TSTP Solution File: GRP617-1 by Leo-III---1.7.7
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%------------------------------------------------------------------------------
% File : Leo-III---1.7.7
% Problem : GRP617-1 : TPTP v8.1.2. Released v3.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n007.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 11:14:32 EDT 2023
% Result : Unsatisfiable 94.60s 18.18s
% Output : Refutation 94.60s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 26
% Syntax : Number of formulae : 45 ( 17 unt; 8 typ; 0 def)
% Number of atoms : 77 ( 6 equ; 0 cnn)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 260 ( 42 ~; 40 |; 0 &; 178 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 7 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 8 ( 8 >; 0 *; 0 +; 0 <<)
% Number of symbols : 10 ( 8 usr; 4 con; 0-3 aty)
% Number of variables : 70 ( 0 ^; 70 !; 0 ?; 70 :)
% Comments :
%------------------------------------------------------------------------------
thf(multiply_type,type,
multiply: $i > $i > $i ).
thf(v_type,type,
v: $i ).
thf(u_type,type,
u: $i ).
thf(product_type,type,
product: $i > $i > $i > $o ).
thf(identity_type,type,
identity: $i ).
thf(subgroup1_member_type,type,
subgroup1_member: $i > $o ).
thf(inverse_type,type,
inverse: $i > $i ).
thf(subgroup2_member_type,type,
subgroup2_member: $i > $o ).
thf(12,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( subgroup1_member @ A )
| ~ ( subgroup1_member @ B )
| ~ ( product @ A @ B @ C )
| ( subgroup1_member @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',closure_of_product1) ).
thf(41,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( subgroup1_member @ A )
| ~ ( subgroup1_member @ B )
| ~ ( product @ A @ B @ C )
| ( subgroup1_member @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(18,axiom,
! [B: $i,A: $i] :
( ~ ( subgroup2_member @ A )
| ( subgroup2_member @ ( multiply @ B @ ( multiply @ A @ ( inverse @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',normality2) ).
thf(49,plain,
! [B: $i,A: $i] :
( ~ ( subgroup2_member @ A )
| ( subgroup2_member @ ( multiply @ B @ ( multiply @ A @ ( inverse @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(11,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(39,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)],[11]) ).
thf(17,axiom,
subgroup2_member @ u,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',u_in_G2) ).
thf(48,plain,
subgroup2_member @ u,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(13,axiom,
! [A: $i] : ( product @ A @ ( inverse @ A ) @ identity ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',right_inverse) ).
thf(43,plain,
! [A: $i] : ( product @ A @ ( inverse @ A ) @ identity ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(16,axiom,
subgroup1_member @ v,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',v_in_G1) ).
thf(47,plain,
subgroup1_member @ v,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(3,axiom,
! [A: $i] : ( product @ A @ identity @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',right_identity) ).
thf(24,plain,
! [A: $i] : ( product @ A @ identity @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(4,axiom,
! [A: $i] :
( ~ ( subgroup1_member @ A )
| ( subgroup1_member @ ( inverse @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',closure_of_inverse1) ).
thf(25,plain,
! [A: $i] :
( ~ ( subgroup1_member @ A )
| ( subgroup1_member @ ( inverse @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(6,axiom,
! [A: $i] :
( ~ ( subgroup2_member @ A )
| ( subgroup2_member @ ( inverse @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',closure_of_inverse2) ).
thf(28,plain,
! [A: $i] :
( ~ ( subgroup2_member @ A )
| ( subgroup2_member @ ( inverse @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(9,axiom,
! [A: $i] :
( ~ ( subgroup1_member @ A )
| ~ ( subgroup2_member @ A )
| ( A = identity ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',trivial_intersection) ).
thf(33,plain,
! [A: $i] :
( ~ ( subgroup1_member @ A )
| ~ ( subgroup2_member @ A )
| ( A = identity ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(8,axiom,
! [A: $i] : ( product @ identity @ A @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',left_identity) ).
thf(32,plain,
! [A: $i] : ( product @ identity @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(15,axiom,
! [B: $i,A: $i] :
( ~ ( subgroup1_member @ A )
| ( subgroup1_member @ ( multiply @ B @ ( multiply @ A @ ( inverse @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',normality1) ).
thf(45,plain,
! [B: $i,A: $i] :
( ~ ( subgroup1_member @ A )
| ( subgroup1_member @ ( multiply @ B @ ( multiply @ A @ ( inverse @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(2,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(22,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)],[2]) ).
thf(14,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)],[14]) ).
thf(5,axiom,
! [A: $i] : ( product @ ( inverse @ A ) @ A @ identity ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',left_inverse) ).
thf(27,plain,
! [A: $i] : ( product @ ( inverse @ A ) @ A @ identity ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(10,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( product @ A @ B @ C )
| ~ ( product @ A @ B @ D )
| ( C = D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',total_function2) ).
thf(36,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( product @ A @ B @ C )
| ~ ( product @ A @ B @ D )
| ( C = D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(7,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( subgroup2_member @ A )
| ~ ( subgroup2_member @ B )
| ~ ( product @ A @ B @ C )
| ( subgroup2_member @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',closure_of_product2) ).
thf(30,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( subgroup2_member @ A )
| ~ ( subgroup2_member @ B )
| ~ ( product @ A @ B @ C )
| ( subgroup2_member @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(1,negated_conjecture,
( ( multiply @ v @ u )
!= ( multiply @ u @ v ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_vu_equals_uv) ).
thf(19,plain,
( ( multiply @ v @ u )
!= ( multiply @ u @ v ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(10665,plain,
$false,
inference(e,[status(thm)],[41,49,39,48,43,47,24,25,28,33,32,45,22,44,27,36,30,19]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.02/0.10 % Problem : GRP617-1 : TPTP v8.1.2. Released v3.1.0.
% 0.12/0.13 % Command : run_Leo-III %s %d
% 0.13/0.35 % Computer : n007.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Fri May 19 01:25:09 EDT 2023
% 0.20/0.35 % CPUTime :
% 0.96/0.92 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.29/1.08 % [INFO] Parsing done (159ms).
% 1.29/1.09 % [INFO] Running in sequential loop mode.
% 1.61/1.32 % [INFO] eprover registered as external prover.
% 1.61/1.32 % [INFO] cvc4 registered as external prover.
% 1.61/1.33 % [INFO] Scanning for conjecture ...
% 1.80/1.38 % [INFO] Found a conjecture and 17 axioms. Running axiom selection ...
% 1.94/1.42 % [INFO] Axiom selection finished. Selected 17 axioms (removed 0 axioms).
% 1.94/1.44 % [INFO] Problem is propositional (TPTP CNF).
% 1.94/1.45 % [INFO] Type checking passed.
% 1.94/1.45 % [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 ...
% 94.60/18.18 % External prover 'e' found a proof!
% 94.60/18.18 % [INFO] Killing All external provers ...
% 94.60/18.18 % Time passed: 17656ms (effective reasoning time: 17084ms)
% 94.60/18.18 % 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)>
% 94.60/18.18 % Axioms used in derivation (17): total_function1, closure_of_product2, left_identity, trivial_intersection, closure_of_inverse1, right_identity, right_inverse, u_in_G2, associativity1, closure_of_inverse2, total_function2, associativity2, v_in_G1, closure_of_product1, normality2, normality1, left_inverse
% 94.60/18.18 % No. of inferences in proof: 37
% 94.60/18.18 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 17656 ms resp. 17084 ms w/o parsing
% 94.60/18.21 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 94.60/18.21 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------