%------------------------------------------------------------------------------
% File : ConnectPP---0.7.2
% Problem : SWV373+1 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/connect++ --verbosity 1 --no-colour --tptp-proof --schedule default --timeout 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n006.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Sep 24 09:03:32 AM UTC 2026
% Result : Theorem 175.81s 181.39s
% Output : Proof 177.61s
% Verified :
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)
% Comments :
%------------------------------------------------------------------------------
fof(transitivity,axiom,
! [U,V,W] :
( ( less_than(V,W)
& less_than(U,V) )
=> less_than(U,W) ),
file('SWV007+0.ax',transitivity) ).
fof(totality,axiom,
! [U,V] :
( less_than(V,U)
| less_than(U,V) ),
file('SWV007+0.ax',totality) ).
fof(reflexivity,axiom,
! [U] : less_than(U,U),
file('SWV007+0.ax',reflexivity) ).
fof(stricly_smaller_definition,axiom,
! [U,V] :
( strictly_less_than(U,V)
<=> ( ~ less_than(V,U)
& less_than(U,V) ) ),
file('SWV007+0.ax',stricly_smaller_definition) ).
fof(bottom_smallest,axiom,
! [U] : less_than(bottom,U),
file('SWV007+0.ax',bottom_smallest) ).
fof(ax18,axiom,
~ isnonempty_slb(create_slb),
file('SWV007+2.ax',ax18) ).
fof(ax19,axiom,
! [U,V,W] : isnonempty_slb(insert_slb(U,pair(V,W))),
file('SWV007+2.ax',ax19) ).
fof(ax20,axiom,
! [U] : ~ contains_slb(create_slb,U),
file('SWV007+2.ax',ax20) ).
fof(ax21,axiom,
! [U,V,W,X] :
( contains_slb(insert_slb(U,pair(V,X)),W)
<=> ( V = W
| contains_slb(U,W) ) ),
file('SWV007+2.ax',ax21) ).
fof(ax22,axiom,
! [U,V] : ~ pair_in_list(create_slb,U,V),
file('SWV007+2.ax',ax22) ).
fof(ax23,axiom,
! [U,V,W,X,Y] :
( pair_in_list(insert_slb(U,pair(V,X)),W,Y)
<=> ( ( X = Y
& V = W )
| pair_in_list(U,W,Y) ) ),
file('SWV007+2.ax',ax23) ).
fof(ax24,axiom,
! [U,V,W] : remove_slb(insert_slb(U,pair(V,W)),V) = U,
file('SWV007+2.ax',ax24) ).
fof(ax25,axiom,
! [U,V,W,X] :
( ( contains_slb(U,W)
& V != W )
=> remove_slb(insert_slb(U,pair(V,X)),W) = insert_slb(remove_slb(U,W),pair(V,X)) ),
file('SWV007+2.ax',ax25) ).
fof(ax26,axiom,
! [U,V,W] : lookup_slb(insert_slb(U,pair(V,W)),V) = W,
file('SWV007+2.ax',ax26) ).
fof(ax27,axiom,
! [U,V,W,X] :
( ( contains_slb(U,W)
& V != W )
=> lookup_slb(insert_slb(U,pair(V,X)),W) = lookup_slb(U,W) ),
file('SWV007+2.ax',ax27) ).
fof(ax28,axiom,
! [U] : update_slb(create_slb,U) = create_slb,
file('SWV007+2.ax',ax28) ).
fof(ax29,axiom,
! [U,V,W,X] :
( strictly_less_than(X,W)
=> update_slb(insert_slb(U,pair(V,X)),W) = insert_slb(update_slb(U,W),pair(V,W)) ),
file('SWV007+2.ax',ax29) ).
fof(ax30,axiom,
! [U,V,W,X] :
( less_than(W,X)
=> update_slb(insert_slb(U,pair(V,X)),W) = insert_slb(update_slb(U,W),pair(V,X)) ),
file('SWV007+2.ax',ax30) ).
fof(ax31,axiom,
! [U] : succ_cpq(U,U),
file('SWV007+3.ax',ax31) ).
fof(ax32,axiom,
! [U,V,W] :
( succ_cpq(U,V)
=> succ_cpq(U,insert_cpq(V,W)) ),
file('SWV007+3.ax',ax32) ).
fof(ax33,axiom,
! [U,V,W] :
( succ_cpq(U,V)
=> succ_cpq(U,remove_cpq(V,W)) ),
file('SWV007+3.ax',ax33) ).
fof(ax34,axiom,
! [U,V] :
( succ_cpq(U,V)
=> succ_cpq(U,findmin_cpq_eff(V)) ),
file('SWV007+3.ax',ax34) ).
fof(ax35,axiom,
! [U,V] :
( succ_cpq(U,V)
=> succ_cpq(U,removemin_cpq_eff(V)) ),
file('SWV007+3.ax',ax35) ).
fof(ax36,axiom,
! [U,V] : check_cpq(triple(U,create_slb,V)),
file('SWV007+3.ax',ax36) ).
fof(ax37,axiom,
! [U,V,W,X,Y] :
( less_than(Y,X)
=> ( check_cpq(triple(U,insert_slb(V,pair(X,Y)),W))
<=> check_cpq(triple(U,V,W)) ) ),
file('SWV007+3.ax',ax37) ).
fof(ax38,axiom,
! [U,V,W,X,Y] :
( strictly_less_than(X,Y)
=> ( check_cpq(triple(U,insert_slb(V,pair(X,Y)),W))
<=> $false ) ),
file('SWV007+3.ax',ax38) ).
fof(ax39,axiom,
! [U,V,W,X] :
( contains_cpq(triple(U,V,W),X)
<=> contains_slb(V,X) ),
file('SWV007+3.ax',ax39) ).
fof(ax40,axiom,
! [U,V] :
( ok(triple(U,V,bad))
<=> $false ),
file('SWV007+3.ax',ax40) ).
fof(ax41,axiom,
! [U,V,W] :
( ~ ok(triple(U,V,W))
=> W = bad ),
file('SWV007+3.ax',ax41) ).
fof(ax42,axiom,
! [U,V,W,X] : insert_cpq(triple(U,V,W),X) = triple(insert_pqp(U,X),insert_slb(V,pair(X,bottom)),W),
file('SWV007+3.ax',ax42) ).
fof(ax43,axiom,
! [U,V,W,X] :
( ~ contains_slb(V,X)
=> remove_cpq(triple(U,V,W),X) = triple(U,V,bad) ),
file('SWV007+3.ax',ax43) ).
fof(ax44,axiom,
! [U,V,W,X] :
( ( less_than(lookup_slb(V,X),X)
& contains_slb(V,X) )
=> remove_cpq(triple(U,V,W),X) = triple(remove_pqp(U,X),remove_slb(V,X),W) ),
file('SWV007+3.ax',ax44) ).
fof(ax45,axiom,
! [U,V,W,X] :
( ( strictly_less_than(X,lookup_slb(V,X))
& contains_slb(V,X) )
=> remove_cpq(triple(U,V,W),X) = triple(remove_pqp(U,X),remove_slb(V,X),bad) ),
file('SWV007+3.ax',ax45) ).
fof(ax46,axiom,
! [U,V] : findmin_cpq_eff(triple(U,create_slb,V)) = triple(U,create_slb,bad),
file('SWV007+3.ax',ax46) ).
