%------------------------------------------------------------------------------
% File : ConnectPP---0.7.2
% Problem : SWV417+1 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/connect++ --verbosity 1 --no-colour --tptp-proof --schedule default --timeout 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n004.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 09:03:37 AM UTC 2026
% Result : Theorem 31.27s 31.54s
% Output : Proof 31.27s
% 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(ax6,axiom,
~ isnonempty_pq(create_pq),
file('SWV007+1.ax',ax6) ).
fof(ax7,axiom,
! [U,V] : isnonempty_pq(insert_pq(U,V)),
file('SWV007+1.ax',ax7) ).
fof(ax8,axiom,
! [U] : ~ contains_pq(create_pq,U),
file('SWV007+1.ax',ax8) ).
fof(ax9,axiom,
! [U,V,W] :
( contains_pq(insert_pq(U,V),W)
<=> ( V = W
| contains_pq(U,W) ) ),
file('SWV007+1.ax',ax9) ).
fof(ax10,axiom,
! [U,V] :
( issmallestelement_pq(U,V)
<=> ! [W] :
( contains_pq(U,W)
=> less_than(V,W) ) ),
file('SWV007+1.ax',ax10) ).
fof(ax11,axiom,
! [U,V] : remove_pq(insert_pq(U,V),V) = U,
file('SWV007+1.ax',ax11) ).
fof(ax12,axiom,
! [U,V,W] :
( ( V != W
& contains_pq(U,W) )
=> remove_pq(insert_pq(U,V),W) = insert_pq(remove_pq(U,W),V) ),
file('SWV007+1.ax',ax12) ).
fof(ax13,axiom,
! [U,V] :
( ( issmallestelement_pq(U,V)
& contains_pq(U,V) )
=> findmin_pq_eff(U,V) = U ),
file('SWV007+1.ax',ax13) ).
fof(ax14,axiom,
! [U,V] :
( ( issmallestelement_pq(U,V)
& contains_pq(U,V) )
=> findmin_pq_res(U,V) = V ),
file('SWV007+1.ax',ax14) ).
fof(ax15,axiom,
! [U,V] :
( ( issmallestelement_pq(U,V)
& contains_pq(U,V) )
=> removemin_pq_eff(U,V) = remove_pq(U,V) ),
file('SWV007+1.ax',ax15) ).
fof(ax16,axiom,
! [U,V] :
( ( issmallestelement_pq(U,V)
& contains_pq(U,V) )
=> removemin_pq_res(U,V) = V ),
file('SWV007+1.ax',ax16) ).
fof(ax17,axiom,
! [U,V,W] : insert_pq(insert_pq(U,V),W) = insert_pq(insert_pq(U,W),V),
file('SWV007+1.ax',ax17) ).
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(ax54,axiom,
! [U,V] : i(triple(U,create_slb,V)) = create_pq,
file('SWV007+4.ax',ax54) ).
fof(ax55,axiom,
! [U,V,W,X,Y] : i(triple(U,insert_slb(V,pair(X,Y)),W)) = insert_pq(i(triple(U,V,W)),X),
file('SWV007+4.ax',ax55) ).
fof(ax56,axiom,
! [U,V] :
( pi_sharp_remove(U,V)
<=> contains_pq(U,V) ),
file('SWV007+4.ax',ax56) ).
fof(ax57,axiom,
! [U,V] :
( pi_remove(U,V)
<=> pi_sharp_remove(i(U),V) ),
file('SWV007+4.ax',ax57) ).
fof(ax58,axiom,
! [U,V] :
( pi_sharp_find_min(U,V)
<=> ( issmallestelement_pq(U,V)
& contains_pq(U,V) ) ),
file('SWV007+4.ax',ax58) ).
fof(ax59,axiom,
! [U] :
( pi_find_min(U)
<=> ? [V] : pi_sharp_find_min(i(U),V) ),
file('SWV007+4.ax',ax59) ).
fof(ax60,axiom,
! [U,V] :
( pi_sharp_removemin(U,V)
<=> ( issmallestelement_pq(U,V)
& contains_pq(U,V) ) ),
file('SWV007+4.ax',ax60) ).
fof(ax61,axiom,
! [U] :
( pi_removemin(U)
<=> ? [V] : pi_sharp_find_min(i(U),V) ),
file('SWV007+4.ax',ax61) ).
fof(ax62,axiom,
! [U] :
( phi(U)
<=> ? [V] :
( check_cpq(V)
& ok(V)
& succ_cpq(U,V) ) ),
file('SWV007+4.ax',ax62) ).
fof(main4_l7,lemma,
! [U,V,W] :
( phi(findmin_cpq_eff(triple(U,V,W)))
=> pi_sharp_find_min(i(triple(U,V,W)),findmin_cpq_res(triple(U,V,W))) ),
file('theBenchmark.p',main4_l7) ).
fof(co4,conjecture,
! [U,V,W] :
( pi_find_min(triple(U,V,W))
=> ( phi(findmin_cpq_eff(triple(U,V,W)))
=> ? [X] :
( findmin_cpq_res(triple(U,V,W)) = findmin_pq_res(i(triple(U,V,W)),X)
& pi_sharp_find_min(i(triple(U,V,W)),X) ) ) ),
file('theBenchmark.p',co4) ).
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]) ).
fof(f_1_3,plain,
! [U_1,U_2,U_0] :
( less_than(U_2,U_0)
| ~ less_than(U_1,U_0)
| ~ less_than(U_2,U_1) ),
inference(definitional_conversion,[status(esa)],[f_1_2]) ).
cnf(f_1_4,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_3]) ).
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]) ).
fof(f_2_3,plain,
! [U_3,U_4] :
( less_than(U_3,U_4)
| less_than(U_4,U_3) ),
inference(definitional_conversion,[status(esa)],[f_2_2]) ).
cnf(f_2_4,plain,
( less_than(U_3,U_4)
| less_than(U_4,U_3) ),
inference(clausify,[status(thm)],[f_2_3]) ).
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]) ).
fof(f_3_3,plain,
! [U_5] : less_than(U_5,U_5),
inference(definitional_conversion,[status(esa)],[f_3_2]) ).
cnf(f_3_4,plain,
less_than(U_5,U_5),
inference(clausify,[status(thm)],[f_3_3]) ).
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]) ).
fof(f_4_4,plain,
( ! [U_10,U_8] :
( ~ less_than(U_8,U_10)
| ~ sP0(U_10,U_8) )
& ! [U_10,U_8] :
( less_than(U_10,U_8)
| ~ sP0(U_10,U_8) )
& ! [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] :
( sP0(U_10,U_8)
| ~ strictly_less_than(U_10,U_8) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP0])],[f_4_3]) ).
cnf(f_4_5,plain,
( sP0(U_10,U_8)
| ~ strictly_less_than(U_10,U_8) ),
inference(clausify,[status(thm)],[f_4_4]) ).
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_4]) ).
cnf(f_4_7,plain,
( less_than(U_10,U_8)
| ~ sP0(U_10,U_8) ),
inference(clausify,[status(thm)],[f_4_4]) ).
cnf(f_4_8,plain,
( ~ less_than(U_8,U_10)
| ~ sP0(U_10,U_8) ),
inference(clausify,[status(thm)],[f_4_4]) ).
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]) ).
fof(f_5_3,plain,
! [U_12] : less_than(bottom,U_12),
inference(definitional_conversion,[status(esa)],[f_5_2]) ).
cnf(f_5_4,plain,
less_than(bottom,U_12),
inference(clausify,[status(thm)],[f_5_3]) ).
fof(f_6_1,plain,
~ isnonempty_pq(create_pq),
inference(fof_nnf,[status(thm)],[ax6]) ).
fof(f_6_2,plain,
~ isnonempty_pq(create_pq),
inference(definitional_conversion,[status(esa)],[f_6_1]) ).
cnf(f_6_3,plain,
~ isnonempty_pq(create_pq),
inference(clausify,[status(thm)],[f_6_2]) ).
fof(f_7_1,plain,
! [U,V] : isnonempty_pq(insert_pq(U,V)),
inference(fof_nnf,[status(thm)],[ax7]) ).
fof(f_7_2,plain,
! [U_14,U_13] : isnonempty_pq(insert_pq(U_14,U_13)),
inference(variable_rename,[status(thm)],[f_7_1]) ).
fof(f_7_3,plain,
! [U_14,U_13] : isnonempty_pq(insert_pq(U_14,U_13)),
inference(definitional_conversion,[status(esa)],[f_7_2]) ).
cnf(f_7_4,plain,
isnonempty_pq(insert_pq(U_14,U_13)),
inference(clausify,[status(thm)],[f_7_3]) ).
fof(f_8_1,plain,
! [U] : ~ contains_pq(create_pq,U),
inference(fof_nnf,[status(thm)],[ax8]) ).
fof(f_8_2,plain,
! [U_15] : ~ contains_pq(create_pq,U_15),
inference(variable_rename,[status(thm)],[f_8_1]) ).
fof(f_8_3,plain,
! [U_15] : ~ contains_pq(create_pq,U_15),
inference(definitional_conversion,[status(esa)],[f_8_2]) ).
cnf(f_8_4,plain,
~ contains_pq(create_pq,U_15),
inference(clausify,[status(thm)],[f_8_3]) ).
fof(f_9_1,plain,
! [U,V,W] :
( ( contains_pq(insert_pq(U,V),W)
| ( V != W
& ~ contains_pq(U,W) ) )
& ( V = W
| contains_pq(U,W)
| ~ contains_pq(insert_pq(U,V),W) ) ),
inference(fof_nnf,[status(thm)],[ax9]) ).
fof(f_9_2,plain,
! [U_18,U_17,U_16] :
( ( contains_pq(insert_pq(U_18,U_17),U_16)
| ( U_17 != U_16
& ~ contains_pq(U_18,U_16) ) )
& ( U_17 = U_16
| contains_pq(U_18,U_16)
| ~ contains_pq(insert_pq(U_18,U_17),U_16) ) ),
inference(variable_rename,[status(thm)],[f_9_1]) ).
fof(f_9_3,plain,
( ! [U_24,U_22,U_20] :
( contains_pq(insert_pq(U_24,U_22),U_20)
| ( U_22 != U_20
& ~ contains_pq(U_24,U_20) ) )
& ! [U_23,U_21,U_19] :
( U_21 = U_19
| contains_pq(U_23,U_19)
| ~ contains_pq(insert_pq(U_23,U_21),U_19) ) ),
inference(miniscope,[status(thm)],[f_9_2]) ).
fof(f_9_4,plain,
( ! [U_20,U_24,U_22] :
( U_22 != U_20
| ~ sP1(U_20,U_24,U_22) )
& ! [U_20,U_24,U_22] :
( ~ contains_pq(U_24,U_20)
| ~ sP1(U_20,U_24,U_22) )
& ! [U_20,U_24,U_22] :
( contains_pq(insert_pq(U_24,U_22),U_20)
| sP1(U_20,U_24,U_22) )
& ! [U_23,U_21,U_19] :
( U_21 = U_19
| contains_pq(U_23,U_19)
| ~ contains_pq(insert_pq(U_23,U_21),U_19) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP1])],[f_9_3]) ).
cnf(f_9_5,plain,
( U_21 = U_19
| contains_pq(U_23,U_19)
| ~ contains_pq(insert_pq(U_23,U_21),U_19) ),
inference(clausify,[status(thm)],[f_9_4]) ).
cnf(f_9_6,plain,
( contains_pq(insert_pq(U_24,U_22),U_20)
| sP1(U_20,U_24,U_22) ),
inference(clausify,[status(thm)],[f_9_4]) ).
cnf(f_9_7,plain,
( ~ contains_pq(U_24,U_20)
| ~ sP1(U_20,U_24,U_22) ),
inference(clausify,[status(thm)],[f_9_4]) ).
cnf(f_9_8,plain,
( U_22 != U_20
| ~ sP1(U_20,U_24,U_22) ),
inference(clausify,[status(thm)],[f_9_4]) ).
