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 : n020.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 : 180 0.12/0.33 % DateTime : Thu Aug 29 09:55:10 EDT 2019 0.12/0.33 % CPUTime : 0.42/0.97 ============================== Prover9 =============================== 0.42/0.97 Prover9 (32) version 2009-11A, November 2009. 0.42/0.97 Process 26784 was started by sandbox on n020.cluster.edu, 0.42/0.97 Thu Aug 29 09:55:11 2019 0.42/0.97 The command was "/export/starexec/sandbox/solver/bin/prover9 -t 180 -f /tmp/Prover9_26630_n020.cluster.edu". 0.42/0.97 ============================== end of head =========================== 0.42/0.97 0.42/0.97 ============================== INPUT ================================= 0.42/0.97 0.42/0.97 % Reading from file /tmp/Prover9_26630_n020.cluster.edu 0.42/0.97 0.42/0.97 set(prolog_style_variables). 0.42/0.97 set(auto2). 0.42/0.97 % set(auto2) -> set(auto). 0.42/0.97 % set(auto) -> set(auto_inference). 0.42/0.97 % set(auto) -> set(auto_setup). 0.42/0.97 % set(auto_setup) -> set(predicate_elim). 0.42/0.97 % set(auto_setup) -> assign(eq_defs, unfold). 0.42/0.97 % set(auto) -> set(auto_limits). 0.42/0.97 % set(auto_limits) -> assign(max_weight, "100.000"). 0.42/0.97 % set(auto_limits) -> assign(sos_limit, 20000). 0.42/0.97 % set(auto) -> set(auto_denials). 0.42/0.97 % set(auto) -> set(auto_process). 0.42/0.97 % set(auto2) -> assign(new_constants, 1). 0.42/0.97 % set(auto2) -> assign(fold_denial_max, 3). 0.42/0.97 % set(auto2) -> assign(max_weight, "200.000"). 0.42/0.97 % set(auto2) -> assign(max_hours, 1). 0.42/0.97 % assign(max_hours, 1) -> assign(max_seconds, 3600). 0.42/0.97 % set(auto2) -> assign(max_seconds, 0). 0.42/0.97 % set(auto2) -> assign(max_minutes, 5). 0.42/0.97 % assign(max_minutes, 5) -> assign(max_seconds, 300). 0.42/0.97 % set(auto2) -> set(sort_initial_sos). 0.42/0.97 % set(auto2) -> assign(sos_limit, -1). 0.42/0.97 % set(auto2) -> assign(lrs_ticks, 3000). 0.42/0.97 % set(auto2) -> assign(max_megs, 400). 0.42/0.97 % set(auto2) -> assign(stats, some). 0.42/0.97 % set(auto2) -> clear(echo_input). 0.42/0.97 % set(auto2) -> set(quiet). 0.42/0.97 % set(auto2) -> clear(print_initial_clauses). 0.42/0.97 % set(auto2) -> clear(print_given). 0.42/0.97 assign(lrs_ticks,-1). 0.42/0.97 assign(sos_limit,10000). 0.42/0.97 assign(order,kbo). 0.42/0.97 set(lex_order_vars). 0.42/0.97 clear(print_given). 0.42/0.97 0.42/0.97 % formulas(sos). % not echoed (14 formulas) 0.42/0.97 0.42/0.97 ============================== end of input ========================== 0.42/0.97 0.42/0.97 % From the command line: assign(max_seconds, 180). 0.42/0.97 0.42/0.97 ============================== PROCESS NON-CLAUSAL FORMULAS ========== 0.42/0.97 0.42/0.97 % Formulas that are not ordinary clauses: 0.42/0.97 1 (all X0 all X1 X0 = join(complement(join(complement(X0),complement(X1))),complement(join(complement(X0),X1)))) # label(maddux3_a_kind_of_de_Morgan) # label(axiom) # label(non_clause). [assumption]. 0.42/0.97 2 (all X0 X0 = composition(X0,one)) # label(composition_identity) # label(axiom) # label(non_clause). [assumption]. 0.42/0.97 3 (all X0 all X1 converse(composition(X0,X1)) = composition(converse(X1),converse(X0))) # label(converse_multiplicativity) # label(axiom) # label(non_clause). [assumption]. 