fof(ax47,axiom,
! [U,V,W,X] :
( ( ~ contains_slb(V,findmin_pqp_res(U))
& V != create_slb )
=> findmin_cpq_eff(triple(U,V,W)) = triple(U,update_slb(V,findmin_pqp_res(U)),bad) ),
file('SWV007+3.ax',ax47) ).
fof(ax48,axiom,
! [U,V,W,X] :
( ( strictly_less_than(findmin_pqp_res(U),lookup_slb(V,findmin_pqp_res(U)))
& contains_slb(V,findmin_pqp_res(U))
& V != create_slb )
=> findmin_cpq_eff(triple(U,V,W)) = triple(U,update_slb(V,findmin_pqp_res(U)),bad) ),
file('SWV007+3.ax',ax48) ).
fof(ax49,axiom,
! [U,V,W,X] :
( ( less_than(lookup_slb(V,findmin_pqp_res(U)),findmin_pqp_res(U))
& contains_slb(V,findmin_pqp_res(U))
& V != create_slb )
=> findmin_cpq_eff(triple(U,V,W)) = triple(U,update_slb(V,findmin_pqp_res(U)),W) ),
file('SWV007+3.ax',ax49) ).
fof(ax50,axiom,
! [U,V] : findmin_cpq_res(triple(U,create_slb,V)) = bottom,
file('SWV007+3.ax',ax50) ).
fof(ax51,axiom,
! [U,V,W,X] :
( V != create_slb
=> findmin_cpq_res(triple(U,V,W)) = findmin_pqp_res(U) ),
file('SWV007+3.ax',ax51) ).
fof(ax52,axiom,
! [U] : removemin_cpq_eff(U) = remove_cpq(findmin_cpq_eff(U),findmin_cpq_res(U)),
file('SWV007+3.ax',ax52) ).
fof(ax53,axiom,
! [U] : removemin_cpq_res(U) = findmin_cpq_res(U),
file('SWV007+3.ax',ax53) ).
fof(l9_l10,lemma,
! [U,V,W] :
( ok(findmin_cpq_eff(triple(U,V,W)))
=> ( less_than(lookup_slb(V,findmin_pqp_res(U)),findmin_pqp_res(U))
& contains_slb(V,findmin_pqp_res(U))
& V != create_slb ) ),
file('theBenchmark.p',l9_l10) ).
fof(l9_co,conjecture,
! [U,V,W] :
( ~ contains_cpq(triple(U,V,W),findmin_cpq_res(triple(U,V,W)))
=> ~ ok(findmin_cpq_eff(triple(U,V,W))) ),
file('theBenchmark.p',l9_co) ).
fof(f_1_1,plain,
! [U,V,W] :
( less_than(U,W)
| ~ less_than(V,W)
| ~ less_than(U,V) ),
inference(fof_nnf,[status(thm)],[transitivity]) ).
fof(f_1_2,plain,
! [U_2,U_1,U_0] :
( less_than(U_2,U_0)
| ~ less_than(U_1,U_0)
| ~ less_than(U_2,U_1) ),
inference(variable_rename,[status(thm)],[f_1_1]) ).
cnf(f_1_3,plain,
( less_than(U_2,U_0)
| ~ less_than(U_1,U_0)
| ~ less_than(U_2,U_1) ),
inference(clausify,[status(thm)],[f_1_2]) ).
fof(f_2_1,plain,
! [U,V] :
( less_than(V,U)
| less_than(U,V) ),
inference(fof_nnf,[status(thm)],[totality]) ).
fof(f_2_2,plain,
! [U_4,U_3] :
( less_than(U_3,U_4)
| less_than(U_4,U_3) ),
inference(variable_rename,[status(thm)],[f_2_1]) ).
cnf(f_2_3,plain,
( less_than(U_3,U_4)
| less_than(U_4,U_3) ),
inference(clausify,[status(thm)],[f_2_2]) ).
fof(f_3_1,plain,
! [U] : less_than(U,U),
inference(fof_nnf,[status(thm)],[reflexivity]) ).
fof(f_3_2,plain,
! [U_5] : less_than(U_5,U_5),
inference(variable_rename,[status(thm)],[f_3_1]) ).
cnf(f_3_3,plain,
less_than(U_5,U_5),
inference(clausify,[status(thm)],[f_3_2]) ).
fof(f_4_1,plain,
! [U,V] :
( ( strictly_less_than(U,V)
| less_than(V,U)
| ~ less_than(U,V) )
& ( ( ~ less_than(V,U)
& less_than(U,V) )
| ~ strictly_less_than(U,V) ) ),
inference(fof_nnf,[status(thm)],[stricly_smaller_definition]) ).
fof(f_4_2,plain,
! [U_7,U_6] :
( ( strictly_less_than(U_7,U_6)
| less_than(U_6,U_7)
| ~ less_than(U_7,U_6) )
& ( ( ~ less_than(U_6,U_7)
& less_than(U_7,U_6) )
| ~ strictly_less_than(U_7,U_6) ) ),
inference(variable_rename,[status(thm)],[f_4_1]) ).
fof(f_4_3,plain,
( ! [U_11,U_9] :
( strictly_less_than(U_11,U_9)
| less_than(U_9,U_11)
| ~ less_than(U_11,U_9) )
& ! [U_10,U_8] :
( ( ~ less_than(U_8,U_10)
& less_than(U_10,U_8) )
| ~ strictly_less_than(U_10,U_8) ) ),
inference(miniscope,[status(thm)],[f_4_2]) ).
cnf(f_4_4,plain,
( less_than(U_10,U_8)
| ~ strictly_less_than(U_10,U_8) ),
inference(clausify,[status(thm)],[f_4_3]) ).
cnf(f_4_5,plain,
( ~ less_than(U_8,U_10)
| ~ strictly_less_than(U_10,U_8) ),
inference(clausify,[status(thm)],[f_4_3]) ).
cnf(f_4_6,plain,
( strictly_less_than(U_11,U_9)
| less_than(U_9,U_11)
| ~ less_than(U_11,U_9) ),
inference(clausify,[status(thm)],[f_4_3]) ).
fof(f_5_1,plain,
! [U] : less_than(bottom,U),
inference(fof_nnf,[status(thm)],[bottom_smallest]) ).
fof(f_5_2,plain,
! [U_12] : less_than(bottom,U_12),
inference(variable_rename,[status(thm)],[f_5_1]) ).
cnf(f_5_3,plain,
less_than(bottom,U_12),
inference(clausify,[status(thm)],[f_5_2]) ).
fof(f_6_1,plain,
~ isnonempty_slb(create_slb),
inference(fof_nnf,[status(thm)],[ax18]) ).
cnf(f_6_2,plain,
~ isnonempty_slb(create_slb),
inference(clausify,[status(thm)],[f_6_1]) ).
fof(f_7_1,plain,
! [U,V,W] : isnonempty_slb(insert_slb(U,pair(V,W))),
inference(fof_nnf,[status(thm)],[ax19]) ).
fof(f_7_2,plain,
! [U_15,U_14,U_13] : isnonempty_slb(insert_slb(U_15,pair(U_14,U_13))),
inference(variable_rename,[status(thm)],[f_7_1]) ).
cnf(f_7_3,plain,
isnonempty_slb(insert_slb(U_15,pair(U_14,U_13))),
inference(clausify,[status(thm)],[f_7_2]) ).
fof(f_8_1,plain,
! [U] : ~ contains_slb(create_slb,U),
inference(fof_nnf,[status(thm)],[ax20]) ).
fof(f_8_2,plain,
! [U_16] : ~ contains_slb(create_slb,U_16),
inference(variable_rename,[status(thm)],[f_8_1]) ).
