds, 0). 0.71/1.09 % set(auto2) -> assign(max_minutes, 5). 0.71/1.09 % assign(max_minutes, 5) -> assign(max_seconds, 300). 0.71/1.09 % set(auto2) -> set(sort_initial_sos). 0.71/1.09 % set(auto2) -> assign(sos_limit, -1). 0.71/1.09 % set(auto2) -> assign(lrs_ticks, 3000). 0.71/1.09 % set(auto2) -> assign(max_megs, 400). 0.71/1.09 % set(auto2) -> assign(stats, some). 0.71/1.09 % set(auto2) -> clear(echo_input). 0.71/1.09 % set(auto2) -> set(quiet). 0.71/1.09 % set(auto2) -> clear(print_initial_clauses). 0.71/1.09 % set(auto2) -> clear(print_given). 0.71/1.09 assign(lrs_ticks,-1). 0.71/1.09 assign(sos_limit,10000). 0.71/1.09 assign(order,kbo). 0.71/1.09 set(lex_order_vars). 0.71/1.09 clear(print_given). 0.71/1.09 0.71/1.09 % formulas(sos). % not echoed (45 formulas) 0.71/1.09 0.71/1.09 ============================== end of input ========================== 0.71/1.09 0.71/1.09 % From the command line: assign(max_seconds, 960). 0.71/1.09 0.71/1.09 ============================== PROCESS NON-CLAUSAL FORMULAS ========== 0.71/1.09 0.71/1.09 % Formulas that are not ordinary clauses: 0.71/1.09 1 and_1 <-> (all X all Y is_a_theorem(implies(and(X,Y),X))) # label(and_1) # label(axiom) # label(non_clause). [assumption]. 0.71/1.09 2 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]. 0.71/1.09 3 (all X all Y is_a_theorem(implies(and(X,Y),Y))) <-> and_2 # label(and_2) # label(axiom) # label(non_clause). [assumption]. 0.71/1.09 4 (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]. 0.71/1.09 5 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]. 0.71/1.09 6 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]. 0.71/1.09 7 kn2 <-> (all P all Q is_a_theorem(implies(and(P,Q),P))) # label(kn2) # label(axiom) # label(non_clause). [assumption]. 0.71/1.09 8 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]. 0.71/1.09 9 or_1 <-> (all X all Y is_a_theorem(implies(X,or(X,Y)))) # label(or_1) # label(axiom) # label(non_clause). [assumption]. 0.71/1.09 10 cn3 <-> (all P is_a_theorem(implies(implies(not(P),P),P))) # label(cn3) # label(axiom) # label(non_clause). [assumption]. 0.71/1.09 11 (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]. 0.71/1.09 12 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]. 0.71/1.09 13 substitution_of_equivalents <-> (all X all Y (is_a_theorem(equiv(X,Y)) -> Y = X)) # label(substitution_of_equivalents) # label(axiom) # label(non_clause). [assumption]. 0.71/1.09 14 (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]. 2.58/2.98 15 (all P all Q is_a_theorem(implies(Q,or(P,Q)))) <-> r2 # label(r2) # label(axiom) # label(non_clause). [assumption]. 2.58/2.98 16 or_2 <-> (all X all Y is_a_theorem(implies(Y,or(X,Y)))) # label(or_2) # label(axiom) # label(non_clause). [assumption]. 2.58/2.98 17 (all P all Q is_a_theorem(implies(P,implies(not(P),Q)))) <-> cn2 # label(cn2) # label(axiom) # label(non_clause). [assumption]. 2.58/2.98 18 (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]. 2.58/2.98 19 r1 <-> (all P is_a_theorem(implies(or(P,P),P))) # label(r1) # label(axiom) # label(non_clause). [assumption]. 2.58/2.98 20 r3 <-> (all P all Q is_a_theorem(implies(or(P,Q),or(Q,P)))) # label(r3) # label(axiom) # label(non_clause). [assumption]. 2.58/2.98 21 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]. 2.58/2.98 22 (all P is_a_theorem(implies(P,and(P,P)))) <-> kn1 # label(kn1) # label(axiom) # label(non_clause). [assumption]. 2.58/2.98 23 (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]. 