TSTP Solution File: GRP033-3 by Leo-III---1.7.7
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Leo-III---1.7.7
% Problem : GRP033-3 : TPTP v8.1.2. Bugfixed v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n029.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 11:13:03 EDT 2023
% Result : Unsatisfiable 2.76s 1.61s
% Output : Refutation 3.08s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 30
% Syntax : Number of formulae : 53 ( 15 unt; 8 typ; 0 def)
% Number of atoms : 101 ( 0 equ; 0 cnn)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 384 ( 58 ~; 56 |; 0 &; 270 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 8 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 10 ( 10 >; 0 *; 0 +; 0 <<)
% Number of symbols : 9 ( 8 usr; 3 con; 0-3 aty)
% Number of variables : 110 ( 0 ^; 110 !; 0 ?; 110 :)
% Comments :
%------------------------------------------------------------------------------
thf(product_type,type,
product: $i > $i > $i > $o ).
thf(j_type,type,
j: $i > $i ).
thf(subgroup_member_type,type,
subgroup_member: $i > $o ).
thf(equalish_type,type,
equalish: $i > $i > $o ).
thf(multiply_type,type,
multiply: $i > $i > $i ).
thf(inverse_type,type,
inverse: $i > $i ).
thf(identity_type,type,
identity: $i ).
thf(a_type,type,
a: $i ).
thf(18,axiom,
! [A: $i] : ( product @ ( inverse @ A ) @ A @ identity ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',left_inverse) ).
thf(53,plain,
! [A: $i] : ( product @ ( inverse @ A ) @ A @ identity ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(11,axiom,
! [A: $i] : ( product @ identity @ A @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',left_identity) ).
thf(41,plain,
! [A: $i] : ( product @ identity @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(14,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( product @ A @ B @ C )
| ~ ( product @ A @ B @ D )
| ( equalish @ C @ D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',total_function2) ).
thf(45,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( product @ A @ B @ C )
| ~ ( product @ A @ B @ D )
| ( equalish @ C @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(10,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( subgroup_member @ A )
| ~ ( subgroup_member @ B )
| ~ ( product @ A @ ( inverse @ B ) @ C )
| ( subgroup_member @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',closure_of_product_and_inverse) ).
thf(39,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( subgroup_member @ A )
| ~ ( subgroup_member @ B )
| ~ ( product @ A @ ( inverse @ B ) @ C )
| ( subgroup_member @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(7,axiom,
! [A: $i] : ( equalish @ A @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reflexivity) ).
thf(35,plain,
! [A: $i] : ( equalish @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(5,axiom,
! [B: $i,A: $i] :
( ~ ( equalish @ A @ B )
| ( equalish @ ( inverse @ A ) @ ( inverse @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',inverse_substitution) ).
thf(31,plain,
! [B: $i,A: $i] :
( ~ ( equalish @ A @ B )
| ( equalish @ ( inverse @ A ) @ ( inverse @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(15,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( equalish @ A @ B )
| ~ ( product @ A @ C @ D )
| ( product @ B @ C @ D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',product_substitution1) ).
thf(47,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( equalish @ A @ B )
| ~ ( product @ A @ C @ D )
| ( product @ B @ C @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(12,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( equalish @ A @ B )
| ~ ( product @ C @ D @ A )
| ( product @ C @ D @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',product_substitution3) ).
thf(42,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( equalish @ A @ B )
| ~ ( product @ C @ D @ A )
| ( product @ C @ D @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(2,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( equalish @ A @ B )
| ~ ( equalish @ B @ C )
| ( equalish @ A @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',transitivity) ).
thf(25,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( equalish @ A @ B )
| ~ ( equalish @ B @ C )
| ( equalish @ A @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(21,axiom,
! [B: $i,A: $i] :
( ~ ( equalish @ A @ B )
| ~ ( subgroup_member @ A )
| ( subgroup_member @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subgroup_member_substitution) ).
thf(57,plain,
! [B: $i,A: $i] :
( ~ ( equalish @ A @ B )
| ~ ( subgroup_member @ A )
| ( subgroup_member @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(4,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( equalish @ A @ B )
| ( equalish @ ( multiply @ C @ A ) @ ( multiply @ C @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',multiply_substitution2) ).
thf(29,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( equalish @ A @ B )
| ( equalish @ ( multiply @ C @ A ) @ ( multiply @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(9,axiom,
! [A: $i] : ( product @ A @ identity @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',right_identity) ).
thf(38,plain,
! [A: $i] : ( product @ A @ identity @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(6,axiom,
! [B: $i,A: $i] :
( ~ ( equalish @ A @ B )
| ( equalish @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',symmetry) ).
thf(33,plain,
! [B: $i,A: $i] :
( ~ ( equalish @ A @ B )
| ( equalish @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(13,axiom,
! [B: $i,A: $i] : ( product @ A @ B @ ( multiply @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',total_function1) ).
