TSTP Solution File: SWV381+1 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : SWV381+1 : TPTP v8.1.0. Released v3.3.0.
% 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 : Wed Jul 20 21:12:28 EDT 2022
% Result : Theorem 2.48s 2.81s
% Output : Refutation 2.48s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SWV381+1 : TPTP v8.1.0. Released v3.3.0.
% 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 : Tue Jun 14 18:56:50 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.43/1.06 ============================== Prover9 ===============================
% 0.43/1.06 Prover9 (32) version 2009-11A, November 2009.
% 0.43/1.06 Process 21864 was started by sandbox2 on n020.cluster.edu,
% 0.43/1.06 Tue Jun 14 18:56:50 2022
% 0.43/1.06 The command was "/export/starexec/sandbox2/solver/bin/prover9 -t 300 -f /tmp/Prover9_21705_n020.cluster.edu".
% 0.43/1.06 ============================== end of head ===========================
% 0.43/1.06
% 0.43/1.06 ============================== INPUT =================================
% 0.43/1.06
% 0.43/1.06 % Reading from file /tmp/Prover9_21705_n020.cluster.edu
% 0.43/1.06
% 0.43/1.06 set(prolog_style_variables).
% 0.43/1.06 set(auto2).
% 0.43/1.06 % set(auto2) -> set(auto).
% 0.43/1.06 % set(auto) -> set(auto_inference).
% 0.43/1.06 % set(auto) -> set(auto_setup).
% 0.43/1.06 % set(auto_setup) -> set(predicate_elim).
% 0.43/1.06 % set(auto_setup) -> assign(eq_defs, unfold).
% 0.43/1.06 % set(auto) -> set(auto_limits).
% 0.43/1.06 % set(auto_limits) -> assign(max_weight, "100.000").
% 0.43/1.06 % set(auto_limits) -> assign(sos_limit, 20000).
% 0.43/1.06 % set(auto) -> set(auto_denials).
% 0.43/1.06 % set(auto) -> set(auto_process).
% 0.43/1.06 % set(auto2) -> assign(new_constants, 1).
% 0.43/1.06 % set(auto2) -> assign(fold_denial_max, 3).
% 0.43/1.06 % set(auto2) -> assign(max_weight, "200.000").
% 0.43/1.06 % set(auto2) -> assign(max_hours, 1).
% 0.43/1.06 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 0.43/1.06 % set(auto2) -> assign(max_seconds, 0).
% 0.43/1.06 % set(auto2) -> assign(max_minutes, 5).
% 0.43/1.06 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 0.43/1.06 % set(auto2) -> set(sort_initial_sos).
% 0.43/1.06 % set(auto2) -> assign(sos_limit, -1).
% 0.43/1.06 % set(auto2) -> assign(lrs_ticks, 3000).
% 0.43/1.06 % set(auto2) -> assign(max_megs, 400).
% 0.43/1.06 % set(auto2) -> assign(stats, some).
% 0.43/1.06 % set(auto2) -> clear(echo_input).
% 0.43/1.06 % set(auto2) -> set(quiet).
% 0.43/1.06 % set(auto2) -> clear(print_initial_clauses).
% 0.43/1.06 % set(auto2) -> clear(print_given).
% 0.43/1.06 assign(lrs_ticks,-1).
% 0.43/1.06 assign(sos_limit,10000).
% 0.43/1.06 assign(order,kbo).
% 0.43/1.06 set(lex_order_vars).
% 0.43/1.06 clear(print_given).
% 0.43/1.06
% 0.43/1.06 % formulas(sos). % not echoed (65 formulas)
% 0.43/1.06
% 0.43/1.06 ============================== end of input ==========================
% 0.43/1.06
% 0.43/1.06 % From the command line: assign(max_seconds, 300).
% 0.43/1.06
% 0.43/1.06 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 0.43/1.06
% 0.43/1.06 % Formulas that are not ordinary clauses:
% 0.43/1.06 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].
% 0.43/1.06 2 (all U all V (less_than(U,V) | less_than(V,U))) # label(totality) # label(axiom) # label(non_clause). [assumption].