0.42/0.97 4 (all X0 meet(X0,complement(X0)) = zero) # label(def_zero) # label(axiom) # label(non_clause). [assumption]. 0.42/0.97 5 (all X0 all X1 meet(X0,X1) = complement(join(complement(X0),complement(X1)))) # label(maddux4_definiton_of_meet) # label(axiom) # label(non_clause). [assumption]. 0.42/0.97 6 (all X0 all X1 converse(join(X0,X1)) = join(converse(X0),converse(X1))) # label(converse_additivity) # label(axiom) # label(non_clause). [assumption]. 0.42/0.97 7 (all X0 join(X0,complement(X0)) = top) # label(def_top) # label(axiom) # label(non_clause). [assumption]. 0.42/0.97 8 (all X0 all X1 all X2 composition(composition(X0,X1),X2) = composition(X0,composition(X1,X2))) # label(composition_associativity) # label(axiom) # label(non_clause). [assumption]. 0.42/0.97 9 (all X0 all X1 all X2 composition(join(X0,X1),X2) = join(composition(X0,X2),composition(X1,X2))) # label(composition_distributivity) # label(axiom) # label(non_clause). [assumption]. 0.42/0.97 10 (all X0 all X1 join(X1,X0) = join(X0,X1)) # label(maddux1_join_commutativity) # label(axiom) # label(non_clause). [assumption]. 0.42/0.97 11 (all X0 X0 = converse(converse(X0))) # label(converse_idempotence) # label(axiom) # label(non_clause). [assumption]. 0.42/0.97 12 (all X0 all X1 all X2 join(X0,join(X1,X2)) = join(join(X0,X1),X2)) # label(maddux2_join_associativity) # label(axiom) # label(non_clause). [assumption]. 0.42/0.97 13 (all X0 all X1 complement(X1) = join(composition(converse(X0),complement(composition(X0,X1))),complement(X1))) # label(converse_cancellativity) # label(axiom) # label(non_clause). [assumption]. 1.19/1.46 14 -(all X0 converse(complement(X0)) = complement(converse(X0))) # label(goals) # label(negated_conjecture) # label(non_clause). [assumption]. 1.19/1.46 1.19/1.46 ============================== end of process non-clausal formulas === 1.19/1.46 1.19/1.46 ============================== PROCESS INITIAL CLAUSES =============== 1.19/1.46 1.19/1.46 ============================== PREDICATE ELIMINATION ================= 1.19/1.46 1.19/1.46 ============================== end predicate elimination ============= 1.19/1.46 1.19/1.46 Auto_denials: 1.19/1.46 % copying label goals to answer in negative clause 1.19/1.46 1.19/1.46 Term ordering decisions: 1.19/1.46 Function symbol KB weights: one=1. top=1. zero=1. c1=1. join=1. composition=1. meet=1. complement=1. converse=1. 1.19/1.46 1.19/1.46 ============================== end of process initial clauses ======== 1.19/1.46 1.19/1.46 ============================== CLAUSES FOR SEARCH ==================== 1.19/1.46 1.19/1.46 ============================== end of clauses for search ============= 1.19/1.46 1.19/1.46 ============================== SEARCH ================================ 1.19/1.46 1.19/1.46 % Starting search at 0.01 seconds. 1.19/1.46 1.19/1.46 ============================== PROOF ================================= 1.19/1.47 % SZS status Theorem 1.19/1.47 % SZS output start Refutation 1.19/1.47 1.19/1.47 % Proof 1 at 0.48 (+ 0.02) seconds: goals. 1.19/1.47 % Length of proof is 78. 1.19/1.47 % Level of proof is 25. 1.19/1.47 % Maximum clause weight is 14.000. 1.19/1.47 % Given clauses 286. 1.19/1.47 1.19/1.47 1 (all X0 all X1 X0 = join(complement(join(complement(X0),complement(X1))),complement(join(complement(X0),X1)))) # label(maddux3_a_kind_of_de_Morgan) # label(axiom) # label(non_clause). [assumption]. 