thf(44,plain,
! [B: $i,A: $i] : ( product @ A @ B @ ( multiply @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(22,axiom,
! [A: $i] : ( product @ A @ ( inverse @ A ) @ identity ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',right_inverse) ).
thf(59,plain,
! [A: $i] : ( product @ A @ ( inverse @ A ) @ identity ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(3,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( equalish @ A @ B )
| ( equalish @ ( multiply @ A @ C ) @ ( multiply @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',multiply_substitution1) ).
thf(27,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( equalish @ A @ B )
| ( equalish @ ( multiply @ A @ C ) @ ( multiply @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(19,axiom,
subgroup_member @ a,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a_is_in_subgroup) ).
thf(54,plain,
subgroup_member @ a,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(16,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( equalish @ A @ B )
| ~ ( product @ C @ A @ D )
| ( product @ C @ B @ D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',product_substitution2) ).
thf(49,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( equalish @ A @ B )
| ~ ( product @ C @ A @ D )
| ( product @ C @ B @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(20,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( product @ A @ B @ C )
| ~ ( product @ B @ D @ E )
| ~ ( product @ C @ D @ F )
| ( product @ A @ E @ F ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',associativity1) ).
thf(55,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( product @ A @ B @ C )
| ~ ( product @ B @ D @ E )
| ~ ( product @ C @ D @ F )
| ( product @ A @ E @ F ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(1,negated_conjecture,
! [A: $i] :
( ~ ( product @ ( j @ A ) @ A @ ( j @ A ) )
| ~ ( product @ A @ ( j @ A ) @ ( j @ A ) )
| ~ ( subgroup_member @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_subgr2) ).
thf(23,plain,
! [A: $i] :
( ~ ( product @ ( j @ A ) @ A @ ( j @ A ) )
| ~ ( product @ A @ ( j @ A ) @ ( j @ A ) )
| ~ ( subgroup_member @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(8,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( product @ A @ B @ C )
| ~ ( product @ B @ D @ E )
| ~ ( product @ A @ E @ F )
| ( product @ C @ D @ F ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',associativity2) ).
thf(36,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( product @ A @ B @ C )
| ~ ( product @ B @ D @ E )
| ~ ( product @ A @ E @ F )
| ( product @ C @ D @ F ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(17,axiom,
! [A: $i] :
( ~ ( subgroup_member @ A )
| ( subgroup_member @ ( j @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subgr2_clause1) ).
thf(51,plain,
! [A: $i] :
( ~ ( subgroup_member @ A )
| ( subgroup_member @ ( j @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(60,plain,
$false,
inference(e,[status(thm)],[53,41,45,39,35,31,47,42,25,57,29,38,33,44,59,27,54,49,55,23,36,51]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : GRP033-3 : TPTP v8.1.2. Bugfixed v4.0.0.
% 0.11/0.15 % Command : run_Leo-III %s %d
% 0.15/0.35 % Computer : n029.cluster.edu
% 0.15/0.35 % Model : x86_64 x86_64
% 0.15/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.35 % Memory : 8042.1875MB
% 0.15/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.35 % CPULimit : 300
% 0.15/0.35 % WCLimit : 300
% 0.15/0.35 % DateTime : Fri May 19 01:53:44 EDT 2023
% 0.15/0.36 % CPUTime :
% 0.86/0.84 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.21/0.96 % [INFO] Parsing done (120ms).
% 1.21/0.97 % [INFO] Running in sequential loop mode.
% 1.53/1.16 % [INFO] eprover registered as external prover.
% 1.53/1.16 % [INFO] cvc4 registered as external prover.
% 1.53/1.16 % [INFO] Scanning for conjecture ...
% 1.83/1.22 % [INFO] Found a conjecture and 21 axioms. Running axiom selection ...
% 1.94/1.25 % [INFO] Axiom selection finished. Selected 21 axioms (removed 0 axioms).
% 1.94/1.27 % [INFO] Problem is propositional (TPTP CNF).
% 1.94/1.27 % [INFO] Type checking passed.
% 1.94/1.28 % [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 ...
% 2.76/1.61 % External prover 'e' found a proof!
% 2.76/1.61 % [INFO] Killing All external provers ...
% 2.76/1.61 % Time passed: 1091ms (effective reasoning time: 638ms)
% 2.76/1.61 % 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)>
% 2.76/1.61 % Axioms used in derivation (21): total_function1, product_substitution2, left_identity, subgr2_clause1, left_inverse, right_inverse, associativity1, closure_of_product_and_inverse, a_is_in_subgroup, total_function2, symmetry, inverse_substitution, subgroup_member_substitution, multiply_substitution1, product_substitution3, reflexivity, right_identity, product_substitution1, multiply_substitution2, transitivity, associativity2
% 2.76/1.61 % No. of inferences in proof: 45
% 2.76/1.61 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 1091 ms resp. 638 ms w/o parsing
% 3.08/1.65 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 3.08/1.65 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------