% 0.43/1.06 3 (all U less_than(U,U)) # label(reflexivity) # label(axiom) # label(non_clause). [assumption].
% 0.43/1.06 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].
% 0.43/1.06 5 (all U less_than(bottom,U)) # label(bottom_smallest) # label(axiom) # label(non_clause). [assumption].
% 0.43/1.06 6 (all U all V isnonempty_pq(insert_pq(U,V))) # label(ax7) # label(axiom) # label(non_clause). [assumption].
% 0.43/1.06 7 (all U -contains_pq(create_pq,U)) # label(ax8) # label(axiom) # label(non_clause). [assumption].
% 0.43/1.06 8 (all U all V all W (contains_pq(insert_pq(U,V),W) <-> contains_pq(U,W) | V = W)) # label(ax9) # label(axiom) # label(non_clause). [assumption].
% 0.43/1.06 9 (all U all V (issmallestelement_pq(U,V) <-> (all W (contains_pq(U,W) -> less_than(V,W))))) # label(ax10) # label(axiom) # label(non_clause). [assumption].
% 0.43/1.06 10 (all U all V remove_pq(insert_pq(U,V),V) = U) # label(ax11) # label(axiom) # label(non_clause). [assumption].
% 0.43/1.06 11 (all U all V all W (contains_pq(U,W) & V != W -> remove_pq(insert_pq(U,V),W) = insert_pq(remove_pq(U,W),V))) # label(ax12) # label(axiom) # label(non_clause). [assumption].
% 0.43/1.06 12 (all U all V (contains_pq(U,V) & issmallestelement_pq(U,V) -> findmin_pq_eff(U,V) = U)) # label(ax13) # label(axiom) # label(non_clause). [assumption].
% 0.43/1.06 13 (all U all V (contains_pq(U,V) & issmallestelement_pq(U,V) -> findmin_pq_res(U,V) = V)) # label(ax14) # label(axiom) # label(non_clause). [assumption].
% 0.43/1.06 14 (all U all V (contains_pq(U,V) & issmallestelement_pq(U,V) -> removemin_pq_eff(U,V) = remove_pq(U,V))) # label(ax15) # label(axiom) # label(non_clause). [assumption].
% 0.43/1.06 15 (all U all V (contains_pq(U,V) & issmallestelement_pq(U,V) -> removemin_pq_res(U,V) = V)) # label(ax16) # label(axiom) # label(non_clause). [assumption].
% 0.43/1.06 16 (all U all V all W insert_pq(insert_pq(U,V),W) = insert_pq(insert_pq(U,W),V)) # label(ax17) # label(axiom) # label(non_clause). [assumption].
% 0.43/1.06 17 (all U all V all W isnonempty_slb(insert_slb(U,pair(V,W)))) # label(ax19) # label(axiom) # label(non_clause). [assumption].
% 0.43/1.06 18 (all U -contains_slb(create_slb,U)) # label(ax20) # label(axiom) # label(non_clause). [assumption].
% 0.43/1.06 19 (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].
% 0.43/1.06 20 (all U all V -pair_in_list(create_slb,U,V)) # label(ax22) # label(axiom) # label(non_clause). [assumption].
% 0.43/1.06 21 (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].
% 0.43/1.06 22 (all U all V all W remove_slb(insert_slb(U,pair(V,W)),V) = U) # label(ax24) # label(axiom) # label(non_clause). [assumption].
% 0.43/1.06 23 (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].
% 0.43/1.06 24 (all U all V all W lookup_slb(insert_slb(U,pair(V,W)),V) = W) # label(ax26) # label(axiom) # label(non_clause). [assumption].
% 0.43/1.06 25 (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].
% 0.43/1.06 26 (all U update_slb(create_slb,U) = create_slb) # label(ax28) # label(axiom) # label(non_clause). [assumption].
% 0.43/1.06 27 (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].
% 0.43/1.06 28 (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].
% 0.43/1.06 29 (all U succ_cpq(U,U)) # label(ax31) # label(axiom) # label(non_clause). [assumption].