fof(f_10_1,plain,
! [U,V] :
( ( issmallestelement_pq(U,V)
| ? [W] :
( ~ less_than(V,W)
& contains_pq(U,W) ) )
& ( ! [W] :
( less_than(V,W)
| ~ contains_pq(U,W) )
| ~ issmallestelement_pq(U,V) ) ),
inference(fof_nnf,[status(thm)],[ax10]) ).
fof(f_10_2,plain,
! [U_28,U_27] :
( ( issmallestelement_pq(U_28,U_27)
| ? [U_26] :
( ~ less_than(U_27,U_26)
& contains_pq(U_28,U_26) ) )
& ( ! [U_25] :
( less_than(U_27,U_25)
| ~ contains_pq(U_28,U_25) )
| ~ issmallestelement_pq(U_28,U_27) ) ),
inference(variable_rename,[status(thm)],[f_10_1]) ).
fof(f_10_3,plain,
( ! [U_32,U_30] :
( issmallestelement_pq(U_32,U_30)
| ? [U_26] :
( ~ less_than(U_30,U_26)
& contains_pq(U_32,U_26) ) )
& ! [U_31,U_29] :
( ! [U_25] :
( less_than(U_29,U_25)
| ~ contains_pq(U_31,U_25) )
| ~ issmallestelement_pq(U_31,U_29) ) ),
inference(miniscope,[status(thm)],[f_10_2]) ).
fof(f_10_4,plain,
( ! [U_32,U_30] :
( issmallestelement_pq(U_32,U_30)
| ( ~ less_than(U_30,sK1(U_32,U_30))
& contains_pq(U_32,sK1(U_32,U_30)) ) )
& ! [U_31,U_29] :
( ! [U_25] :
( less_than(U_29,U_25)
| ~ contains_pq(U_31,U_25) )
| ~ issmallestelement_pq(U_31,U_29) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(U_26,sK1(U_32,U_30))],[f_10_3]) ).
fof(f_10_5,plain,
( ! [U_30,U_32] :
( ~ less_than(U_30,sK1(U_32,U_30))
| ~ sP2(U_30,U_32) )
& ! [U_30,U_32] :
( contains_pq(U_32,sK1(U_32,U_30))
| ~ sP2(U_30,U_32) )
& ! [U_30,U_32] :
( issmallestelement_pq(U_32,U_30)
| sP2(U_30,U_32) )
& ! [U_25,U_29,U_31] :
( less_than(U_29,U_25)
| ~ contains_pq(U_31,U_25)
| ~ issmallestelement_pq(U_31,U_29) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP2])],[f_10_4]) ).
cnf(f_10_6,plain,
( less_than(U_29,U_25)
| ~ contains_pq(U_31,U_25)
| ~ issmallestelement_pq(U_31,U_29) ),
inference(clausify,[status(thm)],[f_10_5]) ).
cnf(f_10_7,plain,
( issmallestelement_pq(U_32,U_30)
| sP2(U_30,U_32) ),
inference(clausify,[status(thm)],[f_10_5]) ).
cnf(f_10_8,plain,
( contains_pq(U_32,sK1(U_32,U_30))
| ~ sP2(U_30,U_32) ),
inference(clausify,[status(thm)],[f_10_5]) ).
cnf(f_10_9,plain,
( ~ less_than(U_30,sK1(U_32,U_30))
| ~ sP2(U_30,U_32) ),
inference(clausify,[status(thm)],[f_10_5]) ).
fof(f_11_1,plain,
! [U,V] : remove_pq(insert_pq(U,V),V) = U,
inference(fof_nnf,[status(thm)],[ax11]) ).
fof(f_11_2,plain,
! [U_34,U_33] : remove_pq(insert_pq(U_34,U_33),U_33) = U_34,
inference(variable_rename,[status(thm)],[f_11_1]) ).
fof(f_11_3,plain,
! [U_34,U_33] : remove_pq(insert_pq(U_34,U_33),U_33) = U_34,
inference(definitional_conversion,[status(esa)],[f_11_2]) ).
cnf(f_11_4,plain,
remove_pq(insert_pq(U_34,U_33),U_33) = U_34,
inference(clausify,[status(thm)],[f_11_3]) ).
fof(f_12_1,plain,
! [U,V,W] :
( remove_pq(insert_pq(U,V),W) = insert_pq(remove_pq(U,W),V)
| V = W
| ~ contains_pq(U,W) ),
inference(fof_nnf,[status(thm)],[ax12]) ).
fof(f_12_2,plain,
! [U_37,U_36,U_35] :
( remove_pq(insert_pq(U_37,U_36),U_35) = insert_pq(remove_pq(U_37,U_35),U_36)
| U_36 = U_35
| ~ contains_pq(U_37,U_35) ),
inference(variable_rename,[status(thm)],[f_12_1]) ).
fof(f_12_3,plain,
! [U_35,U_36,U_37] :
( remove_pq(insert_pq(U_37,U_36),U_35) = insert_pq(remove_pq(U_37,U_35),U_36)
| U_36 = U_35
| ~ contains_pq(U_37,U_35) ),
inference(definitional_conversion,[status(esa)],[f_12_2]) ).
cnf(f_12_4,plain,
( remove_pq(insert_pq(U_37,U_36),U_35) = insert_pq(remove_pq(U_37,U_35),U_36)
| U_36 = U_35
| ~ contains_pq(U_37,U_35) ),
inference(clausify,[status(thm)],[f_12_3]) ).
fof(f_13_1,plain,
! [U,V] :
( findmin_pq_eff(U,V) = U
| ~ issmallestelement_pq(U,V)
| ~ contains_pq(U,V) ),
inference(fof_nnf,[status(thm)],[ax13]) ).
fof(f_13_2,plain,
! [U_39,U_38] :
( findmin_pq_eff(U_39,U_38) = U_39
| ~ issmallestelement_pq(U_39,U_38)
| ~ contains_pq(U_39,U_38) ),
inference(variable_rename,[status(thm)],[f_13_1]) ).
fof(f_13_3,plain,
! [U_39,U_38] :
( findmin_pq_eff(U_39,U_38) = U_39
| ~ issmallestelement_pq(U_39,U_38)
| ~ contains_pq(U_39,U_38) ),
inference(definitional_conversion,[status(esa)],[f_13_2]) ).
cnf(f_13_4,plain,
( findmin_pq_eff(U_39,U_38) = U_39
| ~ issmallestelement_pq(U_39,U_38)
| ~ contains_pq(U_39,U_38) ),
inference(clausify,[status(thm)],[f_13_3]) ).
fof(f_14_1,plain,
! [U,V] :
( findmin_pq_res(U,V) = V
| ~ issmallestelement_pq(U,V)
| ~ contains_pq(U,V) ),
inference(fof_nnf,[status(thm)],[ax14]) ).
fof(f_14_2,plain,
! [U_41,U_40] :
( findmin_pq_res(U_41,U_40) = U_40
| ~ issmallestelement_pq(U_41,U_40)
| ~ contains_pq(U_41,U_40) ),
inference(variable_rename,[status(thm)],[f_14_1]) ).
fof(f_14_3,plain,
! [U_41,U_40] :
( findmin_pq_res(U_41,U_40) = U_40
| ~ issmallestelement_pq(U_41,U_40)
| ~ contains_pq(U_41,U_40) ),
inference(definitional_conversion,[status(esa)],[f_14_2]) ).
cnf(f_14_4,plain,
( findmin_pq_res(U_41,U_40) = U_40
| ~ issmallestelement_pq(U_41,U_40)
| ~ contains_pq(U_41,U_40) ),
inference(clausify,[status(thm)],[f_14_3]) ).
fof(f_15_1,plain,
! [U,V] :
( removemin_pq_eff(U,V) = remove_pq(U,V)
| ~ issmallestelement_pq(U,V)
| ~ contains_pq(U,V) ),
inference(fof_nnf,[status(thm)],[ax15]) ).
fof(f_15_2,plain,
! [U_43,U_42] :
( removemin_pq_eff(U_43,U_42) = remove_pq(U_43,U_42)
| ~ issmallestelement_pq(U_43,U_42)
| ~ contains_pq(U_43,U_42) ),
inference(variable_rename,[status(thm)],[f_15_1]) ).
fof(f_15_3,plain,
! [U_42,U_43] :
( removemin_pq_eff(U_43,U_42) = remove_pq(U_43,U_42)
| ~ issmallestelement_pq(U_43,U_42)
| ~ contains_pq(U_43,U_42) ),
inference(definitional_conversion,[status(esa)],[f_15_2]) ).
cnf(f_15_4,plain,
( removemin_pq_eff(U_43,U_42) = remove_pq(U_43,U_42)
| ~ issmallestelement_pq(U_43,U_42)
| ~ contains_pq(U_43,U_42) ),
inference(clausify,[status(thm)],[f_15_3]) ).
fof(f_16_1,plain,
! [U,V] :
( removemin_pq_res(U,V) = V
| ~ issmallestelement_pq(U,V)
| ~ contains_pq(U,V) ),
inference(fof_nnf,[status(thm)],[ax16]) ).
fof(f_16_2,plain,
! [U_45,U_44] :
( removemin_pq_res(U_45,U_44) = U_44
| ~ issmallestelement_pq(U_45,U_44)
| ~ contains_pq(U_45,U_44) ),
inference(variable_rename,[status(thm)],[f_16_1]) ).
fof(f_16_3,plain,
! [U_44,U_45] :
( removemin_pq_res(U_45,U_44) = U_44
| ~ issmallestelement_pq(U_45,U_44)
| ~ contains_pq(U_45,U_44) ),
inference(definitional_conversion,[status(esa)],[f_16_2]) ).
cnf(f_16_4,plain,
( removemin_pq_res(U_45,U_44) = U_44
| ~ issmallestelement_pq(U_45,U_44)
| ~ contains_pq(U_45,U_44) ),
inference(clausify,[status(thm)],[f_16_3]) ).
fof(f_17_1,plain,
! [U,V,W] : insert_pq(insert_pq(U,V),W) = insert_pq(insert_pq(U,W),V),
inference(fof_nnf,[status(thm)],[ax17]) ).
fof(f_17_2,plain,
! [U_48,U_47,U_46] : insert_pq(insert_pq(U_48,U_47),U_46) = insert_pq(insert_pq(U_48,U_46),U_47),
inference(variable_rename,[status(thm)],[f_17_1]) ).
fof(f_17_3,plain,
! [U_46,U_48,U_47] : insert_pq(insert_pq(U_48,U_47),U_46) = insert_pq(insert_pq(U_48,U_46),U_47),
inference(definitional_conversion,[status(esa)],[f_17_2]) ).
cnf(f_17_4,plain,
insert_pq(insert_pq(U_48,U_47),U_46) = insert_pq(insert_pq(U_48,U_46),U_47),
inference(clausify,[status(thm)],[f_17_3]) ).
fof(f_18_1,plain,
~ isnonempty_slb(create_slb),
inference(fof_nnf,[status(thm)],[ax18]) ).
fof(f_18_2,plain,
~ isnonempty_slb(create_slb),
inference(definitional_conversion,[status(esa)],[f_18_1]) ).
cnf(f_18_3,plain,
~ isnonempty_slb(create_slb),
inference(clausify,[status(thm)],[f_18_2]) ).
fof(f_19_1,plain,
! [U,V,W] : isnonempty_slb(insert_slb(U,pair(V,W))),
inference(fof_nnf,[status(thm)],[ax19]) ).
fof(f_19_2,plain,
! [U_51,U_50,U_49] : isnonempty_slb(insert_slb(U_51,pair(U_50,U_49))),
inference(variable_rename,[status(thm)],[f_19_1]) ).
fof(f_19_3,plain,
! [U_49,U_50,U_51] : isnonempty_slb(insert_slb(U_51,pair(U_50,U_49))),
inference(definitional_conversion,[status(esa)],[f_19_2]) ).
cnf(f_19_4,plain,
isnonempty_slb(insert_slb(U_51,pair(U_50,U_49))),
inference(clausify,[status(thm)],[f_19_3]) ).
