0.03/0.12 % Problem : theBenchmark.p : TPTP v0.0.0. Released v0.0.0. 0.03/0.12 % Command : tptp2X_and_run_prover9 %d %s 0.12/0.33 % Computer : n009.cluster.edu 0.12/0.33 % Model : x86_64 x86_64 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz 0.12/0.33 % Memory : 8042.1875MB 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64 0.12/0.33 % CPULimit : 1440 0.12/0.33 % WCLimit : 180 0.12/0.33 % DateTime : Mon Jul 3 06:18:41 EDT 2023 0.12/0.33 % CPUTime : 0.71/0.97 ============================== Prover9 =============================== 0.71/0.97 Prover9 (32) version 2009-11A, November 2009. 0.71/0.97 Process 21976 was started by sandbox on n009.cluster.edu, 0.71/0.97 Mon Jul 3 06:18:42 2023 0.71/0.97 The command was "/export/starexec/sandbox/solver/bin/prover9 -t 1440 -f /tmp/Prover9_21823_n009.cluster.edu". 0.71/0.97 ============================== end of head =========================== 0.71/0.97 0.71/0.97 ============================== INPUT ================================= 0.71/0.97 0.71/0.97 % Reading from file /tmp/Prover9_21823_n009.cluster.edu 0.71/0.97 0.71/0.97 set(prolog_style_variables). 0.71/0.97 set(auto2). 0.71/0.97 % set(auto2) -> set(auto). 0.71/0.97 % set(auto) -> set(auto_inference). 0.71/0.97 % set(auto) -> set(auto_setup). 0.71/0.97 % set(auto_setup) -> set(predicate_elim). 0.71/0.97 % set(auto_setup) -> assign(eq_defs, unfold). 0.71/0.97 % set(auto) -> set(auto_limits). 0.71/0.97 % set(auto_limits) -> assign(max_weight, "100.000"). 0.71/0.97 % set(auto_limits) -> assign(sos_limit, 20000). 0.71/0.97 % set(auto) -> set(auto_denials). 0.71/0.97 % set(auto) -> set(auto_process). 0.71/0.97 % set(auto2) -> assign(new_constants, 1). 0.71/0.97 % set(auto2) -> assign(fold_denial_max, 3). 0.71/0.97 % set(auto2) -> assign(max_weight, "200.000"). 0.71/0.97 % set(auto2) -> assign(max_hours, 1). 0.71/0.97 % assign(max_hours, 1) -> assign(max_seconds, 3600). 0.71/0.97 % set(auto2) -> assign(max_seconds, 0). 0.71/0.97 % set(auto2) -> assign(max_minutes, 5). 0.71/0.97 % assign(max_minutes, 5) -> assign(max_seconds, 300). 0.71/0.97 % set(auto2) -> set(sort_initial_sos). 0.71/0.97 % set(auto2) -> assign(sos_limit, -1). 0.71/0.97 % set(auto2) -> assign(lrs_ticks, 3000). 0.71/0.97 % set(auto2) -> assign(max_megs, 400). 0.71/0.97 % set(auto2) -> assign(stats, some). 0.71/0.97 % set(auto2) -> clear(echo_input). 0.71/0.97 % set(auto2) -> set(quiet). 0.71/0.97 % set(auto2) -> clear(print_initial_clauses). 0.71/0.97 % set(auto2) -> clear(print_given). 0.71/0.97 assign(lrs_ticks,-1). 0.71/0.97 assign(sos_limit,10000). 0.71/0.97 assign(order,kbo). 0.71/0.97 set(lex_order_vars). 0.71/0.97 clear(print_given). 0.71/0.97 0.71/0.97 % formulas(sos). % not echoed (18 formulas) 0.71/0.97 0.71/0.97 ============================== end of input ========================== 0.71/0.97 0.71/0.97 % From the command line: assign(max_seconds, 1440). 0.71/0.97 0.71/0.97 ============================== PROCESS NON-CLAUSAL FORMULAS ========== 0.71/0.97 0.71/0.97 % Formulas that are not ordinary clauses: 0.71/0.97 1 (all A all B (leq(A,B) <-> addition(A,B) = B)) # label(order) # label(axiom) # label(non_clause). [assumption]. 