% 0.43/1.06 30 (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].
% 0.43/1.06 31 (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].
% 0.43/1.06 32 (all U all V (succ_cpq(U,V) -> succ_cpq(U,findmin_cpq_eff(V)))) # label(ax34) # label(axiom) # label(non_clause). [assumption].
% 0.43/1.06 33 (all U all V (succ_cpq(U,V) -> succ_cpq(U,removemin_cpq_eff(V)))) # label(ax35) # label(axiom) # label(non_clause). [assumption].
% 0.43/1.06 34 (all U all V check_cpq(triple(U,create_slb,V))) # label(ax36) # label(axiom) # label(non_clause). [assumption].
% 0.43/1.06 35 (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].
% 0.43/1.06 36 (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].
% 0.43/1.06 37 (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].
% 0.43/1.06 38 (all U all V (ok(triple(U,V,bad)) <-> $F)) # label(ax40) # label(axiom) # label(non_clause). [assumption].
% 0.43/1.06 39 (all U all V all W (-ok(triple(U,V,W)) -> W = bad)) # label(ax41) # label(axiom) # label(non_clause). [assumption].
% 0.43/1.06 40 (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].
% 0.43/1.06 41 (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].
% 0.43/1.06 42 (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].
% 0.43/1.07 43 (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].
% 0.43/1.07 44 (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].
% 0.43/1.07 45 (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].
% 0.43/1.07 46 (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].
% 0.43/1.07 47 (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].
% 0.43/1.07 48 (all U all V findmin_cpq_res(triple(U,create_slb,V)) = bottom) # label(ax50) # label(axiom) # label(non_clause). [assumption].
% 0.43/1.07 49 (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].
% 0.43/1.07 50 (all U removemin_cpq_eff(U) = remove_cpq(findmin_cpq_eff(U),findmin_cpq_res(U))) # label(ax52) # label(axiom) # label(non_clause). [assumption].
% 0.43/1.07 51 (all U removemin_cpq_res(U) = findmin_cpq_res(U)) # label(ax53) # label(axiom) # label(non_clause). [assumption].
% 0.43/1.07 52 (all U all V i(triple(U,create_slb,V)) = create_pq) # label(ax54) # label(axiom) # label(non_clause). [assumption].
% 0.43/1.07 53 (all U all V all W all X all Y i(triple(U,insert_slb(V,pair(X,Y)),W)) = insert_pq(i(triple(U,V,W)),X)) # label(ax55) # label(axiom) # label(non_clause). [assumption].
% 0.43/1.07 54 (all U all V (pi_sharp_remove(U,V) <-> contains_pq(U,V))) # label(ax56) # label(axiom) # label(non_clause). [assumption].
% 0.43/1.07 55 (all U all V (pi_remove(U,V) <-> pi_sharp_remove(i(U),V))) # label(ax57) # label(axiom) # label(non_clause). [assumption].
% 0.43/1.07 56 (all U all V (pi_sharp_find_min(U,V) <-> contains_pq(U,V) & issmallestelement_pq(U,V))) # label(ax58) # label(axiom) # label(non_clause). [assumption].
% 0.43/1.07 57 (all U (pi_find_min(U) <-> (exists V pi_sharp_find_min(i(U),V)))) # label(ax59) # label(axiom) # label(non_clause). [assumption].
% 0.43/1.07 58 (all U all V (pi_sharp_removemin(U,V) <-> contains_pq(U,V) & issmallestelement_pq(U,V))) # label(ax60) # label(axiom) # label(non_clause). [assumption].
% 0.43/1.07 59 (all U (pi_removemin(U) <-> (exists V pi_sharp_find_min(i(U),V)))) # label(ax61) # label(axiom) # label(non_clause). [assumption].
% 0.43/1.07 60 (all U (phi(U) <-> (exists V (succ_cpq(U,V) & ok(V) & check_cpq(V))))) # label(ax62) # label(axiom) # label(non_clause). [assumption].