fof(f_20_1,plain,
! [U] : ~ contains_slb(create_slb,U),
inference(fof_nnf,[status(thm)],[ax20]) ).
fof(f_20_2,plain,
! [U_52] : ~ contains_slb(create_slb,U_52),
inference(variable_rename,[status(thm)],[f_20_1]) ).
fof(f_20_3,plain,
! [U_52] : ~ contains_slb(create_slb,U_52),
inference(definitional_conversion,[status(esa)],[f_20_2]) ).
cnf(f_20_4,plain,
~ contains_slb(create_slb,U_52),
inference(clausify,[status(thm)],[f_20_3]) ).
fof(f_21_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_21_2,plain,
! [U_56,U_55,U_54,U_53] :
( ( contains_slb(insert_slb(U_56,pair(U_55,U_53)),U_54)
| ( U_55 != U_54
& ~ contains_slb(U_56,U_54) ) )
& ( U_55 = U_54
| contains_slb(U_56,U_54)
| ~ contains_slb(insert_slb(U_56,pair(U_55,U_53)),U_54) ) ),
inference(variable_rename,[status(thm)],[f_21_1]) ).
fof(f_21_3,plain,
( ! [U_64,U_62,U_60] :
( ! [U_58] : contains_slb(insert_slb(U_64,pair(U_62,U_58)),U_60)
| ( U_62 != U_60
& ~ contains_slb(U_64,U_60) ) )
& ! [U_63,U_61,U_59] :
( ! [U_57] : ~ contains_slb(insert_slb(U_63,pair(U_61,U_57)),U_59)
| U_61 = U_59
| contains_slb(U_63,U_59) ) ),
inference(miniscope,[status(thm)],[f_21_2]) ).
fof(f_21_4,plain,
( ! [U_60,U_62,U_64] :
( U_62 != U_60
| ~ sP3(U_60,U_62,U_64) )
& ! [U_60,U_62,U_64] :
( ~ contains_slb(U_64,U_60)
| ~ sP3(U_60,U_62,U_64) )
& ! [U_60,U_58,U_62,U_64] :
( contains_slb(insert_slb(U_64,pair(U_62,U_58)),U_60)
| sP3(U_60,U_62,U_64) )
& ! [U_61,U_59,U_63,U_57] :
( ~ contains_slb(insert_slb(U_63,pair(U_61,U_57)),U_59)
| U_61 = U_59
| contains_slb(U_63,U_59) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP3])],[f_21_3]) ).
cnf(f_21_5,plain,
( ~ contains_slb(insert_slb(U_63,pair(U_61,U_57)),U_59)
| U_61 = U_59
| contains_slb(U_63,U_59) ),
inference(clausify,[status(thm)],[f_21_4]) ).
cnf(f_21_6,plain,
( contains_slb(insert_slb(U_64,pair(U_62,U_58)),U_60)
| sP3(U_60,U_62,U_64) ),
inference(clausify,[status(thm)],[f_21_4]) ).
cnf(f_21_7,plain,
( ~ contains_slb(U_64,U_60)
| ~ sP3(U_60,U_62,U_64) ),
inference(clausify,[status(thm)],[f_21_4]) ).
cnf(f_21_8,plain,
( U_62 != U_60
| ~ sP3(U_60,U_62,U_64) ),
inference(clausify,[status(thm)],[f_21_4]) ).
fof(f_22_1,plain,
! [U,V] : ~ pair_in_list(create_slb,U,V),
inference(fof_nnf,[status(thm)],[ax22]) ).
fof(f_22_2,plain,
! [U_66,U_65] : ~ pair_in_list(create_slb,U_66,U_65),
inference(variable_rename,[status(thm)],[f_22_1]) ).
fof(f_22_3,plain,
! [U_66,U_65] : ~ pair_in_list(create_slb,U_66,U_65),
inference(definitional_conversion,[status(esa)],[f_22_2]) ).
cnf(f_22_4,plain,
~ pair_in_list(create_slb,U_66,U_65),
inference(clausify,[status(thm)],[f_22_3]) ).
fof(f_23_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_23_2,plain,
! [U_71,U_70,U_69,U_68,U_67] :
( ( pair_in_list(insert_slb(U_71,pair(U_70,U_68)),U_69,U_67)
| ( ( U_68 != U_67
| U_70 != U_69 )
& ~ pair_in_list(U_71,U_69,U_67) ) )
& ( ( U_68 = U_67
& U_70 = U_69 )
| pair_in_list(U_71,U_69,U_67)
| ~ pair_in_list(insert_slb(U_71,pair(U_70,U_68)),U_69,U_67) ) ),
inference(variable_rename,[status(thm)],[f_23_1]) ).
fof(f_23_3,plain,
( ! [U_81,U_79,U_77,U_75,U_73] :
( pair_in_list(insert_slb(U_81,pair(U_79,U_75)),U_77,U_73)
| ( ( U_75 != U_73
| U_79 != U_77 )
& ~ pair_in_list(U_81,U_77,U_73) ) )
& ! [U_80,U_78,U_76,U_74,U_72] :
( ( U_74 = U_72
& U_78 = U_76 )
| pair_in_list(U_80,U_76,U_72)
| ~ pair_in_list(insert_slb(U_80,pair(U_78,U_74)),U_76,U_72) ) ),
inference(miniscope,[status(thm)],[f_23_2]) ).
fof(f_23_4,plain,
( ! [U_75,U_79,U_73,U_77,U_81] :
( U_75 != U_73
| U_79 != U_77
| ~ sP5(U_75,U_79,U_73,U_77,U_81) )
& ! [U_75,U_79,U_73,U_77,U_81] :
( ~ pair_in_list(U_81,U_77,U_73)
| ~ sP5(U_75,U_79,U_73,U_77,U_81) )
& ! [U_76,U_72,U_74,U_78] :
( U_74 = U_72
| ~ sP4(U_76,U_72,U_74,U_78) )
& ! [U_76,U_72,U_74,U_78] :
( U_78 = U_76
| ~ sP4(U_76,U_72,U_74,U_78) )
& ! [U_75,U_79,U_73,U_77,U_81] :
( pair_in_list(insert_slb(U_81,pair(U_79,U_75)),U_77,U_73)
| sP5(U_75,U_79,U_73,U_77,U_81) )
& ! [U_80,U_76,U_72,U_74,U_78] :
( sP4(U_76,U_72,U_74,U_78)
| pair_in_list(U_80,U_76,U_72)
| ~ pair_in_list(insert_slb(U_80,pair(U_78,U_74)),U_76,U_72) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP4,sP5])],[f_23_3]) ).
cnf(f_23_5,plain,
( sP4(U_76,U_72,U_74,U_78)
| pair_in_list(U_80,U_76,U_72)
| ~ pair_in_list(insert_slb(U_80,pair(U_78,U_74)),U_76,U_72) ),
inference(clausify,[status(thm)],[f_23_4]) ).
cnf(f_23_6,plain,
( pair_in_list(insert_slb(U_81,pair(U_79,U_75)),U_77,U_73)
| sP5(U_75,U_79,U_73,U_77,U_81) ),
inference(clausify,[status(thm)],[f_23_4]) ).
cnf(f_23_7,plain,
( U_78 = U_76
| ~ sP4(U_76,U_72,U_74,U_78) ),
inference(clausify,[status(thm)],[f_23_4]) ).
cnf(f_23_8,plain,
( U_74 = U_72
| ~ sP4(U_76,U_72,U_74,U_78) ),
inference(clausify,[status(thm)],[f_23_4]) ).
cnf(f_23_9,plain,
( ~ pair_in_list(U_81,U_77,U_73)
| ~ sP5(U_75,U_79,U_73,U_77,U_81) ),
inference(clausify,[status(thm)],[f_23_4]) ).
cnf(f_23_10,plain,
( U_75 != U_73
| U_79 != U_77
| ~ sP5(U_75,U_79,U_73,U_77,U_81) ),
inference(clausify,[status(thm)],[f_23_4]) ).
fof(f_24_1,plain,
! [U,V,W] : remove_slb(insert_slb(U,pair(V,W)),V) = U,
inference(fof_nnf,[status(thm)],[ax24]) ).
fof(f_24_2,plain,
! [U_84,U_83,U_82] : remove_slb(insert_slb(U_84,pair(U_83,U_82)),U_83) = U_84,
inference(variable_rename,[status(thm)],[f_24_1]) ).
fof(f_24_3,plain,
! [U_84,U_82,U_83] : remove_slb(insert_slb(U_84,pair(U_83,U_82)),U_83) = U_84,
inference(definitional_conversion,[status(esa)],[f_24_2]) ).
cnf(f_24_4,plain,
remove_slb(insert_slb(U_84,pair(U_83,U_82)),U_83) = U_84,
inference(clausify,[status(thm)],[f_24_3]) ).
fof(f_25_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_25_2,plain,
! [U_88,U_87,U_86,U_85] :
( remove_slb(insert_slb(U_88,pair(U_87,U_85)),U_86) = insert_slb(remove_slb(U_88,U_86),pair(U_87,U_85))
| ~ contains_slb(U_88,U_86)
| U_87 = U_86 ),
inference(variable_rename,[status(thm)],[f_25_1]) ).
fof(f_25_3,plain,
! [U_88,U_87,U_86] :
( ! [U_85] : remove_slb(insert_slb(U_88,pair(U_87,U_85)),U_86) = insert_slb(remove_slb(U_88,U_86),pair(U_87,U_85))
| ~ contains_slb(U_88,U_86)
| U_87 = U_86 ),
inference(miniscope,[status(thm)],[f_25_2]) ).
fof(f_25_4,plain,
! [U_86,U_88,U_85,U_87] :
( remove_slb(insert_slb(U_88,pair(U_87,U_85)),U_86) = insert_slb(remove_slb(U_88,U_86),pair(U_87,U_85))
| ~ contains_slb(U_88,U_86)
| U_87 = U_86 ),
inference(definitional_conversion,[status(esa)],[f_25_3]) ).
cnf(f_25_5,plain,
( remove_slb(insert_slb(U_88,pair(U_87,U_85)),U_86) = insert_slb(remove_slb(U_88,U_86),pair(U_87,U_85))
| ~ contains_slb(U_88,U_86)
| U_87 = U_86 ),
inference(clausify,[status(thm)],[f_25_4]) ).
fof(f_26_1,plain,
! [U,V,W] : lookup_slb(insert_slb(U,pair(V,W)),V) = W,
inference(fof_nnf,[status(thm)],[ax26]) ).
fof(f_26_2,plain,
! [U_91,U_90,U_89] : lookup_slb(insert_slb(U_91,pair(U_90,U_89)),U_90) = U_89,
inference(variable_rename,[status(thm)],[f_26_1]) ).
fof(f_26_3,plain,
! [U_89,U_90,U_91] : lookup_slb(insert_slb(U_91,pair(U_90,U_89)),U_90) = U_89,
inference(definitional_conversion,[status(esa)],[f_26_2]) ).
cnf(f_26_4,plain,
lookup_slb(insert_slb(U_91,pair(U_90,U_89)),U_90) = U_89,
inference(clausify,[status(thm)],[f_26_3]) ).
fof(f_27_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_27_2,plain,
! [U_95,U_94,U_93,U_92] :
( lookup_slb(insert_slb(U_95,pair(U_94,U_92)),U_93) = lookup_slb(U_95,U_93)
| ~ contains_slb(U_95,U_93)
| U_94 = U_93 ),
inference(variable_rename,[status(thm)],[f_27_1]) ).
fof(f_27_3,plain,
! [U_95,U_94,U_93] :
( ! [U_92] : lookup_slb(insert_slb(U_95,pair(U_94,U_92)),U_93) = lookup_slb(U_95,U_93)
| ~ contains_slb(U_95,U_93)
| U_94 = U_93 ),
inference(miniscope,[status(thm)],[f_27_2]) ).
fof(f_27_4,plain,
! [U_93,U_94,U_95,U_92] :
( lookup_slb(insert_slb(U_95,pair(U_94,U_92)),U_93) = lookup_slb(U_95,U_93)
| ~ contains_slb(U_95,U_93)
| U_94 = U_93 ),
inference(definitional_conversion,[status(esa)],[f_27_3]) ).
