0.08/0.13 % Problem : theBenchmark.p : TPTP v0.0.0. Released v0.0.0. 0.08/0.14 % Command : tptp2X_and_run_prover9 %d %s 0.13/0.35 % Computer : n007.cluster.edu 0.13/0.35 % Model : x86_64 x86_64 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz 0.13/0.35 % Memory : 8042.1875MB 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64 0.13/0.35 % CPULimit : 960 0.13/0.35 % WCLimit : 120 0.13/0.35 % DateTime : Tue Aug 9 03:24:27 EDT 2022 0.13/0.35 % CPUTime : 0.75/1.02 ============================== Prover9 =============================== 0.75/1.02 Prover9 (32) version 2009-11A, November 2009. 0.75/1.02 Process 30505 was started by sandbox on n007.cluster.edu, 0.75/1.02 Tue Aug 9 03:24:27 2022 0.75/1.02 The command was "/export/starexec/sandbox/solver/bin/prover9 -t 960 -f /tmp/Prover9_30352_n007.cluster.edu". 0.75/1.02 ============================== end of head =========================== 0.75/1.02 0.75/1.02 ============================== INPUT ================================= 0.75/1.02 0.75/1.02 % Reading from file /tmp/Prover9_30352_n007.cluster.edu 0.75/1.02 0.75/1.02 set(prolog_style_variables). 0.75/1.02 set(auto2). 0.75/1.02 % set(auto2) -> set(auto). 0.75/1.02 % set(auto) -> set(auto_inference). 0.75/1.02 % set(auto) -> set(auto_setup). 0.75/1.02 % set(auto_setup) -> set(predicate_elim). 0.75/1.02 % set(auto_setup) -> assign(eq_defs, unfold). 0.75/1.02 % set(auto) -> set(auto_limits). 0.75/1.02 % set(auto_limits) -> assign(max_weight, "100.000"). 0.75/1.02 % set(auto_limits) -> assign(sos_limit, 20000). 0.75/1.02 % set(auto) -> set(auto_denials). 0.75/1.02 % set(auto) -> set(auto_process). 0.75/1.02 % set(auto2) -> assign(new_constants, 1). 0.75/1.02 % set(auto2) -> assign(fold_denial_max, 3). 0.75/1.02 % set(auto2) -> assign(max_weight, "200.000"). 0.75/1.02 % set(auto2) -> assign(max_hours, 1). 0.75/1.02 % assign(max_hours, 1) -> assign(max_seconds, 3600). 0.75/1.02 % set(auto2) -> assign(max_seconds, 0). 0.75/1.02 % set(auto2) -> assign(max_minutes, 5). 0.75/1.02 % assign(max_minutes, 5) -> assign(max_seconds, 300). 0.75/1.02 % set(auto2) -> set(sort_initial_sos). 0.75/1.02 % set(auto2) -> assign(sos_limit, -1). 0.75/1.02 % set(auto2) -> assign(lrs_ticks, 3000). 0.75/1.02 % set(auto2) -> assign(max_megs, 400). 0.75/1.02 % set(auto2) -> assign(stats, some). 0.75/1.02 % set(auto2) -> clear(echo_input). 0.75/1.02 % set(auto2) -> set(quiet). 0.75/1.02 % set(auto2) -> clear(print_initial_clauses). 0.75/1.02 % set(auto2) -> clear(print_given). 0.75/1.02 assign(lrs_ticks,-1). 0.75/1.02 assign(sos_limit,10000). 0.75/1.02 assign(order,kbo). 0.75/1.02 set(lex_order_vars). 0.75/1.02 clear(print_given). 0.75/1.02 0.75/1.02 % formulas(sos). % not echoed (17 formulas) 0.75/1.02 0.75/1.02 ============================== end of input ========================== 0.75/1.02 0.75/1.02 % From the command line: assign(max_seconds, 960). 0.75/1.02 0.75/1.02 ============================== PROCESS NON-CLAUSAL FORMULAS ========== 0.75/1.02 0.75/1.02 % Formulas that are not ordinary clauses: 0.75/1.02 1 (all A all B (leq(A,B) <-> B = addition(A,B))) # label(order) # label(axiom) # label(non_clause). [assumption]. 0.75/1.02 2 (all A leq(addition(one,multiplication(A,star(A))),star(A))) # label(star_unfold_right) # label(axiom) # label(non_clause). [assumption]. 0.75/1.02 3 (all A all B all C (leq(addition(multiplication(A,B),C),B) -> leq(multiplication(star(A),C),B))) # label(star_induction_left) # label(axiom) # label(non_clause). [assumption]. 