TSTP Solution File: NUM332+1 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : NUM332+1 : TPTP v8.1.0. Released v3.1.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n020.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 600s
% DateTime : Mon Jul 18 13:26:45 EDT 2022
% Result : Theorem 97.70s 98.04s
% Output : Refutation 97.77s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : NUM332+1 : TPTP v8.1.0. Released v3.1.0.
% 0.03/0.13 % Command : tptp2X_and_run_prover9 %d %s
% 0.13/0.34 % Computer : n020.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 600
% 0.13/0.34 % DateTime : Thu Jul 7 00:38:29 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.79/1.11 ============================== Prover9 ===============================
% 0.79/1.11 Prover9 (32) version 2009-11A, November 2009.
% 0.79/1.11 Process 20735 was started by sandbox on n020.cluster.edu,
% 0.79/1.11 Thu Jul 7 00:38:29 2022
% 0.79/1.11 The command was "/export/starexec/sandbox/solver/bin/prover9 -t 300 -f /tmp/Prover9_20582_n020.cluster.edu".
% 0.79/1.11 ============================== end of head ===========================
% 0.79/1.11
% 0.79/1.11 ============================== INPUT =================================
% 0.79/1.11
% 0.79/1.11 % Reading from file /tmp/Prover9_20582_n020.cluster.edu
% 0.79/1.11
% 0.79/1.11 set(prolog_style_variables).
% 0.79/1.11 set(auto2).
% 0.79/1.11 % set(auto2) -> set(auto).
% 0.79/1.11 % set(auto) -> set(auto_inference).
% 0.79/1.11 % set(auto) -> set(auto_setup).
% 0.79/1.11 % set(auto_setup) -> set(predicate_elim).
% 0.79/1.11 % set(auto_setup) -> assign(eq_defs, unfold).
% 0.79/1.11 % set(auto) -> set(auto_limits).
% 0.79/1.11 % set(auto_limits) -> assign(max_weight, "100.000").
% 0.79/1.11 % set(auto_limits) -> assign(sos_limit, 20000).
% 0.79/1.11 % set(auto) -> set(auto_denials).
% 0.79/1.11 % set(auto) -> set(auto_process).
% 0.79/1.11 % set(auto2) -> assign(new_constants, 1).
% 0.79/1.11 % set(auto2) -> assign(fold_denial_max, 3).
% 0.79/1.11 % set(auto2) -> assign(max_weight, "200.000").
% 0.79/1.11 % set(auto2) -> assign(max_hours, 1).
% 0.79/1.11 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 0.79/1.11 % set(auto2) -> assign(max_seconds, 0).
% 0.79/1.11 % set(auto2) -> assign(max_minutes, 5).
% 0.79/1.11 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 0.79/1.11 % set(auto2) -> set(sort_initial_sos).
% 0.79/1.11 % set(auto2) -> assign(sos_limit, -1).
% 0.79/1.11 % set(auto2) -> assign(lrs_ticks, 3000).
% 0.79/1.11 % set(auto2) -> assign(max_megs, 400).
% 0.79/1.11 % set(auto2) -> assign(stats, some).
% 0.79/1.11 % set(auto2) -> clear(echo_input).
% 0.79/1.11 % set(auto2) -> set(quiet).
% 0.79/1.11 % set(auto2) -> clear(print_initial_clauses).
% 0.79/1.11 % set(auto2) -> clear(print_given).
% 0.79/1.11 assign(lrs_ticks,-1).
% 0.79/1.11 assign(sos_limit,10000).
% 0.79/1.11 assign(order,kbo).
% 0.79/1.11 set(lex_order_vars).
% 0.79/1.11 clear(print_given).
% 0.79/1.11
% 0.79/1.11 % formulas(sos). % not echoed (402 formulas)
% 0.79/1.11
% 0.79/1.11 ============================== end of input ==========================
% 0.79/1.11
% 0.79/1.11 % From the command line: assign(max_seconds, 300).