cnf(f_27_5,plain,
( lookup_slb(insert_slb(U_95,pair(U_94,U_92)),U_93) = lookup_slb(U_95,U_93)
| ~ contains_slb(U_95,U_93)
| U_94 = U_93 ),
inference(clausify,[status(thm)],[f_27_4]) ).
fof(f_28_1,plain,
! [U] : update_slb(create_slb,U) = create_slb,
inference(fof_nnf,[status(thm)],[ax28]) ).
fof(f_28_2,plain,
! [U_96] : update_slb(create_slb,U_96) = create_slb,
inference(variable_rename,[status(thm)],[f_28_1]) ).
fof(f_28_3,plain,
! [U_96] : update_slb(create_slb,U_96) = create_slb,
inference(definitional_conversion,[status(esa)],[f_28_2]) ).
cnf(f_28_4,plain,
update_slb(create_slb,U_96) = create_slb,
inference(clausify,[status(thm)],[f_28_3]) ).
fof(f_29_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_29_2,plain,
! [U_100,U_99,U_98,U_97] :
( update_slb(insert_slb(U_100,pair(U_99,U_97)),U_98) = insert_slb(update_slb(U_100,U_98),pair(U_99,U_98))
| ~ strictly_less_than(U_97,U_98) ),
inference(variable_rename,[status(thm)],[f_29_1]) ).
fof(f_29_3,plain,
! [U_97,U_98,U_99,U_100] :
( update_slb(insert_slb(U_100,pair(U_99,U_97)),U_98) = insert_slb(update_slb(U_100,U_98),pair(U_99,U_98))
| ~ strictly_less_than(U_97,U_98) ),
inference(definitional_conversion,[status(esa)],[f_29_2]) ).
cnf(f_29_4,plain,
( update_slb(insert_slb(U_100,pair(U_99,U_97)),U_98) = insert_slb(update_slb(U_100,U_98),pair(U_99,U_98))
| ~ strictly_less_than(U_97,U_98) ),
inference(clausify,[status(thm)],[f_29_3]) ).
fof(f_30_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_30_2,plain,
! [U_104,U_103,U_102,U_101] :
( update_slb(insert_slb(U_104,pair(U_103,U_101)),U_102) = insert_slb(update_slb(U_104,U_102),pair(U_103,U_101))
| ~ less_than(U_102,U_101) ),
inference(variable_rename,[status(thm)],[f_30_1]) ).
fof(f_30_3,plain,
! [U_101,U_102,U_103,U_104] :
( update_slb(insert_slb(U_104,pair(U_103,U_101)),U_102) = insert_slb(update_slb(U_104,U_102),pair(U_103,U_101))
| ~ less_than(U_102,U_101) ),
inference(definitional_conversion,[status(esa)],[f_30_2]) ).
cnf(f_30_4,plain,
( update_slb(insert_slb(U_104,pair(U_103,U_101)),U_102) = insert_slb(update_slb(U_104,U_102),pair(U_103,U_101))
| ~ less_than(U_102,U_101) ),
inference(clausify,[status(thm)],[f_30_3]) ).
fof(f_31_1,plain,
! [U] : succ_cpq(U,U),
inference(fof_nnf,[status(thm)],[ax31]) ).
fof(f_31_2,plain,
! [U_105] : succ_cpq(U_105,U_105),
inference(variable_rename,[status(thm)],[f_31_1]) ).
fof(f_31_3,plain,
! [U_105] : succ_cpq(U_105,U_105),
inference(definitional_conversion,[status(esa)],[f_31_2]) ).
cnf(f_31_4,plain,
succ_cpq(U_105,U_105),
inference(clausify,[status(thm)],[f_31_3]) ).
fof(f_32_1,plain,
! [U,V,W] :
( succ_cpq(U,insert_cpq(V,W))
| ~ succ_cpq(U,V) ),
inference(fof_nnf,[status(thm)],[ax32]) ).
fof(f_32_2,plain,
! [U_108,U_107,U_106] :
( succ_cpq(U_108,insert_cpq(U_107,U_106))
| ~ succ_cpq(U_108,U_107) ),
inference(variable_rename,[status(thm)],[f_32_1]) ).
fof(f_32_3,plain,
! [U_108,U_107] :
( ! [U_106] : succ_cpq(U_108,insert_cpq(U_107,U_106))
| ~ succ_cpq(U_108,U_107) ),
inference(miniscope,[status(thm)],[f_32_2]) ).
fof(f_32_4,plain,
! [U_106,U_107,U_108] :
( succ_cpq(U_108,insert_cpq(U_107,U_106))
| ~ succ_cpq(U_108,U_107) ),
inference(definitional_conversion,[status(esa)],[f_32_3]) ).
cnf(f_32_5,plain,
( succ_cpq(U_108,insert_cpq(U_107,U_106))
| ~ succ_cpq(U_108,U_107) ),
inference(clausify,[status(thm)],[f_32_4]) ).
fof(f_33_1,plain,
! [U,V,W] :
( succ_cpq(U,remove_cpq(V,W))
| ~ succ_cpq(U,V) ),
inference(fof_nnf,[status(thm)],[ax33]) ).
fof(f_33_2,plain,
! [U_111,U_110,U_109] :
( succ_cpq(U_111,remove_cpq(U_110,U_109))
| ~ succ_cpq(U_111,U_110) ),
inference(variable_rename,[status(thm)],[f_33_1]) ).
fof(f_33_3,plain,
! [U_111,U_110] :
( ! [U_109] : succ_cpq(U_111,remove_cpq(U_110,U_109))
| ~ succ_cpq(U_111,U_110) ),
inference(miniscope,[status(thm)],[f_33_2]) ).
fof(f_33_4,plain,
! [U_109,U_110,U_111] :
( succ_cpq(U_111,remove_cpq(U_110,U_109))
| ~ succ_cpq(U_111,U_110) ),
inference(definitional_conversion,[status(esa)],[f_33_3]) ).
cnf(f_33_5,plain,
( succ_cpq(U_111,remove_cpq(U_110,U_109))
| ~ succ_cpq(U_111,U_110) ),
inference(clausify,[status(thm)],[f_33_4]) ).
fof(f_34_1,plain,
! [U,V] :
( succ_cpq(U,findmin_cpq_eff(V))
| ~ succ_cpq(U,V) ),
inference(fof_nnf,[status(thm)],[ax34]) ).
fof(f_34_2,plain,
! [U_113,U_112] :
( succ_cpq(U_113,findmin_cpq_eff(U_112))
| ~ succ_cpq(U_113,U_112) ),
inference(variable_rename,[status(thm)],[f_34_1]) ).
fof(f_34_3,plain,
! [U_112,U_113] :
( succ_cpq(U_113,findmin_cpq_eff(U_112))
| ~ succ_cpq(U_113,U_112) ),
inference(definitional_conversion,[status(esa)],[f_34_2]) ).
cnf(f_34_4,plain,
( succ_cpq(U_113,findmin_cpq_eff(U_112))
| ~ succ_cpq(U_113,U_112) ),
inference(clausify,[status(thm)],[f_34_3]) ).
fof(f_35_1,plain,
! [U,V] :
( succ_cpq(U,removemin_cpq_eff(V))
| ~ succ_cpq(U,V) ),
inference(fof_nnf,[status(thm)],[ax35]) ).
fof(f_35_2,plain,
! [U_115,U_114] :
( succ_cpq(U_115,removemin_cpq_eff(U_114))
| ~ succ_cpq(U_115,U_114) ),
inference(variable_rename,[status(thm)],[f_35_1]) ).
fof(f_35_3,plain,
! [U_114,U_115] :
( succ_cpq(U_115,removemin_cpq_eff(U_114))
| ~ succ_cpq(U_115,U_114) ),
inference(definitional_conversion,[status(esa)],[f_35_2]) ).
cnf(f_35_4,plain,
( succ_cpq(U_115,removemin_cpq_eff(U_114))
| ~ succ_cpq(U_115,U_114) ),
inference(clausify,[status(thm)],[f_35_3]) ).
fof(f_36_1,plain,
! [U,V] : check_cpq(triple(U,create_slb,V)),
inference(fof_nnf,[status(thm)],[ax36]) ).
fof(f_36_2,plain,
! [U_117,U_116] : check_cpq(triple(U_117,create_slb,U_116)),
inference(variable_rename,[status(thm)],[f_36_1]) ).
fof(f_36_3,plain,
! [U_116,U_117] : check_cpq(triple(U_117,create_slb,U_116)),
inference(definitional_conversion,[status(esa)],[f_36_2]) ).
cnf(f_36_4,plain,
check_cpq(triple(U_117,create_slb,U_116)),
inference(clausify,[status(thm)],[f_36_3]) ).
fof(f_37_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_37_2,plain,
! [U_122,U_121,U_120,U_119,U_118] :
( ( ( check_cpq(triple(U_122,insert_slb(U_121,pair(U_119,U_118)),U_120))
| ~ check_cpq(triple(U_122,U_121,U_120)) )
& ( check_cpq(triple(U_122,U_121,U_120))
| ~ check_cpq(triple(U_122,insert_slb(U_121,pair(U_119,U_118)),U_120)) ) )
| ~ less_than(U_118,U_119) ),
inference(variable_rename,[status(thm)],[f_37_1]) ).
fof(f_37_3,plain,
( ! [U_118,U_119,U_120,U_121,U_122] :
( check_cpq(triple(U_122,insert_slb(U_121,pair(U_119,U_118)),U_120))
| ~ check_cpq(triple(U_122,U_121,U_120))
| ~ sP6(U_118,U_119,U_120,U_121,U_122) )
& ! [U_118,U_119,U_120,U_121,U_122] :
( check_cpq(triple(U_122,U_121,U_120))
| ~ check_cpq(triple(U_122,insert_slb(U_121,pair(U_119,U_118)),U_120))
| ~ sP6(U_118,U_119,U_120,U_121,U_122) )
& ! [U_118,U_119,U_120,U_121,U_122] :
( sP6(U_118,U_119,U_120,U_121,U_122)
| ~ less_than(U_118,U_119) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP6])],[f_37_2]) ).
cnf(f_37_4,plain,
( sP6(U_118,U_119,U_120,U_121,U_122)
| ~ less_than(U_118,U_119) ),
inference(clausify,[status(thm)],[f_37_3]) ).
cnf(f_37_5,plain,
( check_cpq(triple(U_122,U_121,U_120))
| ~ check_cpq(triple(U_122,insert_slb(U_121,pair(U_119,U_118)),U_120))
| ~ sP6(U_118,U_119,U_120,U_121,U_122) ),
inference(clausify,[status(thm)],[f_37_3]) ).
cnf(f_37_6,plain,
( check_cpq(triple(U_122,insert_slb(U_121,pair(U_119,U_118)),U_120))
| ~ check_cpq(triple(U_122,U_121,U_120))
| ~ sP6(U_118,U_119,U_120,U_121,U_122) ),
inference(clausify,[status(thm)],[f_37_3]) ).
fof(f_38_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_38_2,plain,
! [U_127,U_126,U_125,U_124,U_123] :
( ( ( check_cpq(triple(U_127,insert_slb(U_126,pair(U_124,U_123)),U_125))
| ~ $false )
& ( $false
| ~ check_cpq(triple(U_127,insert_slb(U_126,pair(U_124,U_123)),U_125)) ) )
| ~ strictly_less_than(U_124,U_123) ),
inference(variable_rename,[status(thm)],[f_38_1]) ).
fof(f_38_3,plain,
( ! [U_127,U_126,U_123,U_124,U_125] :
( check_cpq(triple(U_127,insert_slb(U_126,pair(U_124,U_123)),U_125))
| ~ $false
| ~ sP7(U_127,U_126,U_123,U_124,U_125) )
& ! [U_127,U_126,U_123,U_124,U_125] :
( $false
| ~ check_cpq(triple(U_127,insert_slb(U_126,pair(U_124,U_123)),U_125))
| ~ sP7(U_127,U_126,U_123,U_124,U_125) )
& ! [U_127,U_126,U_123,U_124,U_125] :
( sP7(U_127,U_126,U_123,U_124,U_125)
| ~ strictly_less_than(U_124,U_123) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP7])],[f_38_2]) ).
