%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : GRP033-3 : TPTP v9.3.1. Bugfixed v4.0.0.
% 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 : n001.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 07:19:49 AM UTC 2026
% Result : Unsatisfiable 3.69s 2.43s
% Output : Refutation 3.69s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 22
% Syntax : Number of formulae : 45 ( 15 unt; 0 typ; 0 def)
% Number of atoms : 101 ( 0 equ; 0 cnn)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 384 ( 58 ~; 56 |; 0 &; 270 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 8 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 9 ( 8 usr; 3 con; 0-3 aty)
% Number of variables : 110 ( 0 ^; 110 !; 0 ?; 110 :)
% Comments :
%------------------------------------------------------------------------------
thf(product_decl,type,
product: $i > $i > $i > $o ).
thf(j_decl,type,
j: $i > $i ).
thf(subgroup_member_decl,type,
subgroup_member: $i > $o ).
thf(equalish_decl,type,
equalish: $i > $i > $o ).
thf(multiply_decl,type,
multiply: $i > $i > $i ).
thf(inverse_decl,type,
inverse: $i > $i ).
thf(identity_decl,type,
identity: $i ).
thf(a_decl,type,
a: $i ).
thf(18,axiom,
! [A: $i] : ( identity @ ( A @ ( A @ inverse @ product ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',left_inverse) ).
thf(53,plain,
! [A: $i] : ( identity @ ( A @ ( A @ inverse @ product ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(11,axiom,
! [A: $i] : ( A @ ( A @ ( identity @ product ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',left_identity) ).
thf(41,plain,
! [A: $i] : ( A @ ( A @ ( identity @ product ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(14,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ equalish ) )
| ~ ( D @ ( B @ ( A @ product ) ) )
| ~ ( C @ ( B @ ( A @ product ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',total_function2) ).
thf(45,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ equalish ) )
| ~ ( D @ ( B @ ( A @ product ) ) )
| ~ ( C @ ( B @ ( A @ product ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(10,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ subgroup_member )
| ~ ( C @ ( B @ inverse @ ( A @ product ) ) )
| ~ ( B @ subgroup_member )
| ~ ( A @ subgroup_member ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',closure_of_product_and_inverse) ).
thf(39,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ subgroup_member )
| ~ ( C @ ( B @ inverse @ ( A @ product ) ) )
| ~ ( B @ subgroup_member )
| ~ ( A @ subgroup_member ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(7,axiom,
! [A: $i] : ( A @ ( A @ equalish ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reflexivity) ).
thf(35,plain,
! [A: $i] : ( A @ ( A @ equalish ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(5,axiom,
! [B: $i,A: $i] :
( ( B @ inverse @ ( A @ inverse @ equalish ) )
| ~ ( B @ ( A @ equalish ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',inverse_substitution) ).
thf(31,plain,
! [B: $i,A: $i] :
( ( B @ inverse @ ( A @ inverse @ equalish ) )
| ~ ( B @ ( A @ equalish ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(15,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ ( B @ product ) ) )
| ~ ( D @ ( C @ ( A @ product ) ) )
| ~ ( B @ ( A @ equalish ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',product_substitution1) ).
thf(47,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ ( B @ product ) ) )
| ~ ( D @ ( C @ ( A @ product ) ) )
| ~ ( B @ ( A @ equalish ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(12,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( D @ ( C @ product ) ) )
| ~ ( A @ ( D @ ( C @ product ) ) )
| ~ ( B @ ( A @ equalish ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',product_substitution3) ).
thf(42,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( D @ ( C @ product ) ) )
| ~ ( A @ ( D @ ( C @ product ) ) )
| ~ ( B @ ( A @ equalish ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(2,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( A @ equalish ) )
| ~ ( C @ ( B @ equalish ) )
| ~ ( B @ ( A @ equalish ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',transitivity) ).
thf(25,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( A @ equalish ) )
| ~ ( C @ ( B @ equalish ) )
| ~ ( B @ ( A @ equalish ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(21,axiom,
! [B: $i,A: $i] :
( ( B @ subgroup_member )
| ~ ( A @ subgroup_member )
| ~ ( B @ ( A @ equalish ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subgroup_member_substitution) ).
thf(57,plain,
! [B: $i,A: $i] :
( ( B @ subgroup_member )
| ~ ( A @ subgroup_member )
| ~ ( B @ ( A @ equalish ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(4,axiom,
! [C: $i,B: $i,A: $i] :
( ( B @ ( C @ multiply ) @ ( A @ ( C @ multiply ) @ equalish ) )
| ~ ( B @ ( A @ equalish ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',multiply_substitution2) ).
thf(29,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( C @ multiply ) @ ( A @ ( C @ multiply ) @ equalish ) )
| ~ ( B @ ( A @ equalish ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(9,axiom,
! [A: $i] : ( A @ ( identity @ ( A @ product ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',right_identity) ).
thf(38,plain,
! [A: $i] : ( A @ ( identity @ ( A @ product ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(6,axiom,
! [B: $i,A: $i] :
( ( A @ ( B @ equalish ) )
| ~ ( B @ ( A @ equalish ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',symmetry) ).
thf(33,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ equalish ) )
| ~ ( B @ ( A @ equalish ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(13,axiom,
! [B: $i,A: $i] : ( B @ ( A @ multiply ) @ ( B @ ( A @ product ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',total_function1) ).