% 0.43/1.07 61 (all U all V all W all X (contains_cpq(triple(U,V,W),X) <-> contains_pq(i(triple(U,V,W)),X))) # label(l17_li56) # label(lemma) # label(non_clause). [assumption].
% 0.43/1.07 62 (all U all V all W ((exists X (contains_cpq(triple(U,V,W),X) & strictly_less_than(X,findmin_cpq_res(triple(U,V,W))))) -> -phi(findmin_cpq_eff(triple(U,V,W))))) # label(l17_l18) # label(lemma) # label(non_clause). [assumption].
% 0.43/1.07 63 -(all U all V all W (phi(findmin_cpq_eff(triple(U,V,W))) -> issmallestelement_pq(i(triple(U,V,W)),findmin_cpq_res(triple(U,V,W))))) # label(l17_co) # label(negated_conjecture) # label(non_clause). [assumption].
% 0.43/1.07
% 0.43/1.07 ============================== end of process non-clausal formulas ===
% 0.43/1.07
% 0.43/1.07 ============================== PROCESS INITIAL CLAUSES ===============
% 0.43/1.07
% 0.43/1.07 ============================== PREDICATE ELIMINATION =================
% 0.43/1.07 64 -pi_find_min(A) | pi_sharp_find_min(i(A),f2(A)) # label(ax59) # label(axiom). [clausify(57)].
% 0.43/1.07 65 pi_find_min(A) | -pi_sharp_find_min(i(A),B) # label(ax59) # label(axiom). [clausify(57)].
% 2.48/2.81 Derived: pi_sharp_find_min(i(A),f2(A)) | -pi_sharp_find_min(i(A),B). [resolve(64,a,65,a)].
% 2.48/2.81 66 pi_sharp_removemin(A,B) | -contains_pq(A,B) | -issmallestelement_pq(A,B) # label(ax60) # label(axiom). [clausify(58)].
% 2.48/2.81 67 -pi_sharp_removemin(A,B) | contains_pq(A,B) # label(ax60) # label(axiom). [clausify(58)].
% 2.48/2.81 68 -pi_sharp_removemin(A,B) | issmallestelement_pq(A,B) # label(ax60) # label(axiom). [clausify(58)].
% 2.48/2.81 69 -pi_removemin(A) | pi_sharp_find_min(i(A),f3(A)) # label(ax61) # label(axiom). [clausify(59)].
% 2.48/2.81 70 pi_removemin(A) | -pi_sharp_find_min(i(A),B) # label(ax61) # label(axiom). [clausify(59)].
% 2.48/2.81 Derived: pi_sharp_find_min(i(A),f3(A)) | -pi_sharp_find_min(i(A),B). [resolve(69,a,70,a)].
% 2.48/2.81 71 pi_remove(A,B) | -pi_sharp_remove(i(A),B) # label(ax57) # label(axiom). [clausify(55)].
% 2.48/2.81 72 -pi_remove(A,B) | pi_sharp_remove(i(A),B) # label(ax57) # label(axiom). [clausify(55)].
% 2.48/2.81 73 pi_sharp_remove(A,B) | -contains_pq(A,B) # label(ax56) # label(axiom). [clausify(54)].
% 2.48/2.81 74 -pi_sharp_remove(A,B) | contains_pq(A,B) # label(ax56) # label(axiom). [clausify(54)].
% 2.48/2.81
% 2.48/2.81 ============================== end predicate elimination =============
% 2.48/2.81
% 2.48/2.81 Auto_denials: (non-Horn, no changes).
% 2.48/2.81
% 2.48/2.81 Term ordering decisions:
% 2.48/2.81 Function symbol KB weights: create_slb=1. bad=1. bottom=1. create_pq=1. c1=1. c2=1. c3=1. insert_slb=1. pair=1. insert_pq=1. update_slb=1. lookup_slb=1. remove_cpq=1. remove_slb=1. remove_pq=1. insert_cpq=1. remove_pqp=1. findmin_pq_eff=1. findmin_pq_res=1. insert_pqp=1. removemin_pq_eff=1. removemin_pq_res=1. f1=1. findmin_pqp_res=1. i=1. findmin_cpq_eff=1. findmin_cpq_res=1. removemin_cpq_eff=1. removemin_cpq_res=1. f2=1. f3=1. f4=1. triple=1.
