%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : GRP114-1 : TPTP v9.3.1. Released v1.2.0.
% 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 : n020.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 : Sun Sep 27 07:20:01 AM UTC 2026
% Result : Unsatisfiable 9.73s 4.13s
% Output : Refutation 9.73s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 21
% Syntax : Number of formulae : 43 ( 43 unt; 0 typ; 0 def)
% Number of atoms : 43 ( 42 equ; 0 cnn)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 220 ( 2 ~; 0 |; 0 &; 218 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 3 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 10 ( 8 usr; 3 con; 0-2 aty)
% Number of variables : 76 ( 0 ^; 76 !; 0 ?; 76 :)
% Comments :
%------------------------------------------------------------------------------
thf(multiply_decl,type,
multiply: $i > $i > $i ).
thf(positive_part_decl,type,
positive_part: $i > $i ).
thf(a_decl,type,
a: $i ).
thf(negative_part_decl,type,
negative_part: $i > $i ).
thf(inverse_decl,type,
inverse: $i > $i ).
thf(identity_decl,type,
identity: $i ).
thf(union_decl,type,
union: $i > $i > $i ).
thf(intersection_decl,type,
intersection: $i > $i > $i ).
thf(20,axiom,
! [A: $i] :
( ( A @ negative_part )
= ( identity @ ( A @ intersection ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',negative_part) ).
thf(61,plain,
! [A: $i] :
( ( A @ negative_part )
= ( identity @ ( A @ intersection ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(6,axiom,
! [B: $i,A: $i] :
( ( B @ ( B @ ( A @ union ) @ intersection ) )
= B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',intersection_union_absorbtion) ).
thf(33,plain,
! [B: $i,A: $i] :
( ( B @ ( B @ ( A @ union ) @ intersection ) )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(16,axiom,
! [A: $i] :
( ( A @ positive_part )
= ( identity @ ( A @ union ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',positive_part) ).
thf(53,plain,
! [A: $i] :
( ( A @ positive_part )
= ( identity @ ( A @ union ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(10,axiom,
! [A: $i] :
( ( A @ ( A @ intersection ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',intersection_idempotent) ).
thf(41,plain,
! [A: $i] :
( ( A @ ( A @ intersection ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(12,axiom,
! [B: $i,A: $i] :
( ( B @ ( A @ multiply ) @ inverse )
= ( A @ inverse @ ( B @ inverse @ multiply ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',inverse_product_lemma) ).
thf(45,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ multiply ) @ inverse )
= ( A @ inverse @ ( B @ inverse @ multiply ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(14,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ union ) @ multiply ) )
= ( C @ ( B @ multiply ) @ ( C @ ( A @ multiply ) @ union ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',multiply_union2) ).
thf(49,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ union ) @ multiply ) )
= ( C @ ( B @ multiply ) @ ( C @ ( A @ multiply ) @ union ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(9,axiom,
! [B: $i,A: $i] :
( ( B @ ( A @ union ) )
= ( A @ ( B @ union ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',union_commutative) ).
thf(39,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ union ) )
= ( A @ ( B @ union ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(7,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ union ) @ ( A @ union ) )
= ( C @ ( B @ ( A @ union ) @ union ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',union_associative) ).
thf(35,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ union ) @ ( A @ union ) )
= ( C @ ( B @ ( A @ union ) @ union ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(21,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ multiply ) @ multiply ) )
= ( C @ ( B @ multiply ) @ ( A @ multiply ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',associativity) ).
thf(63,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ multiply ) @ multiply ) )
= ( C @ ( B @ multiply ) @ ( A @ multiply ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(5,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ intersection ) @ ( A @ intersection ) )
= ( C @ ( B @ ( A @ intersection ) @ intersection ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',intersection_associative) ).
thf(31,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ intersection ) @ ( A @ intersection ) )
= ( C @ ( B @ ( A @ intersection ) @ intersection ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(11,axiom,
! [A: $i] :
( ( A @ inverse @ inverse )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',inverse_involution) ).
thf(43,plain,
! [A: $i] :
( ( A @ inverse @ inverse )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(17,axiom,
! [A: $i] :
( ( A @ ( A @ inverse @ multiply ) )
= identity ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',left_inverse) ).
thf(55,plain,
! [A: $i] :
( ( A @ ( A @ inverse @ multiply ) )
= identity ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(15,axiom,
! [A: $i] :
( ( A @ ( identity @ multiply ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',left_identity) ).
