%------------------------------------------------------------------------------
% File : Satallax---3.5
% Problem : ITP049^1 : 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 : n016.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 01:46:49 PM UTC 2025
% Result : Theorem 0.18s 0.51s
% Output : Proof 0.18s
% Verified :
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)
% Comments :
%------------------------------------------------------------------------------
thf(ty_product_prod_nat_nat,type,
product_prod_nat_nat: $tType ).
thf(ty_a,type,
a: $tType ).
thf(ty_set_nat,type,
set_nat: $tType ).
thf(ty_set_Pr1986765409at_nat,type,
set_Pr1986765409at_nat: $tType ).
thf(ty_nat,type,
nat: $tType ).
thf(ty_finite772653738at_nat,type,
finite772653738at_nat: set_Pr1986765409at_nat > $o ).
thf(ty_finite_finite_nat,type,
finite_finite_nat: set_nat > $o ).
thf(ty_s,type,
s: nat ).
thf(ty_edmond475474835dges_a,type,
edmond475474835dges_a: ( product_prod_nat_nat > a ) > nat > nat > set_Pr1986765409at_nat ).
thf(ty_v_a,type,
v_a: ( product_prod_nat_nat > a ) > set_nat ).
thf(ty_t,type,
t: nat ).
thf(ty_c,type,
c: product_prod_nat_nat > a ).
thf(ty_e_a,type,
e_a: ( product_prod_nat_nat > a ) > set_Pr1986765409at_nat ).
thf(ty_finite_Graph_a,type,
finite_Graph_a: ( product_prod_nat_nat > a ) > $o ).
thf(sP1,plain,
( sP1
<=> ( finite_finite_nat @ ( v_a @ c ) ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ( finite772653738at_nat @ ( edmond475474835dges_a @ c @ s @ t ) ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ( finite772653738at_nat @ ( e_a @ c ) ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(conj_0,conjecture,
sP2 ).
thf(h0,negated_conjecture,
~ sP2,
inference(assume_negation,[status(cth)],[conj_0]) ).
thf(h1,assumption,
~ sP1,
introduced(assumption,[]) ).
thf(h2,assumption,
sP3,
introduced(assumption,[]) ).
thf(h3,assumption,
~ sP3,
introduced(assumption,[]) ).
thf(h4,assumption,
sP1,
introduced(assumption,[]) ).
thf(h5,assumption,
finite_Graph_a @ c,
introduced(assumption,[]) ).
thf(h6,assumption,
sP2,
introduced(assumption,[]) ).
thf(fact_3_finite__E,axiom,
sP3 ).
thf(1,plain,
$false,
inference(tab_conflict,[status(thm),assumptions([h3,h3,h3,h1,h0])],[fact_3_finite__E,h3]) ).
thf(2,plain,
$false,
inference(tab_conflict,[status(thm),assumptions([h6,h3,h3,h1,h0])],[fact_3_finite__E,h3]) ).
thf(fact_1__092_060open_062finite_AE_A_092_060Longrightarrow_062_Afinite_AspEdges_092_060close_062,axiom,
( sP3
=> sP2 ) ).
thf(3,plain,
$false,
inference(tab_imp,[status(thm),assumptions([h3,h3,h1,h0]),tab_imp(discharge,[h3]),tab_imp(discharge,[h6])],[fact_1__092_060open_062finite_AE_A_092_060Longrightarrow_062_Afinite_AspEdges_092_060close_062,1,2,h3,h6]) ).
thf(4,plain,
$false,
inference(tab_conflict,[status(thm),assumptions([h3,h5,h3,h1,h0])],[fact_3_finite__E,h3]) ).
thf(5,plain,
$false,
inference(tab_conflict,[status(thm),assumptions([h6,h5,h3,h1,h0])],[fact_3_finite__E,h3]) ).
thf(6,plain,
$false,
inference(tab_imp,[status(thm),assumptions([h5,h3,h1,h0]),tab_imp(discharge,[h3]),tab_imp(discharge,[h6])],[fact_1__092_060open_062finite_AE_A_092_060Longrightarrow_062_Afinite_AspEdges_092_060close_062,4,5,h3,h6]) ).
thf(fact_6_Finite__Graph__EI,axiom,
( sP3
=> ( finite_Graph_a @ c ) ) ).
thf(7,plain,
$false,
inference(tab_imp,[status(thm),assumptions([h3,h1,h0]),tab_imp(discharge,[h3]),tab_imp(discharge,[h5])],[fact_6_Finite__Graph__EI,3,6,h3,h5]) ).
thf(8,plain,
$false,
inference(tab_conflict,[status(thm),assumptions([h3,h3,h4,h1,h0])],[fact_3_finite__E,h3]) ).
thf(9,plain,
$false,
inference(tab_conflict,[status(thm),assumptions([h6,h3,h4,h1,h0])],[fact_3_finite__E,h3]) ).
thf(10,plain,
$false,
inference(tab_imp,[status(thm),assumptions([h3,h4,h1,h0]),tab_imp(discharge,[h3]),tab_imp(discharge,[h6])],[fact_1__092_060open_062finite_AE_A_092_060Longrightarrow_062_Afinite_AspEdges_092_060close_062,8,9,h3,h6]) ).
thf(11,plain,
$false,
inference(tab_conflict,[status(thm),assumptions([h3,h5,h4,h1,h0])],[fact_3_finite__E,h3]) ).
thf(12,plain,
$false,
inference(tab_conflict,[status(thm),assumptions([h6,h5,h4,h1,h0])],[h4,h1]) ).