% 0.79/1.11
% 0.79/1.11 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 0.79/1.12
% 0.79/1.12 % Formulas that are not ordinary clauses:
% 0.79/1.12 1 (all X all Y all Z (rdn_positive_less(rdnn(X),rdnn(Y)) & rdn_positive_less(rdnn(Y),rdnn(Z)) -> rdn_positive_less(rdnn(X),rdnn(Z)))) # label(rdn_positive_less_transitivity) # label(axiom) # label(non_clause). [assumption].
% 0.79/1.12 2 (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].
% 0.79/1.12 3 (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].
% 0.79/1.12 4 (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].
% 0.79/1.12 5 (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].
% 0.79/1.12 6 (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].
% 0.79/1.12 7 (all X all Y all RDN_X all RDN_Y (rdn_translate(X,rdn_pos(RDN_X)) & rdn_translate(Y,rdn_pos(RDN_Y)) & rdn_positive_less(RDN_X,RDN_Y) -> less(X,Y))) # label(less_entry_point_pos_pos) # label(axiom) # label(non_clause). [assumption].
% 0.79/1.12 8 (all X all Y all RDN_X all RDN_Y (rdn_translate(X,rdn_neg(RDN_X)) & rdn_translate(Y,rdn_pos(RDN_Y)) -> less(X,Y))) # label(less_entry_point_neg_pos) # label(axiom) # label(non_clause). [assumption].
% 0.79/1.12 9 (all X all Y all RDN_X all RDN_Y (rdn_translate(X,rdn_neg(RDN_X)) & rdn_translate(Y,rdn_neg(RDN_Y)) & rdn_positive_less(RDN_Y,RDN_X) -> less(X,Y))) # label(less_entry_point_neg_neg) # label(axiom) # label(non_clause). [assumption].
% 0.79/1.12 10 (all X all Y (less(X,Y) <-> -less(Y,X) & Y != X)) # label(less_property) # label(axiom) # label(non_clause). [assumption].
% 0.79/1.12 11 (all X all Y (less_or_equal(X,Y) <-> less(X,Y) | X = Y)) # label(less_or_equal) # label(axiom) # label(non_clause). [assumption].
% 0.79/1.12 12 (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].
% 0.79/1.12 13 (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].
% 0.79/1.12 14 (all X all Y all Z all RDN_X all RDN_Y all RDN_Z (rdn_translate(X,rdn_neg(RDN_X)) & rdn_translate(Y,rdn_neg(RDN_Y)) & rdn_add_with_carry(rdnn(n0),RDN_X,RDN_Y,RDN_Z) & rdn_translate(Z,rdn_neg(RDN_Z)) -> sum(X,Y,Z))) # label(sum_entry_point_neg_neg) # label(axiom) # label(non_clause). [assumption].
% 0.79/1.12 15 (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_neg(RDN_Y)) & rdn_positive_less(RDN_X,RDN_Y) & rdn_add_with_carry(rdnn(n0),RDN_X,RDN_Z,RDN_Y) & rdn_translate(Z,rdn_neg(RDN_Z)) -> sum(X,Y,Z))) # label(sum_entry_point_pos_neg_1) # label(axiom) # label(non_clause). [assumption].
% 0.79/1.12 16 (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_neg(RDN_Y)) & rdn_positive_less(RDN_Y,RDN_X) & 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].
% 0.79/1.12 17 (all POS_X all NEG_X all RDN_X (rdn_translate(POS_X,rdn_pos(RDN_X)) & rdn_translate(NEG_X,rdn_neg(RDN_X)) -> sum(POS_X,NEG_X,n0))) # label(sum_entry_point_posx_negx) # label(axiom) # label(non_clause). [assumption].
