TSTP Solution File: SWV408+1 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : SWV408+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n032.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 : Wed Jul 20 21:12:33 EDT 2022
% Result : Theorem 2.73s 3.03s
% Output : Refutation 2.73s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.10 % Problem : SWV408+1 : TPTP v8.1.0. Released v3.3.0.
% 0.03/0.11 % Command : tptp2X_and_run_prover9 %d %s
% 0.10/0.30 % Computer : n032.cluster.edu
% 0.10/0.30 % Model : x86_64 x86_64
% 0.10/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.30 % Memory : 8042.1875MB
% 0.10/0.30 % OS : Linux 3.10.0-693.el7.x86_64
% 0.10/0.30 % CPULimit : 300
% 0.10/0.30 % WCLimit : 600
% 0.10/0.30 % DateTime : Wed Jun 15 23:13:14 EDT 2022
% 0.10/0.30 % CPUTime :
% 0.56/0.83 ============================== Prover9 ===============================
% 0.56/0.83 Prover9 (32) version 2009-11A, November 2009.
% 0.56/0.83 Process 11922 was started by sandbox on n032.cluster.edu,
% 0.56/0.83 Wed Jun 15 23:13:14 2022
% 0.56/0.83 The command was "/export/starexec/sandbox/solver/bin/prover9 -t 300 -f /tmp/Prover9_11769_n032.cluster.edu".
% 0.56/0.83 ============================== end of head ===========================
% 0.56/0.83
% 0.56/0.83 ============================== INPUT =================================
% 0.56/0.83
% 0.56/0.83 % Reading from file /tmp/Prover9_11769_n032.cluster.edu
% 0.56/0.83
% 0.56/0.83 set(prolog_style_variables).
% 0.56/0.83 set(auto2).
% 0.56/0.83 % set(auto2) -> set(auto).
% 0.56/0.83 % set(auto) -> set(auto_inference).
% 0.56/0.83 % set(auto) -> set(auto_setup).
% 0.56/0.83 % set(auto_setup) -> set(predicate_elim).
% 0.56/0.83 % set(auto_setup) -> assign(eq_defs, unfold).
% 0.56/0.83 % set(auto) -> set(auto_limits).
% 0.56/0.83 % set(auto_limits) -> assign(max_weight, "100.000").
% 0.56/0.83 % set(auto_limits) -> assign(sos_limit, 20000).
% 0.56/0.83 % set(auto) -> set(auto_denials).
% 0.56/0.83 % set(auto) -> set(auto_process).
% 0.56/0.83 % set(auto2) -> assign(new_constants, 1).
% 0.56/0.83 % set(auto2) -> assign(fold_denial_max, 3).
% 0.56/0.83 % set(auto2) -> assign(max_weight, "200.000").
% 0.56/0.83 % set(auto2) -> assign(max_hours, 1).
% 0.56/0.83 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 0.56/0.83 % set(auto2) -> assign(max_seconds, 0).
% 0.56/0.83 % set(auto2) -> assign(max_minutes, 5).
% 0.56/0.83 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 0.56/0.83 % set(auto2) -> set(sort_initial_sos).
% 0.56/0.83 % set(auto2) -> assign(sos_limit, -1).
% 0.56/0.83 % set(auto2) -> assign(lrs_ticks, 3000).
% 0.56/0.83 % set(auto2) -> assign(max_megs, 400).
% 0.56/0.83 % set(auto2) -> assign(stats, some).
% 0.56/0.83 % set(auto2) -> clear(echo_input).
% 0.56/0.83 % set(auto2) -> set(quiet).
% 0.56/0.83 % set(auto2) -> clear(print_initial_clauses).
% 0.56/0.83 % set(auto2) -> clear(print_given).
% 0.56/0.83 assign(lrs_ticks,-1).
% 0.56/0.83 assign(sos_limit,10000).
% 0.56/0.83 assign(order,kbo).
