TSTP Solution File: GRP039-7 by Leo-III---1.7.7
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%------------------------------------------------------------------------------
% File : Leo-III---1.7.7
% Problem : GRP039-7 : TPTP v8.1.2. Bugfixed v1.0.1.
% 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 3.06s 1.65s
% Output : Refutation 3.06s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 25
% Syntax : Number of formulae : 42 ( 25 unt; 9 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 : 6 ( 6 >; 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_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(4,negated_conjecture,
~ ( subgroup_member @ d ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_d_in_O2) ).
thf(20,plain,
~ ( subgroup_member @ d ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(14,axiom,
subgroup_member @ identity,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',identity_in_O2) ).
thf(44,plain,
subgroup_member @ identity,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(2,negated_conjecture,
( ( multiply @ b @ ( inverse @ a ) )
= c ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',b_times_a_inverse_is_c) ).
thf(18,plain,
( ( multiply @ b @ ( inverse @ a ) )
= c ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(16,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(47,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)],[16]) ).
thf(13,axiom,
( ( inverse @ identity )
= identity ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',inverse_of_identity) ).
thf(42,plain,
( ( inverse @ identity )
= identity ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(5,axiom,
! [A: $i] :
( ( multiply @ identity @ A )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',left_identity) ).
thf(24,plain,
! [A: $i] :
( ( multiply @ identity @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
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(28,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(11,axiom,
! [A: $i] :
( ( multiply @ A @ ( inverse @ A ) )
= identity ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',right_inverse) ).
thf(38,plain,
! [A: $i] :
( ( multiply @ A @ ( inverse @ A ) )
= identity ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
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(32,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(15,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(45,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)],[15]) ).
thf(1,negated_conjecture,
subgroup_member @ b,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',b_in_O2) ).
thf(17,plain,
subgroup_member @ b,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(12,axiom,
! [A: $i] :
( ( inverse @ ( inverse @ A ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',inverse_inverse) ).
thf(40,plain,
! [A: $i] :
( ( inverse @ ( inverse @ A ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(6,axiom,
! [A: $i] :
( ( multiply @ ( inverse @ A ) @ A )
= identity ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',left_inverse) ).
thf(26,plain,
! [A: $i] :
( ( multiply @ ( inverse @ A ) @ A )
= identity ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(10,axiom,
! [A: $i] :
( ( multiply @ A @ identity )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',right_identity) ).
thf(36,plain,
! [A: $i] :
( ( multiply @ A @ identity )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(8,axiom,
! [A: $i] :
( ~ ( subgroup_member @ A )
| ( subgroup_member @ ( inverse @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',closure_of_inverse) ).
thf(30,plain,
! [A: $i] :
( ~ ( subgroup_member @ A )
| ( subgroup_member @ ( inverse @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(3,negated_conjecture,
( ( multiply @ a @ c )
= d ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a_times_c_is_d) ).
thf(19,plain,
( ( multiply @ a @ c )
= d ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(72,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
% 0.07/0.11 % Problem : GRP039-7 : TPTP v8.1.2. Bugfixed v1.0.1.
% 0.07/0.15 % Command : run_Leo-III %s %d
% 0.16/0.36 % Computer : n022.cluster.edu
% 0.16/0.36 % Model : x86_64 x86_64
% 0.16/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.36 % Memory : 8042.1875MB
% 0.16/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.36 % CPULimit : 300
% 0.16/0.36 % WCLimit : 300
% 0.16/0.36 % DateTime : Fri May 19 01:41:34 EDT 2023
% 0.16/0.36 % CPUTime :
% 0.83/0.84 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.21/0.95 % [INFO] Parsing done (115ms).
% 1.21/0.96 % [INFO] Running in sequential loop mode.
% 1.55/1.15 % [INFO] eprover registered as external prover.
% 1.55/1.15 % [INFO] cvc4 registered as external prover.
% 1.55/1.15 % [INFO] Scanning for conjecture ...
% 1.79/1.20 % [INFO] Found a conjecture and 12 axioms. Running axiom selection ...
% 1.90/1.22 % [INFO] Axiom selection finished. Selected 12 axioms (removed 0 axioms).
% 1.90/1.23 % [INFO] Problem is propositional (TPTP CNF).
% 1.90/1.23 % [INFO] Type checking passed.
% 1.90/1.24 % [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 ...
% 3.06/1.65 % External prover 'e' found a proof!
% 3.06/1.65 % [INFO] Killing All external provers ...
% 3.06/1.65 % Time passed: 1132ms (effective reasoning time: 683ms)
% 3.06/1.65 % 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)>
% 3.06/1.65 % 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
% 3.06/1.65 % No. of inferences in proof: 33
% 3.06/1.65 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 1132 ms resp. 683 ms w/o parsing
% 3.06/1.67 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 3.06/1.67 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------