%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : ITP039^1 : TPTP v9.3.1. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% Computer : n018.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Sep 30 08:06:31 AM UTC 2026
% Result : Theorem 14.02s 4.47s
% Output : Refutation 14.45s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 1
% Syntax : Number of formulae : 4 ( 4 unt; 0 typ; 0 def)
% Number of atoms : 24 ( 6 equ; 0 cnn)
% Maximal formula atoms : 1 ( 6 avg)
% Number of connectives : 74 ( 2 ~; 0 |; 0 &; 64 @)
% ( 0 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 2 ( 2 avg)
% Number of types : 27 ( 26 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 10 ( 7 usr; 3 con; 0-3 aty)
% Number of variables : 16 ( 0 ^; 16 !; 0 ?; 16 :)
% Comments :
%------------------------------------------------------------------------------
thf(set_Pr754230471real_c_type,type,
set_Pr754230471real_c: $tType ).
thf(produc640052711real_c_type,type,
produc640052711real_c: $tType ).
thf(set_Pr2041213564t_unit_type,type,
set_Pr2041213564t_unit: $tType ).
thf(set_Pr1169339874_sc_sz_type,type,
set_Pr1169339874_sc_sz: $tType ).
thf(produc999471430t_unit_type,type,
produc999471430t_unit: $tType ).
thf(produc1821101996_sc_sz_type,type,
produc1821101996_sc_sz: $tType ).
thf(set_Pr60491591eal_sz_type,type,
set_Pr60491591eal_sz: $tType ).
thf(set_Pr1389752855real_c_type,type,
set_Pr1389752855real_c: $tType ).
thf(set_Pr1774599175_sc_sz_type,type,
set_Pr1774599175_sc_sz: $tType ).
thf(produc1149990247eal_sz_type,type,
produc1149990247eal_sz: $tType ).
thf(produc190496183real_c_type,type,
produc190496183real_c: $tType ).
thf(produc866628903_sc_sz_type,type,
produc866628903_sc_sz: $tType ).
thf(set_De208295462t_unit_type,type,
set_De208295462t_unit: $tType ).
thf(denota610675952t_unit_type,type,
denota610675952t_unit: $tType ).
thf(denota231621370t_unit_type,type,
denota231621370t_unit: $tType ).
thf(set_Su1783761653um_b_c_type,type,
set_Su1783761653um_b_c: $tType ).
thf(set_Fi1407883041real_c_type,type,
set_Fi1407883041real_c: $tType ).
thf(finite1398487019real_c_type,type,
finite1398487019real_c: $tType ).
thf(list_f1238882004_sc_sz_type,type,
list_f1238882004_sc_sz: $tType ).
thf(set_Sum_sum_c_c_type,type,
set_Sum_sum_c_c: $tType ).
thf(formula_sf_sc_sz_type,type,
formula_sf_sc_sz: $tType ).
thf(formula_a_b_c_type,type,
formula_a_b_c: $tType ).
thf(set_o_type,type,
set_o: $tType ).
thf(sz_type,type,
sz: $tType ).
thf(sf_type,type,
sf: $tType ).
thf(sc_type,type,
sc: $tType ).
thf(denota69106024_a_b_c_decl,type,
denota69106024_a_b_c: denota231621370t_unit > denota231621370t_unit > set_Su1783761653um_b_c > $o ).
thf(denota1997846518gree_c_decl,type,
denota1997846518gree_c: produc190496183real_c > produc190496183real_c > set_Sum_sum_c_c > $o ).
thf(denota968303861_a_b_c_decl,type,
denota968303861_a_b_c: denota231621370t_unit > formula_a_b_c > set_Pr1389752855real_c ).
thf(static_FVF_a_b_c_decl,type,
static_FVF_a_b_c: formula_a_b_c > set_Sum_sum_c_c ).
thf(static_SIGF_a_b_c_decl,type,
static_SIGF_a_b_c: formula_a_b_c > set_Su1783761653um_b_c ).
thf(member1895684704real_c_decl,type,
member1895684704real_c: produc190496183real_c > set_Pr1389752855real_c > $o ).
thf(phi_decl,type,
phi: formula_a_b_c ).
