%------------------------------------------------------------------------------
% File : Satallax---3.5
% Problem : ITP077^1 : TPTP v9.2.0. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% Computer : n015.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Oct 9 01:46:54 PM UTC 2025
% Result : Theorem 37.48s 37.61s
% Output : Proof 37.48s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 24
% Syntax : Number of formulae : 73 ( 32 unt; 0 typ; 0 def)
% Number of atoms : 197 ( 25 equ; 0 cnn)
% Maximal formula atoms : 3 ( 2 avg)
% Number of connectives : 147 ( 49 ~; 40 |; 0 &; 51 @)
% ( 0 <=>; 6 =>; 1 <=; 0 <~>)
% Maximal formula depth : 7 ( 2 avg)
% Number of types : 5 ( 4 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 28 ( 26 usr; 24 con; 0-2 aty)
% Number of variables : 1 ( 0 ^; 1 !; 0 ?; 1 :)
% Comments :
%------------------------------------------------------------------------------
thf(ty_a,type,
a: $tType ).
thf(ty_list_set_a,type,
list_set_a: $tType ).
thf(ty_set_list_a,type,
set_list_a: $tType ).
thf(ty_list_a,type,
list_a: $tType ).
thf(ty_a3,type,
a3: a ).
thf(ty_ss1,type,
ss1: list_set_a ).
thf(ty_eigen__0,type,
eigen__0: list_a ).
thf(ty_member_list_a,type,
member_list_a: list_a > set_list_a > $o ).
thf(ty_listset_a,type,
listset_a: list_set_a > set_list_a ).
thf(ty_groups1792256535list_a,type,
groups1792256535list_a: list_a > a ).
thf(conj_0,conjecture,
( a3
= ( groups1792256535list_a @ qs2 ) ) ).
thf(h0,negated_conjecture,
( a3
!= ( groups1792256535list_a @ qs2 ) ),
inference(assume_negation,[status(cth)],[conj_0]) ).
thf(h1,assumption,
~ ( ( a3
= ( groups1792256535list_a @ eigen__0 ) )
=> ~ ( member_list_a @ eigen__0 @ ( listset_a @ ss1 ) ) ),
introduced(assumption,[]) ).
thf(h2,assumption,
( a3
= ( groups1792256535list_a @ eigen__0 ) ),
introduced(assumption,[]) ).
thf(h3,assumption,
member_list_a @ eigen__0 @ ( listset_a @ ss1 ),
introduced(assumption,[]) ).
thf(ax1301,axiom,
( ~ p28
| p247 ),
file('<stdin>',ax1301) ).
thf(ax2012,axiom,
( ~ p15
| p55 ),
file('<stdin>',ax2012) ).
thf(ax1300,axiom,
( ~ p247
| p248 ),
file('<stdin>',ax1300) ).
thf(ax2043,axiom,
p28,
file('<stdin>',ax2043) ).
thf(ax1306,axiom,
( ~ p28
| p243 ),
file('<stdin>',ax1306) ).
thf(pax1,axiom,
( p1
=> ( ( fmset_a @ fqs2 )
= ( fmset_a @ fqs ) ) ),
file('<stdin>',pax1) ).
thf(pax3,axiom,
( p3
=> ( fa3
= ( fgroups1792256535list_a @ fqs ) ) ),
file('<stdin>',pax3) ).
thf(ax1299,axiom,
( ~ p248
| ~ p55
| p246 ),
file('<stdin>',ax1299) ).
thf(ax2056,axiom,
p15,
file('<stdin>',ax2056) ).
thf(ax2013,axiom,
( ~ p15
| p54 ),
file('<stdin>',ax2013) ).
thf(ax1305,axiom,
( ~ p243
| p244 ),
file('<stdin>',ax1305) ).
thf(pax246,axiom,
( p246
=> ( ( fgroups1792256535list_a @ fqs )
= ( fcomm_m543484931mset_a @ ( fmset_a @ fqs ) ) ) ),
file('<stdin>',pax246) ).
thf(ax2070,axiom,
p1,
file('<stdin>',ax2070) ).
thf(ax2068,axiom,
p3,
file('<stdin>',ax2068) ).
thf(ax1304,axiom,
( ~ p244
| ~ p54
| p242 ),
file('<stdin>',ax1304) ).
thf(nax20,axiom,
( p20
<= ( fa3
= ( fgroups1792256535list_a @ fqs2 ) ) ),
file('<stdin>',nax20) ).
