0.12/0.12 % Problem : theBenchmark.p : TPTP v0.0.0. Released v0.0.0. 0.12/0.13 % Command : tptp2X_and_run_prover9 %d %s 0.14/0.34 % Computer : n021.cluster.edu 0.14/0.34 % Model : x86_64 x86_64 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz 0.14/0.34 % Memory : 8042.1875MB 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64 0.14/0.34 % CPULimit : 960 0.14/0.34 % DateTime : Thu Jul 2 07:24:07 EDT 2020 0.14/0.34 % CPUTime : 0.99/1.24 ============================== Prover9 =============================== 0.99/1.24 Prover9 (32) version 2009-11A, November 2009. 0.99/1.24 Process 25855 was started by sandbox2 on n021.cluster.edu, 0.99/1.24 Thu Jul 2 07:24:08 2020 0.99/1.24 The command was "/export/starexec/sandbox2/solver/bin/prover9 -t 960 -f /tmp/Prover9_25702_n021.cluster.edu". 0.99/1.24 ============================== end of head =========================== 0.99/1.24 0.99/1.24 ============================== INPUT ================================= 0.99/1.24 0.99/1.24 % Reading from file /tmp/Prover9_25702_n021.cluster.edu 0.99/1.24 0.99/1.24 set(prolog_style_variables). 0.99/1.24 set(auto2). 0.99/1.24 % set(auto2) -> set(auto). 0.99/1.24 % set(auto) -> set(auto_inference). 0.99/1.24 % set(auto) -> set(auto_setup). 0.99/1.24 % set(auto_setup) -> set(predicate_elim). 0.99/1.24 % set(auto_setup) -> assign(eq_defs, unfold). 0.99/1.24 % set(auto) -> set(auto_limits). 0.99/1.24 % set(auto_limits) -> assign(max_weight, "100.000"). 0.99/1.24 % set(auto_limits) -> assign(sos_limit, 20000). 0.99/1.24 % set(auto) -> set(auto_denials). 0.99/1.24 % set(auto) -> set(auto_process). 0.99/1.24 % set(auto2) -> assign(new_constants, 1). 0.99/1.24 % set(auto2) -> assign(fold_denial_max, 3). 0.99/1.24 % set(auto2) -> assign(max_weight, "200.000"). 0.99/1.24 % set(auto2) -> assign(max_hours, 1). 0.99/1.24 % assign(max_hours, 1) -> assign(max_seconds, 3600). 0.99/1.24 % set(auto2) -> assign(max_seconds, 0). 0.99/1.24 % set(auto2) -> assign(max_minutes, 5). 0.99/1.24 % assign(max_minutes, 5) -> assign(max_seconds, 300). 0.99/1.24 % set(auto2) -> set(sort_initial_sos). 0.99/1.24 % set(auto2) -> assign(sos_limit, -1). 0.99/1.24 % set(auto2) -> assign(lrs_ticks, 3000). 0.99/1.24 % set(auto2) -> assign(max_megs, 400). 0.99/1.24 % set(auto2) -> assign(stats, some). 0.99/1.24 % set(auto2) -> clear(echo_input). 0.99/1.24 % set(auto2) -> set(quiet). 0.99/1.24 % set(auto2) -> clear(print_initial_clauses). 0.99/1.24 % set(auto2) -> clear(print_given). 0.99/1.24 assign(lrs_ticks,-1). 0.99/1.24 assign(sos_limit,10000). 0.99/1.24 assign(order,kbo). 0.99/1.24 set(lex_order_vars). 0.99/1.24 clear(print_given). 