TSTP Solution File: SWV417+2 by Prover9---1109a
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : SWV417+2 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n008.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 21:12:36 EDT 2022
% Result : Unknown 1.29s 1.60s
% Output : None
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11 % Problem : SWV417+2 : TPTP v8.1.0. Released v3.3.0.
% 0.03/0.12 % Command : tptp2X_and_run_prover9 %d %s
% 0.12/0.33 % Computer : n008.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 : 300
% 0.12/0.33 % WCLimit : 600
% 0.12/0.33 % DateTime : Wed Jun 15 18:26:22 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.77/1.04 ============================== Prover9 ===============================
% 0.77/1.04 Prover9 (32) version 2009-11A, November 2009.
% 0.77/1.04 Process 16441 was started by sandbox2 on n008.cluster.edu,
% 0.77/1.04 Wed Jun 15 18:26:23 2022
% 0.77/1.04 The command was "/export/starexec/sandbox2/solver/bin/prover9 -t 300 -f /tmp/Prover9_16288_n008.cluster.edu".
% 0.77/1.04 ============================== end of head ===========================
% 0.77/1.04
% 0.77/1.04 ============================== INPUT =================================
% 0.77/1.04
% 0.77/1.04 % Reading from file /tmp/Prover9_16288_n008.cluster.edu
% 0.77/1.04
% 0.77/1.04 set(prolog_style_variables).
% 0.77/1.04 set(auto2).
% 0.77/1.04 % set(auto2) -> set(auto).
% 0.77/1.04 % set(auto) -> set(auto_inference).
% 0.77/1.04 % set(auto) -> set(auto_setup).
% 0.77/1.04 % set(auto_setup) -> set(predicate_elim).
% 0.77/1.04 % set(auto_setup) -> assign(eq_defs, unfold).
% 0.77/1.04 % set(auto) -> set(auto_limits).
% 0.77/1.04 % set(auto_limits) -> assign(max_weight, "100.000").
% 0.77/1.04 % set(auto_limits) -> assign(sos_limit, 20000).
% 0.77/1.04 % set(auto) -> set(auto_denials).
% 0.77/1.04 % set(auto) -> set(auto_process).
% 0.77/1.04 % set(auto2) -> assign(new_constants, 1).
% 0.77/1.04 % set(auto2) -> assign(fold_denial_max, 3).
% 0.77/1.04 % set(auto2) -> assign(max_weight, "200.000").
% 0.77/1.04 % set(auto2) -> assign(max_hours, 1).
% 0.77/1.04 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 0.77/1.04 % set(auto2) -> assign(max_seconds, 0).
% 0.77/1.04 % set(auto2) -> assign(max_minutes, 5).
% 0.77/1.04 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 0.77/1.04 % set(auto2) -> set(sort_initial_sos).
% 0.77/1.04 % set(auto2) -> assign(sos_limit, -1).
% 0.77/1.04 % set(auto2) -> assign(lrs_ticks, 3000).
% 0.77/1.04 % set(auto2) -> assign(max_megs, 400).
% 0.77/1.04 % set(auto2) -> assign(stats, some).
% 0.77/1.04 % set(auto2) -> clear(echo_input).
% 0.77/1.04 % set(auto2) -> set(quiet).
% 0.77/1.04 % set(auto2) -> clear(print_initial_clauses).
% 0.77/1.04 % set(auto2) -> clear(print_given).
% 0.77/1.04 assign(lrs_ticks,-1).
% 0.77/1.04 assign(sos_limit,10000).
% 0.77/1.04 assign(order,kbo).
% 0.77/1.04 set(lex_order_vars).
% 0.77/1.04 clear(print_given).
% 0.77/1.04
% 0.77/1.04 % formulas(sos). % not echoed (74 formulas)
% 0.77/1.04
% 0.77/1.04 ============================== end of input ==========================
% 0.77/1.04
% 0.77/1.04 % From the command line: assign(max_seconds, 300).
% 0.77/1.04
% 0.77/1.04 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 0.77/1.04
% 0.77/1.04 % Formulas that are not ordinary clauses:
% 0.77/1.04 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].
% 0.77/1.04 2 (all U all V (less_than(U,V) | less_than(V,U))) # label(totality) # label(axiom) # label(non_clause). [assumption].
% 0.77/1.04 3 (all U less_than(U,U)) # label(reflexivity) # label(axiom) # label(non_clause). [assumption].
% 0.77/1.04 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].
% 0.77/1.04 5 (all U less_than(bottom,U)) # label(bottom_smallest) # label(axiom) # label(non_clause). [assumption].
% 0.77/1.04 6 (all U all V isnonempty_pq(insert_pq(U,V))) # label(ax7) # label(axiom) # label(non_clause). [assumption].
% 0.77/1.04 7 (all U -contains_pq(create_pq,U)) # label(ax8) # label(axiom) # label(non_clause). [assumption].
% 0.77/1.04 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].
% 0.77/1.04 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].