% 0.79/1.12 18 (all X all Y all Z all RDN_X all RDN_Y (rdn_translate(X,rdn_neg(RDN_X)) & rdn_translate(Y,rdn_pos(RDN_Y)) & sum(Y,X,Z) -> sum(X,Y,Z))) # label(sum_entry_point_neg_pos) # label(axiom) # label(non_clause). [assumption].
% 0.79/1.12 19 (all X all Y all Z1 all Z2 (sum(X,Y,Z1) & sum(X,Y,Z2) -> Z1 = Z2)) # label(unique_sum) # label(axiom) # label(non_clause). [assumption].
% 0.79/1.12 20 (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].
% 0.79/1.12 21 (all X all Y1 all Y2 all Z (sum(X,Y1,Z) & sum(X,Y2,Z) -> Y1 = Y2)) # label(unique_RHS) # label(axiom) # label(non_clause). [assumption].
% 0.79/1.12 22 (all X all Y all Z (sum(Y,Z,X) <-> difference(X,Y,Z))) # label(minus_entry_point) # label(axiom) # label(non_clause). [assumption].
% 0.79/1.12 23 (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].
% 0.79/1.12 24 (all C all D1 all D2 all ID all RD all IC1 all IC2 (rdn_digit_add(rdnn(D1),rdnn(D2),rdnn(ID),rdnn(IC1)) & rdn_digit_add(rdnn(ID),rdnn(C),rdnn(RD),rdnn(IC2)) & rdn_digit_add(rdnn(IC1),rdnn(IC2),rdnn(n1),rdnn(n0)) -> 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].
% 0.79/1.12 25 (all C all D1 all D2 all O2 all RD all RO all ID all IC1 all IC2 all NC (rdn_digit_add(rdnn(D1),rdnn(D2),rdnn(ID),rdnn(IC1)) & rdn_digit_add(rdnn(ID),rdnn(C),rdnn(RD),rdnn(IC2)) & rdn_digit_add(rdnn(IC1),rdnn(IC2),rdnn(NC),rdnn(n0)) & 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].
% 0.79/1.12 26 (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(D1),rdnn(D2),rdnn(ID),rdnn(IC1)) & rdn_digit_add(rdnn(ID),rdnn(C),rdnn(RD),rdnn(IC2)) & 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_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].
% 97.70/98.04 27 (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].
% 97.70/98.04 28 -(all Z1 all Z2 all Z3 all Z4 (sum(n2,n3,Z1) & sum(Z1,n6,Z2) & sum(n3,n6,Z3) & sum(n2,Z3,Z4) -> Z2 = Z4)) # label(associative_sum) # label(negated_conjecture) # label(non_clause). [assumption].
% 97.70/98.04
% 97.70/98.04 ============================== end of process non-clausal formulas ===
% 97.70/98.04
% 97.70/98.04 ============================== PROCESS INITIAL CLAUSES ===============
% 97.70/98.04
% 97.70/98.04 ============================== PREDICATE ELIMINATION =================
% 97.70/98.04 29 less_or_equal(A,B) | -less(A,B) # label(less_or_equal) # label(axiom). [clausify(11)].
% 97.70/98.04 30 -less_or_equal(A,B) | less(A,B) | B = A # label(less_or_equal) # label(axiom). [clausify(11)].
% 97.70/98.04 31 less_or_equal(A,B) | B != A # label(less_or_equal) # label(axiom). [clausify(11)].
% 97.70/98.04 32 -sum(A,n1,B) | -less(C,B) | less_or_equal(C,A) # label(less_successor) # label(axiom). [clausify(12)].
% 97.70/98.04 Derived: -sum(A,n1,B) | -less(C,B) | less(C,A) | A = C. [resolve(32,c,30,a)].
% 97.70/98.04 33 sum(A,B,C) | -difference(C,A,B) # label(minus_entry_point) # label(axiom). [clausify(22)].
% 97.70/98.04 34 -sum(A,B,C) | difference(C,A,B) # label(minus_entry_point) # label(axiom). [clausify(22)].
