%------------------------------------------------------------------------------
% File : Satallax---3.5
% Problem : ITP039^1 : 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 : n005.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 01:46:47 PM UTC 2025
% Result : Theorem 0.13s 0.38s
% Output : Proof 0.13s
% Verified :
% SZS Type : Derivation
% Derivation depth : 3
% Number of leaves : 1
% Syntax : Number of formulae : 4 ( 4 unt; 0 typ; 0 def)
% Number of atoms : 34 ( 9 equ; 0 cnn)
% Maximal formula atoms : 1 ( 8 avg)
% Number of connectives : 109 ( 1 ~; 0 |; 0 &; 96 @)
% ( 0 <=>; 12 =>; 0 <=; 0 <~>)
% Maximal formula depth : 2 ( 1 avg)
% Number of types : 7 ( 6 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 9 ( 7 usr; 2 con; 0-3 aty)
% Number of variables : 24 ( 0 ^; 24 !; 0 ?; 24 :)
% Comments :
%------------------------------------------------------------------------------
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_denota231621370t_unit,type,
denota231621370t_unit: $tType ).
thf(ty_produc190496183real_c,type,
produc190496183real_c: $tType ).
thf(ty_set_Pr1389752855real_c,type,
set_Pr1389752855real_c: $tType ).
thf(ty_formula_a_b_c,type,
formula_a_b_c: $tType ).
thf(ty_denota1997846518gree_c,type,
denota1997846518gree_c: produc190496183real_c > produc190496183real_c > set_Sum_sum_c_c > $o ).
thf(ty_member1895684704real_c,type,
member1895684704real_c: produc190496183real_c > set_Pr1389752855real_c > $o ).
thf(ty_denota968303861_a_b_c,type,
denota968303861_a_b_c: denota231621370t_unit > formula_a_b_c > set_Pr1389752855real_c ).
thf(ty_static_SIGF_a_b_c,type,
static_SIGF_a_b_c: formula_a_b_c > set_Su1783761653um_b_c ).
thf(ty_phi,type,
phi: formula_a_b_c ).
thf(ty_denota69106024_a_b_c,type,
denota69106024_a_b_c: denota231621370t_unit > denota231621370t_unit > set_Su1783761653um_b_c > $o ).
thf(ty_static_FVF_a_b_c,type,
static_FVF_a_b_c: formula_a_b_c > set_Sum_sum_c_c ).
thf(conj_0,conjecture,
( ( ! [X1: produc190496183real_c,X2: produc190496183real_c,X3: denota231621370t_unit,X4: denota231621370t_unit] :
( ( denota69106024_a_b_c @ X3 @ X4 @ ( static_SIGF_a_b_c @ phi ) )
=> ( ( denota1997846518gree_c @ X1 @ X2 @ ( static_FVF_a_b_c @ phi ) )
=> ( ( member1895684704real_c @ X1 @ ( denota968303861_a_b_c @ X3 @ phi ) )
= ( member1895684704real_c @ X2 @ ( denota968303861_a_b_c @ X4 @ phi ) ) ) ) ) )
= ( ! [X1: produc190496183real_c,X2: produc190496183real_c,X3: denota231621370t_unit,X4: denota231621370t_unit] :
( ( denota69106024_a_b_c @ X3 @ X4 @ ( static_SIGF_a_b_c @ phi ) )
=> ( ( denota1997846518gree_c @ X1 @ X2 @ ( static_FVF_a_b_c @ phi ) )
=> ( ( member1895684704real_c @ X1 @ ( denota968303861_a_b_c @ X3 @ phi ) )
= ( member1895684704real_c @ X2 @ ( denota968303861_a_b_c @ X4 @ phi ) ) ) ) ) ) ) ).
thf(h0,negated_conjecture,
( ( ! [X1: produc190496183real_c,X2: produc190496183real_c,X3: denota231621370t_unit,X4: denota231621370t_unit] :
( ( denota69106024_a_b_c @ X3 @ X4 @ ( static_SIGF_a_b_c @ phi ) )
=> ( ( denota1997846518gree_c @ X1 @ X2 @ ( static_FVF_a_b_c @ phi ) )
=> ( ( member1895684704real_c @ X1 @ ( denota968303861_a_b_c @ X3 @ phi ) )
= ( member1895684704real_c @ X2 @ ( denota968303861_a_b_c @ X4 @ phi ) ) ) ) ) )
!= ( ! [X1: produc190496183real_c,X2: produc190496183real_c,X3: denota231621370t_unit,X4: denota231621370t_unit] :
( ( denota69106024_a_b_c @ X3 @ X4 @ ( static_SIGF_a_b_c @ phi ) )
=> ( ( denota1997846518gree_c @ X1 @ X2 @ ( static_FVF_a_b_c @ phi ) )
=> ( ( member1895684704real_c @ X1 @ ( denota968303861_a_b_c @ X3 @ phi ) )
= ( member1895684704real_c @ X2 @ ( denota968303861_a_b_c @ X4 @ phi ) ) ) ) ) ) ),
inference(assume_negation,[status(cth)],[conj_0]) ).
thf(1,plain,
$false,
inference(tab_negrefl,[status(thm),assumptions([h0])],[h0]) ).
thf(0,theorem,
( ( ! [X1: produc190496183real_c,X2: produc190496183real_c,X3: denota231621370t_unit,X4: denota231621370t_unit] :
( ( denota69106024_a_b_c @ X3 @ X4 @ ( static_SIGF_a_b_c @ phi ) )
=> ( ( denota1997846518gree_c @ X1 @ X2 @ ( static_FVF_a_b_c @ phi ) )
=> ( ( member1895684704real_c @ X1 @ ( denota968303861_a_b_c @ X3 @ phi ) )
= ( member1895684704real_c @ X2 @ ( denota968303861_a_b_c @ X4 @ phi ) ) ) ) ) )
= ( ! [X1: produc190496183real_c,X2: produc190496183real_c,X3: denota231621370t_unit,X4: denota231621370t_unit] :
( ( denota69106024_a_b_c @ X3 @ X4 @ ( static_SIGF_a_b_c @ phi ) )
=> ( ( denota1997846518gree_c @ X1 @ X2 @ ( static_FVF_a_b_c @ phi ) )
=> ( ( member1895684704real_c @ X1 @ ( denota968303861_a_b_c @ X3 @ phi ) )
= ( member1895684704real_c @ X2 @ ( denota968303861_a_b_c @ X4 @ phi ) ) ) ) ) ) ),
inference(contra,[status(thm),contra(discharge,[h0])],[1,h0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.12 % Problem : ITP039^1 : 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 : n005.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 18:50:23 EDT 2025
% 0.13/0.34 % CPUTime :
% 0.13/0.38 % SZS status Theorem
% 0.13/0.38 % Mode: mode507:USE_SINE=true:SINE_TOLERANCE=3.0:SINE_GENERALITY_THRESHOLD=0:SINE_RANK_LIMIT=1.:SINE_DEPTH=1
% 0.13/0.38 % Inferences: 0
% 0.13/0.38 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------