% 0.56/0.83 set(lex_order_vars).
% 0.56/0.83 clear(print_given).
% 0.56/0.83
% 0.56/0.83 % formulas(sos). % not echoed (43 formulas)
% 0.56/0.83
% 0.56/0.83 ============================== end of input ==========================
% 0.56/0.83
% 0.56/0.83 % From the command line: assign(max_seconds, 300).
% 0.56/0.83
% 0.56/0.83 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 0.56/0.83
% 0.56/0.83 % Formulas that are not ordinary clauses:
% 0.56/0.83 1 (all U all V all W (less_than(U,V) & less_than(V,W) -> less_than(U,W))) # label(transitivity) # label(axiom) # label(non_clause). [assumption].
% 0.56/0.83 2 (all U all V (less_than(U,V) | less_than(V,U))) # label(totality) # label(axiom) # label(non_clause). [assumption].
% 0.56/0.83 3 (all U less_than(U,U)) # label(reflexivity) # label(axiom) # label(non_clause). [assumption].
% 0.56/0.83 4 (all U all V (strictly_less_than(U,V) <-> less_than(U,V) & -less_than(V,U))) # label(stricly_smaller_definition) # label(axiom) # label(non_clause). [assumption].
% 0.56/0.83 5 (all U less_than(bottom,U)) # label(bottom_smallest) # label(axiom) # label(non_clause). [assumption].
% 0.56/0.83 6 (all U all V all W isnonempty_slb(insert_slb(U,pair(V,W)))) # label(ax19) # label(axiom) # label(non_clause). [assumption].
% 0.56/0.83 7 (all U -contains_slb(create_slb,U)) # label(ax20) # label(axiom) # label(non_clause). [assumption].
% 0.56/0.83 8 (all U all V all W all X (contains_slb(insert_slb(U,pair(V,X)),W) <-> contains_slb(U,W) | V = W)) # label(ax21) # label(axiom) # label(non_clause). [assumption].
% 0.56/0.83 9 (all U all V -pair_in_list(create_slb,U,V)) # label(ax22) # label(axiom) # label(non_clause). [assumption].
% 0.56/0.83 10 (all U all V all W all X all Y (pair_in_list(insert_slb(U,pair(V,X)),W,Y) <-> pair_in_list(U,W,Y) | V = W & X = Y)) # label(ax23) # label(axiom) # label(non_clause). [assumption].
% 0.56/0.83 11 (all U all V all W remove_slb(insert_slb(U,pair(V,W)),V) = U) # label(ax24) # label(axiom) # label(non_clause). [assumption].
% 0.56/0.83 12 (all U all V all W all X (V != W & contains_slb(U,W) -> remove_slb(insert_slb(U,pair(V,X)),W) = insert_slb(remove_slb(U,W),pair(V,X)))) # label(ax25) # label(axiom) # label(non_clause). [assumption].
% 0.56/0.83 13 (all U all V all W lookup_slb(insert_slb(U,pair(V,W)),V) = W) # label(ax26) # label(axiom) # label(non_clause). [assumption].
% 0.56/0.83 14 (all U all V all W all X (V != W & contains_slb(U,W) -> lookup_slb(insert_slb(U,pair(V,X)),W) = lookup_slb(U,W))) # label(ax27) # label(axiom) # label(non_clause). [assumption].
% 0.56/0.83 15 (all U update_slb(create_slb,U) = create_slb) # label(ax28) # label(axiom) # label(non_clause). [assumption].
% 0.56/0.83 16 (all U all V all W all X (strictly_less_than(X,W) -> update_slb(insert_slb(U,pair(V,X)),W) = insert_slb(update_slb(U,W),pair(V,W)))) # label(ax29) # label(axiom) # label(non_clause). [assumption].