0.75/1.02 4 (all A all B all C addition(multiplication(A,C),multiplication(B,C)) = multiplication(addition(A,B),C)) # label(left_distributivity) # label(axiom) # label(non_clause). [assumption]. 0.75/1.02 5 (all C all B all A addition(addition(A,B),C) = addition(A,addition(B,C))) # label(additive_associativity) # label(axiom) # label(non_clause). [assumption]. 0.75/1.02 6 (all A all B addition(A,B) = addition(B,A)) # label(additive_commutativity) # label(axiom) # label(non_clause). [assumption]. 0.75/1.02 7 (all A multiplication(A,zero) = zero) # label(right_annihilation) # label(axiom) # label(non_clause). [assumption]. 0.75/1.02 8 (all A all B all C multiplication(A,addition(B,C)) = addition(multiplication(A,B),multiplication(A,C))) # label(right_distributivity) # label(axiom) # label(non_clause). [assumption]. 0.75/1.02 9 (all A addition(A,A) = A) # label(additive_idempotence) # label(axiom) # label(non_clause). [assumption]. 0.75/1.02 10 (all A A = multiplication(one,A)) # label(multiplicative_left_identity) # label(axiom) # label(non_clause). [assumption]. 0.75/1.02 11 (all A all B all C (leq(addition(multiplication(A,B),C),A) -> leq(multiplication(C,star(B)),A))) # label(star_induction_right) # label(axiom) # label(non_clause). [assumption]. 0.75/1.02 12 (all A addition(A,zero) = A) # label(additive_identity) # label(axiom) # label(non_clause). [assumption]. 0.75/1.02 13 (all A all B all C multiplication(multiplication(A,B),C) = multiplication(A,multiplication(B,C))) # label(multiplicative_associativity) # label(axiom) # label(non_clause). [assumption]. 0.75/1.02 14 (all A multiplication(A,one) = A) # label(multiplicative_right_identity) # label(axiom) # label(non_clause). [assumption]. 0.95/1.24 15 (all A leq(addition(one,multiplication(star(A),A)),star(A))) # label(star_unfold_left) # label(axiom) # label(non_clause). [assumption]. 0.95/1.24 16 (all A multiplication(zero,A) = zero) # label(left_annihilation) # label(axiom) # label(non_clause). [assumption]. 0.95/1.24 0.95/1.24 ============================== end of process non-clausal formulas === 0.95/1.24 0.95/1.24 ============================== PROCESS INITIAL CLAUSES =============== 0.95/1.24 0.95/1.24 ============================== PREDICATE ELIMINATION ================= 0.95/1.24 0.95/1.24 ============================== end predicate elimination ============= 0.95/1.24 0.95/1.24 Auto_denials: 0.95/1.24 % copying label a to answer in negative clause 0.95/1.24 0.95/1.24 Term ordering decisions: 0.95/1.24 0.95/1.24 % Assigning unary symbol star kb_weight 0 and highest precedence (8). 0.95/1.24 Function symbol KB weights: zero=1. one=1. a=1. multiplication=1. addition=1. star=0. 0.95/1.24 0.95/1.24 ============================== end of process initial clauses ======== 0.95/1.24 0.95/1.24 ============================== CLAUSES FOR SEARCH ==================== 0.95/1.24 0.95/1.24 ============================== end of clauses for search ============= 0.95/1.24 0.95/1.24 ============================== SEARCH ================================ 0.95/1.24 0.95/1.24 % Starting search at 0.01 seconds. 0.95/1.24 0.95/1.24 ============================== PROOF ================================= 0.95/1.24 % SZS status Theorem 0.95/1.24 % SZS output start Refutation 0.95/1.24 0.95/1.24 % Proof 1 at 0.24 (+ 0.00) seconds: a. 0.95/1.24 % Length of proof is 49. 