thf(44,plain,
! [B: $i,A: $i] : ( B @ ( A @ multiply ) @ ( B @ ( A @ product ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(22,axiom,
! [A: $i] : ( identity @ ( A @ inverse @ ( A @ product ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',right_inverse) ).
thf(59,plain,
! [A: $i] : ( identity @ ( A @ inverse @ ( A @ product ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(3,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ multiply ) @ ( C @ ( A @ multiply ) @ equalish ) )
| ~ ( B @ ( A @ equalish ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',multiply_substitution1) ).
thf(27,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ multiply ) @ ( C @ ( A @ multiply ) @ equalish ) )
| ~ ( B @ ( A @ equalish ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(19,axiom,
a @ subgroup_member,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a_is_in_subgroup) ).
thf(54,plain,
a @ subgroup_member,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(16,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( B @ ( C @ product ) ) )
| ~ ( D @ ( A @ ( C @ product ) ) )
| ~ ( B @ ( A @ equalish ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',product_substitution2) ).
thf(49,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( B @ ( C @ product ) ) )
| ~ ( D @ ( A @ ( C @ product ) ) )
| ~ ( B @ ( A @ equalish ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(20,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( F @ ( E @ ( A @ product ) ) )
| ~ ( F @ ( D @ ( C @ product ) ) )
| ~ ( E @ ( D @ ( B @ product ) ) )
| ~ ( C @ ( B @ ( A @ product ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',associativity1) ).
thf(55,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( F @ ( E @ ( A @ product ) ) )
| ~ ( F @ ( D @ ( C @ product ) ) )
| ~ ( E @ ( D @ ( B @ product ) ) )
| ~ ( C @ ( B @ ( A @ product ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(1,negated_conjecture,
! [A: $i] :
( ~ ( A @ subgroup_member )
| ~ ( A @ j @ ( A @ j @ ( A @ product ) ) )
| ~ ( A @ j @ ( A @ ( A @ j @ product ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_subgr2) ).
thf(23,plain,
! [A: $i] :
( ~ ( A @ subgroup_member )
| ~ ( A @ j @ ( A @ j @ ( A @ product ) ) )
| ~ ( A @ j @ ( A @ ( A @ j @ product ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(8,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( F @ ( D @ ( C @ product ) ) )
| ~ ( F @ ( E @ ( A @ product ) ) )
| ~ ( E @ ( D @ ( B @ product ) ) )
| ~ ( C @ ( B @ ( A @ product ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',associativity2) ).
thf(36,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( F @ ( D @ ( C @ product ) ) )
| ~ ( F @ ( E @ ( A @ product ) ) )
| ~ ( E @ ( D @ ( B @ product ) ) )
| ~ ( C @ ( B @ ( A @ product ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(17,axiom,
! [A: $i] :
( ( A @ j @ subgroup_member )
| ~ ( A @ subgroup_member ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subgr2_clause1) ).
thf(51,plain,
! [A: $i] :
( ( A @ j @ subgroup_member )
| ~ ( A @ subgroup_member ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(60,plain,
$false,
inference(e,[status(thm)],[53,41,45,39,35,31,47,42,25,57,29,38,33,44,59,27,54,49,55,23,36,51]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP033-3 : TPTP v9.3.1. Bugfixed v4.0.0.
% 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
% 0.13/0.39 % Computer : n001.cluster.edu
% 0.13/0.39 % Model : x86_64 x86_64
% 0.13/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.39 % Memory : 8046.5625MB
% 0.13/0.39 % OS : Linux 6.8.0-71-generic
% 0.13/0.39 % CPULimit : 300
% 0.13/0.39 % WCLimit : 300
% 0.13/0.39 % DateTime : Fri Sep 25 14:23:55 UTC 2026
% 0.13/0.39 % CPUTime :
% 0.13/0.39 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
% 0.86/0.99 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.21/1.19 % [INFO] Parsing done (198ms).
% 1.37/1.20 % [INFO] Running in sequential loop mode.
% 1.94/1.60 % [INFO] eprover registered as external prover.
% 1.94/1.61 % [INFO] Scanning for conjecture ...
% 1.94/1.70 % [INFO] Found a conjecture (or negated_conjecture) and 21 axioms. Running axiom selection ...
% 2.11/1.76 % [INFO] Axiom selection finished. Selected 21 axioms (removed 0 axioms).
% 2.11/1.79 % [INFO] Problem is propositional (TPTP CNF).
% 2.11/1.79 % [INFO] Type checking passed.
% 2.11/1.80 % [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 ...
% 3.69/2.42 % External prover 'e' found a proof!
% 3.69/2.42 % [INFO] Killing All external provers ...
% 3.69/2.42 % Time passed: 1884ms (effective reasoning time: 1213ms)
% 3.69/2.43 % Axioms used in derivation (21): total_function1, product_substitution2, left_identity, subgr2_clause1, left_inverse, right_inverse, associativity1, closure_of_product_and_inverse, a_is_in_subgroup, total_function2, symmetry, inverse_substitution, subgroup_member_substitution, multiply_substitution1, product_substitution3, reflexivity, right_identity, product_substitution1, multiply_substitution2, transitivity, associativity2
% 3.69/2.43 % No. of inferences in proof: 45
% 3.69/2.43 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p : 1884 ms resp. 1213 ms w/o parsing
% 3.69/2.48 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 3.69/2.48 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------