% 97.70/98.04
% 97.70/98.04 ============================== end predicate elimination =============
% 97.70/98.04
% 97.70/98.04 Auto_denials: (non-Horn, no changes).
% 97.70/98.04
% 97.70/98.04 Term ordering decisions:
% 97.70/98.04 Function symbol KB weights: n1=1. n0=1. n2=1. n3=1. n6=1. n4=1. n5=1. n7=1. n8=1. n9=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. n12=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. c1=1. c2=1. c3=1. c4=1. rdn=1. rdnn=1. rdn_neg=1. rdn_pos=1.
% 97.70/98.04
% 97.70/98.04 ============================== end of process initial clauses ========
% 97.70/98.04
% 97.70/98.04 ============================== CLAUSES FOR SEARCH ====================
% 97.70/98.04
% 97.70/98.04 ============================== end of clauses for search =============
% 97.70/98.04
% 97.70/98.04 ============================== SEARCH ================================
% 97.70/98.04
% 97.70/98.04 % Starting search at 0.07 seconds.
% 97.70/98.04
% 97.70/98.04 NOTE: Back_subsumption disabled, ratio of kept to back_subsumed is 2147483647 (0.00 of 0.25 sec).
% 97.70/98.04
% 97.70/98.04 Low Water (keep): wt=3.000, iters=3357
% 97.70/98.04
% 97.70/98.04 ============================== PROOF =================================
% 97.70/98.04 % SZS status Theorem
% 97.70/98.04 % SZS output start Refutation
% 97.70/98.04
% 97.70/98.04 % Proof 1 at 96.80 (+ 0.14) seconds.
% 97.70/98.04 % Length of proof is 62.
% 97.70/98.04 % Level of proof is 12.
% 97.70/98.04 % Maximum clause weight is 39.000.
% 97.70/98.04 % Given clauses 51688.
% 97.70/98.04
% 97.70/98.04 13 (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].
% 97.70/98.04 19 (all X all Y all Z1 all Z2 (sum(X,Y,Z1) & sum(X,Y,Z2) -> Z1 = Z2)) # label(unique_sum) # label(axiom) # label(non_clause). [assumption].
% 97.70/98.04 23 (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].
% 97.70/98.04 24 (all C all D1 all D2 all ID all RD all IC1 all IC2 (rdn_digit_add(rdnn(D1),rdnn(D2),rdnn(ID),rdnn(IC1)) & rdn_digit_add(rdnn(ID),rdnn(C),rdnn(RD),rdnn(IC2)) & rdn_digit_add(rdnn(IC1),rdnn(IC2),rdnn(n1),rdnn(n0)) -> 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].
% 97.70/98.04 28 -(all Z1 all Z2 all Z3 all Z4 (sum(n2,n3,Z1) & sum(Z1,n6,Z2) & sum(n3,n6,Z3) & sum(n2,Z3,Z4) -> Z2 = Z4)) # label(associative_sum) # label(negated_conjecture) # label(non_clause). [assumption].
% 97.70/98.04 37 rdn_translate(n2,rdn_pos(rdnn(n2))) # label(rdn2) # label(axiom). [assumption].
% 97.70/98.04 38 rdn_translate(n3,rdn_pos(rdnn(n3))) # label(rdn3) # label(axiom). [assumption].
% 97.70/98.04 40 rdn_translate(n5,rdn_pos(rdnn(n5))) # label(rdn5) # label(axiom). [assumption].
% 97.70/98.04 41 rdn_translate(n6,rdn_pos(rdnn(n6))) # label(rdn6) # label(axiom). [assumption].
% 97.70/98.04 44 rdn_translate(n9,rdn_pos(rdnn(n9))) # label(rdn9) # label(axiom). [assumption].
% 97.70/98.04 46 rdn_translate(n11,rdn_pos(rdn(rdnn(n1),rdnn(n1)))) # label(rdn11) # label(axiom). [assumption].