cnf(f_38_4,plain,
( sP7(U_127,U_126,U_123,U_124,U_125)
| ~ strictly_less_than(U_124,U_123) ),
inference(clausify,[status(thm)],[f_38_3]) ).
cnf(f_38_5,plain,
( $false
| ~ check_cpq(triple(U_127,insert_slb(U_126,pair(U_124,U_123)),U_125))
| ~ sP7(U_127,U_126,U_123,U_124,U_125) ),
inference(clausify,[status(thm)],[f_38_3]) ).
cnf(f_38_6,plain,
( check_cpq(triple(U_127,insert_slb(U_126,pair(U_124,U_123)),U_125))
| ~ $false
| ~ sP7(U_127,U_126,U_123,U_124,U_125) ),
inference(clausify,[status(thm)],[f_38_3]) ).
fof(f_39_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_39_2,plain,
! [U_131,U_130,U_129,U_128] :
( ( contains_cpq(triple(U_131,U_130,U_129),U_128)
| ~ contains_slb(U_130,U_128) )
& ( contains_slb(U_130,U_128)
| ~ contains_cpq(triple(U_131,U_130,U_129),U_128) ) ),
inference(variable_rename,[status(thm)],[f_39_1]) ).
fof(f_39_3,plain,
( ! [U_139,U_137,U_135,U_133] :
( contains_cpq(triple(U_139,U_137,U_135),U_133)
| ~ contains_slb(U_137,U_133) )
& ! [U_138,U_136,U_134,U_132] :
( contains_slb(U_136,U_132)
| ~ contains_cpq(triple(U_138,U_136,U_134),U_132) ) ),
inference(miniscope,[status(thm)],[f_39_2]) ).
fof(f_39_4,plain,
( ! [U_135,U_137,U_133,U_139] :
( contains_cpq(triple(U_139,U_137,U_135),U_133)
| ~ contains_slb(U_137,U_133) )
& ! [U_138,U_134,U_136,U_132] :
( contains_slb(U_136,U_132)
| ~ contains_cpq(triple(U_138,U_136,U_134),U_132) ) ),
inference(definitional_conversion,[status(esa)],[f_39_3]) ).
cnf(f_39_5,plain,
( contains_slb(U_136,U_132)
| ~ contains_cpq(triple(U_138,U_136,U_134),U_132) ),
inference(clausify,[status(thm)],[f_39_4]) ).
cnf(f_39_6,plain,
( contains_cpq(triple(U_139,U_137,U_135),U_133)
| ~ contains_slb(U_137,U_133) ),
inference(clausify,[status(thm)],[f_39_4]) ).
fof(f_40_1,plain,
! [U,V] :
( ( ok(triple(U,V,bad))
| ~ $false )
& ( $false
| ~ ok(triple(U,V,bad)) ) ),
inference(fof_nnf,[status(thm)],[ax40]) ).
fof(f_40_2,plain,
! [U_141,U_140] :
( ( ok(triple(U_141,U_140,bad))
| ~ $false )
& ( $false
| ~ ok(triple(U_141,U_140,bad)) ) ),
inference(variable_rename,[status(thm)],[f_40_1]) ).
fof(f_40_3,plain,
( ( ! [U_145,U_143] : ok(triple(U_145,U_143,bad))
| ~ $false )
& ( ! [U_144,U_142] : ~ ok(triple(U_144,U_142,bad))
| $false ) ),
inference(miniscope,[status(thm)],[f_40_2]) ).
fof(f_40_4,plain,
( ! [U_143,U_145] :
( ok(triple(U_145,U_143,bad))
| ~ $false )
& ! [U_142,U_144] :
( ~ ok(triple(U_144,U_142,bad))
| $false ) ),
inference(definitional_conversion,[status(esa)],[f_40_3]) ).
cnf(f_40_5,plain,
( ~ ok(triple(U_144,U_142,bad))
| $false ),
inference(clausify,[status(thm)],[f_40_4]) ).
cnf(f_40_6,plain,
( ok(triple(U_145,U_143,bad))
| ~ $false ),
inference(clausify,[status(thm)],[f_40_4]) ).
fof(f_41_1,plain,
! [U,V,W] :
( W = bad
| ok(triple(U,V,W)) ),
inference(fof_nnf,[status(thm)],[ax41]) ).
fof(f_41_2,plain,
! [U_148,U_147,U_146] :
( U_146 = bad
| ok(triple(U_148,U_147,U_146)) ),
inference(variable_rename,[status(thm)],[f_41_1]) ).
fof(f_41_3,plain,
! [U_148,U_146,U_147] :
( U_146 = bad
| ok(triple(U_148,U_147,U_146)) ),
inference(definitional_conversion,[status(esa)],[f_41_2]) ).
cnf(f_41_4,plain,
( U_146 = bad
| ok(triple(U_148,U_147,U_146)) ),
inference(clausify,[status(thm)],[f_41_3]) ).
fof(f_42_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_42_2,plain,
! [U_152,U_151,U_150,U_149] : insert_cpq(triple(U_152,U_151,U_150),U_149) = triple(insert_pqp(U_152,U_149),insert_slb(U_151,pair(U_149,bottom)),U_150),
inference(variable_rename,[status(thm)],[f_42_1]) ).
fof(f_42_3,plain,
! [U_152,U_149,U_151,U_150] : insert_cpq(triple(U_152,U_151,U_150),U_149) = triple(insert_pqp(U_152,U_149),insert_slb(U_151,pair(U_149,bottom)),U_150),
inference(definitional_conversion,[status(esa)],[f_42_2]) ).
cnf(f_42_4,plain,
insert_cpq(triple(U_152,U_151,U_150),U_149) = triple(insert_pqp(U_152,U_149),insert_slb(U_151,pair(U_149,bottom)),U_150),
inference(clausify,[status(thm)],[f_42_3]) ).
fof(f_43_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_43_2,plain,
! [U_156,U_155,U_154,U_153] :
( remove_cpq(triple(U_156,U_155,U_154),U_153) = triple(U_156,U_155,bad)
| contains_slb(U_155,U_153) ),
inference(variable_rename,[status(thm)],[f_43_1]) ).
fof(f_43_3,plain,
! [U_154,U_153,U_155,U_156] :
( remove_cpq(triple(U_156,U_155,U_154),U_153) = triple(U_156,U_155,bad)
| contains_slb(U_155,U_153) ),
inference(definitional_conversion,[status(esa)],[f_43_2]) ).
cnf(f_43_4,plain,
( remove_cpq(triple(U_156,U_155,U_154),U_153) = triple(U_156,U_155,bad)
| contains_slb(U_155,U_153) ),
inference(clausify,[status(thm)],[f_43_3]) ).
fof(f_44_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_44_2,plain,
! [U_160,U_159,U_158,U_157] :
( remove_cpq(triple(U_160,U_159,U_158),U_157) = triple(remove_pqp(U_160,U_157),remove_slb(U_159,U_157),U_158)
| ~ less_than(lookup_slb(U_159,U_157),U_157)
| ~ contains_slb(U_159,U_157) ),
inference(variable_rename,[status(thm)],[f_44_1]) ).
fof(f_44_3,plain,
! [U_157,U_158,U_159,U_160] :
( remove_cpq(triple(U_160,U_159,U_158),U_157) = triple(remove_pqp(U_160,U_157),remove_slb(U_159,U_157),U_158)
| ~ less_than(lookup_slb(U_159,U_157),U_157)
| ~ contains_slb(U_159,U_157) ),
inference(definitional_conversion,[status(esa)],[f_44_2]) ).
cnf(f_44_4,plain,
( remove_cpq(triple(U_160,U_159,U_158),U_157) = triple(remove_pqp(U_160,U_157),remove_slb(U_159,U_157),U_158)
| ~ less_than(lookup_slb(U_159,U_157),U_157)
| ~ contains_slb(U_159,U_157) ),
inference(clausify,[status(thm)],[f_44_3]) ).
fof(f_45_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_45_2,plain,
! [U_164,U_163,U_162,U_161] :
( remove_cpq(triple(U_164,U_163,U_162),U_161) = triple(remove_pqp(U_164,U_161),remove_slb(U_163,U_161),bad)
| ~ strictly_less_than(U_161,lookup_slb(U_163,U_161))
| ~ contains_slb(U_163,U_161) ),
inference(variable_rename,[status(thm)],[f_45_1]) ).
fof(f_45_3,plain,
! [U_161,U_163,U_164,U_162] :
( remove_cpq(triple(U_164,U_163,U_162),U_161) = triple(remove_pqp(U_164,U_161),remove_slb(U_163,U_161),bad)
| ~ strictly_less_than(U_161,lookup_slb(U_163,U_161))
| ~ contains_slb(U_163,U_161) ),
inference(definitional_conversion,[status(esa)],[f_45_2]) ).
cnf(f_45_4,plain,
( remove_cpq(triple(U_164,U_163,U_162),U_161) = triple(remove_pqp(U_164,U_161),remove_slb(U_163,U_161),bad)
| ~ strictly_less_than(U_161,lookup_slb(U_163,U_161))
| ~ contains_slb(U_163,U_161) ),
inference(clausify,[status(thm)],[f_45_3]) ).
fof(f_46_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_46_2,plain,
! [U_166,U_165] : findmin_cpq_eff(triple(U_166,create_slb,U_165)) = triple(U_166,create_slb,bad),
inference(variable_rename,[status(thm)],[f_46_1]) ).
fof(f_46_3,plain,
! [U_166,U_165] : findmin_cpq_eff(triple(U_166,create_slb,U_165)) = triple(U_166,create_slb,bad),
inference(definitional_conversion,[status(esa)],[f_46_2]) ).
cnf(f_46_4,plain,
findmin_cpq_eff(triple(U_166,create_slb,U_165)) = triple(U_166,create_slb,bad),
inference(clausify,[status(thm)],[f_46_3]) ).
fof(f_47_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_47_2,plain,
! [U_170,U_169,U_168,U_167] :
( findmin_cpq_eff(triple(U_170,U_169,U_168)) = triple(U_170,update_slb(U_169,findmin_pqp_res(U_170)),bad)
| contains_slb(U_169,findmin_pqp_res(U_170))
| U_169 = create_slb ),
inference(variable_rename,[status(thm)],[f_47_1]) ).
fof(f_47_3,plain,
! [U_170,U_169] :
( ! [U_168] : findmin_cpq_eff(triple(U_170,U_169,U_168)) = triple(U_170,update_slb(U_169,findmin_pqp_res(U_170)),bad)
| contains_slb(U_169,findmin_pqp_res(U_170))
| U_169 = create_slb ),
inference(miniscope,[status(thm)],[f_47_2]) ).
fof(f_47_4,plain,
! [U_169,U_170,U_168] :
( findmin_cpq_eff(triple(U_170,U_169,U_168)) = triple(U_170,update_slb(U_169,findmin_pqp_res(U_170)),bad)
| contains_slb(U_169,findmin_pqp_res(U_170))
| U_169 = create_slb ),
inference(definitional_conversion,[status(esa)],[f_47_3]) ).
cnf(f_47_5,plain,
( findmin_cpq_eff(triple(U_170,U_169,U_168)) = triple(U_170,update_slb(U_169,findmin_pqp_res(U_170)),bad)
| contains_slb(U_169,findmin_pqp_res(U_170))
| U_169 = create_slb ),
inference(clausify,[status(thm)],[f_47_4]) ).
fof(f_48_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_48_2,plain,
! [U_174,U_173,U_172,U_171] :
( findmin_cpq_eff(triple(U_174,U_173,U_172)) = triple(U_174,update_slb(U_173,findmin_pqp_res(U_174)),bad)
| ~ strictly_less_than(findmin_pqp_res(U_174),lookup_slb(U_173,findmin_pqp_res(U_174)))
| ~ contains_slb(U_173,findmin_pqp_res(U_174))
| U_173 = create_slb ),
inference(variable_rename,[status(thm)],[f_48_1]) ).