0.99/1.24 0.99/1.24 % formulas(sos). % not echoed (402 formulas) 0.99/1.24 0.99/1.24 ============================== end of input ========================== 0.99/1.24 0.99/1.24 % From the command line: assign(max_seconds, 960). 0.99/1.24 0.99/1.24 ============================== PROCESS NON-CLAUSAL FORMULAS ========== 0.99/1.24 0.99/1.24 % Formulas that are not ordinary clauses: 0.99/1.24 1 (all D all Db all Ob (rdn_non_zero(Ob) -> rdn_positive_less(rdnn(D),rdn(rdnn(Db),Ob)))) # label(rdn_extra_digits_positive_less) # label(axiom) # label(non_clause). [assumption]. 0.99/1.24 2 (all X all Y all Z (sum(X,n1,Y) & less(Z,Y) -> less_or_equal(Z,X))) # label(less_successor) # label(axiom) # label(non_clause). [assumption]. 0.99/1.24 3 (all D all O (rdn_non_zero(O) -> rdn_non_zero(rdn(rdnn(D),O)))) # label(rdn_non_zero_by_structure) # label(axiom) # label(non_clause). [assumption]. 0.99/1.24 4 (all X all Y (less_or_equal(X,Y) <-> less(X,Y) | Y = X)) # label(less_or_equal) # label(axiom) # label(non_clause). [assumption]. 0.99/1.24 5 (all Ds all O all Db (rdn_positive_less(rdnn(Ds),rdnn(Db)) & rdn_non_zero(O) -> rdn_positive_less(rdn(rdnn(Ds),O),rdn(rdnn(Db),O)))) # label(rdn_positive_less_multi_digit_low) # label(axiom) # label(non_clause). [assumption]. 0.99/1.24 6 (all X all Y all RDN_X all RDN_Y (rdn_translate(Y,rdn_neg(RDN_Y)) & rdn_translate(X,rdn_neg(RDN_X)) & rdn_positive_less(RDN_Y,RDN_X) -> less(X,Y))) # label(less_entry_point_neg_neg) # label(axiom) # label(non_clause). [assumption]. 0.99/1.24 7 (all X all Y all RDN_X all RDN_Y (rdn_translate(Y,rdn_pos(RDN_Y)) & rdn_translate(X,rdn_neg(RDN_X)) -> less(X,Y))) # label(less_entry_point_neg_pos) # label(axiom) # label(non_clause). [assumption]. 0.99/1.24 8 (all X all Y all RDN_X all RDN_Y (rdn_positive_less(RDN_X,RDN_Y) & rdn_translate(X,rdn_pos(RDN_X)) & rdn_translate(Y,rdn_pos(RDN_Y)) -> less(X,Y))) # label(less_entry_point_pos_pos) # label(axiom) # label(non_clause). [assumption]. 0.99/1.24 9 (all Ds all Os all Db all Ob (rdn_positive_less(Os,Ob) -> rdn_positive_less(rdn(rdnn(Ds),Os),rdn(rdnn(Db),Ob)))) # label(rdn_positive_less_multi_digit_high) # label(axiom) # label(non_clause). [assumption]. 0.99/1.24 10 (all X all Y (X != Y & -less(Y,X) <-> less(X,Y))) # label(less_property) # label(axiom) # label(non_clause). [assumption]. 0.99/1.24 11 (all X all Y all Z (rdn_positive_less(rdnn(Y),rdnn(Z)) & rdn_positive_less(rdnn(X),rdnn(Y)) -> rdn_positive_less(rdnn(X),rdnn(Z)))) # label(rdn_positive_less_transitivity) # label(axiom) # label(non_clause). [assumption]. 0.99/1.25 12 (all X (rdn_non_zero_digit(rdnn(X)) -> rdn_non_zero(rdnn(X)))) # label(rdn_non_zero_by_digit) # label(axiom) # label(non_clause). [assumption]. 