% 97.70/98.04 321 -rdn_translate(A,rdn_pos(B)) | -rdn_translate(C,rdn_pos(D)) | -rdn_add_with_carry(rdnn(n0),B,D,E) | -rdn_translate(F,rdn_pos(E)) | sum(A,C,F) # label(sum_entry_point_pos_pos) # label(axiom). [clausify(13)].
% 97.70/98.04 327 -sum(A,B,C) | -sum(A,B,D) | D = C # label(unique_sum) # label(axiom). [clausify(19)].
% 97.70/98.04 330 -rdn_digit_add(rdnn(A),rdnn(B),rdnn(C),rdnn(n0)) | -rdn_digit_add(rdnn(C),rdnn(D),rdnn(E),rdnn(n0)) | rdn_add_with_carry(rdnn(D),rdnn(A),rdnn(B),rdnn(E)) # label(add_digit_digit_digit) # label(axiom). [clausify(23)].
% 97.70/98.04 331 -rdn_digit_add(rdnn(A),rdnn(B),rdnn(C),rdnn(D)) | -rdn_digit_add(rdnn(C),rdnn(E),rdnn(F),rdnn(V6)) | -rdn_digit_add(rdnn(D),rdnn(V6),rdnn(n1),rdnn(n0)) | rdn_add_with_carry(rdnn(E),rdnn(A),rdnn(B),rdn(rdnn(F),rdnn(n1))) # label(add_digit_digit_rdn) # label(axiom). [clausify(24)].
% 97.70/98.04 345 rdn_digit_add(rdnn(n1),rdnn(n0),rdnn(n1),rdnn(n0)) # label(rdn_digit_add_n1_n0_n1_n0) # label(axiom). [assumption].
% 97.70/98.04 358 rdn_digit_add(rdnn(n2),rdnn(n3),rdnn(n5),rdnn(n0)) # label(rdn_digit_add_n2_n3_n5_n0) # label(axiom). [assumption].
% 97.70/98.04 364 rdn_digit_add(rdnn(n2),rdnn(n9),rdnn(n1),rdnn(n1)) # label(rdn_digit_add_n2_n9_n1_n1) # label(axiom). [assumption].
% 97.70/98.04 371 rdn_digit_add(rdnn(n3),rdnn(n6),rdnn(n9),rdnn(n0)) # label(rdn_digit_add_n3_n6_n9_n0) # label(axiom). [assumption].
% 97.70/98.04 385 rdn_digit_add(rdnn(n5),rdnn(n0),rdnn(n5),rdnn(n0)) # label(rdn_digit_add_n5_n0_n5_n0) # label(axiom). [assumption].
% 97.70/98.04 391 rdn_digit_add(rdnn(n5),rdnn(n6),rdnn(n1),rdnn(n1)) # label(rdn_digit_add_n5_n6_n1_n1) # label(axiom). [assumption].
% 97.70/98.04 425 rdn_digit_add(rdnn(n9),rdnn(n0),rdnn(n9),rdnn(n0)) # label(rdn_digit_add_n9_n0_n9_n0) # label(axiom). [assumption].
% 97.70/98.04 435 sum(n2,n3,c1) # label(associative_sum) # label(negated_conjecture). [clausify(28)].
% 97.70/98.04 436 sum(c1,n6,c2) # label(associative_sum) # label(negated_conjecture). [clausify(28)].
% 97.70/98.04 437 sum(n3,n6,c3) # label(associative_sum) # label(negated_conjecture). [clausify(28)].
% 97.70/98.04 438 sum(n2,c3,c4) # label(associative_sum) # label(negated_conjecture). [clausify(28)].
% 97.70/98.04 439 c4 != c2 # label(associative_sum) # label(negated_conjecture). [clausify(28)].
% 97.77/98.05 1174 -rdn_digit_add(rdnn(n5),rdnn(A),rdnn(B),rdnn(n0)) | rdn_add_with_carry(rdnn(A),rdnn(n2),rdnn(n3),rdnn(B)). [resolve(358,a,330,a)].