thf(1,conjecture,
( ( ! [A: produc190496183real_c,B: produc190496183real_c,C: denota231621370t_unit,D: denota231621370t_unit] :
( ( denota69106024_a_b_c @ C @ D @ ( static_SIGF_a_b_c @ phi ) )
=> ( ( denota1997846518gree_c @ A @ B @ ( static_FVF_a_b_c @ phi ) )
=> ( ( member1895684704real_c @ A @ ( denota968303861_a_b_c @ C @ phi ) )
= ( member1895684704real_c @ B @ ( denota968303861_a_b_c @ D @ phi ) ) ) ) ) )
= ( ! [A: produc190496183real_c,B: produc190496183real_c,C: denota231621370t_unit,D: denota231621370t_unit] :
( ( denota69106024_a_b_c @ C @ D @ ( static_SIGF_a_b_c @ phi ) )
=> ( ( denota1997846518gree_c @ A @ B @ ( static_FVF_a_b_c @ phi ) )
=> ( ( member1895684704real_c @ A @ ( denota968303861_a_b_c @ C @ phi ) )
= ( member1895684704real_c @ B @ ( denota968303861_a_b_c @ D @ phi ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0) ).
thf(2,negated_conjecture,
( ( ! [A: produc190496183real_c,B: produc190496183real_c,C: denota231621370t_unit,D: denota231621370t_unit] :
( ( denota69106024_a_b_c @ C @ D @ ( static_SIGF_a_b_c @ phi ) )
=> ( ( denota1997846518gree_c @ A @ B @ ( static_FVF_a_b_c @ phi ) )
=> ( ( member1895684704real_c @ A @ ( denota968303861_a_b_c @ C @ phi ) )
= ( member1895684704real_c @ B @ ( denota968303861_a_b_c @ D @ phi ) ) ) ) ) )
!= ( ! [A: produc190496183real_c,B: produc190496183real_c,C: denota231621370t_unit,D: denota231621370t_unit] :
( ( denota69106024_a_b_c @ C @ D @ ( static_SIGF_a_b_c @ phi ) )
=> ( ( denota1997846518gree_c @ A @ B @ ( static_FVF_a_b_c @ phi ) )
=> ( ( member1895684704real_c @ A @ ( denota968303861_a_b_c @ C @ phi ) )
= ( member1895684704real_c @ B @ ( denota968303861_a_b_c @ D @ phi ) ) ) ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(298,plain,
~ $true,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(299,plain,
$false,
inference(simp,[status(thm)],[298]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : ITP039^1 : TPTP v9.3.1. Released v7.5.0.
% 0.00/0.07 % Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% 0.10/0.21 % Computer : n018.cluster.edu
% 0.10/0.21 % Model : x86_64 x86_64
% 0.10/0.21 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.21 % Memory : 8046.5625MB
% 0.10/0.21 % OS : Linux 6.8.0-71-generic
% 0.10/0.21 % CPULimit : 300
% 0.10/0.21 % WCLimit : 300
% 0.10/0.21 % DateTime : Tue Sep 29 19:42:26 UTC 2026
% 0.10/0.21 % CPUTime :
% 0.10/0.21 Running java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% 1.01/0.80 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 2.33/1.23 % [INFO] Parsing done (426ms).
% 2.33/1.25 % [INFO] Running in sequential loop mode.
% 3.50/1.62 % [INFO] eprover registered as external prover.
% 3.50/1.63 % [INFO] Scanning for conjecture ...
% 3.92/1.82 % [INFO] Found a conjecture (or negated_conjecture) and 354 axioms. Running axiom selection ...
% 4.11/1.99 % [INFO] Axiom selection finished. Selected 295 axioms (removed 59 axioms).
% 5.10/2.28 % [INFO] Problem is higher-order (TPTP THF).
% 5.39/2.31 % [INFO] Type checking passed.
% 5.39/2.32 % [CONFIG] Using configuration: timeout(300) with strategy<name(default),share(1.0),primSubst(3),sos(false),unifierCount(4),uniDepth(8),boolExt(true),choice(true),renaming(true),funcspec(false), domConstr(0),specialInstances(39),restrictUniAttempts(true),termOrdering(CPO)>. Searching for refutation ...
% 14.02/4.46 % [INFO] Killing All external provers ...
% 14.02/4.47 % Time passed: 4115ms (effective reasoning time: 3211ms)
% 14.02/4.47 % Solved by strategy<name(default),share(1.0),primSubst(3),sos(false),unifierCount(4),uniDepth(8),boolExt(true),choice(true),renaming(true),funcspec(false), domConstr(0),specialInstances(39),restrictUniAttempts(true),termOrdering(CPO)>
% 14.02/4.47 % Axioms used in derivation (0):
% 14.02/4.47 % No. of inferences in proof: 4
% 14.02/4.47 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 4115 ms resp. 3211 ms w/o parsing
% 14.45/4.51 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 14.45/4.51 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------