%------------------------------------------------------------------------------
% File : ConnectPP---0.7.2
% Problem : SWV409+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 : n011.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 09:03:36 AM UTC 2026
% Result : Theorem 0.80s 1.08s
% Output : Proof 0.80s
% 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(l45_li4647,lemma,
! [U,V] :
( contains_slb(U,V)
=> ? [W] : pair_in_list(U,V,W) ),
file('theBenchmark.p',l45_li4647) ).
fof(l45_l48,lemma,
! [U,V,W,X] :
( ( strictly_less_than(W,X)
& strictly_less_than(V,X)
& pair_in_list(U,V,W) )
=> pair_in_list(update_slb(U,X),V,X) ),
file('theBenchmark.p',l45_l48) ).
fof(l45_l49,lemma,
! [U,V,W,X] :
( ( less_than(X,W)
& strictly_less_than(V,X)
& pair_in_list(U,V,W) )
=> ? [Y] :
( less_than(X,Y)
& pair_in_list(update_slb(U,X),V,Y) ) ),
file('theBenchmark.p',l45_l49) ).
fof(l45_co,conjecture,
! [U,V,W] :
( ( strictly_less_than(V,W)
& contains_slb(U,V) )
=> ( ? [X] :
( less_than(W,X)
& pair_in_list(update_slb(U,W),V,X) )
| pair_in_list(update_slb(U,W),V,W) ) ),
file('theBenchmark.p',l45_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,V] :
( ? [W] : pair_in_list(U,V,W)
| ~ contains_slb(U,V) ),
inference(fof_nnf,[status(thm)],[l45_li4647]) ).
fof(f_19_2,plain,
! [U_71,U_70] :
( ? [U_69] : pair_in_list(U_71,U_70,U_69)
| ~ contains_slb(U_71,U_70) ),
inference(variable_rename,[status(thm)],[f_19_1]) ).
fof(f_19_3,plain,
! [U_71,U_70] :
( pair_in_list(U_71,U_70,sK1(U_71,U_70))
| ~ contains_slb(U_71,U_70) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(U_69,sK1(U_71,U_70))],[f_19_2]) ).
cnf(f_19_4,plain,
( pair_in_list(U_71,U_70,sK1(U_71,U_70))
| ~ contains_slb(U_71,U_70) ),
inference(clausify,[status(thm)],[f_19_3]) ).
fof(f_20_1,plain,
! [U,V,W,X] :
( pair_in_list(update_slb(U,X),V,X)
| ~ strictly_less_than(W,X)
| ~ strictly_less_than(V,X)
| ~ pair_in_list(U,V,W) ),
inference(fof_nnf,[status(thm)],[l45_l48]) ).
fof(f_20_2,plain,
! [U_75,U_74,U_73,U_72] :
( pair_in_list(update_slb(U_75,U_72),U_74,U_72)
| ~ strictly_less_than(U_73,U_72)
| ~ strictly_less_than(U_74,U_72)
| ~ pair_in_list(U_75,U_74,U_73) ),
inference(variable_rename,[status(thm)],[f_20_1]) ).
cnf(f_20_3,plain,
( pair_in_list(update_slb(U_75,U_72),U_74,U_72)
| ~ strictly_less_than(U_73,U_72)
| ~ strictly_less_than(U_74,U_72)
| ~ pair_in_list(U_75,U_74,U_73) ),
inference(clausify,[status(thm)],[f_20_2]) ).
fof(f_21_1,plain,
! [U,V,W,X] :
( ? [Y] :
( less_than(X,Y)
& pair_in_list(update_slb(U,X),V,Y) )
| ~ less_than(X,W)
| ~ strictly_less_than(V,X)
| ~ pair_in_list(U,V,W) ),
inference(fof_nnf,[status(thm)],[l45_l49]) ).
fof(f_21_2,plain,
! [U_80,U_79,U_78,U_77] :
( ? [U_76] :
( less_than(U_77,U_76)
& pair_in_list(update_slb(U_80,U_77),U_79,U_76) )
| ~ less_than(U_77,U_78)
| ~ strictly_less_than(U_79,U_77)
| ~ pair_in_list(U_80,U_79,U_78) ),
inference(variable_rename,[status(thm)],[f_21_1]) ).
fof(f_21_3,plain,
! [U_80,U_79,U_78,U_77] :
( ( less_than(U_77,sK2(U_80,U_79,U_78,U_77))
& pair_in_list(update_slb(U_80,U_77),U_79,sK2(U_80,U_79,U_78,U_77)) )
| ~ less_than(U_77,U_78)
| ~ strictly_less_than(U_79,U_77)
| ~ pair_in_list(U_80,U_79,U_78) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2]),skolemize(U_76,sK2(U_80,U_79,U_78,U_77))],[f_21_2]) ).
cnf(f_21_4,plain,
( pair_in_list(update_slb(U_80,U_77),U_79,sK2(U_80,U_79,U_78,U_77))
| ~ less_than(U_77,U_78)
| ~ strictly_less_than(U_79,U_77)
| ~ pair_in_list(U_80,U_79,U_78) ),
inference(clausify,[status(thm)],[f_21_3]) ).