% 97.77/98.05 1194 -rdn_digit_add(rdnn(n1),rdnn(A),rdnn(B),rdnn(C)) | -rdn_digit_add(rdnn(n1),rdnn(C),rdnn(n1),rdnn(n0)) | rdn_add_with_carry(rdnn(A),rdnn(n2),rdnn(n9),rdn(rdnn(B),rdnn(n1))). [resolve(364,a,331,a)].
% 97.77/98.05 1195 rdn_add_with_carry(rdnn(n0),rdnn(n2),rdnn(n9),rdn(rdnn(n1),rdnn(n1))). [factor(1194,a,b),unit_del(a,345)].
% 97.77/98.05 1223 -rdn_digit_add(rdnn(n9),rdnn(A),rdnn(B),rdnn(n0)) | rdn_add_with_carry(rdnn(A),rdnn(n3),rdnn(n6),rdnn(B)). [resolve(371,a,330,a)].
% 97.77/98.05 1287 -rdn_digit_add(rdnn(n1),rdnn(A),rdnn(B),rdnn(C)) | -rdn_digit_add(rdnn(n1),rdnn(C),rdnn(n1),rdnn(n0)) | rdn_add_with_carry(rdnn(A),rdnn(n5),rdnn(n6),rdn(rdnn(B),rdnn(n1))). [resolve(391,a,331,a)].
% 97.77/98.05 1288 rdn_add_with_carry(rdnn(n0),rdnn(n5),rdnn(n6),rdn(rdnn(n1),rdnn(n1))). [factor(1287,a,b),unit_del(a,345)].
% 97.77/98.05 1401 -sum(n2,n3,A) | c1 = A. [resolve(435,a,327,b)].
% 97.77/98.05 1409 -sum(n3,n6,A) | c3 = A. [resolve(437,a,327,b)].
% 97.77/98.05 12161 rdn_add_with_carry(rdnn(n0),rdnn(n2),rdnn(n3),rdnn(n5)). [resolve(1174,a,385,a)].
% 97.77/98.05 12426 -rdn_translate(A,rdn_pos(rdnn(n2))) | -rdn_translate(B,rdn_pos(rdnn(n9))) | -rdn_translate(C,rdn_pos(rdn(rdnn(n1),rdnn(n1)))) | sum(A,B,C). [resolve(1195,a,321,c)].
% 97.77/98.05 12788 rdn_add_with_carry(rdnn(n0),rdnn(n3),rdnn(n6),rdnn(n9)). [resolve(1223,a,425,a)].
% 97.77/98.05 13435 -rdn_translate(A,rdn_pos(rdnn(n5))) | -rdn_translate(B,rdn_pos(rdnn(n6))) | -rdn_translate(C,rdn_pos(rdn(rdnn(n1),rdnn(n1)))) | sum(A,B,C). [resolve(1288,a,321,c)].
% 97.77/98.05 17263 -rdn_translate(A,rdn_pos(rdnn(n2))) | -rdn_translate(B,rdn_pos(rdnn(n3))) | -rdn_translate(C,rdn_pos(rdnn(n5))) | sum(A,B,C). [resolve(12161,a,321,c)].
% 97.77/98.05 17321 -rdn_translate(A,rdn_pos(rdnn(n3))) | -rdn_translate(B,rdn_pos(rdnn(n6))) | -rdn_translate(C,rdn_pos(rdnn(n9))) | sum(A,B,C). [resolve(12788,a,321,c)].
% 97.77/98.05 23366 -rdn_translate(A,rdn_pos(rdnn(n9))) | -rdn_translate(B,rdn_pos(rdn(rdnn(n1),rdnn(n1)))) | sum(n2,A,B). [resolve(12426,a,37,a)].