cnf(f_8_3,plain,
~ contains_slb(create_slb,U_16),
inference(clausify,[status(thm)],[f_8_2]) ).
fof(f_9_1,plain,
! [U,V,W,X] :
( ( contains_slb(insert_slb(U,pair(V,X)),W)
| ( V != W
& ~ contains_slb(U,W) ) )
& ( V = W
| contains_slb(U,W)
| ~ contains_slb(insert_slb(U,pair(V,X)),W) ) ),
inference(fof_nnf,[status(thm)],[ax21]) ).
fof(f_9_2,plain,
! [U_20,U_19,U_18,U_17] :
( ( contains_slb(insert_slb(U_20,pair(U_19,U_17)),U_18)
| ( U_19 != U_18
& ~ contains_slb(U_20,U_18) ) )
& ( U_19 = U_18
| contains_slb(U_20,U_18)
| ~ contains_slb(insert_slb(U_20,pair(U_19,U_17)),U_18) ) ),
inference(variable_rename,[status(thm)],[f_9_1]) ).
fof(f_9_3,plain,
( ! [U_28,U_26,U_24] :
( ! [U_22] : contains_slb(insert_slb(U_28,pair(U_26,U_22)),U_24)
| ( U_26 != U_24
& ~ contains_slb(U_28,U_24) ) )
& ! [U_27,U_25,U_23] :
( ! [U_21] : ~ contains_slb(insert_slb(U_27,pair(U_25,U_21)),U_23)
| U_25 = U_23
| contains_slb(U_27,U_23) ) ),
inference(miniscope,[status(thm)],[f_9_2]) ).
cnf(f_9_4,plain,
( ~ contains_slb(insert_slb(U_27,pair(U_25,U_21)),U_23)
| U_25 = U_23
| contains_slb(U_27,U_23) ),
inference(clausify,[status(thm)],[f_9_3]) ).
cnf(f_9_5,plain,
( ~ contains_slb(U_28,U_24)
| contains_slb(insert_slb(U_28,pair(U_26,U_22)),U_24) ),
inference(clausify,[status(thm)],[f_9_3]) ).
cnf(f_9_6,plain,
( U_26 != U_24
| contains_slb(insert_slb(U_28,pair(U_26,U_22)),U_24) ),
inference(clausify,[status(thm)],[f_9_3]) ).
fof(f_10_1,plain,
! [U,V] : ~ pair_in_list(create_slb,U,V),
inference(fof_nnf,[status(thm)],[ax22]) ).
fof(f_10_2,plain,
! [U_30,U_29] : ~ pair_in_list(create_slb,U_30,U_29),
inference(variable_rename,[status(thm)],[f_10_1]) ).
cnf(f_10_3,plain,
~ pair_in_list(create_slb,U_30,U_29),
inference(clausify,[status(thm)],[f_10_2]) ).
fof(f_11_1,plain,
! [U,V,W,X,Y] :
( ( pair_in_list(insert_slb(U,pair(V,X)),W,Y)
| ( ( X != Y
| V != W )
& ~ pair_in_list(U,W,Y) ) )
& ( ( X = Y
& V = W )
| pair_in_list(U,W,Y)
| ~ pair_in_list(insert_slb(U,pair(V,X)),W,Y) ) ),
inference(fof_nnf,[status(thm)],[ax23]) ).
fof(f_11_2,plain,
! [U_35,U_34,U_33,U_32,U_31] :
( ( pair_in_list(insert_slb(U_35,pair(U_34,U_32)),U_33,U_31)
| ( ( U_32 != U_31
| U_34 != U_33 )
& ~ pair_in_list(U_35,U_33,U_31) ) )
& ( ( U_32 = U_31
& U_34 = U_33 )
| pair_in_list(U_35,U_33,U_31)
| ~ pair_in_list(insert_slb(U_35,pair(U_34,U_32)),U_33,U_31) ) ),
inference(variable_rename,[status(thm)],[f_11_1]) ).
fof(f_11_3,plain,
( ! [U_45,U_43,U_41,U_39,U_37] :
( pair_in_list(insert_slb(U_45,pair(U_43,U_39)),U_41,U_37)
| ( ( U_39 != U_37
| U_43 != U_41 )
& ~ pair_in_list(U_45,U_41,U_37) ) )
& ! [U_44,U_42,U_40,U_38,U_36] :
( ( U_38 = U_36
& U_42 = U_40 )
| pair_in_list(U_44,U_40,U_36)
| ~ pair_in_list(insert_slb(U_44,pair(U_42,U_38)),U_40,U_36) ) ),
inference(miniscope,[status(thm)],[f_11_2]) ).
cnf(f_11_4,plain,
( U_42 = U_40
| pair_in_list(U_44,U_40,U_36)
| ~ pair_in_list(insert_slb(U_44,pair(U_42,U_38)),U_40,U_36) ),
inference(clausify,[status(thm)],[f_11_3]) ).
cnf(f_11_5,plain,
( U_38 = U_36
| pair_in_list(U_44,U_40,U_36)
| ~ pair_in_list(insert_slb(U_44,pair(U_42,U_38)),U_40,U_36) ),
inference(clausify,[status(thm)],[f_11_3]) ).
cnf(f_11_6,plain,
( ~ pair_in_list(U_45,U_41,U_37)
| pair_in_list(insert_slb(U_45,pair(U_43,U_39)),U_41,U_37) ),
inference(clausify,[status(thm)],[f_11_3]) ).
cnf(f_11_7,plain,
( U_39 != U_37
| U_43 != U_41
| pair_in_list(insert_slb(U_45,pair(U_43,U_39)),U_41,U_37) ),
inference(clausify,[status(thm)],[f_11_3]) ).
fof(f_12_1,plain,
! [U,V,W] : remove_slb(insert_slb(U,pair(V,W)),V) = U,
inference(fof_nnf,[status(thm)],[ax24]) ).
fof(f_12_2,plain,
! [U_48,U_47,U_46] : remove_slb(insert_slb(U_48,pair(U_47,U_46)),U_47) = U_48,
inference(variable_rename,[status(thm)],[f_12_1]) ).
cnf(f_12_3,plain,
remove_slb(insert_slb(U_48,pair(U_47,U_46)),U_47) = U_48,
inference(clausify,[status(thm)],[f_12_2]) ).
fof(f_13_1,plain,
! [U,V,W,X] :
( remove_slb(insert_slb(U,pair(V,X)),W) = insert_slb(remove_slb(U,W),pair(V,X))
| ~ contains_slb(U,W)
| V = W ),
inference(fof_nnf,[status(thm)],[ax25]) ).
fof(f_13_2,plain,
! [U_52,U_51,U_50,U_49] :
( remove_slb(insert_slb(U_52,pair(U_51,U_49)),U_50) = insert_slb(remove_slb(U_52,U_50),pair(U_51,U_49))
| ~ contains_slb(U_52,U_50)
| U_51 = U_50 ),
inference(variable_rename,[status(thm)],[f_13_1]) ).
fof(f_13_3,plain,
! [U_52,U_51,U_50] :
( ! [U_49] : remove_slb(insert_slb(U_52,pair(U_51,U_49)),U_50) = insert_slb(remove_slb(U_52,U_50),pair(U_51,U_49))
| ~ contains_slb(U_52,U_50)
| U_51 = U_50 ),
inference(miniscope,[status(thm)],[f_13_2]) ).