0.95/1.24 % Level of proof is 15. 0.95/1.24 % Maximum clause weight is 13.000. 0.95/1.24 % Given clauses 233. 0.95/1.24 0.95/1.24 1 (all A all B (leq(A,B) <-> B = addition(A,B))) # label(order) # label(axiom) # label(non_clause). [assumption]. 0.95/1.24 2 (all A leq(addition(one,multiplication(A,star(A))),star(A))) # label(star_unfold_right) # label(axiom) # label(non_clause). [assumption]. 0.95/1.24 4 (all A all B all C addition(multiplication(A,C),multiplication(B,C)) = multiplication(addition(A,B),C)) # label(left_distributivity) # label(axiom) # label(non_clause). [assumption]. 0.95/1.24 5 (all C all B all A addition(addition(A,B),C) = addition(A,addition(B,C))) # label(additive_associativity) # label(axiom) # label(non_clause). [assumption]. 0.95/1.24 6 (all A all B addition(A,B) = addition(B,A)) # label(additive_commutativity) # label(axiom) # label(non_clause). [assumption]. 0.95/1.24 8 (all A all B all C multiplication(A,addition(B,C)) = addition(multiplication(A,B),multiplication(A,C))) # label(right_distributivity) # label(axiom) # label(non_clause). [assumption]. 0.95/1.24 9 (all A addition(A,A) = A) # label(additive_idempotence) # label(axiom) # label(non_clause). [assumption]. 0.95/1.24 10 (all A A = multiplication(one,A)) # label(multiplicative_left_identity) # label(axiom) # label(non_clause). [assumption]. 0.95/1.24 14 (all A multiplication(A,one) = A) # label(multiplicative_right_identity) # label(axiom) # label(non_clause). [assumption]. 0.95/1.24 15 (all A leq(addition(one,multiplication(star(A),A)),star(A))) # label(star_unfold_left) # label(axiom) # label(non_clause). [assumption]. 0.95/1.24 18 addition(A,A) = A # label(additive_idempotence) # label(axiom). [clausify(9)]. 0.95/1.24 19 multiplication(one,A) = A # label(multiplicative_left_identity) # label(axiom). [clausify(10)]. 0.95/1.24 21 multiplication(A,one) = A # label(multiplicative_right_identity) # label(axiom). [clausify(14)]. 0.95/1.24 23 addition(A,B) = addition(B,A) # label(additive_commutativity) # label(axiom). [clausify(6)]. 0.95/1.24 24 leq(addition(one,multiplication(A,star(A))),star(A)) # label(star_unfold_right) # label(axiom). [clausify(2)]. 0.95/1.24 25 leq(addition(one,multiplication(star(A),A)),star(A)) # label(star_unfold_left) # label(axiom). [clausify(15)]. 0.95/1.24 26 addition(addition(A,B),C) = addition(A,addition(B,C)) # label(additive_associativity) # label(axiom). [clausify(5)]. 0.95/1.24 27 addition(A,addition(B,C)) = addition(C,addition(A,B)). [copy(26),rewrite([23(2)]),flip(a)]. 0.95/1.24 29 multiplication(addition(A,B),C) = addition(multiplication(A,C),multiplication(B,C)) # label(left_distributivity) # label(axiom). [clausify(4)]. 0.95/1.24 30 addition(multiplication(A,B),multiplication(C,B)) = multiplication(addition(A,C),B). [copy(29),flip(a)]. 0.95/1.24 31 multiplication(A,addition(B,C)) = addition(multiplication(A,B),multiplication(A,C)) # label(right_distributivity) # label(axiom). [clausify(8)]. 0.95/1.24 32 addition(multiplication(A,B),multiplication(A,C)) = multiplication(A,addition(B,C)). [copy(31),flip(a)]. 0.95/1.24 33 -leq(multiplication(a,a),star(a)) # label(a) # label(negated_conjecture) # answer(a). [assumption]. 0.95/1.24 34 -leq(A,B) | addition(A,B) = B # label(order) # label(axiom). [clausify(1)]. 0.95/1.24 35 leq(A,B) | addition(A,B) != B # label(order) # label(axiom). [clausify(1)]. 