0.71/0.97 2 (all A all B addition(A,B) = addition(B,A)) # label(additive_commutativity) # label(axiom) # label(non_clause). [assumption]. 0.71/0.97 3 (all A zero = multiplication(A,zero)) # label(right_annihilation) # label(axiom) # label(non_clause). [assumption]. 0.71/0.97 4 (all A all B all C multiplication(addition(A,B),C) = addition(multiplication(A,C),multiplication(B,C))) # label(left_distributivity) # label(axiom) # label(non_clause). [assumption]. 0.71/0.97 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]. 0.71/0.97 6 (all A addition(A,A) = A) # label(additive_idempotence) # label(axiom) # label(non_clause). [assumption]. 0.71/0.97 7 (all A A = multiplication(A,one)) # label(multiplicative_right_identity) # label(axiom) # label(non_clause). [assumption]. 0.71/0.97 8 (all A multiplication(one,A) = A) # label(multiplicative_left_identity) # label(axiom) # label(non_clause). [assumption]. 0.71/0.97 9 (all A multiplication(zero,A) = zero) # label(left_annihilation) # label(axiom) # label(non_clause). [assumption]. 0.71/0.97 10 (all A all B all C multiplication(A,multiplication(B,C)) = multiplication(multiplication(A,B),C)) # label(multiplicative_associativity) # label(axiom) # label(non_clause). [assumption]. 0.71/0.97 11 (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]. 0.71/0.97 12 (all A addition(A,zero) = A) # label(additive_identity) # label(axiom) # label(non_clause). [assumption]. 0.71/0.97 13 (all X0 addition(domain(X0),one) = one) # label(domain3) # label(axiom) # label(non_clause). [assumption]. 0.71/0.97 14 (all X0 all X1 domain(multiplication(X0,domain(X1))) = domain(multiplication(X0,X1))) # label(domain2) # label(axiom) # label(non_clause). [assumption]. 0.71/0.97 15 (all X0 addition(X0,multiplication(domain(X0),X0)) = multiplication(domain(X0),X0)) # label(domain1) # label(axiom) # label(non_clause). [assumption]. 0.91/1.19 16 (all X0 all X1 domain(addition(X0,X1)) = addition(domain(X0),domain(X1))) # label(domain5) # label(axiom) # label(non_clause). [assumption]. 0.91/1.19 17 -(all X0 ((all X1 (multiplication(domain(X1),antidomain(X1)) = zero & addition(domain(X1),antidomain(X1)) = one)) -> domain(antidomain(X0)) = antidomain(X0))) # label(goals) # label(negated_conjecture) # label(non_clause). [assumption]. 0.91/1.19 0.91/1.19 ============================== end of process non-clausal formulas === 0.91/1.19 0.91/1.19 ============================== PROCESS INITIAL CLAUSES =============== 0.91/1.19 0.91/1.19 ============================== PREDICATE ELIMINATION ================= 0.91/1.19 18 leq(A,B) | addition(A,B) != B # label(order) # label(axiom). [clausify(1)]. 0.91/1.19 19 -leq(A,B) | addition(A,B) = B # label(order) # label(axiom). [clausify(1)]. 0.91/1.19 0.91/1.19 ============================== end predicate elimination ============= 0.91/1.19 0.91/1.19 Auto_denials: 0.91/1.19 % copying label goals to answer in negative clause 0.91/1.19 0.91/1.19 Term ordering decisions: 0.91/1.19 Function symbol KB weights: zero=1. one=1. c1=1. multiplication=1. addition=1. domain=1. antidomain=1. 