2.58/2.98 24 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]. 2.58/2.98 25 (all X all Y is_a_theorem(implies(X,implies(Y,X)))) <-> implies_1 # label(implies_1) # label(axiom) # label(non_clause). [assumption]. 2.58/2.98 26 (all X all Y all Z is_a_theorem(implies(implies(X,Y),implies(implies(Y,Z),implies(X,Z))))) <-> implies_3 # label(implies_3) # label(axiom) # label(non_clause). [assumption]. 2.58/2.98 27 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]. 2.58/2.98 28 op_implies_or -> (all X all Y or(not(X),Y) = implies(X,Y)) # label(op_implies_or) # label(axiom) # label(non_clause). [assumption]. 2.58/2.98 29 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]. 2.58/2.98 30 op_or -> (all X all Y not(and(not(X),not(Y))) = or(X,Y)) # label(op_or) # label(axiom) # label(non_clause). [assumption]. 2.58/2.98 31 op_and -> (all X all Y and(X,Y) = not(or(not(X),not(Y)))) # label(op_and) # label(axiom) # label(non_clause). [assumption]. 2.58/2.98 2.58/2.98 ============================== end of process non-clausal formulas === 2.58/2.98 2.58/2.98 ============================== PROCESS INITIAL CLAUSES =============== 2.58/2.98 2.58/2.98 ============================== PREDICATE ELIMINATION ================= 2.58/2.98 2.58/2.98 ============================== end predicate elimination ============= 2.58/2.98 2.58/2.98 Auto_denials: (non-Horn, no changes). 2.58/2.98 2.58/2.98 Term ordering decisions: 2.58/2.98 2.58/2.98 % Assigning unary symbol not kb_weight 0 and highest precedence (93). 2.58/2.98 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. 2.58/2.98 2.58/2.98 ============================== end of process initial clauses ======== 2.58/2.98 2.58/2.98 ============================== CLAUSES FOR SEARCH ==================== 2.58/2.98 2.58/2.98 ============================== end of clauses for search ============= 2.58/2.98 2.58/2.98 ============================== SEARCH ================================ 2.58/2.98 2.58/2.98 % Starting search at 0.02 seconds. 2.58/2.98 2.58/2.98 Low Water (keep): wt=26.000, iters=3402 2.58/2.98 2.58/2.98 Low Water (keep): wt=21.000, iters=3382 2.58/2.98 2.58/2.98 Low Water (keep): wt=20.000, iters=3363 2.58/2.98 2.58/2.98 Low Water (keep): wt=19.000, iters=3336 2.58/2.98 2.58/2.98 Low Water (keep): wt=18.000, iters=3353 2.58/2.98 2.58/2.98 Low Water (keep): wt=17.000, iters=3358 2.58/2.98 2.58/2.98 Low Water (keep): wt=16.000, iters=3371 2.58/2.98 2.58/2.98 Low Water (keep): wt=15.000, iters=3349 2.58/2.98 2.58/2.98 Low Water (keep): wt=14.000, iters=3337 2.58/2.98 2.58/2.98 NOTE: Back_subsumption disabled, ratio of kept to back_subsumed is 24 (0.00 of 1.86 sec). 42.38/42.76 42.38/42.76 Low Water (keep): wt=13.000, iters=3333 42.38/42.76 42.38/42.76 Low Water (displace): id=8065, wt=38.000 42.38/42.76 42.38/42.76 Low Water (displace): id=8063, wt=36.000 42.38/42.76 42.38/42.76 Low Water (displace): id=15203, wt=35.000 42.38/42.76 42.38/42.76 Low Water (displace): id=12017, wt=34.000 42.38/42.76 42.38/42.76 Low Water (displace): id=15462, wt=33.000 42.38/42.76 42.38/42.76 Low Water (displace): id=15730, wt=32.000 42.38/42.76 42.38/42.76 Low Water (displace): id=15548, wt=30.000 42.38/42.76 42.38/42.76 Low Water (displace): id=16092, wt=29.000 42.38/42.76 42.38/42.76 Low Water (displace): id=14078, wt=28.000 42.38/42.76 42.38/42.76 Low Water (displace): id=16093, wt=27.000 42.38/42.76 42.38/42.76 Low Water (displace): id=16118, wt=26.000 