% 0.77/1.04 10 (all U all V remove_pq(insert_pq(U,V),V) = U) # label(ax11) # label(axiom) # label(non_clause). [assumption].
% 0.77/1.04 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].
% 0.77/1.04 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].
% 0.77/1.04 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].
% 0.77/1.04 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].
% 0.77/1.04 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].
% 0.77/1.04 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].
% 0.77/1.04 17 (all U all V all W isnonempty_slb(insert_slb(U,pair(V,W)))) # label(ax19) # label(axiom) # label(non_clause). [assumption].
% 0.77/1.04 18 (all U -contains_slb(create_slb,U)) # label(ax20) # label(axiom) # label(non_clause). [assumption].
% 0.77/1.04 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].
% 0.77/1.04 20 (all U all V -pair_in_list(create_slb,U,V)) # label(ax22) # label(axiom) # label(non_clause). [assumption].
% 0.77/1.04 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].
% 0.77/1.04 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].
% 0.77/1.04 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].
% 0.77/1.04 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].
% 0.77/1.04 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].
% 0.77/1.04 26 (all U update_slb(create_slb,U) = create_slb) # label(ax28) # label(axiom) # label(non_clause). [assumption].
% 0.77/1.04 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].
% 0.77/1.04 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].
% 0.77/1.04 29 (all U succ_cpq(U,U)) # label(ax31) # label(axiom) # label(non_clause). [assumption].
% 0.77/1.04 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].
% 0.77/1.04 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].
% 0.77/1.04 32 (all U all V (succ_cpq(U,V) -> succ_cpq(U,findmin_cpq_eff(V)))) # label(ax34) # label(axiom) # label(non_clause). [assumption].
% 0.77/1.04 33 (all U all V (succ_cpq(U,V) -> succ_cpq(U,removemin_cpq_eff(V)))) # label(ax35) # label(axiom) # label(non_clause). [assumption].
% 0.77/1.04 34 (all U all V check_cpq(triple(U,create_slb,V))) # label(ax36) # label(axiom) # label(non_clause). [assumption].
% 0.77/1.04 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].
% 0.77/1.04 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].
% 0.77/1.04 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].
% 0.77/1.04 38 (all U all V (ok(triple(U,V,bad)) <-> $F)) # label(ax40) # label(axiom) # label(non_clause). [assumption].
% 0.77/1.04 39 (all U all V all W (-ok(triple(U,V,W)) -> W = bad)) # label(ax41) # label(axiom) # label(non_clause). [assumption].
% 0.77/1.04 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].
% 0.77/1.04 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].
% 0.77/1.04 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].
% 0.77/1.05 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].
% 0.77/1.05 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].
% 0.77/1.05 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].
% 0.77/1.05 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].
% 0.77/1.05 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].
% 0.77/1.05 48 (all U all V findmin_cpq_res(triple(U,create_slb,V)) = bottom) # label(ax50) # label(axiom) # label(non_clause). [assumption].
% 0.77/1.05 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].
% 0.77/1.05 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].
% 0.77/1.05 51 (all U removemin_cpq_res(U) = findmin_cpq_res(U)) # label(ax53) # label(axiom) # label(non_clause). [assumption].
% 0.77/1.05 52 (all U all V i(triple(U,create_slb,V)) = create_pq) # label(ax54) # label(axiom) # label(non_clause). [assumption].
% 0.77/1.05 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].
% 0.77/1.05 54 (all U all V (pi_sharp_remove(U,V) <-> contains_pq(U,V))) # label(ax56) # label(axiom) # label(non_clause). [assumption].
% 0.77/1.05 55 (all U all V (pi_remove(U,V) <-> pi_sharp_remove(i(U),V))) # label(ax57) # label(axiom) # label(non_clause). [assumption].
% 0.77/1.05 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].
% 0.77/1.05 57 (all U (pi_find_min(U) <-> (exists V pi_sharp_find_min(i(U),V)))) # label(ax59) # label(axiom) # label(non_clause). [assumption].
% 0.77/1.05 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].
% 0.77/1.05 59 (all U (pi_removemin(U) <-> (exists V pi_sharp_find_min(i(U),V)))) # label(ax61) # label(axiom) # label(non_clause). [assumption].
% 0.77/1.05 60 (all U (phi(U) <-> (exists V (succ_cpq(U,V) & ok(V) & check_cpq(V))))) # label(ax62) # label(axiom) # label(non_clause). [assumption].
% 0.77/1.05 61 (all U all V all W (contains_cpq(triple(U,create_slb,V),W) <-> contains_pq(i(triple(U,create_slb,V)),W))) & (all X ((all Y all Z all X1 (contains_cpq(triple(Y,X,Z),X1) <-> contains_pq(i(triple(Y,X,Z)),X1))) -> (all X2 all X3 all X4 all X5 all X6 (contains_cpq(triple(X2,insert_slb(X,pair(X4,X5)),X3),X6) <-> contains_pq(i(triple(X2,insert_slb(X,pair(X4,X5)),X3)),X6))))) -> (all X7 all X8 all X9 all X10 (contains_cpq(triple(X7,X8,X9),X10) <-> contains_pq(i(triple(X7,X8,X9)),X10))) # label(big4_induction1) # label(axiom) # label(non_clause). [assumption].