0.95/1.24 42 addition(A,addition(A,B)) = addition(A,B). [para(27(a,1),18(a,1)),rewrite([23(1),23(2),27(2,R),18(1),23(3)])]. 0.95/1.24 44 multiplication(addition(A,one),B) = addition(B,multiplication(A,B)). [para(19(a,1),30(a,1,1)),rewrite([23(4)]),flip(a)]. 0.95/1.24 48 multiplication(A,addition(B,one)) = addition(A,multiplication(A,B)). [para(21(a,1),32(a,1,1)),rewrite([23(4)]),flip(a)]. 0.95/1.24 49 addition(star(A),addition(one,multiplication(star(A),A))) = star(A). [hyper(34,a,25,a),rewrite([23(6)])]. 0.95/1.24 50 addition(star(A),addition(one,multiplication(A,star(A)))) = star(A). [hyper(34,a,24,a),rewrite([23(6)])]. 0.95/1.24 53 addition(star(a),multiplication(a,a)) != star(a) # answer(a). [ur(35,a,33,a),rewrite([23(6)])]. 0.95/1.24 78 leq(A,addition(A,B)). [hyper(35,b,42,a)]. 0.95/1.24 80 leq(multiplication(A,B),multiplication(A,addition(B,C))). [para(32(a,1),78(a,2))]. 0.95/1.24 170 multiplication(addition(A,one),A) = multiplication(A,addition(A,one)). [para(48(a,2),44(a,2))]. 0.95/1.24 192 addition(one,addition(star(A),multiplication(star(A),A))) = star(A). [para(49(a,1),27(a,1)),rewrite([27(7),23(6)]),flip(a)]. 0.95/1.24 214 addition(one,addition(star(A),multiplication(A,star(A)))) = star(A). [para(50(a,1),27(a,1)),rewrite([27(7),23(6)]),flip(a)]. 0.95/1.24 365 addition(one,star(A)) = star(A). [para(192(a,1),42(a,1,2)),rewrite([192(9)])]. 0.95/1.24 369 leq(A,multiplication(A,star(B))). [para(192(a,1),80(a,2,2)),rewrite([21(2)])]. 0.95/1.24 389 leq(addition(A,one),addition(star(B),multiplication(A,star(B)))). [para(44(a,1),369(a,2))]. 0.95/1.24 473 addition(star(A),multiplication(A,star(A))) = star(A). [para(214(a,1),27(a,1)),rewrite([365(6),23(5)]),flip(a)]. 0.95/1.24 481 multiplication(addition(A,one),star(A)) = star(A). [para(473(a,1),44(a,2))]. 0.95/1.24 493 leq(addition(A,one),star(A)). [para(473(a,1),389(a,2))]. 0.95/1.24 514 addition(A,star(A)) = star(A). [hyper(34,a,493,a),rewrite([23(4),27(4,R),365(3)])]. 0.95/1.24 522 leq(multiplication(A,B),multiplication(A,star(B))). [para(514(a,1),80(a,2,2))]. 0.95/1.24 557 leq(multiplication(A,addition(A,one)),star(A)). [para(170(a,1),522(a,1)),rewrite([481(7)])]. 0.95/1.24 561 leq(addition(A,multiplication(A,A)),star(A)). [para(48(a,1),557(a,1))]. 0.95/1.24 570 addition(A,addition(star(A),multiplication(A,A))) = star(A). [hyper(34,a,561,a),rewrite([23(4),27(4,R),23(3)])]. 0.95/1.24 1987 addition(star(A),multiplication(A,A)) = star(A). [para(570(a,1),27(a,1)),rewrite([514(4),23(4)]),flip(a)]. 0.95/1.24 1988 $F # answer(a). [resolve(1987,a,53,a)]. 0.95/1.24 0.95/1.24 % SZS output end Refutation 0.95/1.24 ============================== end of proof ========================== 0.95/1.24 0.95/1.24 ============================== STATISTICS ============================ 0.95/1.24 0.95/1.24 Given=233. Generated=6741. Kept=1966. proofs=1. 0.95/1.24 Usable=207. Sos=1605. Demods=273. Limbo=0, Disabled=171. Hints=0. 0.95/1.24 Megabytes=2.00. 0.95/1.24 User_CPU=0.24, System_CPU=0.00, Wall_clock=0. 0.95/1.24 0.95/1.24 ============================== end of statistics ===================== 0.95/1.24 0.95/1.24 ============================== end of search ========================= 0.95/1.24 0.95/1.24 THEOREM PROVED 0.95/1.24 % SZS status Theorem 0.95/1.24 0.95/1.24 Exiting with 1 proof. 0.95/1.24 0.95/1.24 Process 30505 exit (max_proofs) Tue Aug 9 03:24:27 2022 0.95/1.24 Prover9 interrupted 0.95/1.25 EOF