% 0.56/0.83 17 (all U all V all W all X (less_than(W,X) -> update_slb(insert_slb(U,pair(V,X)),W) = insert_slb(update_slb(U,W),pair(V,X)))) # label(ax30) # label(axiom) # label(non_clause). [assumption].
% 0.56/0.83 18 (all U succ_cpq(U,U)) # label(ax31) # label(axiom) # label(non_clause). [assumption].
% 0.56/0.83 19 (all U all V all W (succ_cpq(U,V) -> succ_cpq(U,insert_cpq(V,W)))) # label(ax32) # label(axiom) # label(non_clause). [assumption].
% 0.56/0.83 20 (all U all V all W (succ_cpq(U,V) -> succ_cpq(U,remove_cpq(V,W)))) # label(ax33) # label(axiom) # label(non_clause). [assumption].
% 0.56/0.83 21 (all U all V (succ_cpq(U,V) -> succ_cpq(U,findmin_cpq_eff(V)))) # label(ax34) # label(axiom) # label(non_clause). [assumption].
% 0.56/0.83 22 (all U all V (succ_cpq(U,V) -> succ_cpq(U,removemin_cpq_eff(V)))) # label(ax35) # label(axiom) # label(non_clause). [assumption].
% 0.56/0.83 23 (all U all V check_cpq(triple(U,create_slb,V))) # label(ax36) # label(axiom) # label(non_clause). [assumption].
% 0.56/0.83 24 (all U all V all W all X all Y (less_than(Y,X) -> (check_cpq(triple(U,insert_slb(V,pair(X,Y)),W)) <-> check_cpq(triple(U,V,W))))) # label(ax37) # label(axiom) # label(non_clause). [assumption].
% 0.56/0.83 25 (all U all V all W all X all Y (strictly_less_than(X,Y) -> (check_cpq(triple(U,insert_slb(V,pair(X,Y)),W)) <-> $F))) # label(ax38) # label(axiom) # label(non_clause). [assumption].
% 0.56/0.83 26 (all U all V all W all X (contains_cpq(triple(U,V,W),X) <-> contains_slb(V,X))) # label(ax39) # label(axiom) # label(non_clause). [assumption].
% 0.56/0.83 27 (all U all V (ok(triple(U,V,bad)) <-> $F)) # label(ax40) # label(axiom) # label(non_clause). [assumption].
% 0.56/0.83 28 (all U all V all W (-ok(triple(U,V,W)) -> W = bad)) # label(ax41) # label(axiom) # label(non_clause). [assumption].
% 0.56/0.83 29 (all U all V all W all X insert_cpq(triple(U,V,W),X) = triple(insert_pqp(U,X),insert_slb(V,pair(X,bottom)),W)) # label(ax42) # label(axiom) # label(non_clause). [assumption].
% 0.56/0.83 30 (all U all V all W all X (-contains_slb(V,X) -> remove_cpq(triple(U,V,W),X) = triple(U,V,bad))) # label(ax43) # label(axiom) # label(non_clause). [assumption].
% 0.56/0.83 31 (all U all V all W all X (contains_slb(V,X) & less_than(lookup_slb(V,X),X) -> remove_cpq(triple(U,V,W),X) = triple(remove_pqp(U,X),remove_slb(V,X),W))) # label(ax44) # label(axiom) # label(non_clause). [assumption].
% 0.56/0.83 32 (all U all V all W all X (contains_slb(V,X) & strictly_less_than(X,lookup_slb(V,X)) -> remove_cpq(triple(U,V,W),X) = triple(remove_pqp(U,X),remove_slb(V,X),bad))) # label(ax45) # label(axiom) # label(non_clause). [assumption].
% 0.56/0.83 33 (all U all V findmin_cpq_eff(triple(U,create_slb,V)) = triple(U,create_slb,bad)) # label(ax46) # label(axiom) # label(non_clause). [assumption].
