%------------------------------------------------------------------------------
% File : Lash---1.13
% Problem : ITP038^1 : TPTP v9.2.0. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : lash -P picomus -M modes -p tstp -t %d %s
% Computer : n023.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 01:44:52 PM UTC 2025
% Result : Theorem 0.19s 0.46s
% Output : Proof 0.19s
% Verified :
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)
% Comments :
%------------------------------------------------------------------------------
thf(ty_denota231621370t_unit,type,
denota231621370t_unit: $tType ).
thf(ty_real,type,
real: $tType ).
thf(ty_set_Sum_sum_c_c,type,
set_Sum_sum_c_c: $tType ).
thf(ty_set_Su1783761653um_b_c,type,
set_Su1783761653um_b_c: $tType ).
thf(ty_a,type,
a: $tType ).
thf(ty_finite1398487019real_c,type,
finite1398487019real_c: $tType ).
thf(ty_sum_su737395349um_b_c,type,
sum_su737395349um_b_c: $tType ).
thf(ty_set_a,type,
set_a: $tType ).
thf(ty_produc190496183real_c,type,
produc190496183real_c: $tType ).
thf(ty_trm_a_c,type,
trm_a_c: $tType ).
thf(ty_plus_a_c,type,
plus_a_c: trm_a_c > trm_a_c > trm_a_c ).
thf(ty_nu2,type,
nu2: produc190496183real_c ).
thf(ty_static_FVDiff_a_c,type,
static_FVDiff_a_c: trm_a_c > set_Sum_sum_c_c ).
thf(ty_produc314122909real_c,type,
produc314122909real_c: produc190496183real_c > finite1398487019real_c ).
thf(ty_member_a,type,
member_a: a > set_a > $o ).
thf(ty_j,type,
j: denota231621370t_unit ).
thf(ty_denota229585092_a_b_c,type,
denota229585092_a_b_c: denota231621370t_unit > trm_a_c > finite1398487019real_c > finite1398487019real_c > real ).
thf(ty_t1,type,
t1: trm_a_c ).
thf(ty_denota1997846518gree_c,type,
denota1997846518gree_c: produc190496183real_c > produc190496183real_c > set_Sum_sum_c_c > $o ).
thf(ty_nu,type,
nu: produc190496183real_c ).
thf(ty_static_SIGT_a_c,type,
static_SIGT_a_c: trm_a_c > set_a ).
thf(ty_produc2010422875real_c,type,
produc2010422875real_c: produc190496183real_c > finite1398487019real_c ).
thf(ty_collec2086029184um_b_c,type,
collec2086029184um_b_c: ( sum_su737395349um_b_c > $o ) > set_Su1783761653um_b_c ).
thf(ty_i,type,
i: denota231621370t_unit ).
thf(ty_sum_In2139678582um_b_c,type,
sum_In2139678582um_b_c: a > sum_su737395349um_b_c ).
thf(ty_t2,type,
t2: trm_a_c ).
thf(ty_denota69106024_a_b_c,type,
denota69106024_a_b_c: denota231621370t_unit > denota231621370t_unit > set_Su1783761653um_b_c > $o ).
thf(sP1,plain,
( sP1
<=> ( denota1997846518gree_c @ nu @ nu2 @ ( static_FVDiff_a_c @ ( plus_a_c @ t1 @ t2 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ( sP1
=> ( denota1997846518gree_c @ nu @ nu2 @ ( static_FVDiff_a_c @ t2 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ! [X1: produc190496183real_c,X2: trm_a_c,X3: trm_a_c] :
( ( denota1997846518gree_c @ nu @ X1 @ ( static_FVDiff_a_c @ ( plus_a_c @ X2 @ X3 ) ) )
=> ( denota1997846518gree_c @ nu @ X1 @ ( static_FVDiff_a_c @ X3 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> ( denota69106024_a_b_c @ i @ j
@ ( collec2086029184um_b_c
@ ^ [X1: sum_su737395349um_b_c] :
~ ! [X2: a] :
( ( X1
= ( sum_In2139678582um_b_c @ X2 ) )
=> ~ ( member_a @ X2 @ ( static_SIGT_a_c @ t2 ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(sP5,plain,
( sP5
<=> ( denota1997846518gree_c @ nu @ nu2 @ ( static_FVDiff_a_c @ t1 ) ) ),
introduced(definition,[new_symbols(definition,[sP5])]) ).
thf(sP6,plain,
( sP6
<=> ! [X1: produc190496183real_c,X2: produc190496183real_c,X3: trm_a_c,X4: trm_a_c] :
( ( denota1997846518gree_c @ X1 @ X2 @ ( static_FVDiff_a_c @ ( plus_a_c @ X3 @ X4 ) ) )
=> ( denota1997846518gree_c @ X1 @ X2 @ ( static_FVDiff_a_c @ X4 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP6])]) ).