% 0.77/1.05 62 (all U all V all W all X all Y all Z (succ_cpq(triple(U,V,W),triple(X,Y,Z)) -> (-ok(triple(X,Y,Z)) -> -ok(im_succ_cpq(triple(X,Y,Z)))))) -> (all X1 all X2 all X3 (-ok(triple(X1,X2,X3)) -> (all X4 all X5 all X6 (succ_cpq(triple(X1,X2,X3),triple(X4,X5,X6)) -> -ok(triple(X4,X5,X6)))))) # label(big4_induction2) # label(axiom) # label(non_clause). [assumption].
% 0.77/1.05 63 (all U all V all W all X (-ok(triple(U,V,W)) -> -ok(insert_cpq(triple(U,V,W),X)))) & (all Y all Z all X1 all X2 (-ok(triple(Y,Z,X1)) -> -ok(remove_cpq(triple(Y,Z,X1),X2)))) & (all X3 all X4 all X5 (-ok(triple(X3,X4,X5)) -> -ok(findmin_cpq_eff(triple(X3,X4,X5))))) & (all X6 all X7 all X8 (-ok(triple(X6,X7,X8)) -> -ok(removemin_cpq_eff(triple(X6,X7,X8))))) -> (all X9 (-ok(X9) -> -ok(im_succ_cpq(X9)))) # label(big4_induction3) # label(axiom) # label(non_clause). [assumption].
% 0.77/1.05 64 (all U all V all W all X all Y all Z (succ_cpq(triple(U,V,W),triple(X,Y,Z)) -> (-check_cpq(triple(X,Y,Z)) | -ok(triple(X,Y,Z)) -> -check_cpq(im_succ_cpq(triple(X,Y,Z))) | -ok(im_succ_cpq(triple(X,Y,Z)))))) -> (all X1 all X2 all X3 (-check_cpq(triple(X1,X2,X3)) | -ok(triple(X1,X2,X3)) -> (all X4 all X5 all X6 (succ_cpq(triple(X1,X2,X3),triple(X4,X5,X6)) -> -ok(triple(X4,X5,X6)) | -check_cpq(triple(X4,X5,X6)))))) # label(big4_induction4) # label(axiom) # label(non_clause). [assumption].
% 0.77/1.05 65 (all U all V all W (-check_cpq(triple(U,V,W)) -> (all X (-check_cpq(insert_cpq(triple(U,V,W),X)) | -ok(insert_cpq(triple(U,V,W),X)))))) & (all Y all Z all X1 (-check_cpq(triple(Y,Z,X1)) -> (all X2 (-check_cpq(remove_cpq(triple(Y,Z,X1),X2)) | -ok(remove_cpq(triple(Y,Z,X1),X2)))))) & (all X3 all X4 all X5 (-check_cpq(triple(X3,X4,X5)) -> -check_cpq(findmin_cpq_eff(triple(X3,X4,X5))) | -ok(findmin_cpq_eff(triple(X3,X4,X5))))) & (all X6 all X7 all X8 (-check_cpq(triple(X6,X7,X8)) -> -check_cpq(removemin_cpq_eff(triple(X6,X7,X8))) | -ok(removemin_cpq_eff(triple(X6,X7,X8))))) -> (all X9 all X10 all X11 (-check_cpq(triple(X9,X10,X11)) -> -check_cpq(im_succ_cpq(triple(X9,X10,X11))) | -ok(im_succ_cpq(triple(X9,X10,X11))))) # label(big4_induction5) # label(axiom) # label(non_clause). [assumption].
% 0.77/1.05 66 (all U all V (pair_in_list(create_slb,U,V) -> (all W (contains_slb(create_slb,W) -> pair_in_list(remove_slb(create_slb,W),U,V) | U = W)))) & (all X ((all Y all Z (pair_in_list(X,Y,Z) -> (all X1 (contains_slb(X,X1) -> pair_in_list(remove_slb(X,X1),Y,Z) | Y = X1)))) -> (all X2 all X3 all X4 all X5 (pair_in_list(insert_slb(X,pair(X4,X5)),X2,X3) -> (all X4 (contains_slb(insert_slb(X,pair(X4,X5)),X4) -> pair_in_list(remove_slb(insert_slb(X,pair(X4,X5)),X4),X2,X3) | X2 = X4)))))) -> (all X6 all X7 all X8 (pair_in_list(X6,X7,X8) -> (all X9 (contains_slb(X6,X9) -> pair_in_list(remove_slb(X6,X9),X7,X8) | X7 = X9)))) # label(big4_induction6) # label(axiom) # label(non_clause). [assumption].
