%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : ITP039^2 : TPTP v9.3.1. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% Computer : n006.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 15.57s 5.94s
% Output : Refutation 15.57s
% 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 : 48 ( 6 equ; 0 cnn)
% Maximal formula atoms : 1 ( 12 avg)
% Number of connectives : 274 ( 2 ~; 0 |; 0 &; 264 @)
% ( 0 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 2 ( 2 avg)
% Number of types : 9 ( 8 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 16 ( 13 usr; 9 con; 0-6 aty)
% Number of variables : 16 ( 0 ^; 16 !; 0 ?; 16 :)
% Comments :
%------------------------------------------------------------------------------
thf(product_unit_type,type,
product_unit: $tType ).
thf(real_type,type,
real: $tType ).
thf(sz_type,type,
sz: $tType ).
thf(sf_type,type,
sf: $tType ).
thf(sc_type,type,
sc: $tType ).
thf(c_type,type,
c: $tType ).
thf(b_type,type,
b: $tType ).
thf(a_type,type,
a: $tType ).
thf(denotational_Iagree_decl,type,
denotational_Iagree:
!>[TA: $tType,TB: $tType,TC: $tType] : ( ( denota1663640101rp_ext @ TC @ TB @ TA @ product_unit ) > ( denota1663640101rp_ext @ TC @ TB @ TA @ product_unit ) > ( set @ ( sum_sum @ TC @ ( sum_sum @ TB @ TA ) ) ) > $o ) ).
thf(denotational_Vagree_decl,type,
denotational_Vagree:
!>[TA: $tType] : ( ( product_prod @ ( finite_Cartesian_vec @ real @ TA ) @ ( finite_Cartesian_vec @ real @ TA ) ) > ( product_prod @ ( finite_Cartesian_vec @ real @ TA ) @ ( finite_Cartesian_vec @ real @ TA ) ) > ( set @ ( sum_sum @ TA @ TA ) ) > $o ) ).
thf(denotational_fml_sem_decl,type,
denotational_fml_sem:
!>[TA: $tType,TB: $tType,TC: $tType] : ( ( denota1663640101rp_ext @ TC @ TB @ TA @ product_unit ) > ( formula @ TC @ TB @ TA ) > ( set @ ( product_prod @ ( finite_Cartesian_vec @ real @ TA ) @ ( finite_Cartesian_vec @ real @ TA ) ) ) ) ).
thf(static_FVF_decl,type,
static_FVF:
!>[TA: $tType,TB: $tType,TC: $tType] : ( ( formula @ TC @ TB @ TA ) > ( set @ ( sum_sum @ TA @ TA ) ) ) ).
thf(static_SIGF_decl,type,
static_SIGF:
!>[TA: $tType,TB: $tType,TC: $tType] : ( ( formula @ TC @ TB @ TA ) > ( set @ ( sum_sum @ TC @ ( sum_sum @ TB @ TA ) ) ) ) ).
thf(member_decl,type,
member:
!>[TA: $tType] : ( TA > ( set @ TA ) > $o ) ).
thf(phi_decl,type,
phi: formula @ a @ b @ c ).
thf(1,conjecture,
( ( ! [A: product_prod @ ( finite_Cartesian_vec @ real @ c ) @ ( finite_Cartesian_vec @ real @ c ),B: product_prod @ ( finite_Cartesian_vec @ real @ c ) @ ( finite_Cartesian_vec @ real @ c ),C: denota1663640101rp_ext @ a @ b @ c @ product_unit,D: denota1663640101rp_ext @ a @ b @ c @ product_unit] :
( ( denotational_Iagree @ a @ b @ c @ C @ D @ ( static_SIGF @ a @ b @ c @ phi ) )
=> ( ( denotational_Vagree @ c @ A @ B @ ( static_FVF @ a @ b @ c @ phi ) )
=> ( ( member @ ( product_prod @ ( finite_Cartesian_vec @ real @ c ) @ ( finite_Cartesian_vec @ real @ c ) ) @ A @ ( denotational_fml_sem @ a @ b @ c @ C @ phi ) )
= ( member @ ( product_prod @ ( finite_Cartesian_vec @ real @ c ) @ ( finite_Cartesian_vec @ real @ c ) ) @ B @ ( denotational_fml_sem @ a @ b @ c @ D @ phi ) ) ) ) ) )
= ( ! [A: product_prod @ ( finite_Cartesian_vec @ real @ c ) @ ( finite_Cartesian_vec @ real @ c ),B: product_prod @ ( finite_Cartesian_vec @ real @ c ) @ ( finite_Cartesian_vec @ real @ c ),C: denota1663640101rp_ext @ a @ b @ c @ product_unit,D: denota1663640101rp_ext @ a @ b @ c @ product_unit] :
( ( denotational_Iagree @ a @ b @ c @ C @ D @ ( static_SIGF @ a @ b @ c @ phi ) )
=> ( ( denotational_Vagree @ c @ A @ B @ ( static_FVF @ a @ b @ c @ phi ) )
=> ( ( member @ ( product_prod @ ( finite_Cartesian_vec @ real @ c ) @ ( finite_Cartesian_vec @ real @ c ) ) @ A @ ( denotational_fml_sem @ a @ b @ c @ C @ phi ) )
= ( member @ ( product_prod @ ( finite_Cartesian_vec @ real @ c ) @ ( finite_Cartesian_vec @ real @ c ) ) @ B @ ( denotational_fml_sem @ a @ b @ c @ D @ phi ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0) ).