1.19/1.47 2 (all X0 X0 = composition(X0,one)) # label(composition_identity) # label(axiom) # label(non_clause). [assumption]. 1.19/1.47 3 (all X0 all X1 converse(composition(X0,X1)) = composition(converse(X1),converse(X0))) # label(converse_multiplicativity) # label(axiom) # label(non_clause). [assumption]. 1.19/1.47 4 (all X0 meet(X0,complement(X0)) = zero) # label(def_zero) # label(axiom) # label(non_clause). [assumption]. 1.19/1.47 5 (all X0 all X1 meet(X0,X1) = complement(join(complement(X0),complement(X1)))) # label(maddux4_definiton_of_meet) # label(axiom) # label(non_clause). [assumption]. 1.19/1.47 6 (all X0 all X1 converse(join(X0,X1)) = join(converse(X0),converse(X1))) # label(converse_additivity) # label(axiom) # label(non_clause). [assumption]. 1.19/1.47 7 (all X0 join(X0,complement(X0)) = top) # label(def_top) # label(axiom) # label(non_clause). [assumption]. 1.19/1.47 8 (all X0 all X1 all X2 composition(composition(X0,X1),X2) = composition(X0,composition(X1,X2))) # label(composition_associativity) # label(axiom) # label(non_clause). [assumption]. 1.19/1.47 10 (all X0 all X1 join(X1,X0) = join(X0,X1)) # label(maddux1_join_commutativity) # label(axiom) # label(non_clause). [assumption]. 1.19/1.47 11 (all X0 X0 = converse(converse(X0))) # label(converse_idempotence) # label(axiom) # label(non_clause). [assumption]. 1.19/1.47 12 (all X0 all X1 all X2 join(X0,join(X1,X2)) = join(join(X0,X1),X2)) # label(maddux2_join_associativity) # label(axiom) # label(non_clause). [assumption]. 1.19/1.47 13 (all X0 all X1 complement(X1) = join(composition(converse(X0),complement(composition(X0,X1))),complement(X1))) # label(converse_cancellativity) # label(axiom) # label(non_clause). [assumption]. 1.19/1.47 14 -(all X0 converse(complement(X0)) = complement(converse(X0))) # label(goals) # label(negated_conjecture) # label(non_clause). [assumption]. 1.19/1.47 15 composition(A,one) = A # label(composition_identity) # label(axiom). [clausify(2)]. 1.19/1.47 16 converse(converse(A)) = A # label(converse_idempotence) # label(axiom). [clausify(11)]. 1.19/1.47 17 meet(A,complement(A)) = zero # label(def_zero) # label(axiom). [clausify(4)]. 1.19/1.47 18 join(A,complement(A)) = top # label(def_top) # label(axiom). [clausify(7)]. 1.19/1.47 19 join(A,B) = join(B,A) # label(maddux1_join_commutativity) # label(axiom). [clausify(10)]. 1.19/1.47 20 converse(composition(A,B)) = composition(converse(B),converse(A)) # label(converse_multiplicativity) # label(axiom). [clausify(3)]. 1.19/1.47 21 composition(converse(A),converse(B)) = converse(composition(B,A)). [copy(20),flip(a)]. 1.19/1.47 22 meet(A,B) = complement(join(complement(A),complement(B))) # label(maddux4_definiton_of_meet) # label(axiom). [clausify(5)]. 1.19/1.47 23 converse(join(A,B)) = join(converse(A),converse(B)) # label(converse_additivity) # label(axiom). [clausify(6)]. 1.19/1.47 24 join(converse(A),converse(B)) = converse(join(A,B)). [copy(23),flip(a)]. 1.19/1.47 25 composition(composition(A,B),C) = composition(A,composition(B,C)) # label(composition_associativity) # label(axiom). [clausify(8)]. 1.19/1.47 26 join(join(A,B),C) = join(A,join(B,C)) # label(maddux2_join_associativity) # label(axiom). [clausify(12)]. 1.19/1.47 27 join(A,join(B,C)) = join(C,join(A,B)). [copy(26),rewrite([19(2)]),flip(a)]. 