fof(f_48_3,plain,
! [U_174,U_173] :
( ! [U_172] : findmin_cpq_eff(triple(U_174,U_173,U_172)) = triple(U_174,update_slb(U_173,findmin_pqp_res(U_174)),bad)
| ~ strictly_less_than(findmin_pqp_res(U_174),lookup_slb(U_173,findmin_pqp_res(U_174)))
| ~ contains_slb(U_173,findmin_pqp_res(U_174))
| U_173 = create_slb ),
inference(miniscope,[status(thm)],[f_48_2]) ).
fof(f_48_4,plain,
! [U_172,U_173,U_174] :
( findmin_cpq_eff(triple(U_174,U_173,U_172)) = triple(U_174,update_slb(U_173,findmin_pqp_res(U_174)),bad)
| ~ strictly_less_than(findmin_pqp_res(U_174),lookup_slb(U_173,findmin_pqp_res(U_174)))
| ~ contains_slb(U_173,findmin_pqp_res(U_174))
| U_173 = create_slb ),
inference(definitional_conversion,[status(esa)],[f_48_3]) ).
cnf(f_48_5,plain,
( findmin_cpq_eff(triple(U_174,U_173,U_172)) = triple(U_174,update_slb(U_173,findmin_pqp_res(U_174)),bad)
| ~ strictly_less_than(findmin_pqp_res(U_174),lookup_slb(U_173,findmin_pqp_res(U_174)))
| ~ contains_slb(U_173,findmin_pqp_res(U_174))
| U_173 = create_slb ),
inference(clausify,[status(thm)],[f_48_4]) ).
fof(f_49_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_49_2,plain,
! [U_178,U_177,U_176,U_175] :
( findmin_cpq_eff(triple(U_178,U_177,U_176)) = triple(U_178,update_slb(U_177,findmin_pqp_res(U_178)),U_176)
| ~ less_than(lookup_slb(U_177,findmin_pqp_res(U_178)),findmin_pqp_res(U_178))
| ~ contains_slb(U_177,findmin_pqp_res(U_178))
| U_177 = create_slb ),
inference(variable_rename,[status(thm)],[f_49_1]) ).
fof(f_49_3,plain,
! [U_178,U_177] :
( ! [U_176] : findmin_cpq_eff(triple(U_178,U_177,U_176)) = triple(U_178,update_slb(U_177,findmin_pqp_res(U_178)),U_176)
| ~ less_than(lookup_slb(U_177,findmin_pqp_res(U_178)),findmin_pqp_res(U_178))
| ~ contains_slb(U_177,findmin_pqp_res(U_178))
| U_177 = create_slb ),
inference(miniscope,[status(thm)],[f_49_2]) ).
fof(f_49_4,plain,
! [U_177,U_178,U_176] :
( findmin_cpq_eff(triple(U_178,U_177,U_176)) = triple(U_178,update_slb(U_177,findmin_pqp_res(U_178)),U_176)
| ~ less_than(lookup_slb(U_177,findmin_pqp_res(U_178)),findmin_pqp_res(U_178))
| ~ contains_slb(U_177,findmin_pqp_res(U_178))
| U_177 = create_slb ),
inference(definitional_conversion,[status(esa)],[f_49_3]) ).
cnf(f_49_5,plain,
( findmin_cpq_eff(triple(U_178,U_177,U_176)) = triple(U_178,update_slb(U_177,findmin_pqp_res(U_178)),U_176)
| ~ less_than(lookup_slb(U_177,findmin_pqp_res(U_178)),findmin_pqp_res(U_178))
| ~ contains_slb(U_177,findmin_pqp_res(U_178))
| U_177 = create_slb ),
inference(clausify,[status(thm)],[f_49_4]) ).
fof(f_50_1,plain,
! [U,V] : findmin_cpq_res(triple(U,create_slb,V)) = bottom,
inference(fof_nnf,[status(thm)],[ax50]) ).
fof(f_50_2,plain,
! [U_180,U_179] : findmin_cpq_res(triple(U_180,create_slb,U_179)) = bottom,
inference(variable_rename,[status(thm)],[f_50_1]) ).
fof(f_50_3,plain,
! [U_180,U_179] : findmin_cpq_res(triple(U_180,create_slb,U_179)) = bottom,
inference(definitional_conversion,[status(esa)],[f_50_2]) ).
cnf(f_50_4,plain,
findmin_cpq_res(triple(U_180,create_slb,U_179)) = bottom,
inference(clausify,[status(thm)],[f_50_3]) ).
fof(f_51_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_51_2,plain,
! [U_184,U_183,U_182,U_181] :
( findmin_cpq_res(triple(U_184,U_183,U_182)) = findmin_pqp_res(U_184)
| U_183 = create_slb ),
inference(variable_rename,[status(thm)],[f_51_1]) ).
fof(f_51_3,plain,
! [U_184,U_183] :
( ! [U_182] : findmin_cpq_res(triple(U_184,U_183,U_182)) = findmin_pqp_res(U_184)
| U_183 = create_slb ),
inference(miniscope,[status(thm)],[f_51_2]) ).
fof(f_51_4,plain,
! [U_182,U_183,U_184] :
( findmin_cpq_res(triple(U_184,U_183,U_182)) = findmin_pqp_res(U_184)
| U_183 = create_slb ),
inference(definitional_conversion,[status(esa)],[f_51_3]) ).
cnf(f_51_5,plain,
( findmin_cpq_res(triple(U_184,U_183,U_182)) = findmin_pqp_res(U_184)
| U_183 = create_slb ),
inference(clausify,[status(thm)],[f_51_4]) ).
fof(f_52_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_52_2,plain,
! [U_185] : removemin_cpq_eff(U_185) = remove_cpq(findmin_cpq_eff(U_185),findmin_cpq_res(U_185)),
inference(variable_rename,[status(thm)],[f_52_1]) ).
fof(f_52_3,plain,
! [U_185] : removemin_cpq_eff(U_185) = remove_cpq(findmin_cpq_eff(U_185),findmin_cpq_res(U_185)),
inference(definitional_conversion,[status(esa)],[f_52_2]) ).
cnf(f_52_4,plain,
removemin_cpq_eff(U_185) = remove_cpq(findmin_cpq_eff(U_185),findmin_cpq_res(U_185)),
inference(clausify,[status(thm)],[f_52_3]) ).
fof(f_53_1,plain,
! [U] : removemin_cpq_res(U) = findmin_cpq_res(U),
inference(fof_nnf,[status(thm)],[ax53]) ).
fof(f_53_2,plain,
! [U_186] : removemin_cpq_res(U_186) = findmin_cpq_res(U_186),
inference(variable_rename,[status(thm)],[f_53_1]) ).
fof(f_53_3,plain,
! [U_186] : removemin_cpq_res(U_186) = findmin_cpq_res(U_186),
inference(definitional_conversion,[status(esa)],[f_53_2]) ).
cnf(f_53_4,plain,
removemin_cpq_res(U_186) = findmin_cpq_res(U_186),
inference(clausify,[status(thm)],[f_53_3]) ).
fof(f_54_1,plain,
! [U,V] : i(triple(U,create_slb,V)) = create_pq,
inference(fof_nnf,[status(thm)],[ax54]) ).
fof(f_54_2,plain,
! [U_188,U_187] : i(triple(U_188,create_slb,U_187)) = create_pq,
inference(variable_rename,[status(thm)],[f_54_1]) ).
fof(f_54_3,plain,
! [U_187,U_188] : i(triple(U_188,create_slb,U_187)) = create_pq,
inference(definitional_conversion,[status(esa)],[f_54_2]) ).
cnf(f_54_4,plain,
i(triple(U_188,create_slb,U_187)) = create_pq,
inference(clausify,[status(thm)],[f_54_3]) ).
fof(f_55_1,plain,
! [U,V,W,X,Y] : i(triple(U,insert_slb(V,pair(X,Y)),W)) = insert_pq(i(triple(U,V,W)),X),
inference(fof_nnf,[status(thm)],[ax55]) ).
fof(f_55_2,plain,
! [U_193,U_192,U_191,U_190,U_189] : i(triple(U_193,insert_slb(U_192,pair(U_190,U_189)),U_191)) = insert_pq(i(triple(U_193,U_192,U_191)),U_190),
inference(variable_rename,[status(thm)],[f_55_1]) ).
fof(f_55_3,plain,
! [U_189,U_190,U_191,U_192,U_193] : i(triple(U_193,insert_slb(U_192,pair(U_190,U_189)),U_191)) = insert_pq(i(triple(U_193,U_192,U_191)),U_190),
inference(definitional_conversion,[status(esa)],[f_55_2]) ).
cnf(f_55_4,plain,
i(triple(U_193,insert_slb(U_192,pair(U_190,U_189)),U_191)) = insert_pq(i(triple(U_193,U_192,U_191)),U_190),
inference(clausify,[status(thm)],[f_55_3]) ).
fof(f_56_1,plain,
! [U,V] :
( ( pi_sharp_remove(U,V)
| ~ contains_pq(U,V) )
& ( contains_pq(U,V)
| ~ pi_sharp_remove(U,V) ) ),
inference(fof_nnf,[status(thm)],[ax56]) ).
fof(f_56_2,plain,
! [U_195,U_194] :
( ( pi_sharp_remove(U_195,U_194)
| ~ contains_pq(U_195,U_194) )
& ( contains_pq(U_195,U_194)
| ~ pi_sharp_remove(U_195,U_194) ) ),
inference(variable_rename,[status(thm)],[f_56_1]) ).
fof(f_56_3,plain,
( ! [U_199,U_197] :
( pi_sharp_remove(U_199,U_197)
| ~ contains_pq(U_199,U_197) )
& ! [U_198,U_196] :
( contains_pq(U_198,U_196)
| ~ pi_sharp_remove(U_198,U_196) ) ),
inference(miniscope,[status(thm)],[f_56_2]) ).
fof(f_56_4,plain,
( ! [U_199,U_197] :
( pi_sharp_remove(U_199,U_197)
| ~ contains_pq(U_199,U_197) )
& ! [U_198,U_196] :
( contains_pq(U_198,U_196)
| ~ pi_sharp_remove(U_198,U_196) ) ),
inference(definitional_conversion,[status(esa)],[f_56_3]) ).
cnf(f_56_5,plain,
( contains_pq(U_198,U_196)
| ~ pi_sharp_remove(U_198,U_196) ),
inference(clausify,[status(thm)],[f_56_4]) ).
cnf(f_56_6,plain,
( pi_sharp_remove(U_199,U_197)
| ~ contains_pq(U_199,U_197) ),
inference(clausify,[status(thm)],[f_56_4]) ).
fof(f_57_1,plain,
! [U,V] :
( ( pi_remove(U,V)
| ~ pi_sharp_remove(i(U),V) )
& ( pi_sharp_remove(i(U),V)
| ~ pi_remove(U,V) ) ),
inference(fof_nnf,[status(thm)],[ax57]) ).
fof(f_57_2,plain,
! [U_201,U_200] :
( ( pi_remove(U_201,U_200)
| ~ pi_sharp_remove(i(U_201),U_200) )
& ( pi_sharp_remove(i(U_201),U_200)
| ~ pi_remove(U_201,U_200) ) ),
inference(variable_rename,[status(thm)],[f_57_1]) ).
fof(f_57_3,plain,
( ! [U_205,U_203] :
( pi_remove(U_205,U_203)
| ~ pi_sharp_remove(i(U_205),U_203) )
& ! [U_204,U_202] :
( pi_sharp_remove(i(U_204),U_202)
| ~ pi_remove(U_204,U_202) ) ),
inference(miniscope,[status(thm)],[f_57_2]) ).
fof(f_57_4,plain,
( ! [U_205,U_203] :
( pi_remove(U_205,U_203)
| ~ pi_sharp_remove(i(U_205),U_203) )
& ! [U_202,U_204] :
( pi_sharp_remove(i(U_204),U_202)
| ~ pi_remove(U_204,U_202) ) ),
inference(definitional_conversion,[status(esa)],[f_57_3]) ).