% 2.48/2.81
% 2.48/2.81 ============================== end of process initial clauses ========
% 2.48/2.81
% 2.48/2.81 ============================== CLAUSES FOR SEARCH ====================
% 2.48/2.81
% 2.48/2.81 ============================== end of clauses for search =============
% 2.48/2.81
% 2.48/2.81 ============================== SEARCH ================================
% 2.48/2.81
% 2.48/2.81 % Starting search at 0.03 seconds.
% 2.48/2.81
% 2.48/2.81 NOTE: Back_subsumption disabled, ratio of kept to back_subsumed is 33 (0.00 of 0.30 sec).
% 2.48/2.81
% 2.48/2.81 Low Water (keep): wt=54.000, iters=3359
% 2.48/2.81
% 2.48/2.81 Low Water (keep): wt=52.000, iters=3362
% 2.48/2.81
% 2.48/2.81 Low Water (keep): wt=49.000, iters=3379
% 2.48/2.81
% 2.48/2.81 Low Water (keep): wt=48.000, iters=3342
% 2.48/2.81
% 2.48/2.81 Low Water (keep): wt=43.000, iters=3355
% 2.48/2.81
% 2.48/2.81 Low Water (keep): wt=40.000, iters=3417
% 2.48/2.81
% 2.48/2.81 Low Water (keep): wt=39.000, iters=3360
% 2.48/2.81
% 2.48/2.81 Low Water (keep): wt=36.000, iters=3426
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% 2.48/2.81 Low Water (keep): wt=35.000, iters=3451
% 2.48/2.81
% 2.48/2.81 Low Water (keep): wt=33.000, iters=3503
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% 2.48/2.81 Low Water (keep): wt=32.000, iters=3505
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% 2.48/2.81 Low Water (keep): wt=31.000, iters=3343
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% 2.48/2.81 Low Water (keep): wt=30.000, iters=3367
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% 2.48/2.81 Low Water (keep): wt=29.000, iters=3373
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% 2.48/2.81 Low Water (keep): wt=28.000, iters=3358
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% 2.48/2.81 Low Water (keep): wt=27.000, iters=3358
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% 2.48/2.81 Low Water (keep): wt=25.000, iters=3334
% 2.48/2.81
% 2.48/2.81 ============================== PROOF =================================
% 2.48/2.81 % SZS status Theorem
% 2.48/2.81 % SZS output start Refutation
% 2.48/2.81
% 2.48/2.81 % Proof 1 at 1.73 (+ 0.03) seconds.
% 2.48/2.81 % Length of proof is 20.
% 2.48/2.81 % Level of proof is 5.
% 2.48/2.81 % Maximum clause weight is 19.000.
% 2.48/2.81 % Given clauses 1543.
% 2.48/2.81
% 2.48/2.81 2 (all U all V (less_than(U,V) | less_than(V,U))) # label(totality) # label(axiom) # label(non_clause). [assumption].
% 2.48/2.81 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].
% 2.48/2.81 9 (all U all V (issmallestelement_pq(U,V) <-> (all W (contains_pq(U,W) -> less_than(V,W))))) # label(ax10) # label(axiom) # label(non_clause). [assumption].
% 2.48/2.81 61 (all U all V all W all X (contains_cpq(triple(U,V,W),X) <-> contains_pq(i(triple(U,V,W)),X))) # label(l17_li56) # label(lemma) # label(non_clause). [assumption].
% 2.48/2.81 62 (all U all V all W ((exists X (contains_cpq(triple(U,V,W),X) & strictly_less_than(X,findmin_cpq_res(triple(U,V,W))))) -> -phi(findmin_cpq_eff(triple(U,V,W))))) # label(l17_l18) # label(lemma) # label(non_clause). [assumption].
% 2.48/2.81 63 -(all U all V all W (phi(findmin_cpq_eff(triple(U,V,W))) -> issmallestelement_pq(i(triple(U,V,W)),findmin_cpq_res(triple(U,V,W))))) # label(l17_co) # label(negated_conjecture) # label(non_clause). [assumption].