thf(ax2051,axiom,
~ p20,
file('<stdin>',ax2051) ).
thf(pax242,axiom,
( p242
=> ( ( fgroups1792256535list_a @ fqs2 )
= ( fcomm_m543484931mset_a @ ( fmset_a @ fqs2 ) ) ) ),
file('<stdin>',pax242) ).
thf(c_0_18,plain,
( ~ p28
| p247 ),
inference(fof_simplification,[status(thm)],[ax1301]) ).
thf(c_0_19,plain,
( ~ p15
| p55 ),
inference(fof_simplification,[status(thm)],[ax2012]) ).
thf(c_0_20,plain,
( ~ p247
| p248 ),
inference(fof_simplification,[status(thm)],[ax1300]) ).
thf(c_0_21,plain,
( p247
| ~ p28 ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
thf(c_0_22,plain,
p28,
inference(split_conjunct,[status(thm)],[ax2043]) ).
thf(c_0_23,plain,
( ~ p28
| p243 ),
inference(fof_simplification,[status(thm)],[ax1306]) ).
thf(c_0_24,plain,
( ~ p1
| ( ( fmset_a @ fqs2 )
= ( fmset_a @ fqs ) ) ),
inference(fof_nnf,[status(thm)],[pax1]) ).
thf(c_0_25,plain,
( ~ p3
| ( fa3
= ( fgroups1792256535list_a @ fqs ) ) ),
inference(fof_nnf,[status(thm)],[pax3]) ).
thf(c_0_26,plain,
( ~ p248
| ~ p55
| p246 ),
inference(fof_simplification,[status(thm)],[ax1299]) ).
thf(c_0_27,plain,
( p55
| ~ p15 ),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
thf(c_0_28,plain,
p15,
inference(split_conjunct,[status(thm)],[ax2056]) ).
thf(c_0_29,plain,
( p248
| ~ p247 ),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
thf(c_0_30,plain,
p247,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_21,c_0_22])]) ).
thf(c_0_31,plain,
( ~ p15
| p54 ),
inference(fof_simplification,[status(thm)],[ax2013]) ).
thf(c_0_32,plain,
( ~ p243
| p244 ),
inference(fof_simplification,[status(thm)],[ax1305]) ).
thf(c_0_33,plain,
( p243
| ~ p28 ),
inference(split_conjunct,[status(thm)],[c_0_23]) ).
thf(c_0_34,plain,
( ~ p246
| ( ( fgroups1792256535list_a @ fqs )
= ( fcomm_m543484931mset_a @ ( fmset_a @ fqs ) ) ) ),
inference(fof_nnf,[status(thm)],[pax246]) ).
thf(c_0_35,plain,
( ( ( fmset_a @ fqs2 )
= ( fmset_a @ fqs ) )
| ~ p1 ),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
thf(c_0_36,plain,
p1,
inference(split_conjunct,[status(thm)],[ax2070]) ).
thf(c_0_37,plain,
( ( fa3
= ( fgroups1792256535list_a @ fqs ) )
| ~ p3 ),
inference(split_conjunct,[status(thm)],[c_0_25]) ).
thf(c_0_38,plain,
p3,
inference(split_conjunct,[status(thm)],[ax2068]) ).
thf(c_0_39,plain,
( p246
| ~ p248
| ~ p55 ),
inference(split_conjunct,[status(thm)],[c_0_26]) ).
thf(c_0_40,plain,
p55,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_27,c_0_28])]) ).
thf(c_0_41,plain,
p248,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_29,c_0_30])]) ).
thf(c_0_42,plain,
( ~ p244
| ~ p54
| p242 ),
inference(fof_simplification,[status(thm)],[ax1304]) ).
thf(c_0_43,plain,
( p54
| ~ p15 ),
inference(split_conjunct,[status(thm)],[c_0_31]) ).
thf(c_0_44,plain,
( p244
| ~ p243 ),
inference(split_conjunct,[status(thm)],[c_0_32]) ).
thf(c_0_45,plain,
p243,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_33,c_0_22])]) ).
thf(c_0_46,plain,
( ( fa3
!= ( fgroups1792256535list_a @ fqs2 ) )
| p20 ),
inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[nax20])]) ).
thf(c_0_47,plain,
~ p20,
inference(fof_simplification,[status(thm)],[ax2051]) ).
thf(c_0_48,plain,
( ~ p242
| ( ( fgroups1792256535list_a @ fqs2 )
= ( fcomm_m543484931mset_a @ ( fmset_a @ fqs2 ) ) ) ),
inference(fof_nnf,[status(thm)],[pax242]) ).
