%------------------------------------------------------------------------------
% File : Satallax---3.5
% Problem : ITP161^1 : 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 : n006.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 01:47:09 PM UTC 2025
% Result : Theorem 28.03s 28.66s
% Output : Proof 28.03s
% Verified :
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)
% Comments :
%------------------------------------------------------------------------------
thf(ty_a,type,
a: $tType ).
thf(ty_refine424419629nres_a,type,
refine424419629nres_a: $tType ).
thf(ty_refine432681134nres_b,type,
refine432681134nres_b: $tType ).
thf(ty_set_a,type,
set_a: $tType ).
thf(ty_member_a,type,
member_a: a > set_a > $o ).
thf(ty_refine436832839nd_a_b,type,
refine436832839nd_a_b: refine424419629nres_a > ( a > refine432681134nres_b ) > refine432681134nres_b ).
thf(ty_ord_le527798542nres_b,type,
ord_le527798542nres_b: refine432681134nres_b > refine432681134nres_b > $o ).
thf(ty_phi,type,
phi: a > $o ).
thf(ty_collect_a,type,
collect_a: ( a > $o ) > set_a ).
thf(ty_f,type,
f: a > refine432681134nres_b ).
thf(ty_refine1198353288_RES_a,type,
refine1198353288_RES_a: set_a > refine424419629nres_a ).
thf(ty_m,type,
m: refine432681134nres_b ).
thf(ty_x,type,
x: a ).
thf(sP1,plain,
( sP1
<=> ( member_a @ x @ ( collect_a @ phi ) ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ! [X1: a > refine432681134nres_b] :
( sP1
=> ( ( ord_le527798542nres_b @ m @ ( X1 @ x ) )
=> ( ord_le527798542nres_b @ m @ ( refine436832839nd_a_b @ ( refine1198353288_RES_a @ ( collect_a @ phi ) ) @ X1 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ( sP1
=> ( ( ord_le527798542nres_b @ m @ ( f @ x ) )
=> ( ord_le527798542nres_b @ m @ ( refine436832839nd_a_b @ ( refine1198353288_RES_a @ ( collect_a @ phi ) ) @ f ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> ( sP1
= ( phi @ x ) ) ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(sP5,plain,
( sP5
<=> ! [X1: a,X2: set_a,X3: refine432681134nres_b,X4: a > refine432681134nres_b] :
( ( member_a @ X1 @ X2 )
=> ( ( ord_le527798542nres_b @ X3 @ ( X4 @ X1 ) )
=> ( ord_le527798542nres_b @ X3 @ ( refine436832839nd_a_b @ ( refine1198353288_RES_a @ X2 ) @ X4 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP5])]) ).
thf(sP6,plain,
( sP6
<=> ! [X1: refine432681134nres_b,X2: a > refine432681134nres_b] :
( sP1
=> ( ( ord_le527798542nres_b @ X1 @ ( X2 @ x ) )
=> ( ord_le527798542nres_b @ X1 @ ( refine436832839nd_a_b @ ( refine1198353288_RES_a @ ( collect_a @ phi ) ) @ X2 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP6])]) ).
thf(sP7,plain,
( sP7
<=> ! [X1: a,X2: a > $o] :
( ( member_a @ X1 @ ( collect_a @ X2 ) )
= ( X2 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP7])]) ).
thf(sP8,plain,
( sP8
<=> ! [X1: set_a,X2: refine432681134nres_b,X3: a > refine432681134nres_b] :
( ( member_a @ x @ X1 )
=> ( ( ord_le527798542nres_b @ X2 @ ( X3 @ x ) )
=> ( ord_le527798542nres_b @ X2 @ ( refine436832839nd_a_b @ ( refine1198353288_RES_a @ X1 ) @ X3 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP8])]) ).
thf(sP9,plain,
( sP9
<=> ( ord_le527798542nres_b @ m @ ( f @ x ) ) ),
introduced(definition,[new_symbols(definition,[sP9])]) ).
thf(sP10,plain,
( sP10
<=> ( ord_le527798542nres_b @ m @ ( refine436832839nd_a_b @ ( refine1198353288_RES_a @ ( collect_a @ phi ) ) @ f ) ) ),
introduced(definition,[new_symbols(definition,[sP10])]) ).
thf(sP11,plain,
( sP11
<=> ( sP9
=> sP10 ) ),
introduced(definition,[new_symbols(definition,[sP11])]) ).
thf(sP12,plain,
( sP12
<=> ( phi @ x ) ),
introduced(definition,[new_symbols(definition,[sP12])]) ).
thf(sP13,plain,
( sP13
<=> ! [X1: a > $o] :
( ( member_a @ x @ ( collect_a @ X1 ) )
= ( X1 @ x ) ) ),
introduced(definition,[new_symbols(definition,[sP13])]) ).
thf(conj_0,conjecture,
sP10 ).
thf(h0,negated_conjecture,
~ sP10,
inference(assume_negation,[status(cth)],[conj_0]) ).
thf(1,plain,
( ~ sP4
| sP1
| ~ sP12 ),
inference(prop_rule,[status(thm)],[]) ).
thf(2,plain,
( ~ sP11
| ~ sP9
| sP10 ),
inference(prop_rule,[status(thm)],[]) ).
thf(3,plain,
( ~ sP3
| ~ sP1
| sP11 ),
inference(prop_rule,[status(thm)],[]) ).
thf(4,plain,
( ~ sP13
| sP4 ),
inference(all_rule,[status(thm)],[]) ).
thf(5,plain,
( ~ sP2
| sP3 ),
inference(all_rule,[status(thm)],[]) ).
thf(6,plain,
( ~ sP6
| sP2 ),
inference(all_rule,[status(thm)],[]) ).
thf(7,plain,
( ~ sP8
| sP6 ),
inference(all_rule,[status(thm)],[]) ).
thf(8,plain,
( ~ sP7
| sP13 ),
inference(all_rule,[status(thm)],[]) ).
thf(9,plain,
( ~ sP5
| sP8 ),
inference(all_rule,[status(thm)],[]) ).
thf(fact_0_assms_I1_J,axiom,
sP12 ).
thf(fact_1_assms_I2_J,axiom,
sP9 ).
thf(fact_35_RES__bind__choose,axiom,
sP5 ).
thf(fact_107_mem__Collect__eq,axiom,
sP7 ).
thf(10,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h0])],[1,2,3,4,5,6,7,8,9,fact_0_assms_I1_J,fact_1_assms_I2_J,fact_35_RES__bind__choose,fact_107_mem__Collect__eq,h0]) ).
thf(0,theorem,
sP10,
inference(contra,[status(thm),contra(discharge,[h0])],[10,h0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.13 % Problem : ITP161^1 : 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
% 0.15/0.35 % Computer : n006.cluster.edu
% 0.15/0.35 % Model : x86_64 x86_64
% 0.15/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.35 % Memory : 8042.1875MB
% 0.15/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.35 % CPULimit : 300
% 0.15/0.35 % WCLimit : 300
% 0.15/0.35 % DateTime : Wed Oct 8 18:23:23 EDT 2025
% 0.15/0.35 % CPUTime :
% 28.03/28.66 % SZS status Theorem
% 28.03/28.66 % Mode: mode9:USE_SINE=true:SINE_TOLERANCE=2.0:SINE_GENERALITY_THRESHOLD=16:SINE_RANK_LIMIT=1.:SINE_DEPTH=0
% 28.03/28.66 % Inferences: 11702
% 28.03/28.66 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------