%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : GRP039-7 : TPTP v9.3.1. Bugfixed v1.0.1.
% 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 : n002.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 07:19:51 AM UTC 2026
% Result : Unsatisfiable 3.52s 7.38s
% Output : Refutation 3.84s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 16
% Syntax : Number of formulae : 33 ( 25 unt; 0 typ; 0 def)
% Number of atoms : 49 ( 22 equ; 0 cnn)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 122 ( 10 ~; 16 |; 0 &; 96 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 11 ( 9 usr; 6 con; 0-2 aty)
% Number of variables : 32 ( 0 ^; 32 !; 0 ?; 32 :)
% Comments :
%------------------------------------------------------------------------------
thf(subgroup_member_decl,type,
subgroup_member: $i > $o ).
thf(b_decl,type,
b: $i ).
thf(multiply_decl,type,
multiply: $i > $i > $i ).
thf(inverse_decl,type,
inverse: $i > $i ).
thf(a_decl,type,
a: $i ).
thf(c_decl,type,
c: $i ).
thf(d_decl,type,
d: $i ).
thf(identity_decl,type,
identity: $i ).
thf(element_in_O2_decl,type,
element_in_O2: $i > $i > $i ).
thf(4,negated_conjecture,
~ ( d @ subgroup_member ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_d_in_O2) ).
thf(20,plain,
~ ( d @ subgroup_member ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(14,axiom,
identity @ subgroup_member,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',identity_in_O2) ).
thf(44,plain,
identity @ subgroup_member,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(2,negated_conjecture,
( ( a @ inverse @ ( b @ multiply ) )
= c ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',b_times_a_inverse_is_c) ).
thf(18,plain,
( ( a @ inverse @ ( b @ multiply ) )
= c ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(16,axiom,
! [B: $i,A: $i] :
( ( ( B @ ( A @ element_in_O2 ) @ ( A @ multiply ) )
= B )
| ( B @ subgroup_member )
| ( A @ subgroup_member ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',property_of_O2) ).
thf(47,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ element_in_O2 ) @ ( A @ multiply ) )
= B )
| ( B @ subgroup_member )
| ( A @ subgroup_member ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(13,axiom,
( ( identity @ inverse )
= identity ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',inverse_of_identity) ).
thf(42,plain,
( ( identity @ inverse )
= identity ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(5,axiom,
! [A: $i] :
( ( A @ ( identity @ multiply ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',left_identity) ).
thf(24,plain,
! [A: $i] :
( ( A @ ( identity @ multiply ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(7,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(28,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)],[7]) ).
thf(11,axiom,
! [A: $i] :
( ( A @ inverse @ ( A @ multiply ) )
= identity ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',right_inverse) ).
thf(38,plain,
! [A: $i] :
( ( A @ inverse @ ( A @ multiply ) )
= identity ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(9,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ subgroup_member )
| ( ( B @ ( A @ multiply ) )
!= C )
| ~ ( B @ subgroup_member )
| ~ ( A @ subgroup_member ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',closure_of_multiply) ).
thf(32,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ subgroup_member )
| ( ( B @ ( A @ multiply ) )
!= C )
| ~ ( B @ subgroup_member )
| ~ ( A @ subgroup_member ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(15,axiom,
! [B: $i,A: $i] :
( ( B @ ( A @ element_in_O2 ) @ subgroup_member )
| ( B @ subgroup_member )
| ( A @ subgroup_member ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',an_element_in_O2) ).
thf(45,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ element_in_O2 ) @ subgroup_member )
| ( B @ subgroup_member )
| ( A @ subgroup_member ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(1,negated_conjecture,
b @ subgroup_member,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',b_in_O2) ).
thf(17,plain,
b @ subgroup_member,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(12,axiom,
! [A: $i] :
( ( A @ inverse @ inverse )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',inverse_inverse) ).
thf(40,plain,
! [A: $i] :
( ( A @ inverse @ inverse )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(6,axiom,
! [A: $i] :
( ( A @ ( A @ inverse @ multiply ) )
= identity ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',left_inverse) ).
thf(26,plain,
! [A: $i] :
( ( A @ ( A @ inverse @ multiply ) )
= identity ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(10,axiom,
! [A: $i] :
( ( identity @ ( A @ multiply ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',right_identity) ).
thf(36,plain,
! [A: $i] :
( ( identity @ ( A @ multiply ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(8,axiom,
! [A: $i] :
( ( A @ inverse @ subgroup_member )
| ~ ( A @ subgroup_member ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',closure_of_inverse) ).
thf(30,plain,
! [A: $i] :
( ( A @ inverse @ subgroup_member )
| ~ ( A @ subgroup_member ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(3,negated_conjecture,
( ( c @ ( a @ multiply ) )
= d ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a_times_c_is_d) ).
thf(19,plain,
( ( c @ ( a @ multiply ) )
= d ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(53,plain,
$false,
inference(e,[status(thm)],[20,44,18,47,42,24,28,38,32,45,17,40,26,36,30,19]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP039-7 : TPTP v9.3.1. Bugfixed v1.0.1.
% 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
% 0.14/5.41 % Computer : n002.cluster.edu
% 0.14/5.41 % Model : x86_64 x86_64
% 0.14/5.41 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/5.41 % Memory : 8046.5625MB
% 0.14/5.41 % OS : Linux 6.8.0-71-generic
% 0.14/5.41 % CPULimit : 300
% 0.14/5.41 % WCLimit : 300
% 0.14/5.41 % DateTime : Fri Sep 25 14:22:11 UTC 2026
% 0.14/5.41 % CPUTime :
% 0.14/5.41 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
% 0.18/6.00 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.42/6.21 % [INFO] Parsing done (207ms).
% 1.42/6.23 % [INFO] Running in sequential loop mode.
% 2.12/6.63 % [INFO] eprover registered as external prover.
% 2.12/6.64 % [INFO] Scanning for conjecture ...
% 2.31/6.73 % [INFO] Found a conjecture (or negated_conjecture) and 12 axioms. Running axiom selection ...
% 2.31/6.77 % [INFO] Axiom selection finished. Selected 12 axioms (removed 0 axioms).
% 2.31/6.79 % [INFO] Problem is propositional (TPTP CNF).
% 2.31/6.79 % [INFO] Type checking passed.
% 2.47/6.80 % [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 ...
% 3.52/7.38 % External prover 'e' found a proof!
% 3.52/7.38 % [INFO] Killing All external provers ...
% 3.52/7.38 % Time passed: 1823ms (effective reasoning time: 1147ms)
% 3.52/7.38 % Axioms used in derivation (12): associativity, identity_in_O2, property_of_O2, inverse_of_identity, left_inverse, right_identity, right_inverse, an_element_in_O2, inverse_inverse, closure_of_inverse, closure_of_multiply, left_identity
% 3.52/7.38 % No. of inferences in proof: 33
% 3.52/7.38 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p : 1823 ms resp. 1147 ms w/o parsing
% 3.84/7.43 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 3.84/7.43 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------