thf(sP7,plain,
( sP7
<=> ( denota1997846518gree_c @ nu @ nu2 @ ( static_FVDiff_a_c @ t2 ) ) ),
introduced(definition,[new_symbols(definition,[sP7])]) ).
thf(sP8,plain,
( sP8
<=> ( denota69106024_a_b_c @ i @ j
@ ( collec2086029184um_b_c
@ ^ [X1: sum_su737395349um_b_c] :
~ ! [X2: a] :
( ( X1
= ( sum_In2139678582um_b_c @ X2 ) )
=> ~ ( member_a @ X2 @ ( static_SIGT_a_c @ t1 ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP8])]) ).
thf(sP9,plain,
( sP9
<=> ! [X1: trm_a_c,X2: trm_a_c] :
( ( denota1997846518gree_c @ nu @ nu2 @ ( static_FVDiff_a_c @ ( plus_a_c @ X1 @ X2 ) ) )
=> ( denota1997846518gree_c @ nu @ nu2 @ ( static_FVDiff_a_c @ X2 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP9])]) ).
thf(sP10,plain,
( sP10
<=> ! [X1: trm_a_c] :
( ( denota1997846518gree_c @ nu @ nu2 @ ( static_FVDiff_a_c @ ( plus_a_c @ t1 @ X1 ) ) )
=> ( denota1997846518gree_c @ nu @ nu2 @ ( static_FVDiff_a_c @ 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(h1,assumption,
~ sP5,
introduced(assumption,[]) ).
thf(h2,assumption,
( sP8
=> ( ( denota229585092_a_b_c @ i @ t1 @ ( produc2010422875real_c @ nu ) @ ( produc314122909real_c @ nu ) )
= ( denota229585092_a_b_c @ j @ t1 @ ( produc2010422875real_c @ nu2 ) @ ( produc314122909real_c @ nu2 ) ) ) ),
introduced(assumption,[]) ).
thf(h3,assumption,
~ sP7,
introduced(assumption,[]) ).
thf(h4,assumption,
( sP4
=> ( ( denota229585092_a_b_c @ i @ t2 @ ( produc2010422875real_c @ nu ) @ ( produc314122909real_c @ nu ) )
= ( denota229585092_a_b_c @ j @ t2 @ ( produc2010422875real_c @ nu2 ) @ ( produc314122909real_c @ nu2 ) ) ) ),
introduced(assumption,[]) ).
thf(fact_3_agree1,axiom,
sP5 ).
thf(1,plain,
$false,
inference(tab_conflict,[status(thm),assumptions([h3,h1,h0])],[fact_3_agree1,h1]) ).
thf(h5,assumption,
~ sP4,
introduced(assumption,[]) ).
thf(h6,assumption,
( ( denota229585092_a_b_c @ i @ t2 @ ( produc2010422875real_c @ nu ) @ ( produc314122909real_c @ nu ) )
= ( denota229585092_a_b_c @ j @ t2 @ ( produc2010422875real_c @ nu2 ) @ ( produc314122909real_c @ nu2 ) ) ),
introduced(assumption,[]) ).
thf(fact_34_IA2,axiom,
sP4 ).
thf(2,plain,
$false,
inference(tab_conflict,[status(thm),assumptions([h5,h4,h1,h0])],[fact_34_IA2,h5]) ).
thf(3,plain,
$false,
inference(tab_conflict,[status(thm),assumptions([h6,h4,h1,h0])],[fact_3_agree1,h1]) ).
thf(4,plain,
$false,
inference(tab_imp,[status(thm),assumptions([h4,h1,h0]),tab_imp(discharge,[h5]),tab_imp(discharge,[h6])],[h4,2,3,h5,h6]) ).
thf(fact_22_IH2,axiom,
( sP7
=> ( sP4
=> ( ( denota229585092_a_b_c @ i @ t2 @ ( produc2010422875real_c @ nu ) @ ( produc314122909real_c @ nu ) )
= ( denota229585092_a_b_c @ j @ t2 @ ( produc2010422875real_c @ nu2 ) @ ( produc314122909real_c @ nu2 ) ) ) ) ) ).
thf(5,plain,
$false,
inference(tab_imp,[status(thm),assumptions([h1,h0]),tab_imp(discharge,[h3]),tab_imp(discharge,[h4])],[fact_22_IH2,1,4,h3,h4]) ).
thf(h7,assumption,
~ sP8,
introduced(assumption,[]) ).
thf(h8,assumption,
( ( denota229585092_a_b_c @ i @ t1 @ ( produc2010422875real_c @ nu ) @ ( produc314122909real_c @ nu ) )
= ( denota229585092_a_b_c @ j @ t1 @ ( produc2010422875real_c @ nu2 ) @ ( produc314122909real_c @ nu2 ) ) ),
introduced(assumption,[]) ).