thf(c_0_49,plain,
( ( ( fgroups1792256535list_a @ fqs )
= ( fcomm_m543484931mset_a @ ( fmset_a @ fqs ) ) )
| ~ p246 ),
inference(split_conjunct,[status(thm)],[c_0_34]) ).
thf(c_0_50,plain,
( ( fmset_a @ fqs )
= ( fmset_a @ fqs2 ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_35,c_0_36])]) ).
thf(c_0_51,plain,
( ( fgroups1792256535list_a @ fqs )
= fa3 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_37,c_0_38])]) ).
thf(c_0_52,plain,
p246,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_39,c_0_40]),c_0_41])]) ).
thf(c_0_53,plain,
( p242
| ~ p244
| ~ p54 ),
inference(split_conjunct,[status(thm)],[c_0_42]) ).
thf(c_0_54,plain,
p54,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_43,c_0_28])]) ).
thf(c_0_55,plain,
p244,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_44,c_0_45])]) ).
thf(c_0_56,plain,
( p20
| ( fa3
!= ( fgroups1792256535list_a @ fqs2 ) ) ),
inference(split_conjunct,[status(thm)],[c_0_46]) ).
thf(c_0_57,plain,
~ p20,
inference(split_conjunct,[status(thm)],[c_0_47]) ).
thf(c_0_58,plain,
( ( ( fgroups1792256535list_a @ fqs2 )
= ( fcomm_m543484931mset_a @ ( fmset_a @ fqs2 ) ) )
| ~ p242 ),
inference(split_conjunct,[status(thm)],[c_0_48]) ).
thf(c_0_59,plain,
( ( fcomm_m543484931mset_a @ ( fmset_a @ fqs2 ) )
= fa3 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_49,c_0_50]),c_0_51]),c_0_52])]) ).
thf(c_0_60,plain,
p242,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_53,c_0_54]),c_0_55])]) ).
thf(c_0_61,plain,
( ( fgroups1792256535list_a @ fqs2 )
!= fa3 ),
inference(sr,[status(thm)],[c_0_56,c_0_57]) ).
thf(c_0_62,plain,
$false,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_58,c_0_59]),c_0_60])]),c_0_61]),
[proof] ).
thf(1,plain,
$false,
inference(eprover,[status(thm),assumptions([h2,h3,h1,h0])],[]) ).
thf(2,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h1,h0]),tab_negimp(discharge,[h2,h3])],[h1,1,h2,h3]) ).
thf(fact_4__092_060open_062_092_060And_062thesis_O_A_I_092_060And_062qs_O_A_092_060lbrakk_062a_A_061_Asum__list_Aqs_059_Aqs_A_092_060in_062_Alistset_Ass1_092_060rbrakk_062_A_092_060Longrightarrow_062_Athesis_J_A_092_060Longrightarrow_062_Athesis_092_060close_062,axiom,
~ ! [X1: list_a] :
( ( a3
= ( groups1792256535list_a @ X1 ) )
=> ~ ( member_list_a @ X1 @ ( listset_a @ ss1 ) ) ) ).
thf(3,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h0]),tab_negall(discharge,[h1]),tab_negall(eigenvar,eigen__0)],[fact_4__092_060open_062_092_060And_062thesis_O_A_I_092_060And_062qs_O_A_092_060lbrakk_062a_A_061_Asum__list_Aqs_059_Aqs_A_092_060in_062_Alistset_Ass1_092_060rbrakk_062_A_092_060Longrightarrow_062_Athesis_J_A_092_060Longrightarrow_062_Athesis_092_060close_062,2,h1]) ).
thf(0,theorem,
( a3
= ( groups1792256535list_a @ qs2 ) ),
inference(contra,[status(thm),contra(discharge,[h0])],[3,h0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.13 % Problem : ITP077^1 : TPTP v9.2.0. Released v7.5.0.
% 0.12/0.13 % Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% 0.14/0.35 % Computer : n015.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Wed Oct 8 17:52:08 EDT 2025
% 0.14/0.35 % CPUTime :
% 37.48/37.61 % SZS status Theorem
% 37.48/37.61 % Mode: mode478:USE_SINE=true:SINE_TOLERANCE=2.0:SINE_GENERALITY_THRESHOLD=16:SINE_RANK_LIMIT=1.:SINE_DEPTH=0
% 37.48/37.61 % Inferences: 1652
% 37.48/37.61 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------