0.99/1.25 13 (all X all Y all Z1 all Z2 (sum(X,Y,Z2) & sum(X,Y,Z1) -> Z2 = Z1)) # label(unique_sum) # label(axiom) # label(non_clause). [assumption]. 0.99/1.25 14 (all C all D1 all D2 all ID all RD all IC1 all IC2 (rdn_digit_add(rdnn(ID),rdnn(C),rdnn(RD),rdnn(IC2)) & rdn_digit_add(rdnn(IC1),rdnn(IC2),rdnn(n1),rdnn(n0)) & rdn_digit_add(rdnn(D1),rdnn(D2),rdnn(ID),rdnn(IC1)) -> rdn_add_with_carry(rdnn(C),rdnn(D1),rdnn(D2),rdn(rdnn(RD),rdnn(n1))))) # label(add_digit_digit_rdn) # label(axiom) # label(non_clause). [assumption]. 0.99/1.25 15 (all C all D1 all O1 all D2 all RD all RO (rdn_add_with_carry(rdnn(C),rdnn(D2),rdn(rdnn(D1),O1),rdn(rdnn(RD),RO)) -> rdn_add_with_carry(rdnn(C),rdn(rdnn(D1),O1),rdnn(D2),rdn(rdnn(RD),RO)))) # label(add_rdn_digit_rdn) # label(axiom) # label(non_clause). [assumption]. 0.99/1.25 16 (all X all Y all Z all RDN_X all RDN_Y (rdn_translate(X,rdn_neg(RDN_X)) & sum(Y,X,Z) & rdn_translate(Y,rdn_pos(RDN_Y)) -> sum(X,Y,Z))) # label(sum_entry_point_neg_pos) # label(axiom) # label(non_clause). [assumption]. 0.99/1.25 17 (all X all Y all Z all RDN_X all RDN_Y all RDN_Z (rdn_translate(Z,rdn_neg(RDN_Z)) & rdn_positive_less(RDN_X,RDN_Y) & rdn_translate(X,rdn_pos(RDN_X)) & rdn_translate(Y,rdn_neg(RDN_Y)) & rdn_add_with_carry(rdnn(n0),RDN_X,RDN_Z,RDN_Y) -> sum(X,Y,Z))) # label(sum_entry_point_pos_neg_1) # label(axiom) # label(non_clause). [assumption]. 0.99/1.25 18 (all X all Y all Z all RDN_X all RDN_Y all RDN_Z (rdn_translate(X,rdn_pos(RDN_X)) & rdn_translate(Y,rdn_pos(RDN_Y)) & rdn_add_with_carry(rdnn(n0),RDN_X,RDN_Y,RDN_Z) & rdn_translate(Z,rdn_pos(RDN_Z)) -> sum(X,Y,Z))) # label(sum_entry_point_pos_pos) # label(axiom) # label(non_clause). [assumption]. 0.99/1.25 19 (all X all Y all Z (sum(Y,Z,X) <-> difference(X,Y,Z))) # label(minus_entry_point) # label(axiom) # label(non_clause). [assumption]. 0.99/1.25 20 (all C all D1 all D2 all RD all ID (rdn_digit_add(rdnn(D1),rdnn(D2),rdnn(ID),rdnn(n0)) & rdn_digit_add(rdnn(ID),rdnn(C),rdnn(RD),rdnn(n0)) -> rdn_add_with_carry(rdnn(C),rdnn(D1),rdnn(D2),rdnn(RD)))) # label(add_digit_digit_digit) # label(axiom) # label(non_clause). [assumption]. 0.99/1.25 21 (all X all Y1 all Y2 all Z (sum(X,Y2,Z) & sum(X,Y1,Z) -> Y2 = Y1)) # label(unique_RHS) # label(axiom) # label(non_clause). [assumption]. 0.99/1.25 22 (all X all Y all Z all RDN_X all RDN_Y all RDN_Z (rdn_positive_less(RDN_Y,RDN_X) & rdn_translate(X,rdn_pos(RDN_X)) & rdn_translate(Y,rdn_neg(RDN_Y)) & rdn_add_with_carry(rdnn(n0),RDN_Y,RDN_Z,RDN_X) & rdn_translate(Z,rdn_pos(RDN_Z)) -> sum(X,Y,Z))) # label(sum_entry_point_pos_neg_2) # label(axiom) # label(non_clause). [assumption]. 