% 0.56/0.83 34 (all U all V all W all X (V != create_slb & -contains_slb(V,findmin_pqp_res(U)) -> findmin_cpq_eff(triple(U,V,W)) = triple(U,update_slb(V,findmin_pqp_res(U)),bad))) # label(ax47) # label(axiom) # label(non_clause). [assumption].
% 0.56/0.83 35 (all U all V all W all X (V != create_slb & contains_slb(V,findmin_pqp_res(U)) & strictly_less_than(findmin_pqp_res(U),lookup_slb(V,findmin_pqp_res(U))) -> findmin_cpq_eff(triple(U,V,W)) = triple(U,update_slb(V,findmin_pqp_res(U)),bad))) # label(ax48) # label(axiom) # label(non_clause). [assumption].
% 0.56/0.83 36 (all U all V all W all X (V != create_slb & contains_slb(V,findmin_pqp_res(U)) & less_than(lookup_slb(V,findmin_pqp_res(U)),findmin_pqp_res(U)) -> findmin_cpq_eff(triple(U,V,W)) = triple(U,update_slb(V,findmin_pqp_res(U)),W))) # label(ax49) # label(axiom) # label(non_clause). [assumption].
% 0.56/0.83 37 (all U all V findmin_cpq_res(triple(U,create_slb,V)) = bottom) # label(ax50) # label(axiom) # label(non_clause). [assumption].
% 0.56/0.83 38 (all U all V all W all X (V != create_slb -> findmin_cpq_res(triple(U,V,W)) = findmin_pqp_res(U))) # label(ax51) # label(axiom) # label(non_clause). [assumption].
% 0.56/0.83 39 (all U removemin_cpq_eff(U) = remove_cpq(findmin_cpq_eff(U),findmin_cpq_res(U))) # label(ax52) # label(axiom) # label(non_clause). [assumption].
% 2.73/3.03 40 (all U removemin_cpq_res(U) = findmin_cpq_res(U)) # label(ax53) # label(axiom) # label(non_clause). [assumption].
% 2.73/3.03 41 (all U all V all W (contains_slb(U,V) & strictly_less_than(V,W) -> pair_in_list(update_slb(U,W),V,W) | (exists X (pair_in_list(update_slb(U,W),V,X) & less_than(W,X))))) # label(l44_l45) # label(lemma) # label(non_clause). [assumption].
% 2.73/3.03 42 -(all U all V all W all X (contains_slb(V,X) & strictly_less_than(X,findmin_cpq_res(triple(U,V,W))) -> pair_in_list(update_slb(V,findmin_pqp_res(U)),X,findmin_pqp_res(U)) | (exists Y (pair_in_list(update_slb(V,findmin_pqp_res(U)),X,Y) & less_than(findmin_pqp_res(U),Y))))) # label(l44_co) # label(negated_conjecture) # label(non_clause). [assumption].
% 2.73/3.03
% 2.73/3.03 ============================== end of process non-clausal formulas ===
% 2.73/3.03
% 2.73/3.03 ============================== PROCESS INITIAL CLAUSES ===============
% 2.73/3.03
% 2.73/3.03 ============================== PREDICATE ELIMINATION =================
% 2.73/3.03
% 2.73/3.03 ============================== end predicate elimination =============
% 2.73/3.03
% 2.73/3.03 Auto_denials: (non-Horn, no changes).
% 2.73/3.03
% 2.73/3.03 Term ordering decisions:
% 2.73/3.03 Function symbol KB weights: create_slb=1. bad=1. bottom=1. c1=1. c2=1. c3=1. c4=1. insert_slb=1. pair=1. update_slb=1. lookup_slb=1. remove_cpq=1. remove_slb=1. insert_cpq=1. remove_pqp=1. insert_pqp=1. findmin_pqp_res=1. findmin_cpq_eff=1. findmin_cpq_res=1. removemin_cpq_eff=1. removemin_cpq_res=1. triple=1. f1=1.