0.91/1.19 0.91/1.19 ============================== end of process initial clauses ======== 0.91/1.19 0.91/1.19 ============================== CLAUSES FOR SEARCH ==================== 0.91/1.19 0.91/1.19 ============================== end of clauses for search ============= 0.91/1.19 0.91/1.19 ============================== SEARCH ================================ 0.91/1.19 0.91/1.19 % Starting search at 0.01 seconds. 0.91/1.19 0.91/1.19 ============================== PROOF ================================= 0.91/1.19 % SZS status Theorem 0.91/1.19 % SZS output start Refutation 0.91/1.19 0.91/1.19 % Proof 1 at 0.21 (+ 0.02) seconds: goals. 0.91/1.19 % Length of proof is 62. 0.91/1.19 % Level of proof is 14. 0.91/1.19 % Maximum clause weight is 24.000. 0.91/1.19 % Given clauses 188. 0.91/1.19 0.91/1.19 2 (all A all B addition(A,B) = addition(B,A)) # label(additive_commutativity) # label(axiom) # label(non_clause). [assumption]. 0.91/1.19 4 (all A all B all C multiplication(addition(A,B),C) = addition(multiplication(A,C),multiplication(B,C))) # label(left_distributivity) # label(axiom) # label(non_clause). [assumption]. 0.91/1.19 7 (all A A = multiplication(A,one)) # label(multiplicative_right_identity) # label(axiom) # label(non_clause). [assumption]. 0.91/1.19 8 (all A multiplication(one,A) = A) # label(multiplicative_left_identity) # label(axiom) # label(non_clause). [assumption]. 0.91/1.19 9 (all A multiplication(zero,A) = zero) # label(left_annihilation) # label(axiom) # label(non_clause). [assumption]. 0.91/1.19 10 (all A all B all C multiplication(A,multiplication(B,C)) = multiplication(multiplication(A,B),C)) # label(multiplicative_associativity) # label(axiom) # label(non_clause). [assumption]. 0.91/1.19 11 (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]. 0.91/1.19 12 (all A addition(A,zero) = A) # label(additive_identity) # label(axiom) # label(non_clause). [assumption]. 0.91/1.19 13 (all X0 addition(domain(X0),one) = one) # label(domain3) # label(axiom) # label(non_clause). [assumption]. 0.91/1.19 14 (all X0 all X1 domain(multiplication(X0,domain(X1))) = domain(multiplication(X0,X1))) # label(domain2) # label(axiom) # label(non_clause). [assumption]. 0.91/1.19 15 (all X0 addition(X0,multiplication(domain(X0),X0)) = multiplication(domain(X0),X0)) # label(domain1) # label(axiom) # label(non_clause). [assumption]. 0.91/1.19 16 (all X0 all X1 domain(addition(X0,X1)) = addition(domain(X0),domain(X1))) # label(domain5) # label(axiom) # label(non_clause). [assumption]. 0.91/1.19 17 -(all X0 ((all X1 (multiplication(domain(X1),antidomain(X1)) = zero & addition(domain(X1),antidomain(X1)) = one)) -> domain(antidomain(X0)) = antidomain(X0))) # label(goals) # label(negated_conjecture) # label(non_clause). [assumption]. 0.91/1.19 20 domain(zero) = zero # label(domain4) # label(axiom). [assumption]. 0.91/1.19 23 multiplication(A,one) = A # label(multiplicative_right_identity) # label(axiom). [clausify(7)]. 0.91/1.19 24 multiplication(one,A) = A # label(multiplicative_left_identity) # label(axiom). [clausify(8)]. 