cnf(f_57_5,plain,
( pi_sharp_remove(i(U_204),U_202)
| ~ pi_remove(U_204,U_202) ),
inference(clausify,[status(thm)],[f_57_4]) ).
cnf(f_57_6,plain,
( pi_remove(U_205,U_203)
| ~ pi_sharp_remove(i(U_205),U_203) ),
inference(clausify,[status(thm)],[f_57_4]) ).
fof(f_58_1,plain,
! [U,V] :
( ( pi_sharp_find_min(U,V)
| ~ issmallestelement_pq(U,V)
| ~ contains_pq(U,V) )
& ( ( issmallestelement_pq(U,V)
& contains_pq(U,V) )
| ~ pi_sharp_find_min(U,V) ) ),
inference(fof_nnf,[status(thm)],[ax58]) ).
fof(f_58_2,plain,
! [U_207,U_206] :
( ( pi_sharp_find_min(U_207,U_206)
| ~ issmallestelement_pq(U_207,U_206)
| ~ contains_pq(U_207,U_206) )
& ( ( issmallestelement_pq(U_207,U_206)
& contains_pq(U_207,U_206) )
| ~ pi_sharp_find_min(U_207,U_206) ) ),
inference(variable_rename,[status(thm)],[f_58_1]) ).
fof(f_58_3,plain,
( ! [U_211,U_209] :
( pi_sharp_find_min(U_211,U_209)
| ~ issmallestelement_pq(U_211,U_209)
| ~ contains_pq(U_211,U_209) )
& ! [U_210,U_208] :
( ( issmallestelement_pq(U_210,U_208)
& contains_pq(U_210,U_208) )
| ~ pi_sharp_find_min(U_210,U_208) ) ),
inference(miniscope,[status(thm)],[f_58_2]) ).
fof(f_58_4,plain,
( ! [U_210,U_208] :
( issmallestelement_pq(U_210,U_208)
| ~ sP8(U_210,U_208) )
& ! [U_210,U_208] :
( contains_pq(U_210,U_208)
| ~ sP8(U_210,U_208) )
& ! [U_211,U_209] :
( pi_sharp_find_min(U_211,U_209)
| ~ issmallestelement_pq(U_211,U_209)
| ~ contains_pq(U_211,U_209) )
& ! [U_210,U_208] :
( sP8(U_210,U_208)
| ~ pi_sharp_find_min(U_210,U_208) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP8])],[f_58_3]) ).
cnf(f_58_5,plain,
( sP8(U_210,U_208)
| ~ pi_sharp_find_min(U_210,U_208) ),
inference(clausify,[status(thm)],[f_58_4]) ).
cnf(f_58_6,plain,
( pi_sharp_find_min(U_211,U_209)
| ~ issmallestelement_pq(U_211,U_209)
| ~ contains_pq(U_211,U_209) ),
inference(clausify,[status(thm)],[f_58_4]) ).
cnf(f_58_7,plain,
( contains_pq(U_210,U_208)
| ~ sP8(U_210,U_208) ),
inference(clausify,[status(thm)],[f_58_4]) ).
cnf(f_58_8,plain,
( issmallestelement_pq(U_210,U_208)
| ~ sP8(U_210,U_208) ),
inference(clausify,[status(thm)],[f_58_4]) ).
fof(f_59_1,plain,
! [U] :
( ( pi_find_min(U)
| ! [V] : ~ pi_sharp_find_min(i(U),V) )
& ( ? [V] : pi_sharp_find_min(i(U),V)
| ~ pi_find_min(U) ) ),
inference(fof_nnf,[status(thm)],[ax59]) ).
fof(f_59_2,plain,
! [U_214] :
( ( pi_find_min(U_214)
| ! [U_213] : ~ pi_sharp_find_min(i(U_214),U_213) )
& ( ? [U_212] : pi_sharp_find_min(i(U_214),U_212)
| ~ pi_find_min(U_214) ) ),
inference(variable_rename,[status(thm)],[f_59_1]) ).
fof(f_59_3,plain,
( ! [U_216] :
( pi_find_min(U_216)
| ! [U_213] : ~ pi_sharp_find_min(i(U_216),U_213) )
& ! [U_215] :
( ? [U_212] : pi_sharp_find_min(i(U_215),U_212)
| ~ pi_find_min(U_215) ) ),
inference(miniscope,[status(thm)],[f_59_2]) ).
fof(f_59_4,plain,
( ! [U_216] :
( pi_find_min(U_216)
| ! [U_213] : ~ pi_sharp_find_min(i(U_216),U_213) )
& ! [U_215] :
( pi_sharp_find_min(i(U_215),sK2(U_215))
| ~ pi_find_min(U_215) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2]),skolemize(U_212,sK2(U_215))],[f_59_3]) ).
fof(f_59_5,plain,
( ! [U_216,U_213] :
( pi_find_min(U_216)
| ~ pi_sharp_find_min(i(U_216),U_213) )
& ! [U_215] :
( pi_sharp_find_min(i(U_215),sK2(U_215))
| ~ pi_find_min(U_215) ) ),
inference(definitional_conversion,[status(esa)],[f_59_4]) ).
cnf(f_59_6,plain,
( pi_sharp_find_min(i(U_215),sK2(U_215))
| ~ pi_find_min(U_215) ),
inference(clausify,[status(thm)],[f_59_5]) ).
cnf(f_59_7,plain,
( pi_find_min(U_216)
| ~ pi_sharp_find_min(i(U_216),U_213) ),
inference(clausify,[status(thm)],[f_59_5]) ).
fof(f_60_1,plain,
! [U,V] :
( ( pi_sharp_removemin(U,V)
| ~ issmallestelement_pq(U,V)
| ~ contains_pq(U,V) )
& ( ( issmallestelement_pq(U,V)
& contains_pq(U,V) )
| ~ pi_sharp_removemin(U,V) ) ),
inference(fof_nnf,[status(thm)],[ax60]) ).
fof(f_60_2,plain,
! [U_218,U_217] :
( ( pi_sharp_removemin(U_218,U_217)
| ~ issmallestelement_pq(U_218,U_217)
| ~ contains_pq(U_218,U_217) )
& ( ( issmallestelement_pq(U_218,U_217)
& contains_pq(U_218,U_217) )
| ~ pi_sharp_removemin(U_218,U_217) ) ),
inference(variable_rename,[status(thm)],[f_60_1]) ).
fof(f_60_3,plain,
( ! [U_222,U_220] :
( pi_sharp_removemin(U_222,U_220)
| ~ issmallestelement_pq(U_222,U_220)
| ~ contains_pq(U_222,U_220) )
& ! [U_221,U_219] :
( ( issmallestelement_pq(U_221,U_219)
& contains_pq(U_221,U_219) )
| ~ pi_sharp_removemin(U_221,U_219) ) ),
inference(miniscope,[status(thm)],[f_60_2]) ).
fof(f_60_4,plain,
( ! [U_221,U_219] :
( issmallestelement_pq(U_221,U_219)
| ~ sP9(U_221,U_219) )
& ! [U_221,U_219] :
( contains_pq(U_221,U_219)
| ~ sP9(U_221,U_219) )
& ! [U_222,U_220] :
( pi_sharp_removemin(U_222,U_220)
| ~ issmallestelement_pq(U_222,U_220)
| ~ contains_pq(U_222,U_220) )
& ! [U_221,U_219] :
( sP9(U_221,U_219)
| ~ pi_sharp_removemin(U_221,U_219) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP9])],[f_60_3]) ).
cnf(f_60_5,plain,
( sP9(U_221,U_219)
| ~ pi_sharp_removemin(U_221,U_219) ),
inference(clausify,[status(thm)],[f_60_4]) ).
cnf(f_60_6,plain,
( pi_sharp_removemin(U_222,U_220)
| ~ issmallestelement_pq(U_222,U_220)
| ~ contains_pq(U_222,U_220) ),
inference(clausify,[status(thm)],[f_60_4]) ).
cnf(f_60_7,plain,
( contains_pq(U_221,U_219)
| ~ sP9(U_221,U_219) ),
inference(clausify,[status(thm)],[f_60_4]) ).
cnf(f_60_8,plain,
( issmallestelement_pq(U_221,U_219)
| ~ sP9(U_221,U_219) ),
inference(clausify,[status(thm)],[f_60_4]) ).
fof(f_61_1,plain,
! [U] :
( ( pi_removemin(U)
| ! [V] : ~ pi_sharp_find_min(i(U),V) )
& ( ? [V] : pi_sharp_find_min(i(U),V)
| ~ pi_removemin(U) ) ),
inference(fof_nnf,[status(thm)],[ax61]) ).
fof(f_61_2,plain,
! [U_225] :
( ( pi_removemin(U_225)
| ! [U_224] : ~ pi_sharp_find_min(i(U_225),U_224) )
& ( ? [U_223] : pi_sharp_find_min(i(U_225),U_223)
| ~ pi_removemin(U_225) ) ),
inference(variable_rename,[status(thm)],[f_61_1]) ).
fof(f_61_3,plain,
( ! [U_227] :
( pi_removemin(U_227)
| ! [U_224] : ~ pi_sharp_find_min(i(U_227),U_224) )
& ! [U_226] :
( ? [U_223] : pi_sharp_find_min(i(U_226),U_223)
| ~ pi_removemin(U_226) ) ),
inference(miniscope,[status(thm)],[f_61_2]) ).
fof(f_61_4,plain,
( ! [U_227] :
( pi_removemin(U_227)
| ! [U_224] : ~ pi_sharp_find_min(i(U_227),U_224) )
& ! [U_226] :
( pi_sharp_find_min(i(U_226),sK3(U_226))
| ~ pi_removemin(U_226) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3]),skolemize(U_223,sK3(U_226))],[f_61_3]) ).
fof(f_61_5,plain,
( ! [U_224,U_227] :
( pi_removemin(U_227)
| ~ pi_sharp_find_min(i(U_227),U_224) )
& ! [U_226] :
( pi_sharp_find_min(i(U_226),sK3(U_226))
| ~ pi_removemin(U_226) ) ),
inference(definitional_conversion,[status(esa)],[f_61_4]) ).
cnf(f_61_6,plain,
( pi_sharp_find_min(i(U_226),sK3(U_226))
| ~ pi_removemin(U_226) ),
inference(clausify,[status(thm)],[f_61_5]) ).
cnf(f_61_7,plain,
( pi_removemin(U_227)
| ~ pi_sharp_find_min(i(U_227),U_224) ),
inference(clausify,[status(thm)],[f_61_5]) ).
fof(f_62_1,plain,
! [U] :
( ( phi(U)
| ! [V] :
( ~ check_cpq(V)
| ~ ok(V)
| ~ succ_cpq(U,V) ) )
& ( ? [V] :
( check_cpq(V)
& ok(V)
& succ_cpq(U,V) )
| ~ phi(U) ) ),
inference(fof_nnf,[status(thm)],[ax62]) ).
fof(f_62_2,plain,
! [U_230] :
( ( phi(U_230)
| ! [U_229] :
( ~ check_cpq(U_229)
| ~ ok(U_229)
| ~ succ_cpq(U_230,U_229) ) )
& ( ? [U_228] :
( check_cpq(U_228)
& ok(U_228)
& succ_cpq(U_230,U_228) )
| ~ phi(U_230) ) ),
inference(variable_rename,[status(thm)],[f_62_1]) ).
fof(f_62_3,plain,
( ! [U_232] :
( phi(U_232)
| ! [U_229] :
( ~ check_cpq(U_229)
| ~ ok(U_229)
| ~ succ_cpq(U_232,U_229) ) )
& ! [U_231] :
( ? [U_228] :
( check_cpq(U_228)
& ok(U_228)
& succ_cpq(U_231,U_228) )
| ~ phi(U_231) ) ),
inference(miniscope,[status(thm)],[f_62_2]) ).