thf(51,plain,
! [A: $i] :
( ( A @ ( identity @ multiply ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(13,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ union ) @ ( A @ multiply ) )
= ( C @ ( A @ multiply ) @ ( B @ ( A @ multiply ) @ union ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',multiply_union1) ).
thf(47,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ union ) @ ( A @ multiply ) )
= ( C @ ( A @ multiply ) @ ( B @ ( A @ multiply ) @ union ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(8,axiom,
! [B: $i,A: $i] :
( ( B @ ( A @ intersection ) )
= ( A @ ( B @ intersection ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',intersection_commutative) ).
thf(37,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ intersection ) )
= ( A @ ( B @ intersection ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(2,axiom,
( ( identity @ inverse )
= identity ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',inverse_of_identity) ).
thf(25,plain,
( ( identity @ inverse )
= identity ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(18,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ intersection ) @ multiply ) )
= ( C @ ( B @ multiply ) @ ( C @ ( A @ multiply ) @ intersection ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',multiply_intersection2) ).
thf(57,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ intersection ) @ multiply ) )
= ( C @ ( B @ multiply ) @ ( C @ ( A @ multiply ) @ intersection ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(4,axiom,
! [B: $i,A: $i] :
( ( B @ ( B @ ( A @ intersection ) @ union ) )
= B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',union_intersection_absorbtion) ).
thf(29,plain,
! [B: $i,A: $i] :
( ( B @ ( B @ ( A @ intersection ) @ union ) )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(1,negated_conjecture,
( ( a @ negative_part @ ( a @ positive_part @ multiply ) )
!= a ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_product) ).
thf(22,plain,
( ( a @ negative_part @ ( a @ positive_part @ multiply ) )
!= a ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(19,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ intersection ) @ ( A @ multiply ) )
= ( C @ ( A @ multiply ) @ ( B @ ( A @ multiply ) @ intersection ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',multiply_intersection1) ).
thf(59,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ intersection ) @ ( A @ multiply ) )
= ( C @ ( A @ multiply ) @ ( B @ ( A @ multiply ) @ intersection ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(3,axiom,
! [A: $i] :
( ( A @ ( A @ union ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',union_idempotent) ).
thf(27,plain,
! [A: $i] :
( ( A @ ( A @ union ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(256,plain,
$false,
inference(e,[status(thm)],[61,33,53,41,45,49,39,35,63,31,43,55,51,47,37,25,57,29,22,59,27]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP114-1 : TPTP v9.3.1. Released v1.2.0.
% 0.00/0.08 % 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
% 0.15/0.41 % Computer : n020.cluster.edu
% 0.15/0.41 % Model : x86_64 x86_64
% 0.15/0.41 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.41 % Memory : 8046.5625MB
% 0.15/0.41 % OS : Linux 6.8.0-71-generic
% 0.15/0.41 % CPULimit : 300
% 0.15/0.41 % WCLimit : 300
% 0.15/0.41 % DateTime : Fri Sep 25 14:23:49 UTC 2026
% 0.15/0.41 % CPUTime :
% 0.15/0.41 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
% 1.26/1.18 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.74/1.45 % [INFO] Parsing done (270ms).
% 1.74/1.47 % [INFO] Running in sequential loop mode.
% 3.04/2.10 % [INFO] eprover registered as external prover.
% 3.04/2.11 % [INFO] Scanning for conjecture ...
% 3.32/2.24 % [INFO] Found a conjecture (or negated_conjecture) and 20 axioms. Running axiom selection ...
% 3.47/2.33 % [INFO] Axiom selection finished. Selected 20 axioms (removed 0 axioms).
% 3.47/2.38 % [INFO] Problem is propositional (TPTP CNF).
% 3.47/2.39 % [INFO] Type checking passed.
% 3.68/2.40 % [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 ...
% 9.73/4.12 % External prover 'e' found a proof!
% 9.73/4.12 % [INFO] Killing All external provers ...
% 9.73/4.13 % Time passed: 3502ms (effective reasoning time: 2642ms)
% 9.73/4.13 % Axioms used in derivation (20): multiply_intersection1, intersection_associative, left_identity, multiply_union1, union_commutative, intersection_commutative, union_idempotent, multiply_intersection2, multiply_union2, associativity, intersection_idempotent, union_intersection_absorbtion, negative_part, inverse_product_lemma, positive_part, inverse_of_identity, intersection_union_absorbtion, left_inverse, union_associative, inverse_involution
% 9.73/4.13 % No. of inferences in proof: 43
% 9.73/4.13 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p : 3502 ms resp. 2642 ms w/o parsing
% 9.73/4.17 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 9.73/4.17 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------