42.38/42.76 42.38/42.76 Low Water (displace): id=13301, wt=25.000 42.38/42.76 42.38/42.76 Low Water (displace): id=16323, wt=24.000 42.38/42.76 42.38/42.76 Low Water (displace): id=16698, wt=23.000 42.38/42.76 42.38/42.76 Low Water (displace): id=16842, wt=22.000 42.38/42.76 42.38/42.76 Low Water (displace): id=17145, wt=12.000 42.38/42.76 42.38/42.76 Low Water (displace): id=17555, wt=10.000 42.38/42.76 42.38/42.76 Low Water (displace): id=19661, wt=9.000 42.38/42.76 42.38/42.76 Low Water (keep): wt=12.000, iters=3333 42.38/42.76 42.38/42.76 Low Water (keep): wt=11.000, iters=3333 42.38/42.76 42.38/42.76 Low Water (keep): wt=10.000, iters=3505 42.38/42.76 42.38/42.76 ============================== PROOF ================================= 42.38/42.76 % SZS status Theorem 42.38/42.76 % SZS output start Refutation 42.38/42.76 42.38/42.76 % Proof 1 at 39.45 (+ 2.23) seconds. 42.38/42.76 % Length of proof is 182. 42.38/42.76 % Level of proof is 34. 42.38/42.76 % Maximum clause weight is 16.000. 42.38/42.76 % Given clauses 3729. 42.38/42.76 42.38/42.76 13 substitution_of_equivalents <-> (all X all Y (is_a_theorem(equiv(X,Y)) -> Y = X)) # label(substitution_of_equivalents) # label(axiom) # label(non_clause). [assumption]. 42.38/42.76 14 (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]. 42.38/42.76 15 (all P all Q is_a_theorem(implies(Q,or(P,Q)))) <-> r2 # label(r2) # label(axiom) # label(non_clause). [assumption]. 42.38/42.76 18 (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]. 42.38/42.76 19 r1 <-> (all P is_a_theorem(implies(or(P,P),P))) # label(r1) # label(axiom) # label(non_clause). [assumption]. 42.38/42.76 20 r3 <-> (all P all Q is_a_theorem(implies(or(P,Q),or(Q,P)))) # label(r3) # label(axiom) # label(non_clause). [assumption]. 42.38/42.76 21 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]. 42.38/42.76 24 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]. 42.38/42.76 27 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]. 42.38/42.76 28 op_implies_or -> (all X all Y or(not(X),Y) = implies(X,Y)) # label(op_implies_or) # label(axiom) # label(non_clause). [assumption]. 42.38/42.76 29 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]. 42.38/42.76 30 op_or -> (all X all Y not(and(not(X),not(Y))) = or(X,Y)) # label(op_or) # label(axiom) # label(non_clause). [assumption]. 42.38/42.76 31 op_and -> (all X all Y and(X,Y) = not(or(not(X),not(Y)))) # label(op_and) # label(axiom) # label(non_clause). [assumption]. 42.38/42.76 32 r4 # label(principia_r4) # label(axiom). [assumption]. 42.38/42.76 33 r3 # label(principia_r3) # label(axiom). [assumption]. 42.38/42.76 34 op_implies_or # label(principia_op_implies_or) # label(axiom). [assumption]. 42.38/42.76 35 modus_ponens # label(principia_modus_ponens) # label(axiom). [assumption]. 42.38/42.76 36 r1 # label(principia_r1) # label(axiom). [assumption]. 42.38/42.76 37 op_and # label(principia_op_and) # label(axiom). [assumption]. 42.38/42.76 38 substitution_of_equivalents # label(substitution_of_equivalents) # label(axiom). [assumption]. 42.38/42.76 39 r5 # label(principia_r5) # label(axiom). [assumption]. 42.38/42.76 40 op_equiv # label(principia_op_equiv) # label(axiom). [assumption]. 42.38/42.76 41 r2 # label(principia_r2) # label(axiom). [assumption]. 42.38/42.76 42 op_or # label(hilbert_op_or) # label(axiom). [assumption]. 42.38/42.76 43 op_implies_and # label(hilbert_op_implies_and) # label(axiom). [assumption]. 