% 2.73/3.03
% 2.73/3.03 ============================== end of process initial clauses ========
% 2.73/3.03
% 2.73/3.03 ============================== CLAUSES FOR SEARCH ====================
% 2.73/3.03
% 2.73/3.03 ============================== end of clauses for search =============
% 2.73/3.03
% 2.73/3.03 ============================== SEARCH ================================
% 2.73/3.03
% 2.73/3.03 % Starting search at 0.01 seconds.
% 2.73/3.03
% 2.73/3.03 NOTE: Back_subsumption disabled, ratio of kept to back_subsumed is 22 (0.00 of 0.23 sec).
% 2.73/3.03
% 2.73/3.03 Low Water (keep): wt=78.000, iters=3380
% 2.73/3.03
% 2.73/3.03 Low Water (keep): wt=70.000, iters=3457
% 2.73/3.03
% 2.73/3.03 Low Water (keep): wt=49.000, iters=3411
% 2.73/3.03
% 2.73/3.03 Low Water (keep): wt=44.000, iters=3333
% 2.73/3.03
% 2.73/3.03 Low Water (keep): wt=42.000, iters=3449
% 2.73/3.03
% 2.73/3.03 Low Water (keep): wt=41.000, iters=3352
% 2.73/3.03
% 2.73/3.03 Low Water (keep): wt=40.000, iters=3335
% 2.73/3.03
% 2.73/3.03 Low Water (keep): wt=39.000, iters=3351
% 2.73/3.03
% 2.73/3.03 Low Water (keep): wt=38.000, iters=3426
% 2.73/3.03
% 2.73/3.03 Low Water (keep): wt=37.000, iters=3542
% 2.73/3.03
% 2.73/3.03 Low Water (keep): wt=34.000, iters=3344
% 2.73/3.03
% 2.73/3.03 Low Water (keep): wt=33.000, iters=3333
% 2.73/3.03
% 2.73/3.03 Low Water (keep): wt=32.000, iters=3334
% 2.73/3.03
% 2.73/3.03 Low Water (keep): wt=31.000, iters=3341
% 2.73/3.03
% 2.73/3.03 Low Water (keep): wt=30.000, iters=3364
% 2.73/3.03
% 2.73/3.03 Low Water (keep): wt=29.000, iters=3484
% 2.73/3.03
% 2.73/3.03 Low Water (keep): wt=27.000, iters=3335
% 2.73/3.03
% 2.73/3.03 Low Water (keep): wt=26.000, iters=3342
% 2.73/3.03
% 2.73/3.03 Low Water (keep): wt=25.000, iters=3400
% 2.73/3.03
% 2.73/3.03 Low Water (keep): wt=23.000, iters=3398
% 2.73/3.03
% 2.73/3.03 Low Water (keep): wt=18.000, iters=3348
% 2.73/3.03
% 2.73/3.03 ============================== PROOF =================================
% 2.73/3.03 % SZS status Theorem
% 2.73/3.03 % SZS output start Refutation
% 2.73/3.03
% 2.73/3.03 % Proof 1 at 2.18 (+ 0.04) seconds.
% 2.73/3.03 % Length of proof is 54.
% 2.73/3.03 % Level of proof is 8.
% 2.73/3.03 % Maximum clause weight is 25.000.
% 2.73/3.03 % Given clauses 3285.
% 2.73/3.03
% 2.73/3.03 1 (all U all V all W (less_than(U,V) & less_than(V,W) -> less_than(U,W))) # label(transitivity) # label(axiom) # label(non_clause). [assumption].
% 2.73/3.03 2 (all U all V (less_than(U,V) | less_than(V,U))) # label(totality) # label(axiom) # label(non_clause). [assumption].
% 2.73/3.03 3 (all U less_than(U,U)) # label(reflexivity) # label(axiom) # label(non_clause). [assumption].
% 2.73/3.03 4 (all U all V (strictly_less_than(U,V) <-> less_than(U,V) & -less_than(V,U))) # label(stricly_smaller_definition) # label(axiom) # label(non_clause). [assumption].
