%------------------------------------------------------------------------------
% File : Satallax---3.5
% Problem : ITP163^1 : 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 : n029.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 26.24s 26.39s
% Output : Proof 26.24s
% 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_set_a,type,
set_a: $tType ).
thf(ty_member_a,type,
member_a: a > set_a > $o ).
thf(ty_phi,type,
phi: a > $o ).
thf(ty_collect_a,type,
collect_a: ( a > $o ) > set_a ).
thf(ty_refine1312857699nres_a,type,
refine1312857699nres_a: refine424419629nres_a > a > $o ).
thf(ty_refine1198353288_RES_a,type,
refine1198353288_RES_a: set_a > refine424419629nres_a ).
thf(ty_x,type,
x: a ).
thf(sP1,plain,
( sP1
<=> ( phi @ x ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ! [X1: a > $o] :
( ( member_a @ x @ ( collect_a @ X1 ) )
= ( X1 @ x ) ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ( ( member_a @ x @ ( collect_a @ phi ) )
= sP1 ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> ! [X1: set_a,X2: a] :
( ( refine1312857699nres_a @ ( refine1198353288_RES_a @ X1 ) @ X2 )
= ( member_a @ X2 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(sP5,plain,
( sP5
<=> ( refine1312857699nres_a @ ( refine1198353288_RES_a @ ( collect_a @ phi ) ) @ x ) ),
introduced(definition,[new_symbols(definition,[sP5])]) ).
thf(sP6,plain,
( sP6
<=> ( member_a @ x @ ( collect_a @ phi ) ) ),
introduced(definition,[new_symbols(definition,[sP6])]) ).
thf(sP7,plain,
( sP7
<=> ( sP5 = sP1 ) ),
introduced(definition,[new_symbols(definition,[sP7])]) ).
thf(sP8,plain,
( sP8
<=> ( sP5 = sP6 ) ),
introduced(definition,[new_symbols(definition,[sP8])]) ).
thf(sP9,plain,
( sP9
<=> ! [X1: a] :
( ( refine1312857699nres_a @ ( refine1198353288_RES_a @ ( collect_a @ phi ) ) @ X1 )
= ( member_a @ X1 @ ( collect_a @ phi ) ) ) ),
introduced(definition,[new_symbols(definition,[sP9])]) ).
thf(sP10,plain,
( sP10
<=> ! [X1: a,X2: a > $o] :
( ( member_a @ X1 @ ( collect_a @ X2 ) )
= ( X2 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP10])]) ).
thf(conj_0,conjecture,
sP7 ).
thf(h0,negated_conjecture,
~ sP7,
inference(assume_negation,[status(cth)],[conj_0]) ).
thf(1,plain,
( ~ sP8
| ~ sP5
| sP6 ),
inference(prop_rule,[status(thm)],[]) ).
thf(2,plain,
( ~ sP8
| sP5
| ~ sP6 ),
inference(prop_rule,[status(thm)],[]) ).
thf(3,plain,
( ~ sP3
| ~ sP6
| sP1 ),
inference(prop_rule,[status(thm)],[]) ).
thf(4,plain,
( ~ sP3
| sP6
| ~ sP1 ),
inference(prop_rule,[status(thm)],[]) ).
thf(5,plain,
( ~ sP2
| sP3 ),
inference(all_rule,[status(thm)],[]) ).
thf(6,plain,
( ~ sP9
| sP8 ),
inference(all_rule,[status(thm)],[]) ).
thf(7,plain,
( ~ sP4
| sP9 ),
inference(all_rule,[status(thm)],[]) ).
thf(8,plain,
( ~ sP10
| sP2 ),
inference(all_rule,[status(thm)],[]) ).
thf(9,plain,
( sP7
| ~ sP5
| ~ sP1 ),
inference(prop_rule,[status(thm)],[]) ).
thf(10,plain,
( sP7
| sP5
| sP1 ),
inference(prop_rule,[status(thm)],[]) ).
thf(fact_2_nf__inres__RES,axiom,
sP4 ).
thf(fact_41_mem__Collect__eq,axiom,
sP10 ).
thf(11,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h0])],[1,2,3,4,5,6,7,8,9,10,fact_2_nf__inres__RES,fact_41_mem__Collect__eq,h0]) ).
thf(0,theorem,
sP7,
inference(contra,[status(thm),contra(discharge,[h0])],[11,h0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.11 % Problem : ITP163^1 : TPTP v9.2.0. Released v7.5.0.
% 0.07/0.12 % Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% 0.11/0.35 % Computer : n029.cluster.edu
% 0.11/0.35 % Model : x86_64 x86_64
% 0.11/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.35 % Memory : 8042.1875MB
% 0.11/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.35 % CPULimit : 300
% 0.11/0.35 % WCLimit : 300
% 0.11/0.35 % DateTime : Wed Oct 8 17:50:23 EDT 2025
% 0.11/0.35 % CPUTime :
% 26.24/26.39 % SZS status Theorem
% 26.24/26.39 % Mode: mode9:USE_SINE=true:SINE_TOLERANCE=2.0:SINE_GENERALITY_THRESHOLD=16:SINE_RANK_LIMIT=1.:SINE_DEPTH=0
% 26.24/26.39 % Inferences: 2920
% 26.24/26.39 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------