42.38/42.76 44 -implies_2 # label(hilbert_implies_2) # label(negated_conjecture). [assumption]. 42.38/42.76 53 is_a_theorem(implies(A,or(B,A))) | -r2 # label(r2) # label(axiom). [clausify(15)]. 42.38/42.76 54 is_a_theorem(implies(A,or(B,A))). [copy(53),unit_del(b,41)]. 42.38/42.76 57 -r1 | is_a_theorem(implies(or(A,A),A)) # label(r1) # label(axiom). [clausify(19)]. 42.38/42.76 58 is_a_theorem(implies(or(A,A),A)). [copy(57),unit_del(a,36)]. 42.38/42.76 66 -substitution_of_equivalents | -is_a_theorem(equiv(A,B)) | B = A # label(substitution_of_equivalents) # label(axiom). [clausify(13)]. 42.38/42.76 67 -is_a_theorem(equiv(A,B)) | B = A. [copy(66),unit_del(a,38)]. 42.38/42.76 74 -r3 | is_a_theorem(implies(or(A,B),or(B,A))) # label(r3) # label(axiom). [clausify(20)]. 42.38/42.76 75 is_a_theorem(implies(or(A,B),or(B,A))). [copy(74),unit_del(a,33)]. 42.38/42.76 79 -modus_ponens | -is_a_theorem(A) | -is_a_theorem(implies(A,B)) | is_a_theorem(B) # label(modus_ponens) # label(axiom). [clausify(24)]. 42.38/42.76 80 -is_a_theorem(A) | -is_a_theorem(implies(A,B)) | is_a_theorem(B). [copy(79),unit_del(a,35)]. 42.38/42.76 81 -op_implies_or | or(not(A),B) = implies(A,B) # label(op_implies_or) # label(axiom). [clausify(28)]. 42.38/42.76 82 or(not(A),B) = implies(A,B). [copy(81),unit_del(a,34)]. 42.38/42.76 83 -op_implies_and | not(and(A,not(B))) = implies(A,B) # label(op_implies_and) # label(axiom). [clausify(27)]. 42.38/42.76 84 not(and(A,not(B))) = implies(A,B). [copy(83),unit_del(a,43)]. 42.38/42.76 87 -is_a_theorem(implies(implies(c38,implies(c38,c39)),implies(c38,c39))) | implies_2 # label(implies_2) # label(axiom). [clausify(18)]. 42.38/42.76 88 -is_a_theorem(implies(implies(c38,implies(c38,c39)),implies(c38,c39))). [copy(87),unit_del(b,44)]. 42.38/42.76 89 -op_or | or(A,B) = not(and(not(A),not(B))) # label(op_or) # label(axiom). [clausify(30)]. 42.38/42.76 90 or(A,B) = implies(not(A),B). [copy(89),rewrite([84(6)]),unit_del(a,42)]. 42.38/42.76 91 -op_and | not(or(not(A),not(B))) = and(A,B) # label(op_and) # label(axiom). [clausify(31)]. 42.38/42.76 92 not(implies(not(not(A)),not(B))) = and(A,B). [copy(91),rewrite([90(4)]),unit_del(a,37)]. 42.38/42.76 93 -op_equiv | equiv(A,B) = and(implies(A,B),implies(B,A)) # label(op_equiv) # label(axiom). [clausify(29)]. 42.38/42.76 94 and(implies(A,B),implies(B,A)) = equiv(A,B). [copy(93),flip(b),unit_del(a,40)]. 42.38/42.76 100 is_a_theorem(implies(implies(A,B),implies(or(C,A),or(C,B)))) | -r5 # label(r5) # label(axiom). [clausify(14)]. 42.38/42.76 101 is_a_theorem(implies(implies(A,B),implies(implies(not(C),A),implies(not(C),B)))). [copy(100),rewrite([90(2),90(4)]),unit_del(b,39)]. 42.38/42.76 102 -r4 | is_a_theorem(implies(or(A,or(B,C)),or(B,or(A,C)))) # label(r4) # label(axiom). [clausify(21)]. 42.38/42.76 103 is_a_theorem(implies(implies(not(A),implies(not(B),C)),implies(not(B),implies(not(A),C)))). [copy(102),rewrite([90(2),90(4),90(6),90(8)]),unit_del(a,32)]. 42.38/42.76 113 implies(not(not(A)),B) = implies(A,B). [back_rewrite(82),rewrite([90(2)])]. 42.38/42.76 114 is_a_theorem(implies(implies(not(A),B),implies(not(B),A))). [back_rewrite(75),rewrite([90(1),90(3)])]. 42.38/42.76 115 is_a_theorem(implies(implies(not(A),A),A)). [back_rewrite(58),rewrite([90(1)])]. 42.38/42.76 116 is_a_theorem(implies(A,implies(not(B),A))). [back_rewrite(54),rewrite([90(1)])]. 42.38/42.76 119 not(implies(A,not(B))) = and(A,B). [back_rewrite(92),rewrite([113(4)])]. 