%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : GRP037-3 : TPTP v9.3.1. Released v1.0.0.
% 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 : Sun Sep 27 07:19:49 AM UTC 2026
% Result : Unsatisfiable 3.89s 2.40s
% Output : Refutation 3.89s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 19
% Syntax : Number of formulae : 39 ( 17 unt; 0 typ; 0 def)
% Number of atoms : 79 ( 8 equ; 0 cnn)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 268 ( 42 ~; 40 |; 0 &; 186 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 7 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 10 ( 8 usr; 4 con; 0-3 aty)
% Number of variables : 76 ( 0 ^; 76 !; 0 ?; 76 :)
% Comments :
%------------------------------------------------------------------------------
thf(inverse_decl,type,
inverse: $i > $i ).
thf(a_decl,type,
a: $i ).
thf(another_inverse_decl,type,
another_inverse: $i > $i ).
thf(product_decl,type,
product: $i > $i > $i > $o ).
thf(multiply_decl,type,
multiply: $i > $i > $i ).
thf(identity_decl,type,
identity: $i ).
thf(subgroup_member_decl,type,
subgroup_member: $i > $o ).
thf(another_identity_decl,type,
another_identity: $i ).
thf(18,axiom,
! [A: $i] :
( ( another_identity @ ( A @ ( A @ another_inverse @ product ) ) )
| ~ ( A @ subgroup_member ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',another_left_inverse) ).
thf(52,plain,
! [A: $i] :
( ( another_identity @ ( A @ ( A @ another_inverse @ product ) ) )
| ~ ( A @ subgroup_member ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(8,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C = D )
| ~ ( D @ ( B @ ( A @ product ) ) )
| ~ ( C @ ( B @ ( A @ product ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',total_function2) ).
thf(33,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C = D )
| ~ ( D @ ( B @ ( A @ product ) ) )
| ~ ( C @ ( B @ ( A @ product ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(12,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D = B )
| ~ ( C @ ( D @ ( A @ product ) ) )
| ~ ( C @ ( B @ ( A @ product ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',product_right_cancellation) ).
thf(41,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D = B )
| ~ ( C @ ( D @ ( A @ product ) ) )
| ~ ( C @ ( B @ ( A @ product ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(7,axiom,
! [A: $i] : ( A @ ( A @ ( identity @ product ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',left_identity) ).
thf(32,plain,
! [A: $i] : ( A @ ( A @ ( identity @ product ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(11,axiom,
! [A: $i] :
( ( A @ ( another_identity @ ( A @ product ) ) )
| ~ ( A @ subgroup_member ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',another_right_identity) ).
thf(39,plain,
! [A: $i] :
( ( A @ ( another_identity @ ( A @ product ) ) )
| ~ ( A @ subgroup_member ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(15,axiom,
! [A: $i] : ( identity @ ( A @ ( A @ inverse @ product ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',left_inverse) ).
thf(48,plain,
! [A: $i] : ( identity @ ( A @ ( A @ inverse @ product ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(17,axiom,
! [A: $i] :
( ( another_identity @ ( A @ another_inverse @ ( A @ product ) ) )
| ~ ( A @ subgroup_member ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',another_right_inverse) ).
thf(50,plain,
! [A: $i] :
( ( another_identity @ ( A @ another_inverse @ ( A @ product ) ) )
| ~ ( A @ subgroup_member ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(2,axiom,
! [B: $i,A: $i] : ( B @ ( A @ multiply ) @ ( B @ ( A @ product ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',total_function1) ).
thf(23,plain,
! [B: $i,A: $i] : ( B @ ( A @ multiply ) @ ( B @ ( A @ product ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(3,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D = A )
| ~ ( C @ ( B @ ( D @ product ) ) )
| ~ ( C @ ( B @ ( A @ product ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',product_left_cancellation) ).
thf(24,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D = A )
| ~ ( C @ ( B @ ( D @ product ) ) )
| ~ ( C @ ( B @ ( A @ product ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(10,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/sandbox/benchmark/theBenchmark.p',associativity1) ).
thf(37,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)],[10]) ).
thf(1,negated_conjecture,
( ( a @ inverse )
!= ( a @ another_inverse ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_two_inverses_are_equal) ).