% 0.77/1.05 67 (all U all V all W all X (pair_in_list(create_slb,W,X) & strictly_less_than(W,X) & ok(remove_cpq(triple(U,create_slb,V),W)) -> pair_in_list(remove_slb(create_slb,W),W,X))) & (all Y ((all Z all X1 all X2 all X3 (pair_in_list(Y,X2,X3) & strictly_less_than(X2,X3) & ok(remove_cpq(triple(Z,Y,X1),X2)) -> pair_in_list(remove_slb(Y,X2),X2,X3))) -> (all X4 all X5 all X6 all X7 all X8 all X9 (pair_in_list(insert_slb(Y,pair(X8,X9)),X6,X7) & strictly_less_than(X6,X7) & ok(remove_cpq(triple(X4,insert_slb(Y,pair(X8,X9)),X5),X6)) -> pair_in_list(remove_slb(insert_slb(Y,pair(X8,X9)),X6),X6,X7))))) -> (all X10 all X11 all X12 all X13 all X14 (pair_in_list(X11,X13,X14) & strictly_less_than(X13,X14) & ok(remove_cpq(triple(X10,X11,X12),X13)) -> pair_in_list(remove_slb(X11,X13),X13,X14))) # label(big4_induction7) # label(axiom) # label(non_clause). [assumption].
% 0.77/1.05 68 (all U all V all W all X (pair_in_list(create_slb,V,W) & less_than(X,W) -> pair_in_list(update_slb(create_slb,X),V,W))) & (all Y ((all Z all X1 all X2 (pair_in_list(Y,Z,X1) & less_than(X2,X1) -> pair_in_list(update_slb(Y,X2),Z,X1))) -> (all X3 all X4 all X5 all X6 all X7 (pair_in_list(insert_slb(Y,pair(X6,X7)),X3,X4) & less_than(X5,X4) -> pair_in_list(update_slb(insert_slb(Y,pair(X6,X7)),X5),X3,X4))))) -> (all X8 all X9 all X10 all X11 (pair_in_list(X8,X9,X10) & less_than(X11,X10) -> pair_in_list(update_slb(X8,X11),X9,X10))) # label(big4_induction8) # label(axiom) # label(non_clause). [assumption].
% 0.77/1.05 69 (all U all V all W all X (pair_in_list(create_slb,V,W) & strictly_less_than(W,X) -> pair_in_list(update_slb(create_slb,X),V,X))) & (all Y ((all Z all X1 all X2 (pair_in_list(Y,Z,X1) & strictly_less_than(X1,X2) -> pair_in_list(update_slb(Y,X2),Z,X2))) -> (all X3 all X4 all X5 all X6 all X7 (pair_in_list(insert_slb(Y,pair(X6,X7)),X3,X4) & strictly_less_than(X4,X5) -> pair_in_list(update_slb(insert_slb(Y,pair(X6,X7)),X5),X3,X5))))) -> (all X8 all X9 all X10 all X11 (pair_in_list(X8,X9,X10) & strictly_less_than(X10,X11) -> pair_in_list(update_slb(X8,X11),X9,X11))) # label(big4_induction9) # label(axiom) # label(non_clause). [assumption].
% 0.77/1.06 70 (all U all V (check_cpq(triple(U,create_slb,V)) <-> (all W all X (pair_in_list(create_slb,W,X) -> less_than(X,W))))) & (all Y ((all Z all X1 (check_cpq(triple(Z,Y,X1)) <-> (all X2 all X3 (pair_in_list(Y,X2,X3) -> less_than(X3,X2))))) -> (all X4 all X5 all X6 all X7 (check_cpq(triple(X4,insert_slb(Y,pair(X6,X7)),X5)) <-> (all X8 all X9 (pair_in_list(insert_slb(Y,pair(X6,X7)),X8,X9) -> less_than(X9,X8))))))) -> (all X10 all X11 all X12 (check_cpq(triple(X10,X11,X12)) <-> (all X13 all X14 (pair_in_list(X11,X13,X14) -> less_than(X14,X13))))) # label(big4_induction10) # label(axiom) # label(non_clause). [assumption].
% 0.77/1.06 71 (all U (contains_slb(create_slb,U) -> (exists V pair_in_list(create_slb,U,V)))) & (all W ((all X (contains_slb(W,X) -> (exists Y pair_in_list(W,X,Y)))) -> (all Z all X1 all X2 (contains_slb(insert_slb(W,pair(X1,X2)),Z) -> (exists X3 pair_in_list(insert_slb(W,pair(X1,X2)),Z,X3)))))) -> (all X4 all X5 (contains_slb(X4,X5) -> (exists X6 pair_in_list(X4,X5,X6)))) # label(big4_induction11) # label(axiom) # label(non_clause). [assumption].