42.38/42.76 121 not(and(A,implies(B,C))) = implies(A,and(B,not(C))). [para(84(a,1),84(a,1,1,2))]. 42.38/42.76 122 -is_a_theorem(implies(A,B)) | is_a_theorem(implies(implies(not(C),A),implies(not(C),B))). [resolve(101,a,80,b)]. 42.38/42.76 125 -is_a_theorem(implies(not(A),implies(not(B),C))) | is_a_theorem(implies(not(B),implies(not(A),C))). [resolve(103,a,80,b)]. 42.38/42.76 130 implies(not(implies(A,B)),C) = implies(and(A,not(B)),C). [para(84(a,1),113(a,1,1,1))]. 42.38/42.76 132 and(implies(A,not(not(B))),implies(B,A)) = equiv(A,not(not(B))). [para(113(a,1),94(a,1,2))]. 42.38/42.76 134 is_a_theorem(implies(implies(A,B),implies(implies(C,A),implies(C,B)))). [para(113(a,1),101(a,1,2,1)),rewrite([113(5)])]. 42.38/42.76 135 is_a_theorem(implies(implies(not(A),implies(B,C)),implies(B,implies(not(A),C)))). [para(113(a,1),103(a,1,1,2)),rewrite([113(8)])]. 42.38/42.76 137 -is_a_theorem(implies(not(A),B)) | is_a_theorem(implies(not(B),A)). [resolve(114,a,80,b)]. 42.38/42.76 141 is_a_theorem(implies(implies(A,B),implies(not(B),not(A)))). [para(113(a,1),114(a,1,1))]. 42.38/42.76 142 is_a_theorem(implies(implies(not(A),not(B)),implies(B,A))). [para(113(a,1),114(a,1,2))]. 42.38/42.76 144 -is_a_theorem(implies(not(A),A)) | is_a_theorem(A). [resolve(115,a,80,b)]. 42.38/42.76 148 is_a_theorem(implies(implies(A,not(A)),not(A))). [para(113(a,1),115(a,1,1))]. 42.38/42.76 152 is_a_theorem(implies(A,implies(B,A))). [para(113(a,1),116(a,1,2))]. 42.38/42.76 158 and(not(not(A)),B) = and(A,B). [para(113(a,1),119(a,1,1)),rewrite([119(3)]),flip(a)]. 42.38/42.76 165 implies(implies(A,B),and(B,not(A))) = not(equiv(A,B)). [para(94(a,1),121(a,1,1)),flip(a)]. 42.38/42.76 194 -is_a_theorem(A) | is_a_theorem(implies(B,A)). [resolve(152,a,80,b)]. 42.38/42.76 199 is_a_theorem(implies(A,implies(B,not(not(A))))). [para(113(a,1),152(a,1))]. 42.38/42.76 204 is_a_theorem(implies(implies(not(A),implies(not(B),B)),implies(not(A),B))). [resolve(122,a,115,a)]. 42.38/42.76 245 -is_a_theorem(A) | is_a_theorem(implies(B,not(not(A)))). [resolve(199,a,80,b)]. 42.38/42.76 341 is_a_theorem(implies(not(A),implies(not(B),not(B)))). [resolve(125,a,152,a)]. 42.38/42.76 344 -is_a_theorem(implies(not(A),implies(B,C))) | is_a_theorem(implies(B,implies(not(A),C))). [para(113(a,1),125(a,1,2)),rewrite([113(9)])]. 42.38/42.76 345 -is_a_theorem(implies(A,implies(not(B),C))) | is_a_theorem(implies(not(B),implies(A,C))). [para(113(a,1),125(a,1)),rewrite([113(8)])]. 42.38/42.76 388 is_a_theorem(implies(not(A),not(A))). [resolve(341,a,144,a)]. 42.38/42.76 429 is_a_theorem(implies(A,not(not(A)))). [para(113(a,1),388(a,1))]. 42.38/42.76 431 is_a_theorem(implies(A,implies(B,B))). [resolve(429,a,245,a),rewrite([119(4),84(3)])]. 42.38/42.76 457 is_a_theorem(implies(A,A)). [resolve(431,a,144,a)]. 42.38/42.76 746 implies(and(A,not(not(B))),C) = implies(and(A,B),C). [para(119(a,1),130(a,1,1)),flip(a)]. 42.38/42.76 999 equiv(A,not(not(B))) = equiv(A,B). [para(132(a,1),158(a,2)),rewrite([119(4),84(3),94(3)]),flip(a)]. 42.38/42.76 1298 -is_a_theorem(equiv(A,B)) | not(not(B)) = A. [para(999(a,1),67(a,1))]. 42.38/42.76 1318 is_a_theorem(implies(and(A,B),B)). [resolve(137,a,199,a),rewrite([119(5),746(4)])]. 42.38/42.76 1320 -is_a_theorem(implies(A,B)) | is_a_theorem(implies(not(B),not(A))). [para(113(a,1),137(a,1))]. 42.38/42.76 1331 -is_a_theorem(implies(A,B)) | is_a_theorem(implies(implies(C,A),implies(C,B))). [resolve(134,a,80,b)]. 42.38/42.76 1629 is_a_theorem(implies(implies(A,implies(B,C)),implies(B,implies(A,C)))). [para(113(a,1),135(a,1,1)),rewrite([113(5)])]. 