%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : GRP039-3 : TPTP v9.3.1. Released v1.0.0.
% 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 : n015.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 07:19:50 AM UTC 2026
% Result : Unsatisfiable 5.80s 3.23s
% Output : Refutation 6.06s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 20
% Syntax : Number of formulae : 41 ( 23 unt; 0 typ; 0 def)
% Number of atoms : 81 ( 8 equ; 0 cnn)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 264 ( 34 ~; 40 |; 0 &; 190 @)
% ( 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 : 12 ( 10 usr; 6 con; 0-3 aty)
% Number of variables : 78 ( 0 ^; 78 !; 0 ?; 78 :)
% Comments :
%------------------------------------------------------------------------------
thf(subgroup_member_decl,type,
subgroup_member: $i > $o ).
thf(b_decl,type,
b: $i ).
thf(product_decl,type,
product: $i > $i > $i > $o ).
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(multiply_decl,type,
multiply: $i > $i > $i ).
thf(9,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C = D )
| ~ ( D @ ( B @ ( A @ product ) ) )
| ~ ( C @ ( B @ ( A @ product ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',total_function2) ).
thf(32,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)],[9]) ).
thf(20,axiom,
! [A: $i] : ( identity @ ( A @ inverse @ ( A @ product ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',right_inverse) ).
thf(54,plain,
! [A: $i] : ( identity @ ( A @ inverse @ ( A @ product ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(12,axiom,
! [B: $i,A: $i] : ( B @ ( A @ multiply ) @ ( B @ ( A @ product ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',total_function1) ).
thf(39,plain,
! [B: $i,A: $i] : ( B @ ( A @ multiply ) @ ( B @ ( A @ product ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(10,axiom,
! [A: $i] :
( ( A @ inverse @ inverse )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',inverse_is_self_cancelling) ).
thf(35,plain,
! [A: $i] :
( ( A @ inverse @ inverse )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(18,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D = A )
| ~ ( C @ ( B @ ( D @ product ) ) )
| ~ ( C @ ( B @ ( A @ product ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',product_left_cancellation) ).
thf(48,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)],[18]) ).
thf(8,axiom,
! [A: $i] : ( A @ ( A @ ( identity @ product ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',left_identity) ).
thf(31,plain,
! [A: $i] : ( A @ ( A @ ( identity @ product ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(15,axiom,
identity @ subgroup_member,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',identity_is_in_subgroup) ).
thf(43,plain,
identity @ subgroup_member,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(19,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D = B )
| ~ ( C @ ( D @ ( A @ product ) ) )
| ~ ( C @ ( B @ ( A @ product ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',product_right_cancellation) ).
thf(51,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)],[19]) ).
thf(14,axiom,
! [A: $i] : ( identity @ ( A @ ( A @ inverse @ product ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',left_inverse) ).
thf(42,plain,
! [A: $i] : ( identity @ ( A @ ( A @ inverse @ product ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(4,negated_conjecture,
~ ( d @ subgroup_member ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_d_is_in_subgroup) ).
thf(24,plain,
~ ( d @ subgroup_member ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(11,axiom,
! [B: $i,A: $i] :
( ( A @ subgroup_member )
| ( B @ subgroup_member )
| ( B @ ( B @ ( A @ element_in_O2 ) @ ( A @ product ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',property_of_O2) ).
thf(37,plain,
! [B: $i,A: $i] :
( ( A @ subgroup_member )
| ( B @ subgroup_member )
| ( B @ ( B @ ( A @ element_in_O2 ) @ ( A @ product ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(17,axiom,
! [B: $i,A: $i] :
( ( A @ subgroup_member )
| ( B @ subgroup_member )
| ( B @ ( A @ element_in_O2 ) @ subgroup_member ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',an_element_in_O2) ).
thf(46,plain,
! [B: $i,A: $i] :
( ( A @ subgroup_member )
| ( B @ subgroup_member )
| ( B @ ( A @ element_in_O2 ) @ subgroup_member ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(7,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(29,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)],[7]) ).
thf(6,axiom,
! [A: $i] : ( A @ ( identity @ ( A @ product ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',right_identity) ).
thf(28,plain,
! [A: $i] : ( A @ ( identity @ ( A @ product ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(1,negated_conjecture,
b @ subgroup_member,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',b_is_in_subgroup) ).
thf(21,plain,
b @ subgroup_member,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(2,negated_conjecture,
c @ ( a @ inverse @ ( b @ product ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',b_times_a_inverse_is_c) ).
thf(22,plain,
c @ ( a @ inverse @ ( b @ product ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(16,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(44,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)],[16]) ).
thf(13,axiom,
! [A: $i] :
( ( A @ inverse @ subgroup_member )
| ~ ( A @ subgroup_member ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subgroup_member_inverse_are_in_subgroup) ).
thf(40,plain,
! [A: $i] :
( ( A @ inverse @ subgroup_member )
| ~ ( A @ subgroup_member ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(5,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(26,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)],[5]) ).
thf(3,negated_conjecture,
d @ ( c @ ( a @ product ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a_times_c_is_d) ).
thf(23,plain,
d @ ( c @ ( a @ product ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(58,plain,
$false,
inference(e,[status(thm)],[32,54,39,35,48,31,43,51,42,24,37,46,29,28,21,22,44,40,26,23]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : GRP039-3 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.11 % 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
% 0.22/0.48 % Computer : n015.cluster.edu
% 0.22/0.48 % Model : x86_64 x86_64
% 0.22/0.48 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.22/0.48 % Memory : 8046.5625MB
% 0.22/0.48 % OS : Linux 6.8.0-71-generic
% 0.22/0.48 % CPULimit : 300
% 0.22/0.48 % WCLimit : 300
% 0.22/0.48 % DateTime : Fri Sep 25 14:22:27 UTC 2026
% 0.22/0.48 % CPUTime :
% 0.22/0.48 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
% 1.26/1.27 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.88/1.54 % [INFO] Parsing done (263ms).
% 1.88/1.56 % [INFO] Running in sequential loop mode.
% 2.92/2.09 % [INFO] eprover registered as external prover.
% 2.92/2.10 % [INFO] Scanning for conjecture ...
% 3.23/2.23 % [INFO] Found a conjecture (or negated_conjecture) and 16 axioms. Running axiom selection ...
% 3.39/2.31 % [INFO] Axiom selection finished. Selected 16 axioms (removed 0 axioms).
% 3.39/2.35 % [INFO] Problem is propositional (TPTP CNF).
% 3.39/2.36 % [INFO] Type checking passed.
% 3.39/2.37 % [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 ...
% 5.80/3.22 % External prover 'e' found a proof!
% 5.80/3.23 % [INFO] Killing All external provers ...
% 5.80/3.23 % Time passed: 2534ms (effective reasoning time: 1659ms)
% 5.80/3.23 % Axioms used in derivation (16): total_function1, left_identity, product_right_cancellation, property_of_O2, left_inverse, right_identity, an_element_in_O2, identity_is_in_subgroup, closure_of_product_and_inverse, total_function2, associativity2, product_left_cancellation, subgroup_member_inverse_are_in_subgroup, right_inverse, associativity1, inverse_is_self_cancelling
% 5.80/3.23 % No. of inferences in proof: 41
% 5.80/3.23 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p : 2534 ms resp. 1659 ms w/o parsing
% 6.06/3.30 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 6.06/3.30 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------