%------------------------------------------------------------------------------
% File : Satallax---3.5
% Problem : ITP162^1 : 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 : n018.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 174.34s 174.28s
% Output : Proof 174.34s
% 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_p,type,
p: a > $o ).
thf(ty_q,type,
q: a > $o ).
thf(ty_ord_le519537037nres_a,type,
ord_le519537037nres_a: refine424419629nres_a > refine424419629nres_a > $o ).
thf(ty_a2,type,
a2: refine424419629nres_a ).
thf(ty_inf_inf_set_a,type,
inf_inf_set_a: set_a > set_a > set_a ).
thf(ty_collect_a,type,
collect_a: ( a > $o ) > set_a ).
thf(ty_inf_in262696383nres_a,type,
inf_in262696383nres_a: refine424419629nres_a > refine424419629nres_a > refine424419629nres_a ).
thf(ty_refine1198353288_RES_a,type,
refine1198353288_RES_a: set_a > refine424419629nres_a ).
thf(sP1,plain,
( sP1
<=> ! [X1: a > $o,X2: a > $o] :
( ( collect_a
@ ^ [X3: a] :
~ ( ( X1 @ X3 )
=> ~ ( X2 @ X3 ) ) )
= ( inf_inf_set_a @ ( collect_a @ X1 ) @ ( collect_a @ X2 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ! [X1: set_a] :
( ( ( collect_a
@ ^ [X2: a] :
~ ( ( p @ X2 )
=> ~ ( q @ X2 ) ) )
= X1 )
=> ~ ( ord_le519537037nres_a @ a2 @ ( refine1198353288_RES_a @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ! [X1: set_a,X2: set_a > $o] :
( ( X2 @ X1 )
=> ! [X3: set_a] :
( ( X1 = X3 )
=> ( X2 @ X3 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> ! [X1: a > $o] :
( ( collect_a
@ ^ [X2: a] :
~ ( ( p @ X2 )
=> ~ ( X1 @ X2 ) ) )
= ( inf_inf_set_a @ ( collect_a @ p ) @ ( collect_a @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(sP5,plain,
( sP5
<=> ( ~ ( ord_le519537037nres_a @ a2
@ ( refine1198353288_RES_a
@ ( collect_a
@ ^ [X1: a] :
~ ( ( p @ X1 )
=> ~ ( q @ X1 ) ) ) ) )
=> sP2 ) ),
introduced(definition,[new_symbols(definition,[sP5])]) ).
thf(sP6,plain,
( sP6
<=> ( ord_le519537037nres_a @ a2 @ ( inf_in262696383nres_a @ ( refine1198353288_RES_a @ ( collect_a @ p ) ) @ ( refine1198353288_RES_a @ ( collect_a @ q ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP6])]) ).
thf(sP7,plain,
( sP7
<=> ( ord_le519537037nres_a @ a2 @ ( refine1198353288_RES_a @ ( inf_inf_set_a @ ( collect_a @ p ) @ ( collect_a @ q ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP7])]) ).
thf(sP8,plain,
( sP8
<=> ( ( ( collect_a
@ ^ [X1: a] :
~ ( ( p @ X1 )
=> ~ ( q @ X1 ) ) )
= ( inf_inf_set_a @ ( collect_a @ p ) @ ( collect_a @ q ) ) )
=> ~ sP7 ) ),
introduced(definition,[new_symbols(definition,[sP8])]) ).
thf(sP9,plain,
( sP9
<=> ( ( collect_a
@ ^ [X1: a] :
~ ( ( p @ X1 )
=> ~ ( q @ X1 ) ) )
= ( inf_inf_set_a @ ( collect_a @ p ) @ ( collect_a @ q ) ) ) ),
introduced(definition,[new_symbols(definition,[sP9])]) ).
thf(sP10,plain,
( sP10
<=> ( ~ sP7
=> ! [X1: refine424419629nres_a] :
( ( X1
= ( refine1198353288_RES_a @ ( inf_inf_set_a @ ( collect_a @ p ) @ ( collect_a @ q ) ) ) )
=> ~ ( ord_le519537037nres_a @ a2 @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP10])]) ).
thf(sP11,plain,
( sP11
<=> ! [X1: set_a] :
( ( inf_in262696383nres_a @ ( refine1198353288_RES_a @ ( collect_a @ p ) ) @ ( refine1198353288_RES_a @ X1 ) )
= ( refine1198353288_RES_a @ ( inf_inf_set_a @ ( collect_a @ p ) @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP11])]) ).
thf(sP12,plain,
( sP12
<=> ! [X1: refine424419629nres_a,X2: refine424419629nres_a > $o] :
( ( X2 @ X1 )
=> ! [X3: refine424419629nres_a] :
( ( X3 = X1 )
=> ( X2 @ X3 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP12])]) ).
thf(sP13,plain,
( sP13
<=> ! [X1: set_a > $o] :
( ( X1
@ ( collect_a
@ ^ [X2: a] :
~ ( ( p @ X2 )
=> ~ ( q @ X2 ) ) ) )
=> ! [X2: set_a] :
( ( ( collect_a
@ ^ [X3: a] :
~ ( ( p @ X3 )
=> ~ ( q @ X3 ) ) )
= X2 )
=> ( X1 @ X2 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP13])]) ).
thf(sP14,plain,
( sP14
<=> ( ord_le519537037nres_a @ a2
@ ( refine1198353288_RES_a
@ ( collect_a
@ ^ [X1: a] :
~ ( ( p @ X1 )
=> ~ ( q @ X1 ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP14])]) ).