42.38/42.76 2862 is_a_theorem(implies(implies(A,not(B)),implies(B,not(A)))). [para(113(a,1),141(a,1,2))]. 42.38/42.76 3161 -is_a_theorem(implies(not(A),not(B))) | is_a_theorem(implies(B,A)). [resolve(142,a,80,b)]. 42.38/42.76 6613 is_a_theorem(implies(A,and(A,A))). [resolve(1320,a,148,a),rewrite([119(5),113(4)])]. 42.38/42.76 6630 -is_a_theorem(A) | is_a_theorem(and(A,A)). [resolve(6613,a,80,b)]. 42.38/42.76 6765 is_a_theorem(equiv(A,A)). [resolve(6630,a,457,a),rewrite([94(3)])]. 42.38/42.76 6959 not(not(A)) = A. [resolve(6765,a,1298,a)]. 42.38/42.76 7031 not(and(A,B)) = implies(A,not(B)). [para(6959(a,1),84(a,1,1,2))]. 42.38/42.76 7032 not(implies(A,B)) = and(A,not(B)). [para(84(a,1),6959(a,1,1))]. 42.38/42.76 7177 implies(implies(not(A),B),and(B,A)) = not(equiv(not(A),B)). [para(6959(a,1),165(a,1,2,2))]. 42.38/42.76 8913 is_a_theorem(implies(and(A,B),and(B,A))). [resolve(2862,a,1320,a),rewrite([7032(3),6959(2),7032(4),6959(3)])]. 42.38/42.76 8915 -is_a_theorem(implies(A,not(B))) | is_a_theorem(implies(B,not(A))). [resolve(2862,a,80,b)]. 42.38/42.76 11775 is_a_theorem(implies(implies(A,implies(not(B),B)),implies(A,B))). [para(6959(a,1),204(a,1,1,1)),rewrite([6959(5)])]. 42.38/42.76 13923 -is_a_theorem(implies(A,implies(not(B),B))) | is_a_theorem(implies(A,B)). [resolve(11775,a,80,b)]. 42.38/42.76 15959 is_a_theorem(implies(implies(A,B),implies(A,and(B,B)))). [resolve(1331,a,6613,a)]. 42.38/42.76 15972 is_a_theorem(implies(implies(A,and(B,C)),implies(A,C))). [resolve(1331,a,1318,a)]. 42.38/42.76 16009 -is_a_theorem(implies(A,B)) | is_a_theorem(implies(A,and(B,B))). [resolve(15959,a,80,b)]. 42.38/42.76 16042 is_a_theorem(implies(implies(not(A),and(B,A)),A)). [resolve(15972,a,13923,a)]. 42.38/42.76 16054 -is_a_theorem(implies(A,and(B,C))) | is_a_theorem(implies(A,C)). [resolve(15972,a,80,b)]. 42.38/42.76 16102 is_a_theorem(implies(A,and(A,implies(B,A)))). [resolve(16042,a,8915,a),rewrite([6959(2),7032(4),7031(3),6959(2)])]. 42.38/42.76 16476 is_a_theorem(not(equiv(A,not(A)))). [resolve(16009,a,148,a),rewrite([165(6)])]. 42.38/42.76 16483 is_a_theorem(not(equiv(not(A),A))). [resolve(16009,a,115,a),rewrite([7177(4)])]. 42.38/42.76 16497 is_a_theorem(implies(A,not(equiv(B,not(B))))). [resolve(16476,a,194,a)]. 42.38/42.76 16644 is_a_theorem(implies(equiv(A,not(A)),B)). [resolve(16497,a,3161,a)]. 42.38/42.76 16689 is_a_theorem(implies(equiv(not(A),A),B)). [para(6959(a,1),16644(a,1,1,2))]. 42.38/42.76 16860 is_a_theorem(implies(and(A,B),A)). [resolve(16054,a,8913,a)]. 42.38/42.76 16910 is_a_theorem(implies(implies(A,and(B,C)),implies(A,B))). [resolve(16860,a,1331,a)]. 42.38/42.76 19809 is_a_theorem(implies(not(equiv(A,B)),implies(implies(A,B),B))). [para(165(a,1),16910(a,1,1))]. 42.38/42.76 22408 is_a_theorem(implies(not(A),implies(implies(not(A),B),B))). [resolve(345,a,457,a)]. 42.38/42.76 22415 is_a_theorem(implies(not(A),implies(implies(not(B),A),B))). [resolve(345,a,142,a),rewrite([6959(4)])]. 42.38/42.76 26052 is_a_theorem(implies(A,implies(implies(A,B),B))). [para(6959(a,1),22408(a,1,1)),rewrite([6959(2)])]. 42.38/42.76 26083 -is_a_theorem(A) | is_a_theorem(implies(implies(A,B),B)). [resolve(26052,a,80,b)]. 42.38/42.76 26156 is_a_theorem(implies(implies(implies(and(A,B),A),C),C)). [resolve(26083,a,16860,a)]. 42.38/42.76 26158 is_a_theorem(implies(implies(implies(equiv(not(A),A),B),C),C)). [resolve(26083,a,16689,a)]. 