% 2.48/2.81 82 less_than(A,B) | less_than(B,A) # label(totality) # label(axiom). [clausify(2)].
% 2.48/2.81 84 phi(findmin_cpq_eff(triple(c1,c2,c3))) # label(l17_co) # label(negated_conjecture). [clausify(63)].
% 2.48/2.81 88 issmallestelement_pq(A,B) | contains_pq(A,f1(A,B)) # label(ax10) # label(axiom). [clausify(9)].
% 2.48/2.81 109 -issmallestelement_pq(i(triple(c1,c2,c3)),findmin_cpq_res(triple(c1,c2,c3))) # label(l17_co) # label(negated_conjecture). [clausify(63)].
% 2.48/2.81 111 -contains_cpq(triple(A,B,C),D) | -strictly_less_than(D,findmin_cpq_res(triple(A,B,C))) | -phi(findmin_cpq_eff(triple(A,B,C))) # label(l17_l18) # label(lemma). [clausify(62)].
% 2.48/2.81 123 issmallestelement_pq(A,B) | -less_than(B,f1(A,B)) # label(ax10) # label(axiom). [clausify(9)].
% 2.48/2.81 127 strictly_less_than(A,B) | -less_than(A,B) | less_than(B,A) # label(stricly_smaller_definition) # label(axiom). [clausify(4)].
% 2.48/2.81 143 contains_cpq(triple(A,B,C),D) | -contains_pq(i(triple(A,B,C)),D) # label(l17_li56) # label(lemma). [clausify(61)].
% 2.48/2.81 171 contains_pq(i(triple(c1,c2,c3)),f1(i(triple(c1,c2,c3)),findmin_cpq_res(triple(c1,c2,c3)))). [resolve(109,a,88,a)].
% 2.48/2.81 190 -less_than(findmin_cpq_res(triple(c1,c2,c3)),f1(i(triple(c1,c2,c3)),findmin_cpq_res(triple(c1,c2,c3)))). [ur(123,a,109,a)].
% 2.48/2.81 195 strictly_less_than(A,B) | less_than(B,A). [resolve(127,b,82,b),merge(c)].
% 2.48/2.81 510 contains_cpq(triple(c1,c2,c3),f1(i(triple(c1,c2,c3)),findmin_cpq_res(triple(c1,c2,c3)))). [resolve(171,a,143,b)].
% 2.48/2.81 11614 -strictly_less_than(f1(i(triple(c1,c2,c3)),findmin_cpq_res(triple(c1,c2,c3))),findmin_cpq_res(triple(c1,c2,c3))). [resolve(510,a,111,a),unit_del(b,84)].
% 2.48/2.81 11616 $F. [resolve(11614,a,195,a),unit_del(a,190)].
% 2.48/2.81
% 2.48/2.81 % SZS output end Refutation
% 2.48/2.81 ============================== end of proof ==========================
% 2.48/2.81
% 2.48/2.81 ============================== STATISTICS ============================
% 2.48/2.81
% 2.48/2.81 Given=1543. Generated=56833. Kept=11538. proofs=1.
% 2.48/2.81 Usable=1539. Sos=9917. Demods=130. Limbo=0, Disabled=175. Hints=0.
% 2.48/2.81 Megabytes=21.60.
% 2.48/2.81 User_CPU=1.73, System_CPU=0.03, Wall_clock=2.
% 2.48/2.81
% 2.48/2.81 ============================== end of statistics =====================
% 2.48/2.81
% 2.48/2.81 ============================== end of search =========================
% 2.48/2.81
% 2.48/2.81 THEOREM PROVED
% 2.48/2.81 % SZS status Theorem
% 2.48/2.81
% 2.48/2.81 Exiting with 1 proof.
% 2.48/2.81
% 2.48/2.81 Process 21864 exit (max_proofs) Tue Jun 14 18:56:52 2022
% 2.48/2.81 Prover9 interrupted
%------------------------------------------------------------------------------