thf(sP15,plain,
( sP15
<=> ! [X1: refine424419629nres_a] :
( ( X1
= ( refine1198353288_RES_a @ ( inf_inf_set_a @ ( collect_a @ p ) @ ( collect_a @ q ) ) ) )
=> ~ ( ord_le519537037nres_a @ a2 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP15])]) ).
thf(sP16,plain,
( sP16
<=> ! [X1: refine424419629nres_a > $o] :
( ( X1 @ ( refine1198353288_RES_a @ ( inf_inf_set_a @ ( collect_a @ p ) @ ( collect_a @ q ) ) ) )
=> ! [X2: refine424419629nres_a] :
( ( X2
= ( refine1198353288_RES_a @ ( inf_inf_set_a @ ( collect_a @ p ) @ ( collect_a @ q ) ) ) )
=> ( X1 @ X2 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP16])]) ).
thf(sP17,plain,
( sP17
<=> ! [X1: set_a,X2: set_a] :
( ( inf_in262696383nres_a @ ( refine1198353288_RES_a @ X1 ) @ ( refine1198353288_RES_a @ X2 ) )
= ( refine1198353288_RES_a @ ( inf_inf_set_a @ X1 @ X2 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP17])]) ).
thf(sP18,plain,
( sP18
<=> ( ( ( inf_in262696383nres_a @ ( refine1198353288_RES_a @ ( collect_a @ p ) ) @ ( refine1198353288_RES_a @ ( collect_a @ q ) ) )
= ( refine1198353288_RES_a @ ( inf_inf_set_a @ ( collect_a @ p ) @ ( collect_a @ q ) ) ) )
=> ~ sP6 ) ),
introduced(definition,[new_symbols(definition,[sP18])]) ).
thf(sP19,plain,
( sP19
<=> ( ( inf_in262696383nres_a @ ( refine1198353288_RES_a @ ( collect_a @ p ) ) @ ( refine1198353288_RES_a @ ( collect_a @ q ) ) )
= ( refine1198353288_RES_a @ ( inf_inf_set_a @ ( collect_a @ p ) @ ( collect_a @ q ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP19])]) ).
thf(conj_0,conjecture,
sP14 ).
thf(h0,negated_conjecture,
~ sP14,
inference(assume_negation,[status(cth)],[conj_0]) ).
thf(1,plain,
( ~ sP17
| sP11 ),
inference(all_rule,[status(thm)],[]) ).
thf(2,plain,
( ~ sP11
| sP19 ),
inference(all_rule,[status(thm)],[]) ).
thf(3,plain,
( ~ sP18
| ~ sP19
| ~ sP6 ),
inference(prop_rule,[status(thm)],[]) ).
thf(4,plain,
( ~ sP15
| sP18 ),
inference(all_rule,[status(thm)],[]) ).
thf(5,plain,
( ~ sP10
| sP7
| sP15 ),
inference(prop_rule,[status(thm)],[]) ).
thf(6,plain,
( ~ sP16
| sP10 ),
inference(all_rule,[status(thm)],[]) ).
thf(7,plain,
( ~ sP12
| sP16 ),
inference(all_rule,[status(thm)],[]) ).
thf(8,plain,
sP12,
inference(eq_ind_sym,[status(thm)],[]) ).
thf(9,plain,
( ~ sP1
| sP4 ),
inference(all_rule,[status(thm)],[]) ).
thf(10,plain,
( ~ sP4
| sP9 ),
inference(all_rule,[status(thm)],[]) ).
thf(11,plain,
( ~ sP8
| ~ sP9
| ~ sP7 ),
inference(prop_rule,[status(thm)],[]) ).
thf(12,plain,
( ~ sP2
| sP8 ),
inference(all_rule,[status(thm)],[]) ).
thf(13,plain,
( ~ sP5
| sP14
| sP2 ),
inference(prop_rule,[status(thm)],[]) ).
thf(14,plain,
( ~ sP13
| sP5 ),
inference(all_rule,[status(thm)],[]) ).
thf(15,plain,
( ~ sP3
| sP13 ),
inference(all_rule,[status(thm)],[]) ).
thf(16,plain,
sP3,
inference(eq_ind,[status(thm)],[]) ).
thf(fact_272_Collect__conj__eq,axiom,
sP1 ).
thf(fact_148_inf__nres_Osimps_I3_J,axiom,
sP17 ).
thf(fact_4__092_060open_062A_A_092_060le_062_Ainf_A_ISPEC_AP_J_A_ISPEC_AQ_J_092_060close_062,axiom,
sP6 ).
thf(17,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h0])],[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,fact_272_Collect__conj__eq,fact_148_inf__nres_Osimps_I3_J,fact_4__092_060open_062A_A_092_060le_062_Ainf_A_ISPEC_AP_J_A_ISPEC_AQ_J_092_060close_062,h0]) ).
thf(0,theorem,
sP14,
inference(contra,[status(thm),contra(discharge,[h0])],[17,h0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.12 % Problem : ITP162^1 : TPTP v9.2.0. Released v7.5.0.
% 0.08/0.13 % Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% 0.13/0.34 % Computer : n018.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Wed Oct 8 17:51:53 EDT 2025
% 0.13/0.34 % CPUTime :
% 174.34/174.28 % SZS status Theorem
% 174.34/174.28 % Mode: mode503:USE_SINE=true:SINE_TOLERANCE=1.2:SINE_GENERALITY_THRESHOLD=0:SINE_RANK_LIMIT=4.:SINE_DEPTH=0
% 174.34/174.28 % Inferences: 85
% 174.34/174.28 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------