42.38/42.76 26298 is_a_theorem(implies(implies(equiv(A,A),B),B)). [resolve(26083,a,6765,a)]. 42.38/42.76 26300 is_a_theorem(implies(implies(implies(A,and(A,A)),B),B)). [resolve(26083,a,6613,a)]. 42.38/42.76 26326 is_a_theorem(implies(implies(implies(and(A,B),B),C),C)). [resolve(26083,a,1318,a)]. 42.38/42.76 26333 is_a_theorem(implies(implies(implies(A,A),B),B)). [resolve(26083,a,457,a)]. 42.38/42.76 26394 -is_a_theorem(implies(equiv(A,A),B)) | is_a_theorem(B). [resolve(26298,a,80,b)]. 42.38/42.76 26434 is_a_theorem(implies(A,and(implies(B,B),A))). [resolve(26333,a,8915,a),rewrite([7032(4),6959(3)])]. 42.38/42.76 26439 -is_a_theorem(implies(implies(A,A),B)) | is_a_theorem(B). [resolve(26333,a,80,b)]. 42.38/42.76 26733 -is_a_theorem(A) | is_a_theorem(and(implies(B,B),A)). [resolve(26434,a,80,b)]. 42.38/42.76 27228 is_a_theorem(and(implies(A,A),implies(B,and(B,implies(C,B))))). [resolve(26733,a,16102,a)]. 42.38/42.76 27548 is_a_theorem(implies(A,implies(implies(not(B),not(A)),B))). [para(6959(a,1),22415(a,1,1))]. 42.38/42.76 33244 -is_a_theorem(implies(implies(and(A,B),A),C)) | is_a_theorem(C). [resolve(26156,a,80,b)]. 42.38/42.76 33446 -is_a_theorem(implies(implies(A,and(A,A)),B)) | is_a_theorem(B). [resolve(26300,a,80,b)]. 42.38/42.76 33526 -is_a_theorem(implies(implies(and(A,B),B),C)) | is_a_theorem(C). [resolve(26326,a,80,b)]. 42.38/42.76 35010 is_a_theorem(implies(implies(not(A),and(B,not(B))),A)). [resolve(27548,a,26439,a),rewrite([7032(3)])]. 42.38/42.76 35011 is_a_theorem(implies(implies(not(A),not(equiv(B,B))),A)). [resolve(27548,a,26394,a)]. 42.38/42.76 48016 -is_a_theorem(implies(not(A),and(B,not(B)))) | is_a_theorem(A). [resolve(35010,a,80,b)]. 42.38/42.76 48094 -is_a_theorem(implies(not(A),not(equiv(B,B)))) | is_a_theorem(A). [resolve(35011,a,80,b)]. 42.38/42.76 55955 -is_a_theorem(implies(not(A),and(not(B),B))) | is_a_theorem(A). [para(6959(a,1),48016(a,1,2,2))]. 42.38/42.76 68321 is_a_theorem(implies(implies(A,B),implies(not(equiv(A,B)),B))). [resolve(19809,a,344,a)]. 42.38/42.76 75267 -is_a_theorem(implies(implies(equiv(not(A),A),B),C)) | is_a_theorem(C). [resolve(26158,a,80,b)]. 42.38/42.76 103977 is_a_theorem(implies(not(equiv(equiv(not(A),A),B)),B)). [resolve(75267,a,68321,a)]. 42.38/42.76 104054 is_a_theorem(equiv(equiv(not(A),A),and(not(B),B))). [resolve(103977,a,55955,a)]. 42.38/42.76 104063 is_a_theorem(equiv(equiv(not(A),A),not(equiv(B,B)))). [resolve(103977,a,48094,a)]. 42.38/42.76 104122 is_a_theorem(implies(A,equiv(equiv(not(B),B),not(A)))). [resolve(103977,a,8915,a),rewrite([6959(6)])]. 42.38/42.76 104217 equiv(not(A),A) = and(not(B),B). [resolve(104054,a,67,a),flip(a)]. 42.38/42.76 104223 equiv(not(A),A) = c_0. [new_symbol(104217)]. 42.38/42.76 104225 and(not(A),A) = c_0. [back_rewrite(104217),rewrite([104223(2)]),flip(a)]. 42.38/42.76 104230 is_a_theorem(implies(A,equiv(c_0,not(A)))). [back_rewrite(104122),rewrite([104223(2)])]. 42.38/42.76 104237 is_a_theorem(equiv(c_0,not(equiv(A,A)))). [back_rewrite(104063),rewrite([104223(2)])]. 42.38/42.76 104542 is_a_theorem(not(c_0)). [back_rewrite(16483),rewrite([104223(2)])]. 42.38/42.76 105689 and(A,not(A)) = c_0. [para(6959(a,1),104225(a,1,1))]. 42.38/42.76 106390 implies(A,A) = not(c_0). [para(105689(a,1),7031(a,1,1)),rewrite([6959(4)]),flip(a)]. 42.38/42.76 106654 is_a_theorem(and(not(c_0),implies(A,and(A,implies(B,A))))). [back_rewrite(27228),rewrite([106390(1)])]. 42.38/42.76 106940 equiv(A,A) = and(not(c_0),not(c_0)). [para(106390(a,1),94(a,1,1)),rewrite([106390(3)]),flip(a)]. 