TSTP Solution File: GRP039-2 by Leo-III---1.7.7
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%------------------------------------------------------------------------------
% File : Leo-III---1.7.7
% Problem : GRP039-2 : TPTP v8.1.2. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n022.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Fri May 19 11:13:04 EDT 2023
% Result : Unsatisfiable 2.75s 1.54s
% Output : Refutation 2.84s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 22
% Syntax : Number of formulae : 36 ( 19 unt; 9 typ; 0 def)
% Number of atoms : 43 ( 18 equ; 0 cnn)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 114 ( 10 ~; 16 |; 0 &; 88 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 6 ( 6 >; 0 *; 0 +; 0 <<)
% Number of symbols : 11 ( 9 usr; 6 con; 0-2 aty)
% Number of variables : 30 ( 0 ^; 30 !; 0 ?; 30 :)
% Comments :
%------------------------------------------------------------------------------
thf(subgroup_member_type,type,
subgroup_member: $i > $o ).
thf(b_type,type,
b: $i ).
thf(multiply_type,type,
multiply: $i > $i > $i ).
thf(inverse_type,type,
inverse: $i > $i ).
thf(a_type,type,
a: $i ).
thf(c_type,type,
c: $i ).
thf(d_type,type,
d: $i ).
thf(identity_type,type,
identity: $i ).
thf(element_in_O2_type,type,
element_in_O2: $i > $i > $i ).
thf(1,negated_conjecture,
subgroup_member @ b,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',b_in_O2) ).
thf(14,plain,
subgroup_member @ b,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(9,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( subgroup_member @ A )
| ~ ( subgroup_member @ B )
| ( ( multiply @ A @ B )
!= C )
| ( subgroup_member @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',closure_of_multiply) ).
thf(29,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( subgroup_member @ A )
| ~ ( subgroup_member @ B )
| ( ( multiply @ A @ B )
!= C )
| ( subgroup_member @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(4,negated_conjecture,
~ ( subgroup_member @ d ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_d_in_O2) ).
thf(17,plain,
~ ( subgroup_member @ d ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(8,axiom,
! [A: $i] :
( ~ ( subgroup_member @ A )
| ( subgroup_member @ ( inverse @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',closure_of_inverse) ).
thf(27,plain,
! [A: $i] :
( ~ ( subgroup_member @ A )
| ( subgroup_member @ ( inverse @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(13,axiom,
! [B: $i,A: $i] :
( ( subgroup_member @ A )
| ( subgroup_member @ B )
| ( ( multiply @ A @ ( element_in_O2 @ A @ B ) )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',property_of_O2) ).
thf(39,plain,
! [B: $i,A: $i] :
( ( subgroup_member @ A )
| ( subgroup_member @ B )
| ( ( multiply @ A @ ( element_in_O2 @ A @ B ) )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(11,axiom,
! [A: $i] :
( ( multiply @ A @ ( inverse @ A ) )
= identity ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',right_inverse) ).
thf(35,plain,
! [A: $i] :
( ( multiply @ A @ ( inverse @ A ) )
= identity ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(3,negated_conjecture,
( ( multiply @ a @ c )
= d ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a_times_c_is_d) ).
thf(16,plain,
( ( multiply @ a @ c )
= d ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(6,axiom,
! [A: $i] :
( ( multiply @ ( inverse @ A ) @ A )
= identity ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',left_inverse) ).
thf(23,plain,
! [A: $i] :
( ( multiply @ ( inverse @ A ) @ A )
= identity ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(2,negated_conjecture,
( ( multiply @ b @ ( inverse @ a ) )
= c ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',b_times_a_inverse_is_c) ).
thf(15,plain,
( ( multiply @ b @ ( inverse @ a ) )
= c ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(12,axiom,
! [B: $i,A: $i] :
( ( subgroup_member @ A )
| ( subgroup_member @ B )
| ( subgroup_member @ ( element_in_O2 @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',an_element_in_O2) ).
thf(37,plain,
! [B: $i,A: $i] :
( ( subgroup_member @ A )
| ( subgroup_member @ B )
| ( subgroup_member @ ( element_in_O2 @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(7,axiom,
! [C: $i,B: $i,A: $i] :
( ( multiply @ ( multiply @ A @ B ) @ C )
= ( multiply @ A @ ( multiply @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',associativity) ).
thf(25,plain,
! [C: $i,B: $i,A: $i] :
( ( multiply @ ( multiply @ A @ B ) @ C )
= ( multiply @ A @ ( multiply @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(5,axiom,
! [A: $i] :
( ( multiply @ identity @ A )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',left_identity) ).
thf(21,plain,
! [A: $i] :
( ( multiply @ identity @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(10,axiom,
! [A: $i] :
( ( multiply @ A @ identity )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',right_identity) ).
thf(33,plain,
! [A: $i] :
( ( multiply @ A @ identity )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(44,plain,
$false,
inference(e,[status(thm)],[14,29,17,27,39,35,16,23,15,37,25,21,33]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : GRP039-2 : TPTP v8.1.2. Released v1.0.0.
% 0.06/0.15 % Command : run_Leo-III %s %d
% 0.14/0.36 % Computer : n022.cluster.edu
% 0.14/0.36 % Model : x86_64 x86_64
% 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36 % Memory : 8042.1875MB
% 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36 % CPULimit : 300
% 0.14/0.36 % WCLimit : 300
% 0.14/0.36 % DateTime : Fri May 19 02:03:48 EDT 2023
% 0.14/0.36 % CPUTime :
% 0.91/0.85 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.19/0.97 % [INFO] Parsing done (120ms).
% 1.19/0.98 % [INFO] Running in sequential loop mode.
% 1.65/1.16 % [INFO] eprover registered as external prover.
% 1.65/1.16 % [INFO] cvc4 registered as external prover.
% 1.65/1.17 % [INFO] Scanning for conjecture ...
% 1.77/1.21 % [INFO] Found a conjecture and 9 axioms. Running axiom selection ...
% 1.77/1.23 % [INFO] Axiom selection finished. Selected 9 axioms (removed 0 axioms).
% 1.95/1.24 % [INFO] Problem is propositional (TPTP CNF).
% 1.95/1.25 % [INFO] Type checking passed.
% 1.95/1.25 % [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 ...
% 2.75/1.54 % External prover 'e' found a proof!
% 2.75/1.54 % [INFO] Killing All external provers ...
% 2.75/1.54 % Time passed: 1010ms (effective reasoning time: 558ms)
% 2.75/1.54 % Solved by 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)>
% 2.75/1.54 % Axioms used in derivation (9): associativity, property_of_O2, left_inverse, right_identity, right_inverse, an_element_in_O2, closure_of_inverse, closure_of_multiply, left_identity
% 2.75/1.54 % No. of inferences in proof: 27
% 2.75/1.54 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 1010 ms resp. 558 ms w/o parsing
% 2.84/1.57 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 2.84/1.57 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------