thf(fact_33_IA1,axiom,
sP8 ).
thf(6,plain,
$false,
inference(tab_conflict,[status(thm),assumptions([h3,h7,h2,h0])],[fact_33_IA1,h7]) ).
thf(7,plain,
$false,
inference(tab_conflict,[status(thm),assumptions([h5,h4,h7,h2,h0])],[fact_34_IA2,h5]) ).
thf(8,plain,
$false,
inference(tab_conflict,[status(thm),assumptions([h6,h4,h7,h2,h0])],[fact_33_IA1,h7]) ).
thf(9,plain,
$false,
inference(tab_imp,[status(thm),assumptions([h4,h7,h2,h0]),tab_imp(discharge,[h5]),tab_imp(discharge,[h6])],[h4,7,8,h5,h6]) ).
thf(10,plain,
$false,
inference(tab_imp,[status(thm),assumptions([h7,h2,h0]),tab_imp(discharge,[h3]),tab_imp(discharge,[h4])],[fact_22_IH2,6,9,h3,h4]) ).
thf(11,plain,
( ~ sP2
| ~ sP1
| sP7 ),
inference(prop_rule,[status(thm)],[]) ).
thf(12,plain,
( ~ sP10
| sP2 ),
inference(all_rule,[status(thm)],[]) ).
thf(13,plain,
( ~ sP9
| sP10 ),
inference(all_rule,[status(thm)],[]) ).
thf(14,plain,
( ~ sP3
| sP9 ),
inference(all_rule,[status(thm)],[]) ).
thf(15,plain,
( ~ sP6
| sP3 ),
inference(all_rule,[status(thm)],[]) ).
thf(fact_2_agree,axiom,
sP1 ).
thf(fact_1_agree__plus2,axiom,
sP6 ).
thf(16,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h3,h8,h2,h0])],[11,12,13,14,15,h3,fact_2_agree,fact_1_agree__plus2]) ).
thf(17,plain,
$false,
inference(tab_conflict,[status(thm),assumptions([h5,h4,h8,h2,h0])],[fact_34_IA2,h5]) ).
thf(18,plain,
( ~ sP2
| ~ sP1
| sP7 ),
inference(prop_rule,[status(thm)],[]) ).
thf(19,plain,
( ~ sP10
| sP2 ),
inference(all_rule,[status(thm)],[]) ).
thf(20,plain,
( ~ sP9
| sP10 ),
inference(all_rule,[status(thm)],[]) ).
thf(21,plain,
( ~ sP3
| sP9 ),
inference(all_rule,[status(thm)],[]) ).
thf(22,plain,
( ~ sP6
| sP3 ),
inference(all_rule,[status(thm)],[]) ).
thf(23,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h6,h4,h8,h2,h0])],[18,19,20,21,22,h0,fact_2_agree,fact_1_agree__plus2]) ).
thf(24,plain,
$false,
inference(tab_imp,[status(thm),assumptions([h4,h8,h2,h0]),tab_imp(discharge,[h5]),tab_imp(discharge,[h6])],[h4,17,23,h5,h6]) ).
thf(25,plain,
$false,
inference(tab_imp,[status(thm),assumptions([h8,h2,h0]),tab_imp(discharge,[h3]),tab_imp(discharge,[h4])],[fact_22_IH2,16,24,h3,h4]) ).
thf(26,plain,
$false,
inference(tab_imp,[status(thm),assumptions([h2,h0]),tab_imp(discharge,[h7]),tab_imp(discharge,[h8])],[h2,10,25,h7,h8]) ).
thf(fact_35_IH1,axiom,
( sP5
=> ( sP8
=> ( ( denota229585092_a_b_c @ i @ t1 @ ( produc2010422875real_c @ nu ) @ ( produc314122909real_c @ nu ) )
= ( denota229585092_a_b_c @ j @ t1 @ ( produc2010422875real_c @ nu2 ) @ ( produc314122909real_c @ nu2 ) ) ) ) ) ).
thf(27,plain,
$false,
inference(tab_imp,[status(thm),assumptions([h0]),tab_imp(discharge,[h1]),tab_imp(discharge,[h2])],[fact_35_IH1,5,26,h1,h2]) ).
thf(0,theorem,
sP7,
inference(contra,[status(thm),contra(discharge,[h0])],[27,h0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : ITP038^1 : TPTP v9.2.0. Released v7.5.0.
% 0.03/0.12 % Command : lash -P picomus -M modes -p tstp -t %d %s
% 0.12/0.33 % Computer : n023.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 18:44:53 EDT 2025
% 0.12/0.33 % CPUTime :
% 0.19/0.46 % SZS status Theorem
% 0.19/0.46 % Mode: cade22sinegrackle2x6978
% 0.19/0.46 % Steps: 715
% 0.19/0.46 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------