thf(13,plain,
$false,
inference(tab_imp,[status(thm),assumptions([h5,h4,h1,h0]),tab_imp(discharge,[h3]),tab_imp(discharge,[h6])],[fact_1__092_060open_062finite_AE_A_092_060Longrightarrow_062_Afinite_AspEdges_092_060close_062,11,12,h3,h6]) ).
thf(14,plain,
$false,
inference(tab_imp,[status(thm),assumptions([h4,h1,h0]),tab_imp(discharge,[h3]),tab_imp(discharge,[h5])],[fact_6_Finite__Graph__EI,10,13,h3,h5]) ).
thf(fact_11_Efin__imp__Vfin,axiom,
( sP3
=> sP1 ) ).
thf(15,plain,
$false,
inference(tab_imp,[status(thm),assumptions([h1,h0]),tab_imp(discharge,[h3]),tab_imp(discharge,[h4])],[fact_11_Efin__imp__Vfin,7,14,h3,h4]) ).
thf(16,plain,
$false,
inference(tab_conflict,[status(thm),assumptions([h3,h3,h3,h2,h0])],[h2,h3]) ).
thf(17,plain,
$false,
inference(tab_conflict,[status(thm),assumptions([h6,h3,h3,h2,h0])],[h2,h3]) ).
thf(18,plain,
$false,
inference(tab_imp,[status(thm),assumptions([h3,h3,h2,h0]),tab_imp(discharge,[h3]),tab_imp(discharge,[h6])],[fact_1__092_060open_062finite_AE_A_092_060Longrightarrow_062_Afinite_AspEdges_092_060close_062,16,17,h3,h6]) ).
thf(19,plain,
$false,
inference(tab_conflict,[status(thm),assumptions([h3,h5,h3,h2,h0])],[h2,h3]) ).
thf(20,plain,
$false,
inference(tab_conflict,[status(thm),assumptions([h6,h5,h3,h2,h0])],[h2,h3]) ).
thf(21,plain,
$false,
inference(tab_imp,[status(thm),assumptions([h5,h3,h2,h0]),tab_imp(discharge,[h3]),tab_imp(discharge,[h6])],[fact_1__092_060open_062finite_AE_A_092_060Longrightarrow_062_Afinite_AspEdges_092_060close_062,19,20,h3,h6]) ).
thf(22,plain,
$false,
inference(tab_imp,[status(thm),assumptions([h3,h2,h0]),tab_imp(discharge,[h3]),tab_imp(discharge,[h5])],[fact_6_Finite__Graph__EI,18,21,h3,h5]) ).
thf(23,plain,
$false,
inference(tab_conflict,[status(thm),assumptions([h3,h3,h4,h2,h0])],[h2,h3]) ).
thf(24,plain,
$false,
inference(tab_conflict,[status(thm),assumptions([h6,h3,h4,h2,h0])],[h2,h3]) ).
thf(25,plain,
$false,
inference(tab_imp,[status(thm),assumptions([h3,h4,h2,h0]),tab_imp(discharge,[h3]),tab_imp(discharge,[h6])],[fact_1__092_060open_062finite_AE_A_092_060Longrightarrow_062_Afinite_AspEdges_092_060close_062,23,24,h3,h6]) ).
thf(26,plain,
$false,
inference(tab_conflict,[status(thm),assumptions([h3,h5,h4,h2,h0])],[h2,h3]) ).
thf(27,plain,
$false,
inference(tab_conflict,[status(thm),assumptions([h6,h5,h4,h2,h0])],[h6,h0]) ).
thf(28,plain,
$false,
inference(tab_imp,[status(thm),assumptions([h5,h4,h2,h0]),tab_imp(discharge,[h3]),tab_imp(discharge,[h6])],[fact_1__092_060open_062finite_AE_A_092_060Longrightarrow_062_Afinite_AspEdges_092_060close_062,26,27,h3,h6]) ).
thf(29,plain,
$false,
inference(tab_imp,[status(thm),assumptions([h4,h2,h0]),tab_imp(discharge,[h3]),tab_imp(discharge,[h5])],[fact_6_Finite__Graph__EI,25,28,h3,h5]) ).
thf(30,plain,
$false,
inference(tab_imp,[status(thm),assumptions([h2,h0]),tab_imp(discharge,[h3]),tab_imp(discharge,[h4])],[fact_11_Efin__imp__Vfin,22,29,h3,h4]) ).
thf(fact_25_Vfin__imp__Efin,axiom,
( sP1
=> sP3 ) ).
thf(31,plain,
$false,
inference(tab_imp,[status(thm),assumptions([h0]),tab_imp(discharge,[h1]),tab_imp(discharge,[h2])],[fact_25_Vfin__imp__Efin,15,30,h1,h2]) ).
thf(0,theorem,
sP2,
inference(contra,[status(thm),contra(discharge,[h0])],[31,h0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : ITP049^1 : TPTP v9.2.0. Released v7.5.0.
% 0.03/0.13 % Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% 0.12/0.33 % Computer : n016.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 17:53:23 EDT 2025
% 0.12/0.34 % CPUTime :
% 0.18/0.51 % SZS status Theorem
% 0.18/0.51 % Mode: mode507:USE_SINE=true:SINE_TOLERANCE=3.0:SINE_GENERALITY_THRESHOLD=0:SINE_RANK_LIMIT=1.:SINE_DEPTH=1
% 0.18/0.51 % Inferences: 0
% 0.18/0.51 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------