0.99/1.25 23 (all C all D1 all O1 all D2 all O2 all RD all RO all ID all IC1 all IC2 all RC (rdn_digit_add(rdnn(IC1),rdnn(IC2),rdnn(RC),rdnn(n0)) & rdn_add_with_carry(rdnn(RC),O1,O2,RO) & rdn_non_zero(O1) & rdn_non_zero(O2) & rdn_non_zero(RO) & rdn_digit_add(rdnn(ID),rdnn(C),rdnn(RD),rdnn(IC2)) & rdn_digit_add(rdnn(D1),rdnn(D2),rdnn(ID),rdnn(IC1)) -> rdn_add_with_carry(rdnn(C),rdn(rdnn(D1),O1),rdn(rdnn(D2),O2),rdn(rdnn(RD),RO)))) # label(add_rdn_rdn_rdn) # label(axiom) # label(non_clause). [assumption]. 0.99/1.25 24 (all X all Y all Z all RDN_X all RDN_Y all RDN_Z (rdn_add_with_carry(rdnn(n0),RDN_X,RDN_Y,RDN_Z) & rdn_translate(Z,rdn_neg(RDN_Z)) & rdn_translate(X,rdn_neg(RDN_X)) & rdn_translate(Y,rdn_neg(RDN_Y)) -> sum(X,Y,Z))) # label(sum_entry_point_neg_neg) # label(axiom) # label(non_clause). [assumption]. 0.99/1.25 25 (all POS_X all NEG_X all RDN_X (rdn_translate(NEG_X,rdn_neg(RDN_X)) & rdn_translate(POS_X,rdn_pos(RDN_X)) -> sum(POS_X,NEG_X,n0))) # label(sum_entry_point_posx_negx) # label(axiom) # label(non_clause). [assumption]. 0.99/1.25 26 (all X1 all X2 all Y all Z (sum(X1,Y,Z) & sum(X2,Y,Z) -> X1 = X2)) # label(unique_LHS) # label(axiom) # label(non_clause). [assumption]. 0.99/1.25 27 (all C all D1 all D2 all O2 all RD all RO all ID all IC1 all IC2 all NC (rdn_digit_add(rdnn(IC1),rdnn(IC2),rdnn(NC),rdnn(n0)) & rdn_digit_add(rdnn(D1),rdnn(D2),rdnn(ID),rdnn(IC1)) & rdn_digit_add(rdnn(ID),rdnn(C),rdnn(RD),rdnn(IC2)) & rdn_add_with_carry(rdnn(NC),rdnn(n0),O2,RO) & rdn_non_zero(O2) & rdn_non_zero(RO) -> rdn_add_with_carry(rdnn(C),rdnn(D1),rdn(rdnn(D2),O2),rdn(rdnn(RD),RO)))) # label(add_digit_rdn_rdn) # label(axiom) # label(non_clause). [assumption]. 1.57/1.81 28 -(exists X X != n12) # label(something_not_n12) # label(negated_conjecture) # label(non_clause). [assumption]. 1.57/1.81 1.57/1.81 ============================== end of process non-clausal formulas === 1.57/1.81 1.57/1.81 ============================== PROCESS INITIAL CLAUSES =============== 1.57/1.81 1.57/1.81 ============================== PREDICATE ELIMINATION ================= 1.57/1.81 29 -less_or_equal(A,B) | less(A,B) | B = A # label(less_or_equal) # label(axiom). [clausify(4)]. 1.57/1.81 30 -sum(A,n1,B) | -less(C,B) | less_or_equal(C,A) # label(less_successor) # label(axiom). [clausify(2)]. 1.57/1.81 Derived: less(A,B) | B = A | -sum(B,n1,C) | -less(A,C). [resolve(29,a,30,c)]. 1.57/1.81 31 less_or_equal(A,B) | -less(A,B) # label(less_or_equal) # label(axiom). [clausify(4)]. 1.57/1.81 32 less_or_equal(A,B) | B != A # label(less_or_equal) # label(axiom). [clausify(4)]. 1.57/1.81 33 sum(A,B,C) | -difference(C,A,B) # label(minus_entry_point) # label(axiom). [clausify(19)]. 1.57/1.81 34 -sum(A,B,C) | difference(C,A,B) # label(minus_entry_point) # label(axiom). [clausify(19)]. 