cnf(f_13_4,plain,
( remove_slb(insert_slb(U_52,pair(U_51,U_49)),U_50) = insert_slb(remove_slb(U_52,U_50),pair(U_51,U_49))
| ~ contains_slb(U_52,U_50)
| U_51 = U_50 ),
inference(clausify,[status(thm)],[f_13_3]) ).
fof(f_14_1,plain,
! [U,V,W] : lookup_slb(insert_slb(U,pair(V,W)),V) = W,
inference(fof_nnf,[status(thm)],[ax26]) ).
fof(f_14_2,plain,
! [U_55,U_54,U_53] : lookup_slb(insert_slb(U_55,pair(U_54,U_53)),U_54) = U_53,
inference(variable_rename,[status(thm)],[f_14_1]) ).
cnf(f_14_3,plain,
lookup_slb(insert_slb(U_55,pair(U_54,U_53)),U_54) = U_53,
inference(clausify,[status(thm)],[f_14_2]) ).
fof(f_15_1,plain,
! [U,V,W,X] :
( lookup_slb(insert_slb(U,pair(V,X)),W) = lookup_slb(U,W)
| ~ contains_slb(U,W)
| V = W ),
inference(fof_nnf,[status(thm)],[ax27]) ).
fof(f_15_2,plain,
! [U_59,U_58,U_57,U_56] :
( lookup_slb(insert_slb(U_59,pair(U_58,U_56)),U_57) = lookup_slb(U_59,U_57)
| ~ contains_slb(U_59,U_57)
| U_58 = U_57 ),
inference(variable_rename,[status(thm)],[f_15_1]) ).
fof(f_15_3,plain,
! [U_59,U_58,U_57] :
( ! [U_56] : lookup_slb(insert_slb(U_59,pair(U_58,U_56)),U_57) = lookup_slb(U_59,U_57)
| ~ contains_slb(U_59,U_57)
| U_58 = U_57 ),
inference(miniscope,[status(thm)],[f_15_2]) ).
cnf(f_15_4,plain,
( lookup_slb(insert_slb(U_59,pair(U_58,U_56)),U_57) = lookup_slb(U_59,U_57)
| ~ contains_slb(U_59,U_57)
| U_58 = U_57 ),
inference(clausify,[status(thm)],[f_15_3]) ).
fof(f_16_1,plain,
! [U] : update_slb(create_slb,U) = create_slb,
inference(fof_nnf,[status(thm)],[ax28]) ).
fof(f_16_2,plain,
! [U_60] : update_slb(create_slb,U_60) = create_slb,
inference(variable_rename,[status(thm)],[f_16_1]) ).
cnf(f_16_3,plain,
update_slb(create_slb,U_60) = create_slb,
inference(clausify,[status(thm)],[f_16_2]) ).
fof(f_17_1,plain,
! [U,V,W,X] :
( update_slb(insert_slb(U,pair(V,X)),W) = insert_slb(update_slb(U,W),pair(V,W))
| ~ strictly_less_than(X,W) ),
inference(fof_nnf,[status(thm)],[ax29]) ).
fof(f_17_2,plain,
! [U_64,U_63,U_62,U_61] :
( update_slb(insert_slb(U_64,pair(U_63,U_61)),U_62) = insert_slb(update_slb(U_64,U_62),pair(U_63,U_62))
| ~ strictly_less_than(U_61,U_62) ),
inference(variable_rename,[status(thm)],[f_17_1]) ).
cnf(f_17_3,plain,
( update_slb(insert_slb(U_64,pair(U_63,U_61)),U_62) = insert_slb(update_slb(U_64,U_62),pair(U_63,U_62))
| ~ strictly_less_than(U_61,U_62) ),
inference(clausify,[status(thm)],[f_17_2]) ).
fof(f_18_1,plain,
! [U,V,W,X] :
( update_slb(insert_slb(U,pair(V,X)),W) = insert_slb(update_slb(U,W),pair(V,X))
| ~ less_than(W,X) ),
inference(fof_nnf,[status(thm)],[ax30]) ).
fof(f_18_2,plain,
! [U_68,U_67,U_66,U_65] :
( update_slb(insert_slb(U_68,pair(U_67,U_65)),U_66) = insert_slb(update_slb(U_68,U_66),pair(U_67,U_65))
| ~ less_than(U_66,U_65) ),
inference(variable_rename,[status(thm)],[f_18_1]) ).
cnf(f_18_3,plain,
( update_slb(insert_slb(U_68,pair(U_67,U_65)),U_66) = insert_slb(update_slb(U_68,U_66),pair(U_67,U_65))
| ~ less_than(U_66,U_65) ),
inference(clausify,[status(thm)],[f_18_2]) ).
fof(f_19_1,plain,
! [U] : succ_cpq(U,U),
inference(fof_nnf,[status(thm)],[ax31]) ).
fof(f_19_2,plain,
! [U_69] : succ_cpq(U_69,U_69),
inference(variable_rename,[status(thm)],[f_19_1]) ).
cnf(f_19_3,plain,
succ_cpq(U_69,U_69),
inference(clausify,[status(thm)],[f_19_2]) ).
fof(f_20_1,plain,
! [U,V,W] :
( succ_cpq(U,insert_cpq(V,W))
| ~ succ_cpq(U,V) ),
inference(fof_nnf,[status(thm)],[ax32]) ).
fof(f_20_2,plain,
! [U_72,U_71,U_70] :
( succ_cpq(U_72,insert_cpq(U_71,U_70))
| ~ succ_cpq(U_72,U_71) ),
inference(variable_rename,[status(thm)],[f_20_1]) ).
fof(f_20_3,plain,
! [U_72,U_71] :
( ! [U_70] : succ_cpq(U_72,insert_cpq(U_71,U_70))
| ~ succ_cpq(U_72,U_71) ),
inference(miniscope,[status(thm)],[f_20_2]) ).
cnf(f_20_4,plain,
( succ_cpq(U_72,insert_cpq(U_71,U_70))
| ~ succ_cpq(U_72,U_71) ),
inference(clausify,[status(thm)],[f_20_3]) ).
fof(f_21_1,plain,
! [U,V,W] :
( succ_cpq(U,remove_cpq(V,W))
| ~ succ_cpq(U,V) ),
inference(fof_nnf,[status(thm)],[ax33]) ).
fof(f_21_2,plain,
! [U_75,U_74,U_73] :
( succ_cpq(U_75,remove_cpq(U_74,U_73))
| ~ succ_cpq(U_75,U_74) ),
inference(variable_rename,[status(thm)],[f_21_1]) ).
fof(f_21_3,plain,
! [U_75,U_74] :
( ! [U_73] : succ_cpq(U_75,remove_cpq(U_74,U_73))
| ~ succ_cpq(U_75,U_74) ),
inference(miniscope,[status(thm)],[f_21_2]) ).
cnf(f_21_4,plain,
( succ_cpq(U_75,remove_cpq(U_74,U_73))
| ~ succ_cpq(U_75,U_74) ),
inference(clausify,[status(thm)],[f_21_3]) ).
fof(f_22_1,plain,
! [U,V] :
( succ_cpq(U,findmin_cpq_eff(V))
| ~ succ_cpq(U,V) ),
inference(fof_nnf,[status(thm)],[ax34]) ).
fof(f_22_2,plain,
! [U_77,U_76] :
( succ_cpq(U_77,findmin_cpq_eff(U_76))
| ~ succ_cpq(U_77,U_76) ),
inference(variable_rename,[status(thm)],[f_22_1]) ).