% 2.73/3.03 5 (all U less_than(bottom,U)) # label(bottom_smallest) # label(axiom) # label(non_clause). [assumption].
% 2.73/3.03 23 (all U all V check_cpq(triple(U,create_slb,V))) # label(ax36) # label(axiom) # label(non_clause). [assumption].
% 2.73/3.03 24 (all U all V all W all X all Y (less_than(Y,X) -> (check_cpq(triple(U,insert_slb(V,pair(X,Y)),W)) <-> check_cpq(triple(U,V,W))))) # label(ax37) # label(axiom) # label(non_clause). [assumption].
% 2.73/3.03 25 (all U all V all W all X all Y (strictly_less_than(X,Y) -> (check_cpq(triple(U,insert_slb(V,pair(X,Y)),W)) <-> $F))) # label(ax38) # label(axiom) # label(non_clause). [assumption].
% 2.73/3.03 29 (all U all V all W all X insert_cpq(triple(U,V,W),X) = triple(insert_pqp(U,X),insert_slb(V,pair(X,bottom)),W)) # label(ax42) # label(axiom) # label(non_clause). [assumption].
% 2.73/3.03 37 (all U all V findmin_cpq_res(triple(U,create_slb,V)) = bottom) # label(ax50) # label(axiom) # label(non_clause). [assumption].
% 2.73/3.03 38 (all U all V all W all X (V != create_slb -> findmin_cpq_res(triple(U,V,W)) = findmin_pqp_res(U))) # label(ax51) # label(axiom) # label(non_clause). [assumption].
% 2.73/3.03 41 (all U all V all W (contains_slb(U,V) & strictly_less_than(V,W) -> pair_in_list(update_slb(U,W),V,W) | (exists X (pair_in_list(update_slb(U,W),V,X) & less_than(W,X))))) # label(l44_l45) # label(lemma) # label(non_clause). [assumption].
% 2.73/3.03 42 -(all U all V all W all X (contains_slb(V,X) & strictly_less_than(X,findmin_cpq_res(triple(U,V,W))) -> pair_in_list(update_slb(V,findmin_pqp_res(U)),X,findmin_pqp_res(U)) | (exists Y (pair_in_list(update_slb(V,findmin_pqp_res(U)),X,Y) & less_than(findmin_pqp_res(U),Y))))) # label(l44_co) # label(negated_conjecture) # label(non_clause). [assumption].
% 2.73/3.03 43 less_than(A,A) # label(reflexivity) # label(axiom). [clausify(3)].
% 2.73/3.03 44 less_than(bottom,A) # label(bottom_smallest) # label(axiom). [clausify(5)].
% 2.73/3.03 46 contains_slb(c2,c4) # label(l44_co) # label(negated_conjecture). [clausify(42)].
% 2.73/3.03 48 check_cpq(triple(A,create_slb,B)) # label(ax36) # label(axiom). [clausify(23)].
% 2.73/3.03 50 less_than(A,B) | less_than(B,A) # label(totality) # label(axiom). [clausify(2)].
% 2.73/3.03 52 findmin_cpq_res(triple(A,create_slb,B)) = bottom # label(ax50) # label(axiom). [clausify(37)].
% 2.73/3.03 53 strictly_less_than(c4,findmin_cpq_res(triple(c1,c2,c3))) # label(l44_co) # label(negated_conjecture). [clausify(42)].
% 2.73/3.03 60 create_slb = A | findmin_cpq_res(triple(B,A,C)) = findmin_pqp_res(B) # label(ax51) # label(axiom). [clausify(38)].
% 2.73/3.03 63 triple(insert_pqp(A,B),insert_slb(C,pair(B,bottom)),D) = insert_cpq(triple(A,C,D),B) # label(ax42) # label(axiom). [clausify(29)].