fof(f_62_4,plain,
( ! [U_232] :
( phi(U_232)
| ! [U_229] :
( ~ check_cpq(U_229)
| ~ ok(U_229)
| ~ succ_cpq(U_232,U_229) ) )
& ! [U_231] :
( ( check_cpq(sK4(U_231))
& ok(sK4(U_231))
& succ_cpq(U_231,sK4(U_231)) )
| ~ phi(U_231) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4]),skolemize(U_228,sK4(U_231))],[f_62_3]) ).
fof(f_62_5,plain,
( ! [U_231] :
( check_cpq(sK4(U_231))
| ~ sP10(U_231) )
& ! [U_231] :
( ok(sK4(U_231))
| ~ sP10(U_231) )
& ! [U_231] :
( succ_cpq(U_231,sK4(U_231))
| ~ sP10(U_231) )
& ! [U_229,U_232] :
( phi(U_232)
| ~ check_cpq(U_229)
| ~ ok(U_229)
| ~ succ_cpq(U_232,U_229) )
& ! [U_231] :
( sP10(U_231)
| ~ phi(U_231) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP10])],[f_62_4]) ).
cnf(f_62_6,plain,
( sP10(U_231)
| ~ phi(U_231) ),
inference(clausify,[status(thm)],[f_62_5]) ).
cnf(f_62_7,plain,
( phi(U_232)
| ~ check_cpq(U_229)
| ~ ok(U_229)
| ~ succ_cpq(U_232,U_229) ),
inference(clausify,[status(thm)],[f_62_5]) ).
cnf(f_62_8,plain,
( succ_cpq(U_231,sK4(U_231))
| ~ sP10(U_231) ),
inference(clausify,[status(thm)],[f_62_5]) ).
cnf(f_62_9,plain,
( ok(sK4(U_231))
| ~ sP10(U_231) ),
inference(clausify,[status(thm)],[f_62_5]) ).
cnf(f_62_10,plain,
( check_cpq(sK4(U_231))
| ~ sP10(U_231) ),
inference(clausify,[status(thm)],[f_62_5]) ).
fof(f_63_1,plain,
! [U,V,W] :
( pi_sharp_find_min(i(triple(U,V,W)),findmin_cpq_res(triple(U,V,W)))
| ~ phi(findmin_cpq_eff(triple(U,V,W))) ),
inference(fof_nnf,[status(thm)],[main4_l7]) ).
fof(f_63_2,plain,
! [U_235,U_234,U_233] :
( pi_sharp_find_min(i(triple(U_235,U_234,U_233)),findmin_cpq_res(triple(U_235,U_234,U_233)))
| ~ phi(findmin_cpq_eff(triple(U_235,U_234,U_233))) ),
inference(variable_rename,[status(thm)],[f_63_1]) ).
fof(f_63_3,plain,
! [U_234,U_233,U_235] :
( pi_sharp_find_min(i(triple(U_235,U_234,U_233)),findmin_cpq_res(triple(U_235,U_234,U_233)))
| ~ phi(findmin_cpq_eff(triple(U_235,U_234,U_233))) ),
inference(definitional_conversion,[status(esa)],[f_63_2]) ).
cnf(f_63_4,plain,
( pi_sharp_find_min(i(triple(U_235,U_234,U_233)),findmin_cpq_res(triple(U_235,U_234,U_233)))
| ~ phi(findmin_cpq_eff(triple(U_235,U_234,U_233))) ),
inference(clausify,[status(thm)],[f_63_3]) ).
fof(f_64_1,negated_conjecture,
~ ! [U,V,W] :
( pi_find_min(triple(U,V,W))
=> ( phi(findmin_cpq_eff(triple(U,V,W)))
=> ? [X] :
( findmin_cpq_res(triple(U,V,W)) = findmin_pq_res(i(triple(U,V,W)),X)
& pi_sharp_find_min(i(triple(U,V,W)),X) ) ) ),
inference(negate,[status(cth)],[co4]) ).
fof(f_64_2,negated_conjecture,
? [U,V,W] :
( ! [X] :
( findmin_cpq_res(triple(U,V,W)) != findmin_pq_res(i(triple(U,V,W)),X)
| ~ pi_sharp_find_min(i(triple(U,V,W)),X) )
& phi(findmin_cpq_eff(triple(U,V,W)))
& pi_find_min(triple(U,V,W)) ),
inference(fof_nnf,[status(thm)],[f_64_1]) ).
fof(f_64_3,negated_conjecture,
? [U_239,U_238,U_237] :
( ! [U_236] :
( findmin_cpq_res(triple(U_239,U_238,U_237)) != findmin_pq_res(i(triple(U_239,U_238,U_237)),U_236)
| ~ pi_sharp_find_min(i(triple(U_239,U_238,U_237)),U_236) )
& phi(findmin_cpq_eff(triple(U_239,U_238,U_237)))
& pi_find_min(triple(U_239,U_238,U_237)) ),
inference(variable_rename,[status(thm)],[f_64_2]) ).
fof(f_64_4,negated_conjecture,
? [U_238,U_237] :
( ! [U_236] :
( findmin_cpq_res(triple(sK5,U_238,U_237)) != findmin_pq_res(i(triple(sK5,U_238,U_237)),U_236)
| ~ pi_sharp_find_min(i(triple(sK5,U_238,U_237)),U_236) )
& phi(findmin_cpq_eff(triple(sK5,U_238,U_237)))
& pi_find_min(triple(sK5,U_238,U_237)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK5]),skolemize(U_239,sK5)],[f_64_3]) ).
fof(f_64_5,negated_conjecture,
? [U_237] :
( ! [U_236] :
( findmin_cpq_res(triple(sK5,sK6,U_237)) != findmin_pq_res(i(triple(sK5,sK6,U_237)),U_236)
| ~ pi_sharp_find_min(i(triple(sK5,sK6,U_237)),U_236) )
& phi(findmin_cpq_eff(triple(sK5,sK6,U_237)))
& pi_find_min(triple(sK5,sK6,U_237)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK6]),skolemize(U_238,sK6)],[f_64_4]) ).
fof(f_64_6,negated_conjecture,
( ! [U_236] :
( findmin_cpq_res(triple(sK5,sK6,sK7)) != findmin_pq_res(i(triple(sK5,sK6,sK7)),U_236)
| ~ pi_sharp_find_min(i(triple(sK5,sK6,sK7)),U_236) )
& phi(findmin_cpq_eff(triple(sK5,sK6,sK7)))
& pi_find_min(triple(sK5,sK6,sK7)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK7]),skolemize(U_237,sK7)],[f_64_5]) ).
fof(f_64_7,negated_conjecture,
( ! [U_236] :
( findmin_cpq_res(triple(sK5,sK6,sK7)) != findmin_pq_res(i(triple(sK5,sK6,sK7)),U_236)
| ~ pi_sharp_find_min(i(triple(sK5,sK6,sK7)),U_236) )
& phi(findmin_cpq_eff(triple(sK5,sK6,sK7)))
& pi_find_min(triple(sK5,sK6,sK7)) ),
inference(definitional_conversion,[status(esa)],[f_64_6]) ).
cnf(f_64_8,negated_conjecture,
pi_find_min(triple(sK5,sK6,sK7)),
inference(clausify,[status(thm)],[f_64_7]) ).
cnf(f_64_9,negated_conjecture,
phi(findmin_cpq_eff(triple(sK5,sK6,sK7))),
inference(clausify,[status(thm)],[f_64_7]) ).
cnf(f_64_10,negated_conjecture,
( findmin_cpq_res(triple(sK5,sK6,sK7)) != findmin_pq_res(i(triple(sK5,sK6,sK7)),U_236)
| ~ pi_sharp_find_min(i(triple(sK5,sK6,sK7)),U_236) ),
inference(clausify,[status(thm)],[f_64_7]) ).
cnf(f_38_5_simplified,plain,
( ~ check_cpq(triple(U_127,insert_slb(U_126,pair(U_124,U_123)),U_125))
| ~ sP7(U_127,U_126,U_123,U_124,U_125) ),
inference(simplify_clause,[status(thm)],[f_38_5]) ).
cnf(f_38_6_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_38_6]) ).
cnf(f_40_5_simplified,plain,
~ ok(triple(U_144,U_142,bad)),
inference(simplify_clause,[status(thm)],[f_40_5]) ).
cnf(f_40_6_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_40_6]) ).
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,
( insert_pq(Eq_x_0,Eq_x_1) = insert_pq(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,
( remove_pq(Eq_x_0,Eq_x_1) = remove_pq(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,
( findmin_pq_eff(Eq_x_0,Eq_x_1) = findmin_pq_eff(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,
( findmin_pq_res(Eq_x_0,Eq_x_1) = findmin_pq_res(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,
( removemin_pq_eff(Eq_x_0,Eq_x_1) = removemin_pq_eff(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,
( removemin_pq_res(Eq_x_0,Eq_x_1) = removemin_pq_res(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,
( 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_11,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_12,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_13,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_14,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_15,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_16,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_17,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_18,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_19,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_20,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_21,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_22,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_23,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_24,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_25,axiom,
( i(Eq_x_0) = i(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_26,axiom,
( sK1(Eq_x_0,Eq_x_1) = sK1(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_27,axiom,
( sK2(Eq_x_0) = sK2(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_28,axiom,
( sK3(Eq_x_0) = sK3(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_29,axiom,
( sK4(Eq_x_0) = sK4(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_30,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_31,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_32,axiom,
( isnonempty_pq(Eq_y_0)
| ~ isnonempty_pq(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_33,axiom,
( contains_pq(Eq_y_0,Eq_y_1)
| ~ contains_pq(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_34,axiom,
( issmallestelement_pq(Eq_y_0,Eq_y_1)
| ~ issmallestelement_pq(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_35,axiom,
( isnonempty_slb(Eq_y_0)
| ~ isnonempty_slb(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_36,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_37,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_38,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_39,axiom,
( check_cpq(Eq_y_0)
| ~ check_cpq(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_40,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_41,axiom,
( ok(Eq_y_0)
| ~ ok(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_42,axiom,
( pi_sharp_remove(Eq_y_0,Eq_y_1)
| ~ pi_sharp_remove(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_43,axiom,
( pi_remove(Eq_y_0,Eq_y_1)
| ~ pi_remove(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_44,axiom,
( pi_sharp_find_min(Eq_y_0,Eq_y_1)
| ~ pi_sharp_find_min(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_45,axiom,
( pi_find_min(Eq_y_0)
| ~ pi_find_min(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_46,axiom,
( pi_sharp_removemin(Eq_y_0,Eq_y_1)
| ~ pi_sharp_removemin(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_47,axiom,
( pi_removemin(Eq_y_0)
| ~ pi_removemin(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_48,axiom,
( phi(Eq_y_0)
| ~ phi(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_49,axiom,
( sP0(Eq_y_0,Eq_y_1)
| ~ sP0(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_50,axiom,
( sP1(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP1(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_51,axiom,
( sP2(Eq_y_0,Eq_y_1)
| ~ sP2(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_52,axiom,
( sP3(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP3(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_53,axiom,
( sP4(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| ~ sP4(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_54,axiom,
( sP5(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
| ~ sP5(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4)
| Eq_x_4 != Eq_y_4
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_55,axiom,
( sP6(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
| ~ sP6(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4)
| Eq_x_4 != Eq_y_4
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_56,axiom,
( sP7(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
| ~ sP7(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4)
| Eq_x_4 != Eq_y_4
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_57,axiom,
( sP8(Eq_y_0,Eq_y_1)
| ~ sP8(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_58,axiom,
( sP9(Eq_y_0,Eq_y_1)
| ~ sP9(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_59,axiom,
( sP10(Eq_y_0)
| ~ sP10(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
% 0.00/0.03 % Problem : SWV417+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/sandbox2/solver/bin/connect++ --verbosity 1 --no-colour --tptp-proof --schedule default --timeout 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n004.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Sun Sep 20 03:31:35 UTC 2026
% 0.09/0.36 % CPUTime :
% 31.27/31.54 % SZS status Theorem for theBenchmark
% 31.27/31.54 % SZS output start Proof for theBenchmark
% See solution above
%------------------------------------------------------------------------------