cnf(f_22_3,plain,
( succ_cpq(U_77,findmin_cpq_eff(U_76))
| ~ succ_cpq(U_77,U_76) ),
inference(clausify,[status(thm)],[f_22_2]) ).
fof(f_23_1,plain,
! [U,V] :
( succ_cpq(U,removemin_cpq_eff(V))
| ~ succ_cpq(U,V) ),
inference(fof_nnf,[status(thm)],[ax35]) ).
fof(f_23_2,plain,
! [U_79,U_78] :
( succ_cpq(U_79,removemin_cpq_eff(U_78))
| ~ succ_cpq(U_79,U_78) ),
inference(variable_rename,[status(thm)],[f_23_1]) ).
cnf(f_23_3,plain,
( succ_cpq(U_79,removemin_cpq_eff(U_78))
| ~ succ_cpq(U_79,U_78) ),
inference(clausify,[status(thm)],[f_23_2]) ).
fof(f_24_1,plain,
! [U,V] : check_cpq(triple(U,create_slb,V)),
inference(fof_nnf,[status(thm)],[ax36]) ).
fof(f_24_2,plain,
! [U_81,U_80] : check_cpq(triple(U_81,create_slb,U_80)),
inference(variable_rename,[status(thm)],[f_24_1]) ).
cnf(f_24_3,plain,
check_cpq(triple(U_81,create_slb,U_80)),
inference(clausify,[status(thm)],[f_24_2]) ).
fof(f_25_1,plain,
! [U,V,W,X,Y] :
( ( ( check_cpq(triple(U,insert_slb(V,pair(X,Y)),W))
| ~ check_cpq(triple(U,V,W)) )
& ( check_cpq(triple(U,V,W))
| ~ check_cpq(triple(U,insert_slb(V,pair(X,Y)),W)) ) )
| ~ less_than(Y,X) ),
inference(fof_nnf,[status(thm)],[ax37]) ).
fof(f_25_2,plain,
! [U_86,U_85,U_84,U_83,U_82] :
( ( ( check_cpq(triple(U_86,insert_slb(U_85,pair(U_83,U_82)),U_84))
| ~ check_cpq(triple(U_86,U_85,U_84)) )
& ( check_cpq(triple(U_86,U_85,U_84))
| ~ check_cpq(triple(U_86,insert_slb(U_85,pair(U_83,U_82)),U_84)) ) )
| ~ less_than(U_82,U_83) ),
inference(variable_rename,[status(thm)],[f_25_1]) ).
cnf(f_25_3,plain,
( check_cpq(triple(U_86,U_85,U_84))
| ~ check_cpq(triple(U_86,insert_slb(U_85,pair(U_83,U_82)),U_84))
| ~ less_than(U_82,U_83) ),
inference(clausify,[status(thm)],[f_25_2]) ).
cnf(f_25_4,plain,
( check_cpq(triple(U_86,insert_slb(U_85,pair(U_83,U_82)),U_84))
| ~ check_cpq(triple(U_86,U_85,U_84))
| ~ less_than(U_82,U_83) ),
inference(clausify,[status(thm)],[f_25_2]) ).
fof(f_26_1,plain,
! [U,V,W,X,Y] :
( ( ( check_cpq(triple(U,insert_slb(V,pair(X,Y)),W))
| ~ $false )
& ( $false
| ~ check_cpq(triple(U,insert_slb(V,pair(X,Y)),W)) ) )
| ~ strictly_less_than(X,Y) ),
inference(fof_nnf,[status(thm)],[ax38]) ).
fof(f_26_2,plain,
! [U_91,U_90,U_89,U_88,U_87] :
( ( ( check_cpq(triple(U_91,insert_slb(U_90,pair(U_88,U_87)),U_89))
| ~ $false )
& ( $false
| ~ check_cpq(triple(U_91,insert_slb(U_90,pair(U_88,U_87)),U_89)) ) )
| ~ strictly_less_than(U_88,U_87) ),
inference(variable_rename,[status(thm)],[f_26_1]) ).
cnf(f_26_3,plain,
( $false
| ~ check_cpq(triple(U_91,insert_slb(U_90,pair(U_88,U_87)),U_89))
| ~ strictly_less_than(U_88,U_87) ),
inference(clausify,[status(thm)],[f_26_2]) ).
cnf(f_26_4,plain,
( check_cpq(triple(U_91,insert_slb(U_90,pair(U_88,U_87)),U_89))
| ~ $false
| ~ strictly_less_than(U_88,U_87) ),
inference(clausify,[status(thm)],[f_26_2]) ).
fof(f_27_1,plain,
! [U,V,W,X] :
( ( contains_cpq(triple(U,V,W),X)
| ~ contains_slb(V,X) )
& ( contains_slb(V,X)
| ~ contains_cpq(triple(U,V,W),X) ) ),
inference(fof_nnf,[status(thm)],[ax39]) ).
fof(f_27_2,plain,
! [U_95,U_94,U_93,U_92] :
( ( contains_cpq(triple(U_95,U_94,U_93),U_92)
| ~ contains_slb(U_94,U_92) )
& ( contains_slb(U_94,U_92)
| ~ contains_cpq(triple(U_95,U_94,U_93),U_92) ) ),
inference(variable_rename,[status(thm)],[f_27_1]) ).
fof(f_27_3,plain,
( ! [U_103,U_101,U_99,U_97] :
( contains_cpq(triple(U_103,U_101,U_99),U_97)
| ~ contains_slb(U_101,U_97) )
& ! [U_102,U_100,U_98,U_96] :
( contains_slb(U_100,U_96)
| ~ contains_cpq(triple(U_102,U_100,U_98),U_96) ) ),
inference(miniscope,[status(thm)],[f_27_2]) ).
cnf(f_27_4,plain,
( contains_slb(U_100,U_96)
| ~ contains_cpq(triple(U_102,U_100,U_98),U_96) ),
inference(clausify,[status(thm)],[f_27_3]) ).
cnf(f_27_5,plain,
( contains_cpq(triple(U_103,U_101,U_99),U_97)
| ~ contains_slb(U_101,U_97) ),
inference(clausify,[status(thm)],[f_27_3]) ).
fof(f_28_1,plain,
! [U,V] :
( ( ok(triple(U,V,bad))
| ~ $false )
& ( $false
| ~ ok(triple(U,V,bad)) ) ),
inference(fof_nnf,[status(thm)],[ax40]) ).
fof(f_28_2,plain,
! [U_105,U_104] :
( ( ok(triple(U_105,U_104,bad))
| ~ $false )
& ( $false
| ~ ok(triple(U_105,U_104,bad)) ) ),
inference(variable_rename,[status(thm)],[f_28_1]) ).
fof(f_28_3,plain,
( ( ! [U_109,U_107] : ok(triple(U_109,U_107,bad))
| ~ $false )
& ( ! [U_108,U_106] : ~ ok(triple(U_108,U_106,bad))
| $false ) ),
inference(miniscope,[status(thm)],[f_28_2]) ).
cnf(f_28_4,plain,
( ~ ok(triple(U_108,U_106,bad))
| $false ),
inference(clausify,[status(thm)],[f_28_3]) ).
cnf(f_28_5,plain,
( ok(triple(U_109,U_107,bad))
| ~ $false ),
inference(clausify,[status(thm)],[f_28_3]) ).
fof(f_29_1,plain,
! [U,V,W] :
( W = bad
| ok(triple(U,V,W)) ),
inference(fof_nnf,[status(thm)],[ax41]) ).