0.91/1.19 25 multiplication(zero,A) = zero # label(left_annihilation) # label(axiom). [clausify(9)]. 0.91/1.19 26 addition(A,zero) = A # label(additive_identity) # label(axiom). [clausify(12)]. 0.91/1.19 27 addition(domain(A),one) = one # label(domain3) # label(axiom). [clausify(13)]. 0.91/1.19 28 addition(A,B) = addition(B,A) # label(additive_commutativity) # label(axiom). [clausify(2)]. 0.91/1.19 29 multiplication(domain(A),antidomain(A)) = zero # label(goals) # label(negated_conjecture). [clausify(17)]. 0.91/1.19 30 addition(domain(A),antidomain(A)) = one # label(goals) # label(negated_conjecture). [clausify(17)]. 0.91/1.19 31 domain(multiplication(A,domain(B))) = domain(multiplication(A,B)) # label(domain2) # label(axiom). [clausify(14)]. 0.91/1.19 32 domain(addition(A,B)) = addition(domain(A),domain(B)) # label(domain5) # label(axiom). [clausify(16)]. 0.91/1.19 33 addition(domain(A),domain(B)) = domain(addition(A,B)). [copy(32),flip(a)]. 0.91/1.19 36 multiplication(multiplication(A,B),C) = multiplication(A,multiplication(B,C)) # label(multiplicative_associativity) # label(axiom). [clausify(10)]. 0.91/1.19 37 multiplication(domain(A),A) = addition(A,multiplication(domain(A),A)) # label(domain1) # label(axiom). [clausify(15)]. 0.91/1.19 38 addition(A,multiplication(domain(A),A)) = multiplication(domain(A),A). [copy(37),flip(a)]. 0.91/1.19 39 multiplication(addition(A,B),C) = addition(multiplication(A,C),multiplication(B,C)) # label(left_distributivity) # label(axiom). [clausify(4)]. 0.91/1.19 40 addition(multiplication(A,B),multiplication(C,B)) = multiplication(addition(A,C),B). [copy(39),flip(a)]. 0.91/1.19 41 multiplication(A,addition(B,C)) = addition(multiplication(A,B),multiplication(A,C)) # label(right_distributivity) # label(axiom). [clausify(11)]. 0.91/1.19 42 addition(multiplication(A,B),multiplication(A,C)) = multiplication(A,addition(B,C)). [copy(41),flip(a)]. 0.91/1.19 43 antidomain(c1) != domain(antidomain(c1)) # label(goals) # label(negated_conjecture) # answer(goals). [clausify(17)]. 0.91/1.19 44 domain(antidomain(c1)) != antidomain(c1) # answer(goals). [copy(43),flip(a)]. 0.91/1.19 45 addition(one,domain(A)) = one. [back_rewrite(27),rewrite([28(3)])]. 0.91/1.19 46 domain(antidomain(c1)) = c_0. [new_symbol(44)]. 0.91/1.19 47 antidomain(c1) != c_0 # answer(goals). [back_rewrite(44),rewrite([46(3)]),flip(a)]. 0.91/1.19 51 addition(domain(multiplication(A,B)),antidomain(multiplication(A,domain(B)))) = one. [para(31(a,1),30(a,1,1))]. 0.91/1.19 59 addition(multiplication(A,domain(B)),multiplication(domain(multiplication(A,B)),multiplication(A,domain(B)))) = multiplication(domain(multiplication(A,B)),multiplication(A,domain(B))). [para(31(a,1),38(a,1,2,1)),rewrite([31(11)])]. 0.91/1.19 62 multiplication(addition(A,one),B) = addition(B,multiplication(A,B)). [para(24(a,1),40(a,1,1)),rewrite([28(4)]),flip(a)]. 0.91/1.19 63 addition(zero,multiplication(A,B)) = multiplication(A,B). [para(25(a,1),40(a,1,1)),rewrite([28(5),26(5)])]. 