cnf(f_21_5,plain,
( less_than(U_77,sK2(U_80,U_79,U_78,U_77))
| ~ less_than(U_77,U_78)
| ~ strictly_less_than(U_79,U_77)
| ~ pair_in_list(U_80,U_79,U_78) ),
inference(clausify,[status(thm)],[f_21_3]) ).
fof(f_22_1,negated_conjecture,
~ ! [U,V,W] :
( ( strictly_less_than(V,W)
& contains_slb(U,V) )
=> ( ? [X] :
( less_than(W,X)
& pair_in_list(update_slb(U,W),V,X) )
| pair_in_list(update_slb(U,W),V,W) ) ),
inference(negate,[status(cth)],[l45_co]) ).
fof(f_22_2,negated_conjecture,
? [U,V,W] :
( ! [X] :
( ~ less_than(W,X)
| ~ pair_in_list(update_slb(U,W),V,X) )
& ~ pair_in_list(update_slb(U,W),V,W)
& strictly_less_than(V,W)
& contains_slb(U,V) ),
inference(fof_nnf,[status(thm)],[f_22_1]) ).
fof(f_22_3,negated_conjecture,
? [U_84,U_83,U_82] :
( ! [U_81] :
( ~ less_than(U_82,U_81)
| ~ pair_in_list(update_slb(U_84,U_82),U_83,U_81) )
& ~ pair_in_list(update_slb(U_84,U_82),U_83,U_82)
& strictly_less_than(U_83,U_82)
& contains_slb(U_84,U_83) ),
inference(variable_rename,[status(thm)],[f_22_2]) ).
fof(f_22_4,negated_conjecture,
? [U_83,U_82] :
( ! [U_81] :
( ~ less_than(U_82,U_81)
| ~ pair_in_list(update_slb(sK3,U_82),U_83,U_81) )
& ~ pair_in_list(update_slb(sK3,U_82),U_83,U_82)
& strictly_less_than(U_83,U_82)
& contains_slb(sK3,U_83) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3]),skolemize(U_84,sK3)],[f_22_3]) ).
fof(f_22_5,negated_conjecture,
? [U_82] :
( ! [U_81] :
( ~ less_than(U_82,U_81)
| ~ pair_in_list(update_slb(sK3,U_82),sK4,U_81) )
& ~ pair_in_list(update_slb(sK3,U_82),sK4,U_82)
& strictly_less_than(sK4,U_82)
& contains_slb(sK3,sK4) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4]),skolemize(U_83,sK4)],[f_22_4]) ).
fof(f_22_6,negated_conjecture,
( ! [U_81] :
( ~ less_than(sK5,U_81)
| ~ pair_in_list(update_slb(sK3,sK5),sK4,U_81) )
& ~ pair_in_list(update_slb(sK3,sK5),sK4,sK5)
& strictly_less_than(sK4,sK5)
& contains_slb(sK3,sK4) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK5]),skolemize(U_82,sK5)],[f_22_5]) ).
fof(f_22_7,negated_conjecture,
( ! [U_81] :
( ~ less_than(sK5,U_81)
| ~ pair_in_list(update_slb(sK3,sK5),sK4,U_81) )
& ~ pair_in_list(update_slb(sK3,sK5),sK4,sK5)
& strictly_less_than(sK4,sK5)
& contains_slb(sK3,sK4) ),
inference(definitional_conversion,[status(esa)],[f_22_6]) ).
cnf(f_22_8,negated_conjecture,
contains_slb(sK3,sK4),
inference(clausify,[status(thm)],[f_22_7]) ).
cnf(f_22_9,negated_conjecture,
strictly_less_than(sK4,sK5),
inference(clausify,[status(thm)],[f_22_7]) ).
cnf(f_22_10,negated_conjecture,
~ pair_in_list(update_slb(sK3,sK5),sK4,sK5),
inference(clausify,[status(thm)],[f_22_7]) ).
cnf(f_22_11,negated_conjecture,
( ~ less_than(sK5,U_81)
| ~ pair_in_list(update_slb(sK3,sK5),sK4,U_81) ),
inference(clausify,[status(thm)],[f_22_7]) ).
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,
( 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_10,axiom,
( sK2(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK2(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_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_functions]) ).
cnf(equality_11,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_12,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_13,axiom,
( isnonempty_slb(Eq_y_0)
| ~ isnonempty_slb(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_14,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_15,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(sat_proved,plain,
$false,
inference(cadical,[status(thm)],[]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWV409+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
% 0.10/0.37 % Computer : n011.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Sun Sep 20 03:31:25 UTC 2026
% 0.10/0.38 % CPUTime :
% 0.80/1.08 % SZS status Theorem for theBenchmark
% 0.80/1.08 % SZS output start Proof for theBenchmark
% See solution above
%------------------------------------------------------------------------------