% 2.73/3.03 69 -strictly_less_than(A,B) | -less_than(B,A) # label(stricly_smaller_definition) # label(axiom). [clausify(4)].
% 2.73/3.03 70 -pair_in_list(update_slb(c2,findmin_pqp_res(c1)),c4,findmin_pqp_res(c1)) # label(l44_co) # label(negated_conjecture). [clausify(42)].
% 2.73/3.03 71 -pair_in_list(update_slb(c2,findmin_pqp_res(c1)),c4,A) | -less_than(findmin_pqp_res(c1),A) # label(l44_co) # label(negated_conjecture). [clausify(42)].
% 2.73/3.03 72 -strictly_less_than(A,B) | -check_cpq(triple(C,insert_slb(D,pair(A,B)),E)) # label(ax38) # label(axiom). [clausify(25)].
% 2.73/3.03 79 -less_than(A,B) | -less_than(B,C) | less_than(A,C) # label(transitivity) # label(axiom). [clausify(1)].
% 2.73/3.03 80 strictly_less_than(A,B) | -less_than(A,B) | less_than(B,A) # label(stricly_smaller_definition) # label(axiom). [clausify(4)].
% 2.73/3.03 91 -less_than(A,B) | -check_cpq(triple(C,insert_slb(D,pair(B,A)),E)) | check_cpq(triple(C,D,E)) # label(ax37) # label(axiom). [clausify(24)].
% 2.73/3.03 92 -less_than(A,B) | check_cpq(triple(C,insert_slb(D,pair(B,A)),E)) | -check_cpq(triple(C,D,E)) # label(ax37) # label(axiom). [clausify(24)].
% 2.73/3.03 95 -contains_slb(A,B) | -strictly_less_than(B,C) | pair_in_list(update_slb(A,C),B,C) | less_than(C,f1(A,B,C)) # label(l44_l45) # label(lemma). [clausify(41)].
% 2.73/3.03 97 -contains_slb(A,B) | -strictly_less_than(B,C) | pair_in_list(update_slb(A,C),B,C) | pair_in_list(update_slb(A,C),B,f1(A,B,C)) # label(l44_l45) # label(lemma). [clausify(41)].
% 2.73/3.03 103 c2 = create_slb | strictly_less_than(c4,findmin_pqp_res(c1)). [para(60(b,1),53(a,2)),flip(a)].
% 2.73/3.03 109 -less_than(findmin_cpq_res(triple(c1,c2,c3)),c4). [resolve(69,a,53,a)].
% 2.73/3.03 120 strictly_less_than(A,B) | less_than(B,A). [resolve(80,b,50,b),merge(c)].
% 2.73/3.03 150 -check_cpq(triple(A,insert_slb(B,pair(C,bottom)),D)) | check_cpq(triple(A,B,D)). [resolve(91,a,44,a)].
% 2.73/3.03 153 check_cpq(triple(A,insert_slb(B,pair(C,bottom)),D)) | -check_cpq(triple(A,B,D)). [resolve(92,a,44,a)].
% 2.73/3.03 154 check_cpq(triple(A,insert_slb(B,pair(C,C)),D)) | -check_cpq(triple(A,B,D)). [resolve(92,a,43,a)].
% 2.73/3.03 175 c2 = create_slb | -contains_slb(A,c4) | pair_in_list(update_slb(A,findmin_pqp_res(c1)),c4,findmin_pqp_res(c1)) | pair_in_list(update_slb(A,findmin_pqp_res(c1)),c4,f1(A,c4,findmin_pqp_res(c1))). [resolve(103,b,97,b)].
% 2.73/3.03 176 c2 = create_slb | -contains_slb(A,c4) | pair_in_list(update_slb(A,findmin_pqp_res(c1)),c4,findmin_pqp_res(c1)) | less_than(findmin_pqp_res(c1),f1(A,c4,findmin_pqp_res(c1))). [resolve(103,b,95,b)].