fof(f_29_2,plain,
! [U_112,U_111,U_110] :
( U_110 = bad
| ok(triple(U_112,U_111,U_110)) ),
inference(variable_rename,[status(thm)],[f_29_1]) ).
cnf(f_29_3,plain,
( U_110 = bad
| ok(triple(U_112,U_111,U_110)) ),
inference(clausify,[status(thm)],[f_29_2]) ).
fof(f_30_1,plain,
! [U,V,W,X] : insert_cpq(triple(U,V,W),X) = triple(insert_pqp(U,X),insert_slb(V,pair(X,bottom)),W),
inference(fof_nnf,[status(thm)],[ax42]) ).
fof(f_30_2,plain,
! [U_116,U_115,U_114,U_113] : insert_cpq(triple(U_116,U_115,U_114),U_113) = triple(insert_pqp(U_116,U_113),insert_slb(U_115,pair(U_113,bottom)),U_114),
inference(variable_rename,[status(thm)],[f_30_1]) ).
cnf(f_30_3,plain,
insert_cpq(triple(U_116,U_115,U_114),U_113) = triple(insert_pqp(U_116,U_113),insert_slb(U_115,pair(U_113,bottom)),U_114),
inference(clausify,[status(thm)],[f_30_2]) ).
fof(f_31_1,plain,
! [U,V,W,X] :
( remove_cpq(triple(U,V,W),X) = triple(U,V,bad)
| contains_slb(V,X) ),
inference(fof_nnf,[status(thm)],[ax43]) ).
fof(f_31_2,plain,
! [U_120,U_119,U_118,U_117] :
( remove_cpq(triple(U_120,U_119,U_118),U_117) = triple(U_120,U_119,bad)
| contains_slb(U_119,U_117) ),
inference(variable_rename,[status(thm)],[f_31_1]) ).
cnf(f_31_3,plain,
( remove_cpq(triple(U_120,U_119,U_118),U_117) = triple(U_120,U_119,bad)
| contains_slb(U_119,U_117) ),
inference(clausify,[status(thm)],[f_31_2]) ).
fof(f_32_1,plain,
! [U,V,W,X] :
( remove_cpq(triple(U,V,W),X) = triple(remove_pqp(U,X),remove_slb(V,X),W)
| ~ less_than(lookup_slb(V,X),X)
| ~ contains_slb(V,X) ),
inference(fof_nnf,[status(thm)],[ax44]) ).
fof(f_32_2,plain,
! [U_124,U_123,U_122,U_121] :
( remove_cpq(triple(U_124,U_123,U_122),U_121) = triple(remove_pqp(U_124,U_121),remove_slb(U_123,U_121),U_122)
| ~ less_than(lookup_slb(U_123,U_121),U_121)
| ~ contains_slb(U_123,U_121) ),
inference(variable_rename,[status(thm)],[f_32_1]) ).
cnf(f_32_3,plain,
( remove_cpq(triple(U_124,U_123,U_122),U_121) = triple(remove_pqp(U_124,U_121),remove_slb(U_123,U_121),U_122)
| ~ less_than(lookup_slb(U_123,U_121),U_121)
| ~ contains_slb(U_123,U_121) ),
inference(clausify,[status(thm)],[f_32_2]) ).
fof(f_33_1,plain,
! [U,V,W,X] :
( remove_cpq(triple(U,V,W),X) = triple(remove_pqp(U,X),remove_slb(V,X),bad)
| ~ strictly_less_than(X,lookup_slb(V,X))
| ~ contains_slb(V,X) ),
inference(fof_nnf,[status(thm)],[ax45]) ).
fof(f_33_2,plain,
! [U_128,U_127,U_126,U_125] :
( remove_cpq(triple(U_128,U_127,U_126),U_125) = triple(remove_pqp(U_128,U_125),remove_slb(U_127,U_125),bad)
| ~ strictly_less_than(U_125,lookup_slb(U_127,U_125))
| ~ contains_slb(U_127,U_125) ),
inference(variable_rename,[status(thm)],[f_33_1]) ).
cnf(f_33_3,plain,
( remove_cpq(triple(U_128,U_127,U_126),U_125) = triple(remove_pqp(U_128,U_125),remove_slb(U_127,U_125),bad)
| ~ strictly_less_than(U_125,lookup_slb(U_127,U_125))
| ~ contains_slb(U_127,U_125) ),
inference(clausify,[status(thm)],[f_33_2]) ).
fof(f_34_1,plain,
! [U,V] : findmin_cpq_eff(triple(U,create_slb,V)) = triple(U,create_slb,bad),
inference(fof_nnf,[status(thm)],[ax46]) ).
fof(f_34_2,plain,
! [U_130,U_129] : findmin_cpq_eff(triple(U_130,create_slb,U_129)) = triple(U_130,create_slb,bad),
inference(variable_rename,[status(thm)],[f_34_1]) ).
cnf(f_34_3,plain,
findmin_cpq_eff(triple(U_130,create_slb,U_129)) = triple(U_130,create_slb,bad),
inference(clausify,[status(thm)],[f_34_2]) ).
fof(f_35_1,plain,
! [U,V,W,X] :
( findmin_cpq_eff(triple(U,V,W)) = triple(U,update_slb(V,findmin_pqp_res(U)),bad)
| contains_slb(V,findmin_pqp_res(U))
| V = create_slb ),
inference(fof_nnf,[status(thm)],[ax47]) ).
fof(f_35_2,plain,
! [U_134,U_133,U_132,U_131] :
( findmin_cpq_eff(triple(U_134,U_133,U_132)) = triple(U_134,update_slb(U_133,findmin_pqp_res(U_134)),bad)
| contains_slb(U_133,findmin_pqp_res(U_134))
| U_133 = create_slb ),
inference(variable_rename,[status(thm)],[f_35_1]) ).
fof(f_35_3,plain,
! [U_134,U_133] :
( ! [U_132] : findmin_cpq_eff(triple(U_134,U_133,U_132)) = triple(U_134,update_slb(U_133,findmin_pqp_res(U_134)),bad)
| contains_slb(U_133,findmin_pqp_res(U_134))
| U_133 = create_slb ),
inference(miniscope,[status(thm)],[f_35_2]) ).
cnf(f_35_4,plain,
( findmin_cpq_eff(triple(U_134,U_133,U_132)) = triple(U_134,update_slb(U_133,findmin_pqp_res(U_134)),bad)
| contains_slb(U_133,findmin_pqp_res(U_134))
| U_133 = create_slb ),
inference(clausify,[status(thm)],[f_35_3]) ).
fof(f_36_1,plain,
! [U,V,W,X] :
( findmin_cpq_eff(triple(U,V,W)) = triple(U,update_slb(V,findmin_pqp_res(U)),bad)
| ~ strictly_less_than(findmin_pqp_res(U),lookup_slb(V,findmin_pqp_res(U)))
| ~ contains_slb(V,findmin_pqp_res(U))
| V = create_slb ),
inference(fof_nnf,[status(thm)],[ax48]) ).
fof(f_36_2,plain,
! [U_138,U_137,U_136,U_135] :
( findmin_cpq_eff(triple(U_138,U_137,U_136)) = triple(U_138,update_slb(U_137,findmin_pqp_res(U_138)),bad)
| ~ strictly_less_than(findmin_pqp_res(U_138),lookup_slb(U_137,findmin_pqp_res(U_138)))
| ~ contains_slb(U_137,findmin_pqp_res(U_138))
| U_137 = create_slb ),
inference(variable_rename,[status(thm)],[f_36_1]) ).