thf(20,plain,
( ( a @ inverse )
!= ( a @ another_inverse ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(14,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ subgroup_member )
| ~ ( C @ ( B @ inverse @ ( A @ product ) ) )
| ~ ( B @ subgroup_member )
| ~ ( A @ subgroup_member ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',closure_of_product_and_inverse) ).
thf(46,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)],[14]) ).
thf(5,axiom,
! [A: $i] : ( A @ ( identity @ ( A @ product ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',right_identity) ).
thf(29,plain,
! [A: $i] : ( A @ ( identity @ ( A @ product ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(13,axiom,
! [A: $i] :
( ( A @ another_inverse @ subgroup_member )
| ~ ( A @ subgroup_member ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',another_inverse_in_subgroup) ).
thf(44,plain,
! [A: $i] :
( ( A @ another_inverse @ subgroup_member )
| ~ ( A @ subgroup_member ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(4,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/sandbox/benchmark/theBenchmark.p',associativity2) ).
thf(27,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)],[4]) ).
thf(19,axiom,
! [A: $i] : ( identity @ ( A @ inverse @ ( A @ product ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',right_inverse) ).
thf(54,plain,
! [A: $i] : ( identity @ ( A @ inverse @ ( A @ product ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(16,axiom,
a @ subgroup_member,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a_is_in_subgroup) ).
thf(49,plain,
a @ subgroup_member,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(9,axiom,
another_identity @ subgroup_member,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',another_identity_in_subgroup) ).
thf(36,plain,
another_identity @ subgroup_member,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(6,axiom,
! [A: $i] :
( ( A @ ( A @ ( another_identity @ product ) ) )
| ~ ( A @ subgroup_member ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',another_left_identity) ).
thf(30,plain,
! [A: $i] :
( ( A @ ( A @ ( another_identity @ product ) ) )
| ~ ( A @ subgroup_member ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(55,plain,
$false,
inference(e,[status(thm)],[52,33,41,32,39,48,50,23,24,37,20,46,29,44,27,54,49,36,30]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP037-3 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.07 % 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
% 0.14/0.39 % Computer : n006.cluster.edu
% 0.14/0.39 % Model : x86_64 x86_64
% 0.14/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.39 % Memory : 8046.5625MB
% 0.14/0.39 % OS : Linux 6.8.0-71-generic
% 0.14/0.39 % CPULimit : 300
% 0.14/0.39 % WCLimit : 300
% 0.14/0.39 % DateTime : Fri Sep 25 14:18:41 UTC 2026
% 0.14/0.39 % CPUTime :
% 0.14/0.39 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
% 0.84/0.97 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.19/1.17 % [INFO] Parsing done (197ms).
% 1.19/1.18 % [INFO] Running in sequential loop mode.
% 1.77/1.58 % [INFO] eprover registered as external prover.
% 1.77/1.59 % [INFO] Scanning for conjecture ...
% 1.97/1.67 % [INFO] Found a conjecture (or negated_conjecture) and 18 axioms. Running axiom selection ...
% 2.13/1.73 % [INFO] Axiom selection finished. Selected 18 axioms (removed 0 axioms).
% 2.13/1.76 % [INFO] Problem is propositional (TPTP CNF).
% 2.13/1.76 % [INFO] Type checking passed.
% 2.13/1.77 % [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 ...
% 3.57/2.40 % External prover 'e' found a proof!
% 3.89/2.40 % [INFO] Killing All external provers ...
% 3.89/2.40 % Time passed: 1863ms (effective reasoning time: 1208ms)
% 3.89/2.40 % Axioms used in derivation (18): total_function1, another_inverse_in_subgroup, left_identity, product_right_cancellation, another_left_inverse, left_inverse, right_identity, right_inverse, another_right_identity, another_left_identity, associativity1, a_is_in_subgroup, total_function2, associativity2, another_identity_in_subgroup, product_left_cancellation, another_right_inverse, closure_of_product_and_inverse
% 3.89/2.40 % No. of inferences in proof: 39
% 3.89/2.40 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p : 1863 ms resp. 1208 ms w/o parsing
% 3.89/2.46 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 3.89/2.46 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------