1.19/1.47 30 join(composition(converse(A),complement(composition(A,B))),complement(B)) = complement(B) # label(converse_cancellativity) # label(axiom). [clausify(13)]. 1.19/1.47 31 join(complement(A),composition(converse(B),complement(composition(B,A)))) = complement(A). [copy(30),rewrite([19(6)])]. 1.19/1.47 32 join(complement(join(complement(A),complement(B))),complement(join(complement(A),B))) = A # label(maddux3_a_kind_of_de_Morgan) # label(axiom). [clausify(1)]. 1.19/1.47 33 join(complement(join(A,complement(B))),complement(join(complement(A),complement(B)))) = B. [copy(32),rewrite([19(6),19(8)]),rewrite([19(6)])]. 1.19/1.47 34 converse(complement(c1)) != complement(converse(c1)) # label(goals) # label(negated_conjecture) # answer(goals). [clausify(14)]. 1.19/1.47 35 complement(top) = zero. [back_rewrite(17),rewrite([22(2),18(4)])]. 1.19/1.47 37 converse(composition(converse(A),B)) = composition(converse(B),A). [para(16(a,1),21(a,1,2)),flip(a)]. 1.19/1.47 39 composition(A,composition(one,B)) = composition(A,B). [para(15(a,1),25(a,1,1)),flip(a)]. 1.19/1.47 41 join(A,join(B,complement(A))) = join(B,top). [para(18(a,1),27(a,2,2)),rewrite([19(2)])]. 1.19/1.47 46 join(complement(one),composition(converse(A),complement(A))) = complement(one). [para(15(a,1),31(a,1,2,2,1))]. 1.19/1.47 51 join(zero,complement(join(complement(A),complement(A)))) = A. [para(18(a,1),33(a,1,1,1)),rewrite([35(2)])]. 1.19/1.47 59 join(complement(join(top,complement(A))),complement(join(zero,complement(A)))) = A. [para(35(a,1),33(a,1,2,1,1))]. 1.19/1.47 65 composition(converse(one),A) = A. [para(15(a,1),37(a,1,1)),rewrite([16(2)]),flip(a)]. 1.19/1.47 69 converse(one) = one. [para(65(a,1),15(a,1)),flip(a)]. 1.19/1.47 73 join(complement(A),complement(composition(one,A))) = complement(A). [para(65(a,1),31(a,1,2))]. 1.19/1.47 74 composition(one,A) = A. [para(65(a,1),39(a,2)),rewrite([69(2),39(4)])]. 1.19/1.47 75 join(complement(A),complement(A)) = complement(A). [back_rewrite(73),rewrite([74(3)])]. 1.19/1.47 76 join(zero,complement(complement(A))) = A. [back_rewrite(51),rewrite([75(4)])]. 1.19/1.47 84 converse(join(A,one)) = join(one,converse(A)). [para(69(a,1),24(a,1,1)),rewrite([19(5)]),flip(a)]. 1.19/1.47 100 join(top,complement(A)) = top. [para(75(a,1),41(a,1,2)),rewrite([18(2),19(4)]),flip(a)]. 1.19/1.47 101 join(zero,complement(join(zero,complement(A)))) = A. [back_rewrite(59),rewrite([100(3),35(2)])]. 1.19/1.47 110 join(top,top) = join(A,top). [para(100(a,1),41(a,1,2)),flip(a)]. 1.19/1.47 115 join(A,top) = join(B,top). [para(110(a,1),41(a,2)),rewrite([100(3)])]. 1.19/1.47 116 join(A,top) = c_0. [new_symbol(115)]. 1.19/1.47 119 join(A,join(B,complement(A))) = c_0. [back_rewrite(41),rewrite([116(5)])]. 1.19/1.47 129 c_0 = top. [para(76(a,1),119(a,1,2)),rewrite([19(2),18(2)]),flip(a)]. 1.19/1.47 130 join(A,join(B,complement(A))) = top. [back_rewrite(119),rewrite([129(4)])]. 1.19/1.47 139 join(zero,complement(A)) = complement(A). [para(76(a,1),101(a,1,2,1))]. 1.19/1.47 140 complement(complement(A)) = A. [back_rewrite(101),rewrite([139(4),139(4)])]. 1.19/1.47 141 join(A,zero) = A. [back_rewrite(76),rewrite([140(3),19(2)])]. 1.19/1.47 146 join(complement(join(A,B)),complement(join(B,complement(A)))) = complement(B). [para(140(a,1),33(a,1,1,1,2)),rewrite([140(5),19(4)])]. 