% 0.77/1.06 72 -(all U all V all W (pi_find_min(triple(U,V,W)) -> (phi(findmin_cpq_eff(triple(U,V,W))) -> (exists X (pi_sharp_find_min(i(triple(U,V,W)),X) & findmin_cpq_res(triple(U,V,W)) = findmin_pq_res(i(triple(U,V,W)),X)))))) # label(co4) # label(negated_conjecture) # label(non_clause). [assumption].
% 0.77/1.06
% 0.77/1.06 ============================== end of process non-clausal formulas ===
% 0.77/1.06
% 0.77/1.06 ============================== PROCESS INITIAL CLAUSES ===============
% 0.77/1.06
% 0.77/1.06 ============================== PREDICATE ELIMINATION =================
% 0.77/1.06 73 issmallestelement_pq(A,B) | contains_pq(A,f1(A,B)) # label(ax10) # label(axiom). [clausify(9)].
% 0.77/1.06 74 -issmallestelement_pq(A,B) | -contains_pq(A,C) | less_than(B,C) # label(ax10) # label(axiom). [clausify(9)].
% 0.77/1.06 Derived: contains_pq(A,f1(A,B)) | -contains_pq(A,C) | less_than(B,C). [resolve(73,a,74,a)].
% 0.77/1.06 75 issmallestelement_pq(A,B) | -less_than(B,f1(A,B)) # label(ax10) # label(axiom). [clausify(9)].
% 0.77/1.06 Derived: -less_than(A,f1(B,A)) | -contains_pq(B,C) | less_than(A,C). [resolve(75,a,74,a)].
% 0.77/1.06 76 -contains_pq(A,B) | -issmallestelement_pq(A,B) | findmin_pq_eff(A,B) = A # label(ax13) # label(axiom). [clausify(12)].
% 0.77/1.06 Derived: -contains_pq(A,B) | findmin_pq_eff(A,B) = A | contains_pq(A,f1(A,B)). [resolve(76,b,73,a)].
% 0.77/1.06 Derived: -contains_pq(A,B) | findmin_pq_eff(A,B) = A | -less_than(B,f1(A,B)). [resolve(76,b,75,a)].
% 0.77/1.06 77 -contains_pq(A,B) | -issmallestelement_pq(A,B) | findmin_pq_res(A,B) = B # label(ax14) # label(axiom). [clausify(13)].
% 0.77/1.06 Derived: -contains_pq(A,B) | findmin_pq_res(A,B) = B | contains_pq(A,f1(A,B)). [resolve(77,b,73,a)].
% 0.77/1.06 Derived: -contains_pq(A,B) | findmin_pq_res(A,B) = B | -less_than(B,f1(A,B)). [resolve(77,b,75,a)].
% 0.77/1.06 78 -contains_pq(A,B) | -issmallestelement_pq(A,B) | removemin_pq_eff(A,B) = remove_pq(A,B) # label(ax15) # label(axiom). [clausify(14)].
% 0.77/1.06 Derived: -contains_pq(A,B) | removemin_pq_eff(A,B) = remove_pq(A,B) | contains_pq(A,f1(A,B)). [resolve(78,b,73,a)].
% 0.77/1.06 Derived: -contains_pq(A,B) | removemin_pq_eff(A,B) = remove_pq(A,B) | -less_than(B,f1(A,B)). [resolve(78,b,75,a)].
% 0.77/1.06 79 -contains_pq(A,B) | -issmallestelement_pq(A,B) | removemin_pq_res(A,B) = B # label(ax16) # label(axiom). [clausify(15)].
% 0.77/1.06 Derived: -contains_pq(A,B) | removemin_pq_res(A,B) = B | contains_pq(A,f1(A,B)). [resolve(79,b,73,a)].
% 0.77/1.06 Derived: -contains_pq(A,B) | removemin_pq_res(A,B) = B | -less_than(B,f1(A,B)). [resolve(79,b,75,a)].
% 0.77/1.06 80 -pi_sharp_find_min(A,B) | issmallestelement_pq(A,B) # label(ax58) # label(axiom). [clausify(56)].
% 0.77/1.06 Derived: -pi_sharp_find_min(A,B) | -contains_pq(A,C) | less_than(B,C). [resolve(80,b,74,a)].
% 0.77/1.06 Derived: -pi_sharp_find_min(A,B) | -contains_pq(A,B) | findmin_pq_eff(A,B) = A. [resolve(80,b,76,b)].
% 0.89/1.17 Derived: -pi_sharp_find_min(A,B) | -contains_pq(A,B) | findmin_pq_res(A,B) = B. [resolve(80,b,77,b)].
% 0.89/1.17 Derived: -pi_sharp_find_min(A,B) | -contains_pq(A,B) | removemin_pq_eff(A,B) = remove_pq(A,B). [resolve(80,b,78,b)].
% 0.89/1.17 Derived: -pi_sharp_find_min(A,B) | -contains_pq(A,B) | removemin_pq_res(A,B) = B. [resolve(80,b,79,b)].
% 0.89/1.17 81 pi_sharp_find_min(A,B) | -contains_pq(A,B) | -issmallestelement_pq(A,B) # label(ax58) # label(axiom). [clausify(56)].