0.91/1.19 68 multiplication(domain(multiplication(A,B)),multiplication(A,domain(B))) = multiplication(A,domain(B)). [back_rewrite(59),rewrite([62(8,R),28(4),45(4),24(4)]),flip(a)]. 0.91/1.19 72 addition(A,multiplication(domain(B),A)) = A. [para(45(a,1),40(a,2,1)),rewrite([24(2),24(5)])]. 0.91/1.19 74 multiplication(domain(A),A) = A. [back_rewrite(38),rewrite([72(3)]),flip(a)]. 0.91/1.19 79 addition(one,c_0) = one. [para(46(a,1),45(a,1,2))]. 0.91/1.19 86 addition(A,multiplication(c_0,A)) = A. [para(79(a,1),40(a,2,1)),rewrite([24(2),24(5)])]. 0.91/1.19 96 multiplication(addition(A,domain(B)),B) = addition(B,multiplication(A,B)). [para(74(a,1),40(a,1,1)),rewrite([28(4)]),flip(a)]. 0.91/1.19 98 multiplication(c_0,antidomain(c1)) = antidomain(c1). [para(46(a,1),74(a,1,1))]. 0.91/1.19 115 addition(zero,antidomain(multiplication(domain(A),domain(antidomain(A))))) = one. [para(29(a,1),51(a,1,1,1)),rewrite([20(2)])]. 0.91/1.19 161 addition(zero,antidomain(A)) = antidomain(A). [para(29(a,1),72(a,1,2)),rewrite([28(3)])]. 0.91/1.19 167 antidomain(multiplication(domain(A),domain(antidomain(A)))) = one. [back_rewrite(115),rewrite([161(7)])]. 0.91/1.19 320 antidomain(multiplication(domain(c1),c_0)) = one. [para(46(a,1),167(a,1,1,2))]. 0.91/1.19 330 domain(multiplication(domain(c1),c_0)) = zero. [para(320(a,1),29(a,1,2)),rewrite([23(7)])]. 0.91/1.19 336 multiplication(domain(c1),c_0) = zero. [para(330(a,1),74(a,1,1)),rewrite([25(6)]),flip(a)]. 0.91/1.19 337 multiplication(domain(c1),multiplication(c_0,A)) = zero. [para(336(a,1),36(a,1,1)),rewrite([25(2)]),flip(a)]. 0.91/1.19 665 multiplication(domain(addition(A,B)),B) = B. [para(33(a,1),96(a,1,1)),rewrite([72(6)])]. 0.91/1.19 699 multiplication(domain(A),multiplication(c_0,A)) = multiplication(c_0,A). [para(86(a,1),665(a,1,1,1))]. 0.91/1.19 1031 multiplication(c_0,c1) = zero. [para(699(a,1),337(a,1))]. 0.91/1.19 1046 multiplication(c_0,domain(c1)) = zero. [para(1031(a,1),68(a,1,1,1)),rewrite([20(2),25(6)]),flip(a)]. 0.91/1.19 1049 multiplication(c_0,addition(A,domain(c1))) = multiplication(c_0,A). [para(1046(a,1),42(a,1,1)),rewrite([63(4),28(6)]),flip(a)]. 0.91/1.19 1464 antidomain(c1) = c_0. [para(98(a,1),1049(a,2)),rewrite([28(6),30(6),23(3)]),flip(a)]. 0.91/1.19 1465 $F # answer(goals). [resolve(1464,a,47,a)]. 0.91/1.19 0.91/1.19 % SZS output end Refutation 0.91/1.19 ============================== end of proof ========================== 0.91/1.19 0.91/1.19 ============================== STATISTICS ============================ 0.91/1.19 0.91/1.19 Given=188. Generated=10899. Kept=1439. proofs=1. 0.91/1.19 Usable=178. Sos=1107. Demods=1255. Limbo=4, Disabled=170. Hints=0. 0.91/1.19 Megabytes=1.72. 0.91/1.19 User_CPU=0.21, System_CPU=0.02, Wall_clock=0. 0.91/1.19 0.91/1.19 ============================== end of statistics ===================== 0.91/1.19 0.91/1.19 ============================== end of search ========================= 0.91/1.19 0.91/1.19 THEOREM PROVED 0.91/1.19 % SZS status Theorem 0.91/1.19 0.91/1.19 Exiting with 1 proof. 0.91/1.19 0.91/1.19 Process 21976 exit (max_proofs) Mon Jul 3 06:18:42 2023 0.91/1.19 Prover9 interrupted 0.91/1.19 EOF