fof(f_36_3,plain,
! [U_138,U_137] :
( ! [U_136] : findmin_cpq_eff(triple(U_138,U_137,U_136)) = triple(U_138,update_slb(U_137,findmin_pqp_res(U_138)),bad)
| ~ strictly_less_than(findmin_pqp_res(U_138),lookup_slb(U_137,findmin_pqp_res(U_138)))
| ~ contains_slb(U_137,findmin_pqp_res(U_138))
| U_137 = create_slb ),
inference(miniscope,[status(thm)],[f_36_2]) ).
cnf(f_36_4,plain,
( findmin_cpq_eff(triple(U_138,U_137,U_136)) = triple(U_138,update_slb(U_137,findmin_pqp_res(U_138)),bad)
| ~ strictly_less_than(findmin_pqp_res(U_138),lookup_slb(U_137,findmin_pqp_res(U_138)))
| ~ contains_slb(U_137,findmin_pqp_res(U_138))
| U_137 = create_slb ),
inference(clausify,[status(thm)],[f_36_3]) ).
fof(f_37_1,plain,
! [U,V,W,X] :
( findmin_cpq_eff(triple(U,V,W)) = triple(U,update_slb(V,findmin_pqp_res(U)),W)
| ~ less_than(lookup_slb(V,findmin_pqp_res(U)),findmin_pqp_res(U))
| ~ contains_slb(V,findmin_pqp_res(U))
| V = create_slb ),
inference(fof_nnf,[status(thm)],[ax49]) ).
fof(f_37_2,plain,
! [U_142,U_141,U_140,U_139] :
( findmin_cpq_eff(triple(U_142,U_141,U_140)) = triple(U_142,update_slb(U_141,findmin_pqp_res(U_142)),U_140)
| ~ less_than(lookup_slb(U_141,findmin_pqp_res(U_142)),findmin_pqp_res(U_142))
| ~ contains_slb(U_141,findmin_pqp_res(U_142))
| U_141 = create_slb ),
inference(variable_rename,[status(thm)],[f_37_1]) ).
fof(f_37_3,plain,
! [U_142,U_141] :
( ! [U_140] : findmin_cpq_eff(triple(U_142,U_141,U_140)) = triple(U_142,update_slb(U_141,findmin_pqp_res(U_142)),U_140)
| ~ less_than(lookup_slb(U_141,findmin_pqp_res(U_142)),findmin_pqp_res(U_142))
| ~ contains_slb(U_141,findmin_pqp_res(U_142))
| U_141 = create_slb ),
inference(miniscope,[status(thm)],[f_37_2]) ).
cnf(f_37_4,plain,
( findmin_cpq_eff(triple(U_142,U_141,U_140)) = triple(U_142,update_slb(U_141,findmin_pqp_res(U_142)),U_140)
| ~ less_than(lookup_slb(U_141,findmin_pqp_res(U_142)),findmin_pqp_res(U_142))
| ~ contains_slb(U_141,findmin_pqp_res(U_142))
| U_141 = create_slb ),
inference(clausify,[status(thm)],[f_37_3]) ).
fof(f_38_1,plain,
! [U,V] : findmin_cpq_res(triple(U,create_slb,V)) = bottom,
inference(fof_nnf,[status(thm)],[ax50]) ).
fof(f_38_2,plain,
! [U_144,U_143] : findmin_cpq_res(triple(U_144,create_slb,U_143)) = bottom,
inference(variable_rename,[status(thm)],[f_38_1]) ).
cnf(f_38_3,plain,
findmin_cpq_res(triple(U_144,create_slb,U_143)) = bottom,
inference(clausify,[status(thm)],[f_38_2]) ).
fof(f_39_1,plain,
! [U,V,W,X] :
( findmin_cpq_res(triple(U,V,W)) = findmin_pqp_res(U)
| V = create_slb ),
inference(fof_nnf,[status(thm)],[ax51]) ).
fof(f_39_2,plain,
! [U_148,U_147,U_146,U_145] :
( findmin_cpq_res(triple(U_148,U_147,U_146)) = findmin_pqp_res(U_148)
| U_147 = create_slb ),
inference(variable_rename,[status(thm)],[f_39_1]) ).
fof(f_39_3,plain,
! [U_148,U_147] :
( ! [U_146] : findmin_cpq_res(triple(U_148,U_147,U_146)) = findmin_pqp_res(U_148)
| U_147 = create_slb ),
inference(miniscope,[status(thm)],[f_39_2]) ).
cnf(f_39_4,plain,
( findmin_cpq_res(triple(U_148,U_147,U_146)) = findmin_pqp_res(U_148)
| U_147 = create_slb ),
inference(clausify,[status(thm)],[f_39_3]) ).
fof(f_40_1,plain,
! [U] : removemin_cpq_eff(U) = remove_cpq(findmin_cpq_eff(U),findmin_cpq_res(U)),
inference(fof_nnf,[status(thm)],[ax52]) ).
fof(f_40_2,plain,
! [U_149] : removemin_cpq_eff(U_149) = remove_cpq(findmin_cpq_eff(U_149),findmin_cpq_res(U_149)),
inference(variable_rename,[status(thm)],[f_40_1]) ).
cnf(f_40_3,plain,
removemin_cpq_eff(U_149) = remove_cpq(findmin_cpq_eff(U_149),findmin_cpq_res(U_149)),
inference(clausify,[status(thm)],[f_40_2]) ).
fof(f_41_1,plain,
! [U] : removemin_cpq_res(U) = findmin_cpq_res(U),
inference(fof_nnf,[status(thm)],[ax53]) ).
fof(f_41_2,plain,
! [U_150] : removemin_cpq_res(U_150) = findmin_cpq_res(U_150),
inference(variable_rename,[status(thm)],[f_41_1]) ).
cnf(f_41_3,plain,
removemin_cpq_res(U_150) = findmin_cpq_res(U_150),
inference(clausify,[status(thm)],[f_41_2]) ).
fof(f_42_1,plain,
! [U,V,W] :
( ( less_than(lookup_slb(V,findmin_pqp_res(U)),findmin_pqp_res(U))
& contains_slb(V,findmin_pqp_res(U))
& V != create_slb )
| ~ ok(findmin_cpq_eff(triple(U,V,W))) ),
inference(fof_nnf,[status(thm)],[l9_l10]) ).
fof(f_42_2,plain,
! [U_153,U_152,U_151] :
( ( less_than(lookup_slb(U_152,findmin_pqp_res(U_153)),findmin_pqp_res(U_153))
& contains_slb(U_152,findmin_pqp_res(U_153))
& U_152 != create_slb )
| ~ ok(findmin_cpq_eff(triple(U_153,U_152,U_151))) ),
inference(variable_rename,[status(thm)],[f_42_1]) ).
fof(f_42_3,plain,
! [U_153,U_152] :
( ! [U_151] : ~ ok(findmin_cpq_eff(triple(U_153,U_152,U_151)))
| ( less_than(lookup_slb(U_152,findmin_pqp_res(U_153)),findmin_pqp_res(U_153))
& contains_slb(U_152,findmin_pqp_res(U_153))
& U_152 != create_slb ) ),
inference(miniscope,[status(thm)],[f_42_2]) ).
cnf(f_42_4,plain,
( U_152 != create_slb
| ~ ok(findmin_cpq_eff(triple(U_153,U_152,U_151))) ),
inference(clausify,[status(thm)],[f_42_3]) ).