% 0.89/1.17 Derived: pi_sharp_find_min(A,B) | -contains_pq(A,B) | contains_pq(A,f1(A,B)). [resolve(81,c,73,a)].
% 0.89/1.17 Derived: pi_sharp_find_min(A,B) | -contains_pq(A,B) | -less_than(B,f1(A,B)). [resolve(81,c,75,a)].
% 0.89/1.17 82 -pi_sharp_removemin(A,B) | issmallestelement_pq(A,B) # label(ax60) # label(axiom). [clausify(58)].
% 0.89/1.17 Derived: -pi_sharp_removemin(A,B) | -contains_pq(A,C) | less_than(B,C). [resolve(82,b,74,a)].
% 0.89/1.17 Derived: -pi_sharp_removemin(A,B) | -contains_pq(A,B) | findmin_pq_eff(A,B) = A. [resolve(82,b,76,b)].
% 0.89/1.17 Derived: -pi_sharp_removemin(A,B) | -contains_pq(A,B) | findmin_pq_res(A,B) = B. [resolve(82,b,77,b)].
% 0.89/1.17 Derived: -pi_sharp_removemin(A,B) | -contains_pq(A,B) | removemin_pq_eff(A,B) = remove_pq(A,B). [resolve(82,b,78,b)].
% 0.89/1.17 Derived: -pi_sharp_removemin(A,B) | -contains_pq(A,B) | removemin_pq_res(A,B) = B. [resolve(82,b,79,b)].
% 0.89/1.17 Derived: -pi_sharp_removemin(A,B) | pi_sharp_find_min(A,B) | -contains_pq(A,B). [resolve(82,b,81,c)].
% 0.89/1.17 83 pi_sharp_removemin(A,B) | -contains_pq(A,B) | -issmallestelement_pq(A,B) # label(ax60) # label(axiom). [clausify(58)].
% 0.89/1.17 Derived: pi_sharp_removemin(A,B) | -contains_pq(A,B) | contains_pq(A,f1(A,B)). [resolve(83,c,73,a)].
% 0.89/1.17 Derived: pi_sharp_removemin(A,B) | -contains_pq(A,B) | -less_than(B,f1(A,B)). [resolve(83,c,75,a)].
% 0.89/1.17 Derived: pi_sharp_removemin(A,B) | -contains_pq(A,B) | -pi_sharp_find_min(A,B). [resolve(83,c,80,b)].
% 0.89/1.17 84 pi_remove(A,B) | -pi_sharp_remove(i(A),B) # label(ax57) # label(axiom). [clausify(55)].
% 0.89/1.17 85 -pi_remove(A,B) | pi_sharp_remove(i(A),B) # label(ax57) # label(axiom). [clausify(55)].
% 0.89/1.17 86 pi_sharp_remove(A,B) | -contains_pq(A,B) # label(ax56) # label(axiom). [clausify(54)].
% 0.89/1.17 87 -pi_sharp_remove(A,B) | contains_pq(A,B) # label(ax56) # label(axiom). [clausify(54)].
% 0.89/1.17 88 pi_find_min(A) | -pi_sharp_find_min(i(A),B) # label(ax59) # label(axiom). [clausify(57)].
% 0.89/1.17 89 -pi_find_min(A) | pi_sharp_find_min(i(A),f2(A)) # label(ax59) # label(axiom). [clausify(57)].
% 0.89/1.17 Derived: -pi_sharp_find_min(i(A),B) | pi_sharp_find_min(i(A),f2(A)). [resolve(88,a,89,a)].
% 0.89/1.17 90 pi_find_min(triple(c106,c107,c108)) # label(co4) # label(negated_conjecture). [clausify(72)].
% 0.89/1.17 Derived: pi_sharp_find_min(i(triple(c106,c107,c108)),f2(triple(c106,c107,c108))). [resolve(90,a,89,a)].
% 0.89/1.17 91 pi_sharp_removemin(A,B) | -contains_pq(A,B) | contains_pq(A,f1(A,B)). [resolve(83,c,73,a)].
% 0.89/1.17 92 -pi_sharp_removemin(A,B) | contains_pq(A,B) # label(ax60) # label(axiom). [clausify(58)].
% 0.89/1.17 93 -pi_sharp_removemin(A,B) | -contains_pq(A,C) | less_than(B,C). [resolve(82,b,74,a)].
% 0.89/1.17 94 -pi_sharp_removemin(A,B) | -contains_pq(A,B) | findmin_pq_eff(A,B) = A. [resolve(82,b,76,b)].
% 0.89/1.17 95 -pi_sharp_removemin(A,B) | -contains_pq(A,B) | findmin_pq_res(A,B) = B. [resolve(82,b,77,b)].
% 0.89/1.17 96 -pi_sharp_removemin(A,B) | -contains_pq(A,B) | removemin_pq_eff(A,B) = remove_pq(A,B). [resolve(82,b,78,b)].