1.19/1.47 148 join(A,A) = A. [para(140(a,1),75(a,1,1)),rewrite([140(2),140(3)])]. 1.19/1.47 152 join(A,join(A,B)) = join(A,B). [para(148(a,1),27(a,1)),rewrite([19(3),27(4,R),19(3),27(3,R),148(2)]),flip(a)]. 1.19/1.47 153 join(A,complement(join(B,complement(A)))) = A. [para(33(a,1),152(a,1,2)),rewrite([19(4),33(12)])]. 1.19/1.47 155 join(A,join(B,complement(join(C,complement(A))))) = join(A,B). [para(153(a,1),27(a,2,2)),rewrite([19(4),19(6)])]. 1.19/1.47 158 join(complement(A),complement(join(A,B))) = complement(A). [para(140(a,1),153(a,1,2,1,2)),rewrite([19(2)])]. 1.19/1.47 166 join(complement(one),composition(converse(complement(A)),A)) = complement(one). [para(140(a,1),46(a,1,2,2))]. 1.19/1.47 169 join(complement(converse(A)),complement(converse(join(A,B)))) = complement(converse(A)). [para(24(a,1),158(a,1,2,1))]. 1.19/1.47 219 join(complement(one),converse(complement(one))) = complement(one). [para(15(a,1),166(a,1,2))]. 1.19/1.47 223 converse(complement(one)) = complement(one). [para(219(a,1),24(a,2,1)),rewrite([16(7),19(6),219(6)]),flip(a)]. 1.19/1.47 228 converse(top) = top. [para(223(a,1),84(a,2,2)),rewrite([19(4),18(4),18(6)])]. 1.19/1.47 2509 join(A,complement(join(A,B))) = join(A,complement(B)). [para(146(a,1),155(a,1,2)),flip(a)]. 1.19/1.47 2955 join(complement(converse(A)),converse(join(A,B))) = top. [para(169(a,1),130(a,1,2)),rewrite([19(5)])]. 1.19/1.47 2981 join(A,join(B,converse(complement(converse(A))))) = top. [para(2955(a,1),24(a,2,1)),rewrite([16(6),27(5),19(4),27(5,R),19(4),228(7)])]. 1.19/1.47 3012 join(A,converse(complement(converse(A)))) = top. [para(148(a,1),2981(a,1,2))]. 1.19/1.47 3049 join(A,complement(converse(complement(converse(A))))) = A. [para(3012(a,1),2509(a,1,2,1)),rewrite([35(2),141(2)]),flip(a)]. 1.19/1.47 3050 join(converse(A),complement(converse(complement(A)))) = converse(A). [para(16(a,1),3049(a,1,2,1,1,1))]. 1.19/1.47 3053 join(A,converse(complement(converse(complement(A))))) = converse(complement(converse(complement(A)))). [para(3049(a,1),33(a,1,2,1)),rewrite([140(9),19(8),2509(8),140(6)])]. 1.19/1.47 3172 converse(complement(converse(complement(A)))) = A. [para(3050(a,1),24(a,2,1)),rewrite([16(2),3053(5),16(6)])]. 1.19/1.47 3195 complement(converse(complement(A))) = converse(A). [para(3172(a,1),16(a,1,1)),flip(a)]. 1.19/1.47 3265 converse(complement(A)) = complement(converse(A)). [para(3195(a,1),140(a,1,1)),flip(a)]. 1.19/1.47 3266 $F # answer(goals). [resolve(3265,a,34,a)]. 1.19/1.47 1.19/1.47 % SZS output end Refutation 1.19/1.47 ============================== end of proof ========================== 1.19/1.47 1.19/1.47 ============================== STATISTICS ============================ 1.19/1.47 1.19/1.47 Given=286. Generated=20728. Kept=3245. proofs=1. 1.19/1.47 Usable=232. Sos=2460. Demods=2573. Limbo=3, Disabled=563. Hints=0. 1.19/1.47 Megabytes=4.11. 1.19/1.47 User_CPU=0.48, System_CPU=0.02, Wall_clock=0. 1.19/1.47 1.19/1.47 ============================== end of statistics ===================== 1.19/1.47 1.19/1.47 ============================== end of search ========================= 1.19/1.47 1.19/1.47 THEOREM PROVED 1.19/1.47 % SZS status Theorem 1.19/1.47 1.19/1.47 Exiting with 1 proof. 1.19/1.47 1.19/1.47 Process 26784 exit (max_proofs) Thu Aug 29 09:55:11 2019 1.19/1.47 Prover9 interrupted 1.19/1.47 EOF