42.38/42.76 107271 is_a_theorem(equiv(c_0,and(and(A,B),not(B)))). [resolve(104230,a,33526,a),rewrite([7032(4)])]. 42.38/42.76 107272 is_a_theorem(equiv(c_0,and(A,implies(A,not(A))))). [resolve(104230,a,33446,a),rewrite([7032(4),7031(3)])]. 42.38/42.76 107274 is_a_theorem(equiv(c_0,and(and(A,B),not(A)))). [resolve(104230,a,33244,a),rewrite([7032(4)])]. 42.38/42.76 107373 not(equiv(A,A)) = c_0. [resolve(104237,a,67,a)]. 42.38/42.76 107467 equiv(A,A) = not(c_0). [para(107373(a,1),6959(a,1,1)),flip(a)]. 42.38/42.76 107513 and(not(c_0),not(c_0)) = not(c_0). [back_rewrite(106940),rewrite([107467(1)]),flip(a)]. 42.38/42.76 113277 and(and(A,B),not(B)) = c_0. [resolve(107271,a,67,a)]. 42.38/42.76 113281 implies(and(A,B),B) = not(c_0). [para(113277(a,1),7031(a,1,1)),rewrite([6959(5)]),flip(a)]. 42.38/42.76 113299 and(A,implies(A,not(A))) = c_0. [resolve(107272,a,67,a)]. 42.38/42.76 113308 implies(A,and(A,A)) = not(c_0). [para(113299(a,1),7031(a,1,1)),rewrite([7032(5),6959(4)]),flip(a)]. 42.38/42.76 113311 equiv(A,and(A,A)) = not(c_0). [para(113308(a,1),94(a,1,1)),rewrite([113281(4),107513(5)]),flip(a)]. 42.38/42.76 113313 and(A,A) = A. [para(113311(a,1),67(a,1)),unit_del(a,104542)]. 42.38/42.76 113321 implies(A,not(A)) = not(A). [para(113313(a,1),7031(a,1,1)),flip(a)]. 42.38/42.76 113327 implies(not(A),A) = A. [para(113321(a,1),90(a,2)),rewrite([6959(2),90(1),6959(4)])]. 42.38/42.76 113342 is_a_theorem(implies(implies(A,implies(and(A,not(B)),B)),implies(A,B))). [para(113327(a,1),1629(a,1,2)),rewrite([7032(2)])]. 42.38/42.76 113388 and(and(A,B),not(A)) = c_0. [resolve(107274,a,67,a)]. 42.38/42.76 113481 implies(and(A,B),A) = not(c_0). [para(113388(a,1),7031(a,1,1)),rewrite([6959(5)]),flip(a)]. 42.38/42.76 113502 and(not(c_0),implies(A,and(A,B))) = equiv(and(A,B),A). [para(113481(a,1),94(a,1,1))]. 42.38/42.76 113514 is_a_theorem(equiv(and(A,implies(B,A)),A)). [back_rewrite(106654),rewrite([113502(6)])]. 42.38/42.76 113564 and(A,implies(B,A)) = A. [resolve(113514,a,67,a),flip(a)]. 42.38/42.76 113573 implies(A,and(B,not(A))) = not(A). [para(113564(a,1),7031(a,1,1)),rewrite([7032(3)]),flip(a)]. 42.38/42.76 117988 implies(not(A),and(B,A)) = A. [para(113573(a,1),90(a,2)),rewrite([6959(2),90(2),6959(5)])]. 42.38/42.76 118207 implies(and(A,not(B)),B) = implies(A,B). [para(113564(a,1),117988(a,1,2)),rewrite([7032(2)])]. 42.38/42.76 118229 is_a_theorem(implies(implies(A,implies(A,B)),implies(A,B))). [back_rewrite(113342),rewrite([118207(3)])]. 42.38/42.76 118230 $F. [resolve(118229,a,88,a)]. 42.38/42.76 42.38/42.76 % SZS output end Refutation 42.38/42.76 ============================== end of proof ========================== 42.38/42.76 42.38/42.76 ============================== STATISTICS ============================ 42.38/42.76 42.38/42.76 Given=3729. Generated=3292460. Kept=118178. proofs=1. 42.38/42.76 Usable=1255. Sos=6243. Demods=269. Limbo=22, Disabled=110731. Hints=0. 42.38/42.76 Megabytes=64.77. 42.38/42.76 User_CPU=39.45, System_CPU=2.23, Wall_clock=42. 42.38/42.76 42.38/42.76 ============================== end of statistics ===================== 42.38/42.76 42.38/42.76 ============================== end of search ========================= 42.38/42.76 42.38/42.76 THEOREM PROVED 42.38/42.76 % SZS status Theorem 42.38/42.76 42.38/42.76 Exiting with 1 proof. 42.38/42.76 42.38/42.76 Process 31202 exit (max_proofs) Tue Aug 9 05:12:58 2022 42.38/42.76 Prover9 interrupted 42.38/42.76 EOF