% 0.89/1.17 97 -pi_sharp_removemin(A,B) | -contains_pq(A,B) | removemin_pq_res(A,B) = B. [resolve(82,b,79,b)].
% 0.89/1.17 98 -pi_sharp_removemin(A,B) | pi_sharp_find_min(A,B) | -contains_pq(A,B). [resolve(82,b,81,c)].
% 0.89/1.17 Derived: -contains_pq(A,B) | contains_pq(A,f1(A,B)) | -contains_pq(A,C) | less_than(B,C). [resolve(91,a,93,a)].
% 0.89/1.17 Derived: -contains_pq(A,B) | contains_pq(A,f1(A,B)) | -contains_pq(A,B) | findmin_pq_eff(A,B) = A. [resolve(91,a,94,a)].
% 0.89/1.17 Derived: -contains_pq(A,B) | contains_pq(A,f1(A,B)) | -contains_pq(A,B) | findmin_pq_res(A,B) = B. [resolve(91,a,95,a)].
% 0.89/1.17 Derived: -contains_pq(A,B) | contains_pq(A,f1(A,B)) | -contains_pq(A,B) | removemin_pq_eff(A,B) = remove_pq(A,B). [resolve(91,a,96,a)].
% 0.89/1.17 Derived: -contains_pq(A,B) | contains_pq(A,f1(A,B)) | -contains_pq(A,B) | removemin_pq_res(A,B) = B. [resolve(91,a,97,a)].
% 0.99/1.26 Derived: -contains_pq(A,B) | contains_pq(A,f1(A,B)) | pi_sharp_find_min(A,B) | -contains_pq(A,B). [resolve(91,a,98,a)].
% 0.99/1.26 99 pi_sharp_removemin(A,B) | -contains_pq(A,B) | -less_than(B,f1(A,B)). [resolve(83,c,75,a)].
% 0.99/1.26 Derived: -contains_pq(A,B) | -less_than(B,f1(A,B)) | -contains_pq(A,C) | less_than(B,C). [resolve(99,a,93,a)].
% 0.99/1.26 Derived: -contains_pq(A,B) | -less_than(B,f1(A,B)) | -contains_pq(A,B) | findmin_pq_eff(A,B) = A. [resolve(99,a,94,a)].
% 0.99/1.26 Derived: -contains_pq(A,B) | -less_than(B,f1(A,B)) | -contains_pq(A,B) | findmin_pq_res(A,B) = B. [resolve(99,a,95,a)].
% 0.99/1.26 Derived: -contains_pq(A,B) | -less_than(B,f1(A,B)) | -contains_pq(A,B) | removemin_pq_eff(A,B) = remove_pq(A,B). [resolve(99,a,96,a)].
% 0.99/1.26 Derived: -contains_pq(A,B) | -less_than(B,f1(A,B)) | -contains_pq(A,B) | removemin_pq_res(A,B) = B. [resolve(99,a,97,a)].
% 0.99/1.26 Derived: -contains_pq(A,B) | -less_than(B,f1(A,B)) | pi_sharp_find_min(A,B) | -contains_pq(A,B). [resolve(99,a,98,a)].
% 0.99/1.26 100 pi_sharp_removemin(A,B) | -contains_pq(A,B) | -pi_sharp_find_min(A,B). [resolve(83,c,80,b)].
% 0.99/1.26 Derived: -contains_pq(A,B) | -pi_sharp_find_min(A,B) | -contains_pq(A,C) | less_than(B,C). [resolve(100,a,93,a)].
% 0.99/1.26 Derived: -contains_pq(A,B) | -pi_sharp_find_min(A,B) | -contains_pq(A,B) | findmin_pq_eff(A,B) = A. [resolve(100,a,94,a)].
% 0.99/1.26 Derived: -contains_pq(A,B) | -pi_sharp_find_min(A,B) | -contains_pq(A,B) | findmin_pq_res(A,B) = B. [resolve(100,a,95,a)].
% 0.99/1.26 Derived: -contains_pq(A,B) | -pi_sharp_find_min(A,B) | -contains_pq(A,B) | removemin_pq_eff(A,B) = remove_pq(A,B). [resolve(100,a,96,a)].
% 0.99/1.26 Derived: -contains_pq(A,B) | -pi_sharp_find_min(A,B) | -contains_pq(A,B) | removemin_pq_res(A,B) = B. [resolve(100,a,97,a)].
% 0.99/1.26 101 pi_removemin(A) | -pi_sharp_find_min(i(A),B) # label(ax61) # label(axiom). [clausify(59)].
% 0.99/1.26 102 -pi_removemin(A) | pi_sharp_find_min(i(A),f3(A)) # label(ax61) # label(axiom). [clausify(59)].
% 0.99/1.26 Derived: -pi_sharp_find_min(i(A),B) | pi_sharp_find_min(i(A),f3(A)). [resolve(101,a,102,a)].