% 2.73/3.03 208 -less_than(findmin_cpq_res(triple(c1,c2,c3)),bottom). [ur(79,b,44,a,c,109,a)].
% 2.73/3.03 218 less_than(A,B) | -check_cpq(triple(C,insert_slb(D,pair(B,A)),E)). [resolve(120,a,72,a)].
% 2.73/3.03 1380 check_cpq(triple(A,insert_slb(create_slb,pair(B,B)),C)). [resolve(154,b,48,a)].
% 2.73/3.03 1399 check_cpq(triple(A,insert_slb(insert_slb(create_slb,pair(B,B)),pair(C,bottom)),D)). [resolve(1380,a,153,b)].
% 2.73/3.03 2334 c2 = create_slb | pair_in_list(update_slb(c2,findmin_pqp_res(c1)),c4,f1(c2,c4,findmin_pqp_res(c1))). [resolve(175,b,46,a),unit_del(b,70)].
% 2.73/3.03 2377 c2 = create_slb | less_than(findmin_pqp_res(c1),f1(c2,c4,findmin_pqp_res(c1))). [resolve(176,b,46,a),unit_del(b,70)].
% 2.73/3.03 3753 -check_cpq(triple(A,insert_slb(B,pair(bottom,findmin_cpq_res(triple(c1,c2,c3)))),C)). [ur(218,a,208,a)].
% 2.73/3.03 3756 -check_cpq(triple(A,insert_slb(insert_slb(B,pair(bottom,findmin_cpq_res(triple(c1,c2,c3)))),pair(C,bottom)),D)). [ur(150,b,3753,a)].
% 2.73/3.03 3769 -check_cpq(insert_cpq(triple(A,insert_slb(B,pair(bottom,findmin_cpq_res(triple(c1,c2,c3)))),C),D)). [para(63(a,1),3756(a,1))].
% 2.73/3.03 8157 check_cpq(insert_cpq(triple(A,insert_slb(create_slb,pair(B,B)),C),D)). [para(63(a,1),1399(a,1))].
% 2.73/3.03 12047 c2 = create_slb | -less_than(findmin_pqp_res(c1),f1(c2,c4,findmin_pqp_res(c1))). [resolve(2334,b,71,a)].
% 2.73/3.03 12052 c2 = create_slb. [resolve(12047,b,2377,b),merge(b)].
% 2.73/3.03 13981 -check_cpq(insert_cpq(triple(A,insert_slb(B,pair(bottom,bottom)),C),D)). [back_rewrite(3769),rewrite([12052(3),52(6)])].
% 2.73/3.03 13982 $F. [resolve(13981,a,8157,a)].
% 2.73/3.03
% 2.73/3.03 % SZS output end Refutation
% 2.73/3.03 ============================== end of proof ==========================
% 2.73/3.03
% 2.73/3.03 ============================== STATISTICS ============================
% 2.73/3.03
% 2.73/3.03 Given=3285. Generated=52609. Kept=13936. proofs=1.
% 2.73/3.03 Usable=2314. Sos=6082. Demods=26. Limbo=1929, Disabled=3666. Hints=0.
% 2.73/3.03 Megabytes=18.57.
% 2.73/3.03 User_CPU=2.18, System_CPU=0.04, Wall_clock=3.
% 2.73/3.03
% 2.73/3.03 ============================== end of statistics =====================
% 2.73/3.03
% 2.73/3.03 ============================== end of search =========================
% 2.73/3.03
% 2.73/3.03 THEOREM PROVED
% 2.73/3.03 % SZS status Theorem
% 2.73/3.03
% 2.73/3.03 Exiting with 1 proof.
% 2.73/3.03
% 2.73/3.03 Process 11922 exit (max_proofs) Wed Jun 15 23:13:17 2022
% 2.73/3.03 Prover9 interrupted
%------------------------------------------------------------------------------