1.57/1.81 1.57/1.81 ============================== end predicate elimination ============= 1.57/1.81 1.57/1.81 Auto_denials: (non-Horn, no changes). 1.57/1.81 1.57/1.81 Term ordering decisions: 1.57/1.81 Function symbol KB weights: n1=1. n0=1. n2=1. n3=1. n4=1. n5=1. n6=1. n7=1. n8=1. n9=1. n12=1. n10=1. n100=1. n101=1. n102=1. n103=1. n104=1. n105=1. n106=1. n107=1. n108=1. n109=1. n11=1. n110=1. n111=1. n112=1. n113=1. n114=1. n115=1. n116=1. n117=1. n118=1. n119=1. n120=1. n121=1. n122=1. n123=1. n124=1. n125=1. n126=1. n127=1. n13=1. n14=1. n15=1. n16=1. n17=1. n18=1. n19=1. n20=1. n21=1. n22=1. n23=1. n24=1. n25=1. n26=1. n27=1. n28=1. n29=1. n30=1. n31=1. n32=1. n33=1. n34=1. n35=1. n36=1. n37=1. n38=1. n39=1. n40=1. n41=1. n42=1. n43=1. n44=1. n45=1. n46=1. n47=1. n48=1. n49=1. n50=1. n51=1. n52=1. n53=1. n54=1. n55=1. n56=1. n57=1. n58=1. n59=1. n60=1. n61=1. n62=1. n63=1. n64=1. n65=1. n66=1. n67=1. n68=1. n69=1. n70=1. n71=1. n72=1. n73=1. n74=1. n75=1. n76=1. n77=1. n78=1. n79=1. n80=1. n81=1. n82=1. n83=1. n84=1. n85=1. n86=1. n87=1. n88=1. n89=1. n90=1. n91=1. n92=1. n93=1. n94=1. n95=1. n96=1. n97=1. n98=1. n99=1. nn1=1. nn10=1. nn100=1. nn101=1. nn102=1. nn103=1. nn104=1. nn105=1. nn106=1. nn107=1. nn108=1. nn109=1. nn11=1. nn110=1. nn111=1. nn112=1. nn113=1. nn114=1. nn115=1. nn116=1. nn117=1. nn118=1. nn119=1. nn12=1. nn120=1. nn121=1. nn122=1. nn123=1. nn124=1. nn125=1. nn126=1. nn127=1. nn128=1. nn13=1. nn14=1. nn15=1. nn16=1. nn17=1. nn18=1. nn19=1. nn2=1. nn20=1. nn21=1. nn22=1. nn23=1. nn24=1. nn25=1. nn26=1. nn27=1. nn28=1. nn29=1. nn3=1. nn30=1. nn31=1. nn32=1. nn33=1. nn34=1. nn35=1. nn36=1. nn37=1. nn38=1. nn39=1. nn4=1. nn40=1. nn41=1. nn42=1. nn43=1. nn44=1. nn45=1. nn46=1. nn47=1. nn48=1. nn49=1. nn5=1. nn50=1. nn51=1. nn52=1. nn53=1. nn54=1. nn55=1. nn56=1. nn57=1. nn58=1. nn59=1. nn6=1. nn60=1. nn61=1. nn62=1. nn63=1. nn64=1. nn65=1. nn66=1. nn67=1. nn68=1. nn69=1. nn7=1. nn70=1. nn71=1. nn72=1. nn73=1. nn74=1. nn75=1. nn76=1. nn77=1. nn78=1. nn79=1. nn8=1. nn80=1. nn81=1. nn82=1. nn83=1. nn84=1. nn85=1. nn86=1. nn87=1. nn88=1. nn89=1. nn9=1. nn90=1. nn91=1. nn92=1. nn93=1. nn94=1. nn95=1. nn96=1. nn97=1. nn98=1. nn99=1. rdn=1. rdnn=1. rdn_neg=1. rdn_pos=1. 1.57/1.81 1.57/1.81 ============================== end of process initial clauses ======== 1.57/1.81 1.57/1.81 ============================== CLAUSES FOR SEARCH ==================== 1.57/1.81 1.57/1.81 ============================== end of clauses for search ============= 1.57/1.81 1.57/1.81 ============================== SEARCH ================================ 1.57/1.81 1.57/1.81 % Starting search at 0.12 seconds. 