% 0.99/1.26 103 phi(A) | -succ_cpq(A,B) | -ok(B) | -check_cpq(B) # label(ax62) # label(axiom). [clausify(60)].
% 0.99/1.26 104 -phi(A) | succ_cpq(A,f4(A)) # label(ax62) # label(axiom). [clausify(60)].
% 0.99/1.26 105 -phi(A) | ok(f4(A)) # label(ax62) # label(axiom). [clausify(60)].
% 0.99/1.26 106 -phi(A) | check_cpq(f4(A)) # label(ax62) # label(axiom). [clausify(60)].
% 0.99/1.26 Derived: -succ_cpq(A,B) | -ok(B) | -check_cpq(B) | succ_cpq(A,f4(A)). [resolve(103,a,104,a)].
% 0.99/1.26 Derived: -succ_cpq(A,B) | -ok(B) | -check_cpq(B) | ok(f4(A)). [resolve(103,a,105,a)].
% 0.99/1.26 Derived: -succ_cpq(A,B) | -ok(B) | -check_cpq(B) | check_cpq(f4(A)). [resolve(103,a,106,a)].
% 0.99/1.26 107 phi(findmin_cpq_eff(triple(c106,c107,c108))) # label(co4) # label(negated_conjecture). [clausify(72)].
% 0.99/1.26 Derived: succ_cpq(findmin_cpq_eff(triple(c106,c107,c108)),f4(findmin_cpq_eff(triple(c106,c107,c108)))). [resolve(107,a,104,a)].
% 0.99/1.26 Derived: ok(f4(findmin_cpq_eff(triple(c106,c107,c108)))). [resolve(107,a,105,a)].
% 0.99/1.26 Derived: check_cpq(f4(findmin_cpq_eff(triple(c106,c107,c108)))). [resolve(107,a,106,a)].
% 0.99/1.26
% 0.99/1.26 ============================== end predicate elimination =============
% 0.99/1.26
% 0.99/1.26 Auto_denials: (non-Horn, no changes).
% 0.99/1.26
% 0.99/1.26 Term ordering decisions:
% 0.99/1.26 Function symbol KB weights: create_slb=1. bad=1. bottom=1. create_pq=1. c1=1. c2=1. c3=1. c4=1. c5=1. c6=1. c7=1. c8=1. c9=1. c10=1. c11=1. c12=1. c13=1. c14=1. c15=1. c16=1. c17=1. c18=1. c19=1. c20=1. c21=1. c22=1. c23=1. c24=1. c25=1. c26=1. c27=1. c28=1. c29=1. c30=1. c31=1. c32=1. c33=1. c34=1. c35=1. c36=1. c37=1. c38=1. c39=1. c40=1. c41=1. c42=1. c43=1. c44=1. c45=1. c46=1. c47=1. c48=1. c49=1. c50=1. c51=1. c52=1. c53=1. c54=1. c55=1. c56=1. c57=1. c58=1. c59=1. c60=1. c61=1. c62=1. c63=1. c64=1. c65=1. c66=1. c67=1. c68=1. c69=1. c71=1. c72=1. c73=1. c74=1. c75=1. c76=1. c77=1. c78=1. c79=1. c81=1. c82=1. c83=1. c84=1. c85=1. c86=1. c87=1. c88=1. c89=1. c90=1. c91=1. c92=1. c93=1. c94=1. c95=1. c96=1. c97=1. c98=1. c99=1. c100=1. c101=1. c102=1. c103=1. c104=1. c105=1. c106=1. c107=1. c108=1. insert_slb=1. pair=1. remove_cpq=1. remove_slb=1. insert_cpq=1. update_slb=1. insert_pq=1. remove_pq=1. lookup
% 1.29/1.60 Fatal error: renum_vars_recurse: too many variables
% 1.29/1.60
% 1.29/1.60 _slb=1. findmin_pq_eff=1. findmin_pq_res=1. removemin_pq_eff=1. removemin_pq_res=1. remove_pqp=1. insert_pqp=1. f1=1. f5=1. f6=1. f10=1. im_succ_cpq=1. findmin_cpq_eff=1. removemin_cpq_eff=1. i=1. findmin_pqp_res=1. findmin_cpq_res=1. removemin_cpq_res=1. f2=1. f3=1. f4=1. f9=1. triple=1. f7=1. f8=1.
% 1.29/1.60
% 1.29/1.60 ============================== end of process initial clauses ========
% 1.29/1.60
% 1.29/1.60 ============================== CLAUSES FOR SEARCH ====================
% 1.29/1.60
% 1.29/1.60 ============================== end of clauses for search =============
% 1.29/1.60
% 1.29/1.60 ============================== SEARCH ================================
% 1.29/1.60
% 1.29/1.60 % Starting search at 0.24 seconds.
% 1.29/1.60
% 1.29/1.60 Fatal error: renum_vars_recurse: too many variables
% 1.29/1.60
% 1.29/1.60 Prover9 interrupted
%------------------------------------------------------------------------------