% 97.77/98.05 23948 -rdn_translate(A,rdn_pos(rdnn(n6))) | -rdn_translate(B,rdn_pos(rdn(rdnn(n1),rdnn(n1)))) | sum(n5,A,B). [resolve(13435,a,40,a)].
% 97.77/98.05 36342 -rdn_translate(A,rdn_pos(rdnn(n3))) | -rdn_translate(B,rdn_pos(rdnn(n5))) | sum(n2,A,B). [resolve(17263,a,37,a)].
% 97.77/98.05 36930 -rdn_translate(A,rdn_pos(rdnn(n6))) | -rdn_translate(B,rdn_pos(rdnn(n9))) | sum(n3,A,B). [resolve(17321,a,38,a)].
% 97.77/98.05 48493 -rdn_translate(A,rdn_pos(rdnn(n9))) | sum(n2,A,n11). [resolve(23366,b,46,a)].
% 97.77/98.05 48498 sum(n2,n9,n11). [resolve(48493,a,44,a)].
% 97.77/98.05 48501 -sum(n2,n9,A) | n11 = A. [resolve(48498,a,327,b)].
% 97.77/98.05 50019 -rdn_translate(A,rdn_pos(rdnn(n6))) | sum(n5,A,n11). [resolve(23948,b,46,a)].
% 97.77/98.05 50020 sum(n5,n6,n11). [resolve(50019,a,41,a)].
% 97.77/98.05 50023 -sum(n5,n6,A) | n11 = A. [resolve(50020,a,327,b)].
% 97.77/98.05 53718 -rdn_translate(A,rdn_pos(rdnn(n5))) | sum(n2,n3,A). [resolve(36342,a,38,a)].
% 97.77/98.05 53720 sum(n2,n3,n5). [resolve(53718,a,40,a)].
% 97.77/98.05 53721 c1 = n5. [resolve(53720,a,1401,a)].
% 97.77/98.05 53731 sum(n5,n6,c2). [back_rewrite(436),rewrite([53721(1)])].
% 97.77/98.05 53735 c2 = n11. [resolve(53731,a,50023,a),flip(a)].
% 97.77/98.05 53736 c4 != n11. [back_rewrite(439),rewrite([53735(2)])].
% 97.77/98.05 54737 -rdn_translate(A,rdn_pos(rdnn(n9))) | sum(n3,n6,A). [resolve(36930,a,41,a)].
% 97.77/98.05 54742 sum(n3,n6,n9). [resolve(54737,a,44,a)].
% 97.77/98.05 54743 c3 = n9. [resolve(54742,a,1409,a)].
% 97.77/98.05 54753 sum(n2,n9,c4). [back_rewrite(438),rewrite([54743(2)])].
% 97.77/98.05 54754 $F. [resolve(54753,a,48501,a),flip(a),unit_del(a,53736)].
% 97.77/98.05
% 97.77/98.05 % SZS output end Refutation
% 97.77/98.05 ============================== end of proof ==========================
% 97.77/98.05
% 97.77/98.05 ============================== STATISTICS ============================
% 97.77/98.05
% 97.77/98.05 Given=51688. Generated=166639. Kept=54719. proofs=1.
% 97.77/98.05 Usable=51618. Sos=3023. Demods=3. Limbo=0, Disabled=490. Hints=0.
% 97.77/98.05 Megabytes=126.64.
% 97.77/98.05 User_CPU=96.80, System_CPU=0.14, Wall_clock=97.
% 97.77/98.05
% 97.77/98.05 ============================== end of statistics =====================
% 97.77/98.05
% 97.77/98.05 ============================== end of search =========================
% 97.77/98.05
% 97.77/98.05 THEOREM PROVED
% 97.77/98.05 % SZS status Theorem
% 97.77/98.05
% 97.77/98.05 Exiting with 1 proof.
% 97.77/98.05
% 97.77/98.05 Process 20735 exit (max_proofs) Thu Jul 7 00:40:06 2022
% 97.77/98.05 Prover9 interrupted
%------------------------------------------------------------------------------