thf(2,negated_conjecture,
( ( ! [A: product_prod @ ( finite_Cartesian_vec @ real @ c ) @ ( finite_Cartesian_vec @ real @ c ),B: product_prod @ ( finite_Cartesian_vec @ real @ c ) @ ( finite_Cartesian_vec @ real @ c ),C: denota1663640101rp_ext @ a @ b @ c @ product_unit,D: denota1663640101rp_ext @ a @ b @ c @ product_unit] :
( ( denotational_Iagree @ a @ b @ c @ C @ D @ ( static_SIGF @ a @ b @ c @ phi ) )
=> ( ( denotational_Vagree @ c @ A @ B @ ( static_FVF @ a @ b @ c @ phi ) )
=> ( ( member @ ( product_prod @ ( finite_Cartesian_vec @ real @ c ) @ ( finite_Cartesian_vec @ real @ c ) ) @ A @ ( denotational_fml_sem @ a @ b @ c @ C @ phi ) )
= ( member @ ( product_prod @ ( finite_Cartesian_vec @ real @ c ) @ ( finite_Cartesian_vec @ real @ c ) ) @ B @ ( denotational_fml_sem @ a @ b @ c @ D @ phi ) ) ) ) ) )
!= ( ! [A: product_prod @ ( finite_Cartesian_vec @ real @ c ) @ ( finite_Cartesian_vec @ real @ c ),B: product_prod @ ( finite_Cartesian_vec @ real @ c ) @ ( finite_Cartesian_vec @ real @ c ),C: denota1663640101rp_ext @ a @ b @ c @ product_unit,D: denota1663640101rp_ext @ a @ b @ c @ product_unit] :
( ( denotational_Iagree @ a @ b @ c @ C @ D @ ( static_SIGF @ a @ b @ c @ phi ) )
=> ( ( denotational_Vagree @ c @ A @ B @ ( static_FVF @ a @ b @ c @ phi ) )
=> ( ( member @ ( product_prod @ ( finite_Cartesian_vec @ real @ c ) @ ( finite_Cartesian_vec @ real @ c ) ) @ A @ ( denotational_fml_sem @ a @ b @ c @ C @ phi ) )
= ( member @ ( product_prod @ ( finite_Cartesian_vec @ real @ c ) @ ( finite_Cartesian_vec @ real @ c ) ) @ B @ ( denotational_fml_sem @ a @ b @ c @ D @ phi ) ) ) ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(281,plain,
~ $true,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(282,plain,
$false,
inference(simp,[status(thm)],[281]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ITP039^2 : TPTP v9.3.1. Released v7.5.0.
% 0.00/0.08 % Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% 0.10/0.21 % Computer : n006.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 19:40:09 UTC 2026
% 0.10/0.22 % CPUTime :
% 0.10/0.22 Running java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% 0.87/0.63 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 2.09/1.06 % [INFO] Parsing done (424ms).
% 2.09/1.07 % [INFO] Running in sequential loop mode.
% 3.20/1.46 % [INFO] eprover registered as external prover.
% 3.20/1.47 % [INFO] Scanning for conjecture ...
% 3.63/1.69 % [INFO] Found a conjecture (or negated_conjecture) and 281 axioms. Running axiom selection ...
% 4.21/1.86 % [INFO] Axiom selection finished. Selected 278 axioms (removed 3 axioms).
% 6.02/2.40 % [INFO] Problem is higher-order (TPTP THF).
% 6.43/2.44 % [INFO] Type checking passed.
% 6.43/2.44 % [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 ...
% 15.57/5.93 % [INFO] Killing All external provers ...
% 15.57/5.93 % Time passed: 5626ms (effective reasoning time: 4848ms)
% 15.57/5.93 % 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)>
% 15.57/5.94 % Axioms used in derivation (0):
% 15.57/5.94 % No. of inferences in proof: 4
% 15.57/5.94 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 5626 ms resp. 4848 ms w/o parsing
% 15.57/5.98 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 15.57/5.98 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------