%------------------------------------------------------------------------------
% File : Satallax---3.5
% Problem : ITP098^1 : 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 : n011.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 01:46:57 PM UTC 2025
% Result : Theorem 22.24s 22.51s
% Output : Proof 22.24s
% Verified :
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)
% Comments :
%------------------------------------------------------------------------------
thf(ty_a,type,
a: $tType ).
thf(ty_b,type,
b: $tType ).
thf(ty_set_c,type,
set_c: $tType ).
thf(ty_c,type,
c: $tType ).
thf(ty_set_a,type,
set_a: $tType ).
thf(ty_h,type,
h: c > a ).
thf(ty_inj_on_a_b,type,
inj_on_a_b: ( a > b ) > set_a > $o ).
thf(ty_sup_sup_set_a,type,
sup_sup_set_a: set_a > set_a > set_a ).
thf(ty_top_top_set_c,type,
top_top_set_c: set_c ).
thf(ty_image_c_a,type,
image_c_a: ( c > a ) > set_c > set_a ).
thf(ty_g,type,
g: c > a ).
thf(ty_comp_a_b_c,type,
comp_a_b_c: ( a > b ) > ( c > a ) > c > b ).
thf(ty_f,type,
f: a > b ).
thf(sP1,plain,
( sP1
<=> ( ( comp_a_b_c @ f @ g )
= ( comp_a_b_c @ f @ h ) ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ! [X1: c > a,X2: c > a] :
( ( ( comp_a_b_c @ f @ X1 )
= ( comp_a_b_c @ f @ X2 ) )
=> ( ( inj_on_a_b @ f @ ( sup_sup_set_a @ ( image_c_a @ X1 @ top_top_set_c ) @ ( image_c_a @ X2 @ top_top_set_c ) ) )
=> ( X1 = X2 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ! [X1: a > b,X2: c > a,X3: c > a] :
( ( ( comp_a_b_c @ X1 @ X2 )
= ( comp_a_b_c @ X1 @ X3 ) )
=> ( ( inj_on_a_b @ X1 @ ( sup_sup_set_a @ ( image_c_a @ X2 @ top_top_set_c ) @ ( image_c_a @ X3 @ top_top_set_c ) ) )
=> ( X2 = X3 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> ! [X1: c > a] :
( ( ( comp_a_b_c @ f @ g )
= ( comp_a_b_c @ f @ X1 ) )
=> ( ( inj_on_a_b @ f @ ( sup_sup_set_a @ ( image_c_a @ g @ top_top_set_c ) @ ( image_c_a @ X1 @ top_top_set_c ) ) )
=> ( g = X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(sP5,plain,
( sP5
<=> ( sP1
=> ( ( inj_on_a_b @ f @ ( sup_sup_set_a @ ( image_c_a @ g @ top_top_set_c ) @ ( image_c_a @ h @ top_top_set_c ) ) )
=> ( g = h ) ) ) ),
introduced(definition,[new_symbols(definition,[sP5])]) ).
thf(sP6,plain,
( sP6
<=> ( inj_on_a_b @ f @ ( sup_sup_set_a @ ( image_c_a @ g @ top_top_set_c ) @ ( image_c_a @ h @ top_top_set_c ) ) ) ),
introduced(definition,[new_symbols(definition,[sP6])]) ).
thf(sP7,plain,
( sP7
<=> ( g = h ) ),
introduced(definition,[new_symbols(definition,[sP7])]) ).
thf(sP8,plain,
( sP8
<=> ( sP6
=> sP7 ) ),
introduced(definition,[new_symbols(definition,[sP8])]) ).
thf(conj_2,conjecture,
sP7 ).
thf(h0,negated_conjecture,
~ sP7,
inference(assume_negation,[status(cth)],[conj_2]) ).
thf(1,plain,
( ~ sP3
| sP2 ),
inference(all_rule,[status(thm)],[]) ).
thf(2,plain,
( ~ sP2
| sP4 ),
inference(all_rule,[status(thm)],[]) ).
thf(3,plain,
( ~ sP4
| sP5 ),
inference(all_rule,[status(thm)],[]) ).
thf(4,plain,
( ~ sP5
| ~ sP1
| sP8 ),
inference(prop_rule,[status(thm)],[]) ).
thf(5,plain,
( ~ sP8
| ~ sP6
| sP7 ),
inference(prop_rule,[status(thm)],[]) ).
thf(fact_8_o__inj__on,axiom,
sP3 ).
thf(conj_0,axiom,
sP6 ).
thf(conj_1,axiom,
sP1 ).
thf(6,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h0])],[1,2,3,4,5,fact_8_o__inj__on,conj_0,conj_1,h0]) ).
thf(0,theorem,
sP7,
inference(contra,[status(thm),contra(discharge,[h0])],[6,h0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : ITP098^1 : TPTP v9.2.0. Released v7.5.0.
% 0.06/0.13 % Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% 0.12/0.33 % Computer : n011.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Wed Oct 8 18:36:08 EDT 2025
% 0.12/0.34 % CPUTime :
% 22.24/22.51 % SZS status Theorem
% 22.24/22.51 % Mode: mode454:USE_SINE=true:SINE_TOLERANCE=2.0:SINE_GENERALITY_THRESHOLD=4:SINE_RANK_LIMIT=3.:SINE_DEPTH=0
% 22.24/22.51 % Inferences: 305
% 22.24/22.51 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------