1.57/1.81 1.57/1.81 ============================== PROOF ================================= 1.57/1.81 % SZS status Theorem 1.57/1.81 % SZS output start Refutation 1.57/1.81 1.57/1.81 % Proof 1 at 0.58 (+ 0.01) seconds. 1.57/1.81 % Length of proof is 15. 1.57/1.81 % Level of proof is 6. 1.57/1.81 % Maximum clause weight is 11.000. 1.57/1.81 % Given clauses 401. 1.57/1.81 1.57/1.81 7 (all X all Y all RDN_X all RDN_Y (rdn_translate(Y,rdn_pos(RDN_Y)) & rdn_translate(X,rdn_neg(RDN_X)) -> less(X,Y))) # label(less_entry_point_neg_pos) # label(axiom) # label(non_clause). [assumption]. 1.57/1.81 10 (all X all Y (X != Y & -less(Y,X) <-> less(X,Y))) # label(less_property) # label(axiom) # label(non_clause). [assumption]. 1.57/1.81 28 -(exists X X != n12) # label(something_not_n12) # label(negated_conjecture) # label(non_clause). [assumption]. 1.57/1.81 35 rdn_translate(nn7,rdn_neg(rdnn(n7))) # label(rdnn7) # label(axiom). [assumption]. 1.57/1.81 289 rdn_translate(n88,rdn_pos(rdn(rdnn(n8),rdnn(n8)))) # label(rdn88) # label(axiom). [assumption]. 1.57/1.81 306 -rdn_translate(A,rdn_pos(B)) | -rdn_translate(C,rdn_neg(D)) | less(C,A) # label(less_entry_point_neg_pos) # label(axiom). [clausify(7)]. 1.57/1.81 314 A != B | -less(B,A) # label(less_property) # label(axiom). [clausify(10)]. 1.57/1.81 435 A = n12 # label(something_not_n12) # label(negated_conjecture). [clausify(28)]. 1.57/1.81 436 n12 = A. [copy(435),flip(a)]. 1.57/1.81 755 -rdn_translate(A,rdn_pos(B)) | less(nn7,A). [resolve(306,b,35,a)]. 1.57/1.81 3290 rdn_translate(n88,rdn_pos(n12)). [para(436(a,2),289(a,2,1))]. 1.57/1.81 4193 A = B. [para(436(a,1),436(a,1))]. 1.57/1.81 4247 -less(A,B). [back_unit_del(314),unit_del(a,4193)]. 1.57/1.81 4290 -rdn_translate(A,rdn_pos(B)). [back_unit_del(755),unit_del(b,4247)]. 1.57/1.81 4291 $F. [resolve(4290,a,3290,a)]. 1.57/1.81 1.57/1.81 % SZS output end Refutation 1.57/1.81 ============================== end of proof ========================== 1.57/1.81 1.57/1.81 ============================== STATISTICS ============================ 1.57/1.81 1.57/1.81 Given=401. Generated=4369. Kept=4255. proofs=1. 1.57/1.81 Usable=392. Sos=3779. Demods=0. Limbo=43, Disabled=448. Hints=0. 1.57/1.81 Megabytes=11.84. 1.57/1.81 User_CPU=0.58, System_CPU=0.01, Wall_clock=1. 1.57/1.81 1.57/1.81 ============================== end of statistics ===================== 1.57/1.81 1.57/1.81 ============================== end of search ========================= 1.57/1.81 1.57/1.81 THEOREM PROVED 1.57/1.81 % SZS status Theorem 1.57/1.81 1.57/1.81 Exiting with 1 proof. 1.57/1.81 1.57/1.81 Process 25855 exit (max_proofs) Thu Jul 2 07:24:09 2020 1.57/1.81 Prover9 interrupted 1.57/1.81 EOF