cnf(f_42_5,plain,
( contains_slb(U_152,findmin_pqp_res(U_153))
| ~ ok(findmin_cpq_eff(triple(U_153,U_152,U_151))) ),
inference(clausify,[status(thm)],[f_42_3]) ).
cnf(f_42_6,plain,
( less_than(lookup_slb(U_152,findmin_pqp_res(U_153)),findmin_pqp_res(U_153))
| ~ ok(findmin_cpq_eff(triple(U_153,U_152,U_151))) ),
inference(clausify,[status(thm)],[f_42_3]) ).
fof(f_43_1,negated_conjecture,
~ ! [U,V,W] :
( ~ contains_cpq(triple(U,V,W),findmin_cpq_res(triple(U,V,W)))
=> ~ ok(findmin_cpq_eff(triple(U,V,W))) ),
inference(negate,[status(cth)],[l9_co]) ).
fof(f_43_2,negated_conjecture,
? [U,V,W] :
( ok(findmin_cpq_eff(triple(U,V,W)))
& ~ contains_cpq(triple(U,V,W),findmin_cpq_res(triple(U,V,W))) ),
inference(fof_nnf,[status(thm)],[f_43_1]) ).
fof(f_43_3,negated_conjecture,
? [U_156,U_155,U_154] :
( ok(findmin_cpq_eff(triple(U_156,U_155,U_154)))
& ~ contains_cpq(triple(U_156,U_155,U_154),findmin_cpq_res(triple(U_156,U_155,U_154))) ),
inference(variable_rename,[status(thm)],[f_43_2]) ).
fof(f_43_4,negated_conjecture,
? [U_155,U_154] :
( ok(findmin_cpq_eff(triple(sK1,U_155,U_154)))
& ~ contains_cpq(triple(sK1,U_155,U_154),findmin_cpq_res(triple(sK1,U_155,U_154))) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(U_156,sK1)],[f_43_3]) ).
fof(f_43_5,negated_conjecture,
? [U_154] :
( ok(findmin_cpq_eff(triple(sK1,sK2,U_154)))
& ~ contains_cpq(triple(sK1,sK2,U_154),findmin_cpq_res(triple(sK1,sK2,U_154))) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2]),skolemize(U_155,sK2)],[f_43_4]) ).
fof(f_43_6,negated_conjecture,
( ok(findmin_cpq_eff(triple(sK1,sK2,sK3)))
& ~ contains_cpq(triple(sK1,sK2,sK3),findmin_cpq_res(triple(sK1,sK2,sK3))) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3]),skolemize(U_154,sK3)],[f_43_5]) ).
cnf(f_43_7,negated_conjecture,
~ contains_cpq(triple(sK1,sK2,sK3),findmin_cpq_res(triple(sK1,sK2,sK3))),
inference(clausify,[status(thm)],[f_43_6]) ).
cnf(f_43_8,negated_conjecture,
ok(findmin_cpq_eff(triple(sK1,sK2,sK3))),
inference(clausify,[status(thm)],[f_43_6]) ).
cnf(f_26_3_simplified,plain,
( ~ check_cpq(triple(U_91,insert_slb(U_90,pair(U_88,U_87)),U_89))
| ~ strictly_less_than(U_88,U_87) ),
inference(simplify_clause,[status(thm)],[f_26_3]) ).
cnf(f_26_4_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_26_4]) ).
cnf(f_28_4_simplified,plain,
~ ok(triple(U_108,U_106,bad)),
inference(simplify_clause,[status(thm)],[f_28_4]) ).
cnf(f_28_5_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_28_5]) ).
cnf(equality_1,axiom,
Eq_x_0 = Eq_x_0,
theory(equality,[reflexivity]) ).
cnf(equality_2,axiom,
( Eq_x_1 = Eq_x_0
| Eq_x_0 != Eq_x_1 ),
theory(equality,[symmetry]) ).
cnf(equality_3,axiom,
( Eq_x_0 = Eq_x_2
| Eq_x_1 != Eq_x_2
| Eq_x_0 != Eq_x_1 ),
theory(equality,[transitivity]) ).
cnf(equality_4,axiom,
( pair(Eq_x_0,Eq_x_1) = pair(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_5,axiom,
( insert_slb(Eq_x_0,Eq_x_1) = insert_slb(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_6,axiom,
( remove_slb(Eq_x_0,Eq_x_1) = remove_slb(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_7,axiom,
( lookup_slb(Eq_x_0,Eq_x_1) = lookup_slb(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_8,axiom,
( update_slb(Eq_x_0,Eq_x_1) = update_slb(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_9,axiom,
( insert_cpq(Eq_x_0,Eq_x_1) = insert_cpq(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_10,axiom,
( remove_cpq(Eq_x_0,Eq_x_1) = remove_cpq(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_11,axiom,
( findmin_cpq_eff(Eq_x_0) = findmin_cpq_eff(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_12,axiom,
( removemin_cpq_eff(Eq_x_0) = removemin_cpq_eff(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_13,axiom,
( triple(Eq_x_0,Eq_x_1,Eq_x_2) = triple(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_14,axiom,
( insert_pqp(Eq_x_0,Eq_x_1) = insert_pqp(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_15,axiom,
( remove_pqp(Eq_x_0,Eq_x_1) = remove_pqp(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_16,axiom,
( findmin_pqp_res(Eq_x_0) = findmin_pqp_res(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_17,axiom,
( findmin_cpq_res(Eq_x_0) = findmin_cpq_res(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_18,axiom,
( removemin_cpq_res(Eq_x_0) = removemin_cpq_res(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_19,axiom,
( less_than(Eq_y_0,Eq_y_1)
| ~ less_than(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_20,axiom,
( strictly_less_than(Eq_y_0,Eq_y_1)
| ~ strictly_less_than(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_21,axiom,
( isnonempty_slb(Eq_y_0)
| ~ isnonempty_slb(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_22,axiom,
( contains_slb(Eq_y_0,Eq_y_1)
| ~ contains_slb(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_23,axiom,
( pair_in_list(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ pair_in_list(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_24,axiom,
( succ_cpq(Eq_y_0,Eq_y_1)
| ~ succ_cpq(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_25,axiom,
( check_cpq(Eq_y_0)
| ~ check_cpq(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_26,axiom,
( contains_cpq(Eq_y_0,Eq_y_1)
| ~ contains_cpq(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_27,axiom,
( ok(Eq_y_0)
| ~ ok(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(sat_proved,plain,
$false,
inference(cadical,[status(thm)],[]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SWV373+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.03 This is a FOF_THM_RFO_SEQ problem
% 0.00/0.04 % Command : /export/starexec/sandbox/solver/bin/connect++ --verbosity 1 --no-colour --tptp-proof --schedule default --timeout 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/5.57 % Computer : n006.cluster.edu
% 0.08/5.57 % Model : x86_64 x86_64
% 0.08/5.57 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/5.57 % Memory : 8046.5625MB
% 0.08/5.57 % OS : Linux 6.8.0-71-generic
% 0.08/5.57 % CPULimit : 300
% 0.08/5.57 % WCLimit : 300
% 0.08/5.57 % DateTime : Sun Sep 20 03:28:05 UTC 2026
% 0.08/5.57 % CPUTime :
% 175.81/181.39 % SZS status Theorem for theBenchmark
% 175.81/181.39 % SZS output start Proof for theBenchmark
% See solution above
%------------------------------------------------------------------------------